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{{No newcomer task}} | |||
{{distinguish|Grapheme|Graphane|Graphyne}} | |||
{{Short description|Hexagonal lattice made of carbon atoms}} | |||
{{technical|date=December 2013}} | |||
{{Not to be confused with|Graphite|Grapheme}} | |||
{{Infobox material | |||
| name = Graphene | |||
| image = File:Graphen.jpg | |||
| caption = Graphene is an ] ] made of ] atoms | |||
| type = Allotrope of carbon | |||
| chemical formula = C | |||
| youngs_modulus = ≈1 TPa | |||
| tensile_strength = 130 GPa | |||
| thermal_conductivity = 5300 W⋅m<sup>−1</sup>⋅K<sup>−1</sup> | |||
}} | |||
'''Graphene''' ({{IPAc-en|ˈ|g|r|æ|f|iː|n}})<ref name=camdic/> is a ] consisting of a ] of ]s arranged in a ] planar ].<ref name="geim2007" /><ref name="peres2009" /> The name "graphene" is derived from "]" and the suffix ], indicating the presence of double bonds within the carbon structure. | |||
] made of carbon atoms.]] | |||
Graphene is known for its exceptionally high ], ], ], and being the thinnest two-dimensional material in the world.<ref>{{Cite news |last=Pike |first=Jared |date=2023 |title=Is graphene the best heat conductor ever? Purdue researchers investigate with four-phonon scattering |url=https://engineering.purdue.edu/ME/News/2023/is-graphene-the-best-heat-conductor-ever-purdue-researchers-investigate-with-fourphonon-scattering |url-status=live |archive-url=https://web.archive.org/web/20240304143824/https://engineering.purdue.edu/ME/News/2023/is-graphene-the-best-heat-conductor-ever-purdue-researchers-investigate-with-fourphonon-scattering |archive-date=March 4, 2024 |access-date=October 1, 2024 |work=Purdue University Mechanical Engineering News}}</ref> Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths.<ref name=nair2008/><ref name=zhu2014/> On a microscopic scale, graphene is the strongest material ever measured.<ref name=lee2008/><ref name=cao2020/> | |||
'''Graphene''' is a 2-dimensional, ]line ] of ]. In graphene, carbon atoms are densely packed in a regular ] ] (]) pattern. Graphene can be described as a one-atom thick layer of ]. It is the basic structural element of other allotropes, including graphite, ], ]s and ]s. It can also be considered as an indefinitely large ] molecule, the limiting case of the family of flat ]s. | |||
] | |||
High-quality graphene is strong, light, nearly transparent and an excellent conductor of heat and electricity. Its interactions with other materials and with light and its inherently two-dimensional nature produce unique properties, such as the ] effect, ] of charges and large quantum oscillations. | |||
The existence of graphene was first theorized in 1947 by ] during his research on graphite's electronic properties.<ref>{{cite web |title=Graphene: A Complete Chemical History |url=https://www.acsmaterial.com/blog-detail/graphene-a-complete-chemical-history.html |website=ACS Material |access-date=1 October 2024 |date=20 September 2019 |quote=In 1947, the existence of graphene was theorized by Philip R Wallace as an attempt to understand electronic properties of 3D graphite. He did not use the term “graphene”, but instead referred to it as a “single hexagonal layer.” }}</ref> In 2004, the material was isolated and characterized by ] and ] at the ]<ref name="novo2004" /><ref name="aps2009" /> using a piece of graphite and ].<ref>{{Cite web |title=Discovery of graphene - Graphene - The University of Manchester |url=https://www.graphene.manchester.ac.uk/learn/discovery-of-graphene/ |access-date=2024-10-16 |website=www.graphene.manchester.ac.uk}}</ref> In 2010, Geim and Novoselov were awarded the ] for their "groundbreaking experiments regarding the two-dimensional material graphene".<ref>{{Cite web|title=The Nobel Prize in Physics 2010|url=https://www.nobelprize.org/prizes/physics/2010/summary/|access-date=1 September 2021|publisher=Nobel Foundation|archive-date=22 May 2020|archive-url=https://web.archive.org/web/20200522211920/https://www.nobelprize.org/prizes/physics/2010/summary/|url-status=live}}</ref> While small amounts of graphene are easy to produce using the method by which it was originally isolated, attempts to scale and automate the manufacturing process for mass production have had limited success due to cost-effectiveness and quality control concerns.<ref>{{Cite web |date=2018-04-06 |title=Mass-Producing Graphene |url=https://www.americanscientist.org/article/mass-producing-graphene |access-date=2024-10-16 |website=American Scientist |language=en}}</ref><ref>{{Cite web |last=Joshi |first=Rita |date=2024-04-08 |title=Can Graphene Be Mass Produced? |url=https://www.azonano.com/article.aspx?ArticleID=6716 |access-date=2024-10-16 |website=AZoNano |language=en}}</ref> The global graphene market was $9 million in 2012,<ref name="azon2014" /> with most of the demand from research and development in ], electronics, ],<ref name="mrmak2014" /> and ]. | |||
At the time of its isolation in 2004,<ref name="APS News"> | |||
{{cite journal | |||
|year=2009 | |||
|url=http://www.aps.org/publications/apsnews/200910/loader.cfm?csModule=security/getfile&pageid=187967 | |||
|title=This Month in Physics History: October 22, 2004: Discovery of Graphene | |||
|page=2 | |||
|series=Series II |volume=18 |issue=9 | |||
|journal=] | |||
}}</ref> researchers studying ] were already familiar with graphene's composition, structure and properties, which had been calculated decades earlier. The combination of familiarity, extraordinary properties, surprising ease of isolation and unexpectedly high quality of the obtained graphene enabled a rapid increase in graphene research. ] and ] at the ] won the ] in 2010 "for groundbreaking experiments regarding the ] material graphene".<ref> | |||
{{cite web | |||
|title=The Nobel Prize in Physics 2010 | |||
|url=http://nobelprize.org/nobel_prizes/physics/laureates/2010/ | |||
|publisher=] | |||
|accessdate=2013-12-03 | |||
}}</ref> | |||
{{toclimit|3}} | |||
The ] (International Union of Pure and Applied Chemistry) advises using the term "graphite" for the three-dimensional material and reserving "graphene" for discussions about the properties or reactions of single-atom layers.<ref name=IUPAC2009/> A narrower definition, of "isolated or free-standing graphene", requires that the layer be sufficiently isolated from its environment,<ref name=geim2009a/> but would include layers suspended or transferred to ] or ].<ref name=ried2009/> | |||
== Definition == | |||
== History == | |||
"Graphene" is a combination of ] and the suffix ], named by ],<ref name="termorigin">{{cite journal |doi=10.1351/pac199466091893 |first=H. P. |last=Boehm |first2=R. |last2=Setton |first3=E. |last3=Stumpp |title=Nomenclature and terminology of graphite intercalation compounds |url=http://www.iupac.org/publications/pac/1994/pdf/6609x1893.pdf |format=PDF |journal=Pure and Applied Chemistry |volume=66 |issue=9 |year=1994 |pages=1893–1901 }}</ref> who described single-layer carbon foils in 1962.<ref name="Boehm1962"> | |||
{{main|Discovery of graphene}} | |||
{{cite journal |first=H. P. |last=Boehm |first2=A. |last2=Clauss |first3=G. O. |last3=Fischer |first4=U. |last4=Hofmann |title=Das Adsorptionsverhalten sehr dünner Kohlenstoffolien |journal=Zeitschrift für anorganische und allgemeine Chemie |volume=316 |issue=3–4 |year=1962 |pages=119–127 |doi=10.1002/zaac.19623160303}} | |||
</ref> | |||
], a graphene ], and a ]. Donated to the ] in Stockholm by ] and ] in 2010.]] | |||
The term ''graphene'' first appeared in 1987<ref name="Mouras87"> | |||
{{Cite journal |last=Mouras |first=S. |author2=''et al.'' |title=Synthesis of first stage graphite intercalation compounds with fluorides |journal=Revue de Chimie Minerale |url=http://cat.inist.fr/?aModele=afficheN&cpsidt=7578318 |volume=24 |page=572 |year=1987}} | |||
</ref> to describe single sheets of graphite as one of the constituents of ]s (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of ]s,<ref name="Saito92">{{Cite journal |last=Saito |first=R. |title=Electronic structure of graphene tubules based on C60|doi=10.1103/PhysRevB.46.1804 |journal=Physical Review B |volume=46 |page=1804 |year=1992|bibcode=1992PhRvB..46.1804S |issue=3 |last2=Fujita |first2=Mitsutaka |last3=Dresselhaus |first3=G. |last4=Dresselhaus |first4=M. }}</ref> as well as for epitaxial graphene<ref name="Forbeaux98">{{Cite journal |last=Forbeaux |first=I. |title=Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure |doi=10.1103/PhysRevB.58.16396 |journal=Physical Review B |volume=58 |page=16396 |year=1998 |bibcode=1998PhRvB..5816396F |issue=24 |last2=Themlin |first2=J.-M. |last3=Debever |first3=J.-M. }} | |||
</ref> and polycyclic aromatic hydrocarbons.<ref name="Wang00"> | |||
{{Cite journal |last=Wang |first=S. |title=A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries |doi=10.1149/1.1393559 |journal=Journal of the Electrochemical Society |volume=147 |page=2498 |year=2000 |issue=7 |last2=Yata |first2=S. |last3=Nagano |first3=J. |last4=Okano |first4=Y. |last5=Kinoshita |first5=H. |last6=Kikuta |first6=H. |last7=Yamabe |first7=T. }}</ref> | |||
=== Structure of graphite and its intercalation compounds === | |||
The ] compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene... it is incorrect to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed."<ref name=iupac-gold-book>{{cite web |title=graphene layer |url=http://goldbook.iupac.org/G02683.html |work=IUPAC Gold Book |publisher=International Union of Pure and Applied Chemistry |accessdate=2012-03-31 }}</ref> | |||
In 1859, ] noted the highly ] structure of thermally reduced ].<ref name=geim2012/><ref name=brod1859/> Pioneers in ] attempted to determine the structure of graphite. The lack of large ] graphite specimens contributed to the independent development of ] by ] and ] in 1915, and ] in 1916.<ref name=deb1916/><ref name=deb1917/><ref name=hull1917/> However, neither of their proposed structures was correct. In 1918, Volkmar Kohlschütter and P. Haenni described the properties of ].<ref name=kohl1918/> The structure of graphite was successfully determined from single-crystal X-ray diffraction by ] in 1924,<ref name=bern1924/> although subsequent research has made small modifications to the ] parameters.<ref name=tru1975/><ref name=howe2003/> | |||
Graphene can be considered an "infinite alternant" (only six-member carbon ring) ] (PAH). The largest known isolated PAH molecule consists of 222 atoms and is 10 ]s across.<!-- why is this relevant to graphene? --><ref>{{Cite journal |last=Simpson |first=C. D. |title=Synthesis of a Giant 222 Carbon Graphite Sheet |doi=10.1002/1521-3765(20020315)8:6<1424::AID-CHEM1424>3.0.CO;2-Z |journal=Chemistry – A European Journal |volume=6 |page=1424 |year=2002 |issue=6 |last2=Brand |first2=J. Diedrich |last3=Berresheim |first3=Alexander J. |last4=Przybilla |first4=Laurence |last5=Räder |first5=Hans Joachim |last6=Müllen |first6=Klaus }}</ref> It has proven difficult to synthesize even slightly bigger molecules, and they still remain "a dream of many organic and polymer chemists".<ref name=2Dpolymers>{{Cite journal |last=Sakamoto |first=J. |last2=Van Heijst |first2=Jeroen |last3=Lukin |first3=Oleg |last4=Schlüter |first4=A. Dieter |title=Two-Dimensional Polymers: Just a Dream of Synthetic Chemists? |year=2009 |journal=Angew. Chem. Int. Ed. |pmid=19130514 |volume=48 |issue=16 |doi=10.1002/anie.200801863 |pages=1030–69 }}</ref> | |||
The theory of graphene was first explored by ] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless ] was separately pointed out in 1984 by ],<ref name="Semenoff">{{cite journal |last1=Semenoff |first1=Gordon W. |title=Condensed-Matter Simulation of a Three-Dimensional Anomaly |journal=Physical Review Letters |date=24 December 1984 |volume=53 |issue=26 |pages=2449–2452 |doi=10.1103/PhysRevLett.53.2449 |bibcode=1984PhRvL..53.2449S }}</ref> and by David P. Vincenzo and Eugene J. Mele.<ref name=divi1984/> Semenoff emphasized the occurrence in a magnetic field of an electronic ] precisely at the ]. This level is responsible for the anomalous integer ].<ref name=novo2005/><ref name=gusy2005/><ref name=zhang2005/> | |||
A definition of "isolated or free-standing graphene" was proposed: "graphene is a single atomic plane of graphite, which – and this is essential – is sufficiently isolated from its environment to be considered free-standing."<ref name=Sciencerev09>{{Cite journal |last=Geim |first=A. |year=2009 |title=Graphene: Status and Prospects |journal=Science |pmid=19541989 |volume=324 |issue=5934 |doi=10.1126/science.1158877 |bibcode=2009Sci...324.1530G |pages=1530–4 |arxiv=0906.3799 }}</ref> This definition is narrower than the definition given above and refers to cleaved, transferred and suspended graphene monolayers.{{Citation needed|date=December 2011}} Other forms of graphene, such as graphene grown on various metals, can become free-standing if, for example, suspended or transferred to ] ({{chem|SiO|2}}) or ] (after its ] with hydrogen).<ref name=SiCplusH2>{{Cite journal |last=Riedl |first=C. |last2=Coletti |first2=C. |last3=Iwasaki |first3=T. |last4=Zakharov |first4=A.A. |last5=Starke |first5=U. |year=2009 |title=Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation |journal=Physical Review Letters |volume=103 |page=246804 |doi=10.1103/PhysRevLett.103.246804 |pmid=20366220 |bibcode=2009PhRvL.103x6804R |issue=24|arxiv=0911.1953 }}</ref> | |||
=== Observations of thin graphite layers and related structures === | |||
== History == | |||
] (TEM) images of thin ] samples consisting of a few graphene layers were published by G. Ruess and F. Vogt in 1948.<ref name=ruess1948/> Eventually, single layers were also observed directly.<ref name=meyer2007/> Single layers of graphite were also observed by ] within bulk materials, particularly inside soot obtained by chemical ].<ref name=harris2018/> | |||
In 1859 ] was aware of the highly ] structure of thermally reduced ].<ref>{{cite journal |last=Brodie |first=B. C. |year=1859 |title=On the Atomic Weight of Graphite |journal=] |volume=149 |issue= |pages=249–259 |bibcode=1859RSPT..149..249B |jstor=108699 }}</ref> | |||
From 1961 to 1962, ] published a study of extremely thin flakes of graphite.<ref name=boehm1962b/> The study measured flakes as small as ~0.4 ], which is around 3 atomic layers of amorphous carbon. This was the best possible resolution for TEMs in the 1960s. However, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known method is to analyze the relative intensities of various diffraction spots.<ref name="meyer2007" /> The first reliable TEM observations of monolayers are likely given in references 24 and 26 of Geim and Novoselov's 2007 review.<ref name=geim2007/> | |||
The structure of ] was solved in 1916.<ref>{{cite journal |year=1916 |title=Interferenz an regellos orientierten Teilchen im Röntgenlicht I |journal=Physikalische Zeitschrift |volume=17 |page=277 |last=Debije |first=P |last2=Scherrer |first2=P |authorlink1=Peter Debye }}</ref> by the related method of ],<ref>{{cite journal |last=Friedrich |first=W |year=1913 |title=Eine neue Interferenzerscheinung bei Röntgenstrahlen |journal=Physikalische Zeitschrift |volume=14 |page=317 }}</ref><ref>{{cite journal |last=Hull |first=AW |authorlink=Albert Hull |year=1917 |title=A New Method of X-ray Crystal Analysis |journal=Phys. Rev. |volume=10 |page=661 |doi=10.1103/PhysRev.10.661|issue=6 |bibcode=1917PhRv...10..661H }}</ref> It was studied in detail by V. Kohlschütter and P. Haenni in 1918, who also described the properties of ].<ref name=Kohlschuttler1918> | |||
{{cite journal | |||
|last=Kohlschütter |first=V. | |||
|last2=Haenni |first2=P. | |||
|year=1919 | |||
|title=Zur Kenntnis des Graphitischen Kohlenstoffs und der Graphitsäure | |||
|journal=] | |||
|volume=105 |issue=1 |pages=121–144 | |||
|doi=10.1002/zaac.19191050109 | |||
}}</ref> Its structure was determined from single-crystal diffraction in 1924.<ref>{{cite journal |last=Bernal |first=JD |authorlink=John Desmond Bernal |year=1924 |title=The Structure of Graphite |jstor=94336 |journal=Proc. R. Soc. Lond. |volume=A106 |issue=740 |pages=749–773 }}</ref><ref>{{cite journal |last=Hassel |first=O |last2=Mack |first2=H |year=1924 |title=Über die Kristallstruktur des Graphits |journal=Zeitschrift für Physik |volume=25 |page=317 |doi=10.1007/BF01327534 |bibcode=1924ZPhy...25..317H }}</ref> | |||
In 1975, van Bommel et al. ] grew a single layer of graphite on top of silicon carbide.<ref name="Bom75">{{cite journal|title=LEED and Auger electron observations of the SiC(0001) surface|year=1975|journal=]|volume=48|pages=463–472|issue=2|last1=van Bommel|first1=A.J.|last2=Crombeen|first2=J.E.|last3=van Tooren|first3=A.|doi=10.1016/0039-6028(75)90419-7|bibcode=1975SurSc..48..463V }}</ref> Others grew single layers of carbon atoms on other materials.<ref name=oshi1997/><ref name=forb1998/> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp<sup>2</sup>-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials and, in some cases, hybridization between the ]s of the substrate atoms and π orbitals of graphene, which significantly alter the electronic structure compared to that of free-standing graphene. | |||
The theory of graphene was first explored by ] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by ] and David P. DeVincenzo and Eugene J. Mele.<ref name="devincenzo">{{Cite journal |last=DiVincenzo |first=D. P. |last2=Mele |first2=E. J. |title=Self-Consistent Effective Mass Theory for Intralayer Screening in Graphite Intercalation Compounds |doi=10.1103/PhysRevB.29.1685 |journal=Physical Review B |volume=295 |page=1685 |year=1984|bibcode=1984PhRvB..29.1685D |issue=4 }}</ref> Semenoff emphasized the occurrence in a magnetic field of an electronic ] precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.<ref name="2dgasDiracFermions"/><ref name="Gusynin"/><ref name="Berry'sPhase"/> | |||
Boehm et al. coined the term "graphene" for the hypothetical single-layer structure in 1986.<ref>{{cite journal|doi=10.1016/0008-6223(86)90126-0|title=Nomenclature and terminology of graphite intercalation compounds|journal=Carbon|volume=24|issue=2|pages=241–245|year=1986|last1=Boehm|first1=H.P|last2=Setton|first2=R|last3=Stumpp|first3=E|bibcode=1986Carbo..24..241B |quote=A single carbon layer of the graphitic structure would be the final member of infinite size of this series. The term ''graphene'' layer should be used for such a single carbon layer.}}</ref> The term was used again in 1987 to describe single sheets of graphite as a constituent of ]s,<ref name=mour1987/> which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of ]s by R. Saito and ] and ] in 1992,<ref name=saito1992/> and in the description of ] in 2000 by S. Wang and others.<ref name=wang2000/> | |||
The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948.<ref name=RuessTEM> | |||
{{cite journal |last=Ruess |first=G. |last2=Vogt |first2=F. |year=1948 |title=Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd |journal=] | |||
|volume=78 |issue=3–4 |page=222 | |||
|doi=10.1007/BF01141527 | |||
}}</ref> Later, single graphene layers were also observed directly by electron microscopy.<ref name=Meyer07>{{Cite journal |last=Meyer |first=J. |last2=Geim |first2=A. K. |last3=Katsnelson |first3=M. I. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Roth |first6=S. |title=The structure of suspended graphene sheets |journal=Nature |volume=446 |pages=60–63 |year=2007 |doi=10.1038/nature05545 |pmid=17330039 |issue=7131 |arxiv=cond-mat/0701379 |bibcode=2007Natur.446...60M }}</ref> Before 2004 intercalated graphite compounds were studied under a ] (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962.<ref name=GroxTEM> | |||
{{cite book | |||
|last=Boehm |first=H. P. |last2=Clauss |first2=A. |last3=Fischer |first3=G. |last4=Hofmann |first4=U. |year=1962 | |||
|chapter=Surface Properties of Extremely Thin Graphite Lamellae | |||
|url=http://graphenetimes.com/wp-content/uploads/1961/09/BoehmProcCarbon1962.pdf |format=PDF | |||
|booktitle=Proceedings of the Fifth Conference on Carbon | |||
|publisher=] | |||
}}</ref>{{#tag:ref|This paper reports graphitic flakes that give an additional contrast equivalent of down to ~0.4 nm or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today it is possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.<ref name=Meyer07/> For example, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known way is to analyse relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are probably given in refs. 24 and 26 of {{harvnb|Geim|Novoselov|2007}}}} | |||
Efforts to make thin films of graphite by mechanical exfoliation started in 1990.<ref name=geim2008/> | |||
Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials.<ref name="Oshima97">{{Cite journal |last=Oshima |first=C. |last2=Nagashima |first2=A. |title=Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces |doi=10.1088/0953-8984/9/1/004 |journal=J. Phys.: Condens. Matter |volume=9 |page=1 |year=1997 |bibcode=1997JPCM....9....1O }}</ref> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of ] carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the ]s of the substrate atoms and ] of graphene, which significantly alters the electronic structure of epitaxial graphene. | |||
Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.<ref name=geim2007/> | |||
In 2002, ] and Richard L. Dudman filed for a patent in the US on a method to produce graphene by repeatedly peeling off layers from a graphite flake adhered to a substrate, achieving a graphite thickness of {{convert|0.00001|inch|mm|abbr=off|lk=on}}. The key to success was the ability to quickly and efficiently identify graphene flakes on the substrate using optical microscopy, which provided a small but visible contrast between the graphene and the substrate.<ref name=ruth2002/> | |||
Single layers of graphite were also observed by ] within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990,<ref name=SciAm/> but nothing thinner than 50 to 100 layers was produced before 2004. | |||
] in Stockholm by Andre Geim and Konstantin Novoselov in 2010.]] | |||
Another U.S. patent was filed in the same year by Bor Z. Jang and Wen C. Huang for a method to produce graphene-based on exfoliation followed by attrition.<ref name=jang2002/> | |||
Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.{{sfn|Geim|Novoselov|2007}} Old papers were unearthed<ref name=GroxTEM/> in which researchers tried to isolate graphene starting with intercalated compounds. These papers reported the observation of very thin graphitic fragments (possibly monolayers) by transmission electron microscopy. Neither of the earlier observations was sufficient to "spark the graphene gold rush", which awaited macroscopic samples of extracted atomic planes. | |||
In 2014, inventor ] patented a process for producing single-layer graphene sheets.<ref>{{Cite web |title=Graphene edges closer to widespread production and application |url=https://www.compositesworld.com/articles/cedar-ridge-research-receives-pioneer-patent-for-free-floating-graphene-production-technology |access-date=2022-03-25 |website=www.compositesworld.com |date=10 August 2016 |language=en |archive-date=20 September 2020 |archive-url=https://web.archive.org/web/20200920032954/https://www.compositesworld.com/articles/cedar-ridge-research-receives-pioneer-patent-for-free-floating-graphene-production-technology |url-status=live }}</ref> | |||
One of the very first patents pertaining to the production of graphene was filed in October, 2002 (US Pat. 7071258).<ref>. Patft.uspto.gov. Retrieved on 2014-01-12.</ref> Entitled, "Nano-scaled Graphene Plates", this patent detailed one of the very first large scale graphene production processes. Two years later, in 2004 ] and ] at University of Manchester extracted single-atom-thick crystallites from bulk graphite.<ref name="Nov 04"/> They pulled graphene layers from graphite and transferred them onto thin {{chem|SiO|2}} on a silicon wafer in a process called either micromechanical cleavage or the ] technique. The {{chem|SiO|2}} electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. They may not have been the first to use this technique— {{patent|US|6667100}}, filed in 2002, describes how to process commercially available flexible expanded graphite to achieve a graphite thickness of 0.01 thousandth of an inch. The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast. | |||
=== Full isolation and characterization === | |||
The cleavage technique led directly to the first observation of the ] in graphene,<ref name="2dgasDiracFermions"/><ref name="Berry'sPhase"/> which provided direct evidence of graphene's theoretically predicted ] of massless ]s. The effect was reported soon after by ] and Yuanbo Zhang in 2005. These experiments started after the researchers observed colleagues who were looking for the quantum Hall effect<ref>{{cite journal |last=Kopelevich |first=Y. |last2=Torres |first2=J. |last3=Da Silva |first3=R. |last4=Mrowka |first4=F. |last5=Kempa |first5=H. |last6=Esquinazi |first6=P. |title=Reentrant Metallic Behavior of Graphite in the Quantum Limit |journal=Physical Review Letters |year=2003 |volume=90|page=156402 |doi=10.1103/PhysRevLett.90.156402 |issue=15 |pmid=12732058|arxiv=cond-mat/0209406 |bibcode=2003PhRvL..90o6402K }}</ref> and Dirac fermions<ref>{{cite journal |first=Igor A. |last=Luk’yanchuk |first2=Yakov |last2=Kopelevich |title=Phase Analysis of Quantum Oscillations in Graphite |journal=Physical Review Letters |year=2004 |volume=93|page=166402 |doi=10.1103/PhysRevLett.93.166402 |issue=16 |pmid=15525015 |arxiv=cond-mat/0402058 |bibcode=2004PhRvL..93p6402L }}</ref> in bulk graphite. | |||
], 2010.]] | |||
Graphene was properly isolated and characterized in 2004 by ] and ] at the ].<ref name=novo2004/><ref name=aps2009/> They pulled graphene layers from graphite with a common ] in a process called micro-mechanical cleavage, colloquially referred to as the Scotch tape technique.<ref name=manch2014/> The graphene flakes were then transferred onto a thin ] layer on a ] plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. | |||
Even though graphene on nickel and on silicon carbide have both existed in the laboratory for decades, graphene mechanically exfoliated on {{chem|SiO|2}} provided the first proof of the Dirac fermion nature of electrons.{{Citation needed|date=September 2010}} | |||
This work resulted in the two winning the Nobel Prize in Physics in 2010 for their groundbreaking experiments with graphene.<ref name=ukiop2010/><ref name=nobel2013/><ref name=manch2014/> Their publication and the surprisingly easy preparation method that they described, sparked a "graphene gold rush". Research expanded and split off into many different subfields, exploring different exceptional properties of the material—quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc. | |||
] | |||
Geim and Novoselov received several awards for their pioneering research on graphene, notably the 2010 ].<ref>{{cite web |url=http://physicsworld.com/cws/article/news/43939 |title=Graphene pioneers bag Nobel prize |publisher=], UK |date=5 October 2010 }}</ref> | |||
=== Exploring commercial applications === | |||
== Properties == | |||
Since the early 2000s, several companies and research laboratories have been working to develop commercial applications of graphene. In 2014, a ] was established with that purpose at the University of Manchester, with a £60 million initial funding.<ref name=manch2014f/> In ] two commercial manufacturers, Applied Graphene Materials<ref name=burn2014/> and ]<ref name=gibs2014/><ref name=thej2014/> have begun manufacturing. ]<ref name=canew2015/> is a large-scale graphene powder production facility in ]. | |||
=== Structure === | |||
== Structure == | |||
The ] of isolated, single-layer graphene was studied by ] (TEM) on sheets of graphene suspended between bars of a metallic grid.<ref name=Meyer07/> Electron diffraction patterns showed the expected honeycomb lattice. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson">{{Cite journal |last=Carlsson |first=J. M. |title=Graphene: Buckle or break |doi=10.1038/nmat2051 |journal=Nature Materials |volume=6 |year=2007 |pmid=17972931 |issue=11 |bibcode=2007NatMa...6..801C |pages=801–2 }}</ref><ref name="Fasolino">{{Cite journal |last=Fasolino |first=A. |last2=Los |first2=J. H. |last3=Katsnelson |first3=M. I. |title=Intrinsic ripples in graphene |doi=10.1038/nmat2011 |journal=Nature Materials |volume=6 |year=2007 |pmid=17891144 |issue=11 |bibcode=2007NatMa...6..858F |pages=858–61 |arxiv=0704.1793 }}</ref> or may originate from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on {{chem|SiO|2}} substrates are available<ref name=Ishigami07>{{Cite journal |last=Ishigami |first=Masa |author2=et al. |year=2007 |volume=7 |issue=6 |pages=1643–1648 |title=Atomic Structure of Graphene on SiO<sub>2</sub> |journal=Nano Lett |doi=10.1021/nl070613a |pmid=17497819 |bibcode=2007NanoL...7.1643I }}</ref><ref name="Stolyarova">{{Cite journal |last=Stolyarova |first=Elena |author2=et al. |year=2007 |volume=104 |pages=9209–9212 |title=High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface |journal=Proceedings of the National Academy of Sciences |doi=10.1073/pnas.0703337104 |pmid=17517635 |issue=22 |pmc=1874226 |bibcode=2007PNAS..104.9209S |arxiv=0705.0833 }}</ref> via ]. ] residue, which must be removed to obtain atomic-resolution images, may be the "]s" observed in TEM images, and may explain the observed rippling. Rippling on {{chem|SiO|2}} is caused by conformation of graphene to the underlying {{chem|SiO|2}}, and is not intrinsic.<ref name=Ishigami07/> | |||
Graphene is a single layer of carbon atoms tightly bound in a hexagonal honeycomb lattice. It is an allotrope of carbon in the form of a plane of sp<sup>2</sup>-bonded atoms with a molecular bond length of {{convert|0.142|nm|angstrom|abbr=on|lk=on}}. In a graphene sheet, each atom is connected to its three nearest carbon neighbors by ]s, and a delocalized ], which contributes to a ] that extends over the whole sheet. This type of ] is also seen in ]s.<ref name="zdet2015" /><ref name="harris2018" /> The valence band is touched by a ], making graphene a ] with unusual ] that are best described by theories for massless relativistic particles.<ref name="geim2007" /> Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport is ] over long distances; the material exhibits large ] and large nonlinear ].<ref name="lizhi2015" /> | |||
=== Bonding === | |||
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref>{{Cite journal |last=Kasuya |first=D. |last2=Yudasaka |first2=M. |last3=Takahashi |first3=K. |last4=Kokai |first4=F. |last5=Iijima |first5=S. |title=Selective Production of Single-Wall Carbon Nanohorn Aggregates and Their Formation Mechanism |doi=10.1021/jp020387n |journal=J. Phys. Chem. B |volume=106 |year=2002 |page=4947 |issue=19 }}</ref> However, unlayered graphene with only (hk0) rings has been found in the core of ] graphite onions.<ref>{{Cite journal |author=Bernatowicz |author2=T. J. <!-- check this --> |last3=Gibbons |first3=Patrick C. |last4=Lodders |first4=Katharina |last5=Fegley |first5=Bruce |last6=Amari |first6=Sachiko |last7=Lewis |first7=Roy S. |display-authors=2 |year=1996 |title=Constraints on stellar grain formation from presolar graphite in the Murchison meteorite |journal=Astrophysical Journal |volume=472 |pages=760–782 |doi=10.1086/178105 |bibcode=1996ApJ...472..760B |issue=2 }}</ref> TEM studies show faceting at defects in flat graphene sheets<ref>{{Cite journal |last=Fraundorf |first=P. |last2=Wackenhut |first2=M. |year=2002 |title=The core structure of presolar graphite onions |journal=Astrophysical Journal Letters |volume=578 |page=L153–156 |arxiv=astro-ph/0110585 |doi=10.1086/344633 |bibcode=2002ApJ...578L.153F |issue=2 }}</ref> and suggest a role for two-dimensional crystallization from a melt. | |||
] | |||
] | |||
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as ]s. Bombarded with pure carbon atoms, the atoms perfectly align into ]s, completely filling the holes.<ref name=Manchester>{{Cite journal |year=2012 |doi=10.1021/nl300985q |title=Graphene re-knits its holes |journal=Mesoscale and Nanoscale Physics |arxiv=1207.1487v1 |first=Recep |last=Zan |first2=Quentin M. |last2=Ramasse |first3=Ursel |last3=Bangert |first4=Konstantin S. |last4=Novoselov |volume=12 |issue=8 |page=3936|bibcode=2012NanoL..12.3936Z |last2=Ramasse |last3=Bangert |last4=Novoselov }}</ref><ref>Puiu, Tibi (July 12, 2012) . zmescience.com</ref> | |||
Three of the four outer-] ] of each atom in a graphene sheet occupy three sp<sup>2</sup> ] – a combination of orbitals s, p<sub>x</sub> and p<sub>y</sub> — that are shared with the three nearest atoms, forming σ-bonds. The length of these ] is about 0.142 nanometers.<ref name=coop2012/><ref name=felix2013/> | |||
The remaining outer-shell electron occupies a p<sub>z</sub> orbital that is oriented perpendicularly to the plane. These orbitals hybridize together to form two half-filled bands of free-moving electrons, π, and π∗, which are responsible for most of graphene's notable electronic properties.<ref name=coop2012/> Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of ] (ΔH<sub>hydro</sub>) agree well with the literature reports.<ref name=dixit2019/> | |||
=== Chemical === | |||
Graphene sheets stack to form graphite with an interplanar spacing of {{convert|0.335|nm|angstrom|abbr=on|lk=on}}.<ref>{{Cite book |last=Delhaes |first=Pierre |url=https://books.google.com/books?id=7p2pgNOWPbEC&q=sheet&pg=PA8 |title=Graphite and Precursors |date=2000-12-21 |publisher=CRC Press |isbn=978-90-5699-228-6 |language=en}}</ref> | |||
Graphene is the only form of carbon (and generally all solid materials) in which each single atom is in exposure for chemical reaction from two sides (due to the 2D structure). It is known that carbon atoms at the edge of graphene sheets have special chemical reactivity, and graphene has the highest ratio of edgy carbons (in comparison with similar materials such as carbon nanotubes). In addition, various types of defects within the sheet, which are very common, increase the chemical reactivity.<ref name="Denis">{{Cite journal |last=Denis |first=P. A. |last2=Iribarne |first2=F. |title=Comparative Study of Defect Reactivity in Graphene |doi=10.1021/jp4061945 |journal=Journal of Physical Chemistry C |volume=117 |page=19048 |year=2013 |issue=37 }}</ref> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260 °C <ref name="Yamada3">{{Cite journal |last=Yamada |first=Y. |last2=Murota |first2=K |last3=Fujita |first3=R |last4=Kim |first4=J |author5=et al. |title=Subnanometer vacancy defects introduced on graphene by oxygen gas |doi=10.1021/ja4117268 |journal=Journal of American Chemical Society |volume=136 |issue=6 |pages=2232 |year=2014 }}</ref> and the graphene burns at very low temperature (e.g., 350 °C).<ref name="Eftekhari">{{Cite journal |last=Eftekhari |first=A. |last2=Jafarkhani |first2=P. |title=Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage |doi=10.1021/jp410044v |journal=Journal of Physical Chemistry C |volume=117 |page=25845 |year=2013 |issue=48 }}</ref> In fact, graphene is chemically the most reactive form of carbon, owing to the lateral availability of carbon atoms. | |||
Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. But, determination of structures of graphene with oxygen-<ref name="Yamada">{{Cite journal |last=Yamada |first=Y. |last2=Yasuda |first2=H. |last3=Murota |first3=K. |last4=Nakamura |first4=M. |last5=Sodesawa |first5=T. |last6=Sato |first6=S. |title=Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy |doi=10.1007/s10853-013-7630-0 |journal=Journal of Material Science |volume=48 |page=8171 |year=2013 |issue=23 }}</ref> and nitrogen-<ref name="Yamada2">{{Cite journal |last=Yamada |first=Y. |last2=Kim |first2=J. |last3=Murota |first3=K. |last4=Matsuo |first4=S. |last5=Sato |first5=S. |title=Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy |doi=10.1016/j.carbon.2013.12.061 |journal=Carbon |volume=70 |pages=59 |year=2014 }}</ref> containing functional groups is a difficult task unless the structures are well controlled. | |||
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref name=kasu2002/> However, unlayered graphene displaying only (hk0) rings have been observed in the core of ] graphite onions.<ref name=bern1996/> TEM studies show faceting at defects in flat graphene sheets<ref name=fraun2002/> and suggest a role for two-dimensional crystallization from a melt. | |||
In 2013, ] physicists reported that sheets of Graphene one atom thick are a hundred times more chemically reactive than thicker sheets.<ref>{{cite web |url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected |publisher=Phys.org |date=1 February 2013 }}</ref> | |||
=== |
=== Geometry === | ||
] image of graphene|alt=]] | |||
The ] of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of a metallic grid.<ref name=meyer2007/> Some of these images showed a "rippling" of the flat sheet, with an amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,<ref name=geim2007/><ref name=carl2007/><ref name=faso2007/> or may originate from the ubiquitous dirt seen in all TEM images of graphene. ] residue, which must be removed to obtain atomic-resolution images, may be the "]s" observed in TEM images, and may explain the observed rippling.<ref>{{Cite journal |last1=Meyer |first1=Jannik C. |last2=Geim |first2=A. K. |last3=Katsnelson |first3=M. I. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Roth |first6=S. |date=March 2007 |title=The structure of suspended graphene sheets |url=https://www.nature.com/articles/nature05545 |journal=Nature |language=en |volume=446 |issue=7131 |pages=60–63 |doi=10.1038/nature05545 |pmid=17330039 |arxiv=cond-mat/0701379 |bibcode=2007Natur.446...60M |issn=1476-4687}}</ref> | |||
The ] length in graphene is about 0.142 ]s.<ref>{{cite arXiv |eprint=0804.4086 |first=Raji |last=Heyrovska|title=Atomic Structures of Graphene, Benzene and Methane with Bond Lengths as Sums of the Single, Double and Resonance Bond Radii of Carbon |class=physics.gen-ph |year=2008 }}</ref> Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm. | |||
The hexagonal structure is also seen in ] (STM) images of graphene supported on silicon dioxide substrates<ref name=ishi2007/> The rippling seen in these images is caused by the conformation of graphene to the substrates' lattice and is not intrinsic.<ref name=ishi2007/> | |||
=== Electronic === | |||
{{close paraphrasing|section|source=http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons|date=March 2014}} | |||
] band structure for zig-zag orientation. Tightbinding calculations show that zigzag orientation is always metallic.]] | |||
=== Stability === | |||
] band structure for armchair orientation. Tightbinding calculations show that armchair orientation can be semiconducting or metallic depending on width (chirality).]] | |||
] show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm and becomes the most stable ] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=shen2006/> | |||
Graphene differs from most three-dimensional materials. Intrinsic graphene is a ] or zero-gap ]. Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. The energy-momentum relation (]) is linear for low energies near the six corners of the two-dimensional hexagonal ], leading to zero ] for electrons and ].<ref name="E-Phonon">{{Cite book |last=Charlier |first=J.-C. |last2=Eklund |first2=P.C.|last3=Zhu|first3=J. |last4=Ferrari |first4=A.C. |chapter=Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes |title=from Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications, Ed. A. Jorio, G. Dresselhaus, and M.S. Dresselhaus |location=Berlin/Heidelberg |publisher=Springer-Verlag |year=2008 }}</ref> Due to this linear (or "]") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like ] particles described by the ] for spin-1/2 particles.<ref name="Semenoff">{{Cite journal |last=Semenoff |first=G. W. |title=Condensed-Matter Simulation of a Three-Dimensional Anomaly |doi=10.1103/PhysRevLett.53.2449 |journal=Physical Review Letters |volume=53 |page=2449 |year=1984 |bibcode=1984PhRvL..53.2449S |issue=26 }}</ref><ref name=CBE>{{Cite journal |last=Avouris |first=P. |last2=Chen |first2=Z. |last3=Perebeinos |first3=V. |title=Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal=Nature Nanotechnology |volume=2 |year=2007 |pmid=18654384 |issue=10 |bibcode=2007NatNa...2..605A |pages=605–15 }}</ref> Hence, the electrons and holes are called Dirac ] and the six corners of the Brillouin zone are called the Dirac points.<ref name="Semenoff"/> The equation describing the electrons' linear dispersion relation is <math>E=\hbar v_F\sqrt{k_x^2+k_y^2}</math>; where the ] ''v<sub>F</sub>'' ~ {{val|e=6|u=m/s}}, and the ] ''k'' is measured from the Dirac points (the zero of energy is chosen here to coincide with the Dirac points).<ref name=CBE/> | |||
== Electronic properties == | |||
Electrical resistance in 40-nanometer-wide ]s of epitaxially-applied graphene changes in discrete steps following ] principles. Graphene nanoribbons can act more like ]s or ]s, allowing electrons to flow smoothly along the material's edges. In conductors such as copper, resistance increases in proportion to the length as electrons encounter more and more impurities while moving through the conductor. Electrons travel ballistically, similar to those observed in cylindrical ]s, exceeding theoretical conductance predictions for graphene by a factor of 10. Electrons in the nanoribbons can move tens or hundreds of microns without scattering.<ref name=k1402></ref><ref>{{cite doi|10.1038/nature12952 }}</ref> | |||
{{main|Electronic properties of graphene}} | |||
] | |||
Graphene is a zero-gap ] because its conduction and ] meet at the ]. The Dirac points are six locations in ] on the edge of the ], divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene a ] of <math>g_{v} = 2</math>. In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero.<ref name=coop2012/> | |||
If the in-plane direction is confined rather than infinite, its electronic structure changes. These confined structures are referred to as ]s. If the nanoribbon has a "zig-zag" edge, the bandgap remains zero. If it has an "armchair" edge, the bandgap is non-zero. | |||
The measured graphene nanoribbons were approximately 40 nanometers wide that had been grown on the edges of three-dimensional structures etched into ] wafers. When the wafers are heated to approximately {{convert|1000|C|F}}, silicon is preferentially driven off along the edges, forming graphene nanoribbons whose structure is determined by the pattern of the three-dimensional surface.<ref name=k1402/> | |||
Graphene's honeycomb structure can be viewed as two interleaving triangular lattices. This perspective has been used to calculate the band structure for a single graphite layer using a tight-binding approximation.<ref name=coop2012/> | |||
The nanoribbons have perfectly smooth edges, annealed by the fabrication process. Electrons on the edge flow more like photons in ], helping them avoid scattering. Ballistic conductance extended for up to 16 microns. Electron mobility measurements surpassing one million correspond to a ] of one ohm per square— two orders of magnitude lower than what is observed in two-dimensional graphene and one tenth of theoretical predictions.<ref name=k1402/> | |||
Transport is dominated by two modes. One is ballistic and temperature independent; while the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres.<ref name=k1402/> | |||
Theoretical explanations of the phenomenon are incomplete, although they may produce a new type of electronic transport similar to what is observed in ]s.<ref name=k1402/> | |||
=== |
=== Electronic spectrum === | ||
Electrons propagating through the graphene honeycomb lattice effectively lose their mass, producing ]s described by a 2D analogue of the ] rather than the ] for spin-{{sfrac|1|2}} particles.<ref name="Castro" /><ref name="E-Phonon">{{cite book |url={{google books |plainurl=yes |id=ammoVEI-H2gC}} |last1=Charlier |first1=J.-C. |last2=Eklund |first2=P.C. |last3=Zhu |first3=J. |last4=Ferrari |first4=A.C. |chapter=Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes |title=Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications |editor1-first=A. |editor1-last=Jorio |editor2-first=G. |editor2-last=Dresselhaus |editor3-first=M.S. |editor3-last=Dresselhaus |editor-link3=Mildred Dresselhaus|location=Berlin/Heidelberg |publisher=Springer-Verlag |year=2008|page=673}}</ref> | |||
Graphene's unit cell has two identical carbon atoms and two zero-energy states: one in which the electron resides on atom A, the other in which the electron resides on atom B. Both states exist at exactly zero energy. However, if the two atoms in the unit cell are not identical, the situation changes. Hunt et al. show that placing hBN in contact with graphene can alter the potential felt at atom A versus atom B enough that the electrons develop a mass and accompanying band gap of about 30 meV.<ref name=sci1306>{{cite doi|10.1126/science.1240317 }}</ref> | |||
=== Dispersion relation === | |||
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via ]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.<ref name=sci1306/> | |||
]{{citation needed|date=July 2020}}|220x220px]] | |||
The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by ] and ]. This effect provided direct evidence of graphene's theoretically predicted ] of massless ]s and proof of the Dirac fermion nature of electrons.<ref name=novo2005/><ref name=zhang2005/> These effects were previously observed in bulk graphite by Yakov Kopelevich, Igor A. Luk'yanchuk, and others, in 2003–2004.<ref name=kope2003/><ref name=luky2004/> | |||
If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of ]s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against ]ing and could carry currents without dissipation.<ref name=sci1306/> | |||
When atoms are placed onto the graphene hexagonal lattice, the overlap between the ''p''<sub>z</sub>(π) orbitals and the ''s'' or the ''p''<sub>x</sub> and ''p''<sub>y</sub> orbitals is zero by symmetry. Therefore, ''p''<sub>z</sub> electrons forming the π bands in graphene can be treated independently. Within this π-band approximation, using a conventional ] model, the ] (restricted to first-nearest-neighbor interactions only) that produces the energy of the electrons with wave vector ''k'' is:<ref name="Semenoff" /><ref name="Wallace">{{cite journal |last=Wallace |first=P.R. |s2cid=53633968 |title=The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume=71 |year=1947 |pages=622–634 |bibcode=1947PhRv...71..622W |issue=9}}</ref> | |||
==== Electron transport ==== | |||
:<math>E(k_x,k_y)=\pm\,\gamma_0\sqrt{1+4\cos^2{\tfrac{1}{2}ak_x}+4\cos{\tfrac{1}{2}ak_x} \cdot \cos{\tfrac{\sqrt{3}}{2}ak_y}}</math> | |||
Experimental results from transport measurements show that graphene has a remarkably high ] at room temperature, with reported values in excess of {{val|fmt=commas|15000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.{{sfn|Geim|Novoselov|2007}} Additionally, the symmetry of the experimentally measured conductance indicates that hole and electron mobilities should be nearly the same.<ref name="E-Phonon"/> The mobility is nearly independent of temperature between {{val|10|u=K}} and {{val|100|u=K}},<ref name="2dgasDiracFermions">{{Cite journal |last=Novoselov |first=K. S. |title=Two-dimensional gas of massless Dirac fermions in graphene |doi=10.1038/nature04233 |journal=Nature |volume=438 |pages=197–200 |year=2005 |pmid=16281030 |issue=7065 |arxiv=cond-mat/0509330 |bibcode=2005Natur.438..197N |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Jiang |first4=D. |last5=Katsnelson |first5=M. I. |last6=Grigorieva |first6=I. V. |last7=Dubonos |first7=S. V. |last8=Firsov |first8=A. A. }}</ref><ref name="GiantMobility">{{Cite journal |last=Morozov |first=S.V. |title=Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal=Physical Review Letters |volume=100 |page=016602 |year=2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M |issue=1 |last2=Novoselov |first2=K. |last3=Katsnelson |first3=M. |last4=Schedin |first4=F. |last5=Elias |first5=D. |last6=Jaszczak |first6=J. |last7=Geim |first7=A. |arxiv=0710.5304 }}</ref><ref name=E-ph>{{Cite journal |last=Chen |first=J. H. |title=Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO<sub>2</sub> |doi=10.1038/nnano.2008.58 |journal=Nature Nanotechnology |volume=3 |year=2008 |pmid=18654504 |issue=4 |pages=206–9 |last2=Jang |first2=Chaun |last3=Xiao |first3=Shudong |last4=Ishigami |first4=Masa |last5=Fuhrer |first5=Michael S. }}</ref> which implies that the dominant scattering mechanism is ]. Scattering by the acoustic ]s of graphene intrinsically limits room temperature mobility to {{val|fmt=commas|200000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}} at a carrier density of {{val|e=12|u=cm<sup>−2</sup>}}.<ref name=E-ph/><ref name="GrapheneMC">{{Cite journal |last=Akturk |first=A. |last2=Goldsman |first2=N. |title=Electron transport and full-band electron–phonon interactions in graphene |doi=10.1063/1.2890147 |journal=Journal of Applied Physics |volume=103 |page=053702 |year=2008 |bibcode=2008JAP...103e3702A |issue=5 }}</ref> The corresponding ] of the graphene sheet would be {{val|e=-6|u=Ω·cm}}. This is less than the resistivity of ], the lowest known at room temperature.<ref name="UMDnews">. Newsdesk.umd.edu (2008-03-24). Retrieved on 2014-01-12.</ref> However, for graphene on {{chem|SiO|2}} substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons. This limits mobility to {{val|fmt=commas|40000|u=cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>}}.<ref name=E-ph/> | |||
with the nearest-neighbor (π orbitals) hopping energy ''γ''<sub>0</sub> ≈ {{val|2.8 |u=eV}} and the ] {{nowrap|''a'' ≈ {{val|2.46 |u=Å}}}}. The conduction and valence bands correspond to the different signs. With one ''p''<sub>z</sub> electron per atom in this model, the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the ''K'' point in the Brillouin zone), where there is a zero density of states but no band gap. Thus, graphene exhibits a semi-metallic (or zero-gap semiconductor) character, although this is not true for a graphene sheet rolled into a ] due to its curvature. Two of the six Dirac points are independent, while the rest are equivalent by symmetry. Near the ''K''-points, the energy depends ''linearly'' on the wave vector, similar to a relativistic particle.<ref name="Semenoff"/><ref name="CBE">{{Cite journal |last1=Avouris |first1=P. |last2=Chen |first2=Z. |last3=Perebeinos |first3=V. |title=Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal=Nature Nanotechnology |volume=2 |year=2007 |pmid=18654384 |issue=10 |bibcode=2007NatNa...2..605A |pages=605–15}}</ref> Since an elementary cell of the lattice has a basis of two atoms, the ] has an effective ]. | |||
Despite zero carrier density near the Dirac points, graphene exhibits a minimum ] on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon"/> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of order <math>4e^2/h</math> or greater{{sfn|Geim|Novoselov|2007}} and depend on impurity concentration.<ref name=K>{{Cite journal |last=Chen |first=J. H. |title=Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal=Nature Physics |volume=4 |pages=377–381 |year=2008 |bibcode=2008NatPh...4..377C |issue=5 |last2=Jang |first2=C. |last3=Adam |first3=S. |last4=Fuhrer |first4=M. S. |last5=Williams |first5=E. D. |last6=Ishigami |first6=M. |arxiv=0708.2408 }}</ref> | |||
Consequently, at low energies even neglecting the true spin, electrons can be described by an equation formally equivalent to the massless ]. Hence, the electrons and holes are called Dirac ].<ref name="Semenoff" /> This pseudo-relativistic description is restricted to the ], i.e., to vanishing rest mass ''M''<sub>0</sub>, leading to interesting additional features:<ref name="Semenoff" /><ref name="cabra2">{{cite journal |last1=Lamas |first1=C.A. |first2=D.C. |last2=Cabra |first3=N. |last3=Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |page=75108 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406 |bibcode=2009PhRvB..80g5108L|s2cid=119213419 }}</ref> | |||
Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in vacuum.<ref name="K" /><ref name="ChemDoping">{{Cite journal |last=Schedin |first=F. |title=Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal=Nature Materials |volume=6 |pages=652–655 |year=2007 |pmid=17660825 |issue=9 |bibcode=2007NatMa...6..652S |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Hill |first4=E. W. |last5=Blake |first5=P. |last6=Katsnelson |first6=M. I. |last7=Novoselov |first7=K. S. }}</ref> Even for ] concentrations in excess of 10<sup>12</sup> cm<sup>−2</sup> carrier mobility exhibits no observable change.<ref name="ChemDoping"/> Graphene doped with ] in ] at low temperature can reduce mobility 20-fold.<ref name="K" /><ref name="GrapheneCharge">{{Cite journal |last=Adam |first=S. |title=A self-consistent theory for graphene transport |journal=Proc. Nat. Acad. Sci. USA |volume=104 |arxiv=0705.1540 |year=2007 |doi=10.1073/pnas.0704772104 |pmid=18003926 |issue=47 |pmc=2141788 |bibcode=2007PNAS..10418392A |pages=18392–7 |last2=Hwang |first2=E. H. |last3=Galitski |first3=V. M. |last4=Das Sarma |first4=S. }}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium. | |||
:<math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math> | |||
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum<ref>{{Cite journal |first=Hadar |last=Steinberg |first2=Gilad |last2=Barak |first3=Amir |last3=Yacoby |author4=et al. |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi=10.1038/nphys810 |bibcode=2008NatPh...4..116S |arxiv=0803.0744 }}</ref>) is thought to occur. It may therefore be a suitable material for constructing ]s<ref>{{Cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |first=Agung |last=Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode=2010arXiv1003.4590T |issue=11–12 }}</ref> using ]ic circuits.<ref>{{Cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |first=Jiannis K. |last=Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |page=375 |bibcode=2009ConPh..50..375P |issue=2 }}<br/>, M. Franz, University of British Columbia, January 5, 2008</ref> | |||
Here ''v<sub>F</sub>'' ~ {{val |e=6 |u=m/s}} (.003 c) is the ] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the ], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro" /> | |||
=== Optical === | |||
The equation describing the electrons' linear dispersion relation is: | |||
] above}}Photograph of graphene in transmitted light. This one-atom-thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light.]] | |||
:<math>E(q)=\hbar v_F q</math> | |||
Graphene's unique optical properties produce an unexpectedly high ] for an atomic monolayer in vacuum, absorbing ''πα'' ≈ 2.3% of white ], where ''α'' is the ].<ref>{{Cite journal |title=Universal infrared conductance of graphite |first=A. B. |last=Kuzmenko |first2=E. |last2=Van Heumen |first3=F. |last3=Carbone |first4=D. |last4=Van Der Marel |journal=Physical Review Letters |volume=100 |page=117401 |doi=10.1103/PhysRevLett.100.117401 |year=2008 |pmid=18517825 |issue=11 |bibcode=2008PhRvL.100k7401K |arxiv=0712.0835 }}</ref> This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole ] meeting each other at the ]... is qualitatively different from more common ]s".<ref>{{Cite journal |title=Fine Structure Constant Defines Visual Transparency of Graphene |url=http://onnes.ph.man.ac.uk/nano/Publications/Science_2008fsc.pdf |format=PDF |last=Nair |first=R. R. |journal=] |year=2008 |doi=10.1126/science.1156965 |volume=320 |page=1308 |pmid=18388259 |issue=5881 |bibcode=2008Sci...320.1308N |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. }} </ref> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, the interatomic distance, hopping value and frequency cancel when optical conductance is calculated using ] in the thin-film limit. | |||
where the ] ''q'' is measured from the Brillouin zone vertex K, <math>q=\left|\mathbf{k}-\mathrm{K}\right|</math>, and the zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice.<ref name="CBE" /> | |||
Although confirmed experimentally, the measurement is not precise enough to improve on other techniques for determining the ].<ref>{{Cite news |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |publisher=ScienceDaily |date=4 April 2008 }}</ref> | |||
=== Single-atom wave propagation === | |||
Graphene's ] can be tuned from 0 to 0.25 eV (about 5 micrometre wavelength) by applying voltage to a dual-gate bilayer graphene ] (FET) at room temperature.<ref>{{Cite journal |doi=10.1038/nature08105 |journal=Nature |last=Zhang |first=Y. |volume=459 |pages=820–823 |date=11 June 2009 |title=Direct observation of a widely tunable bandgap in bilayer graphene |pmid=19516337 |issue=7248 |bibcode=2009Natur.459..820Z |last2=Tang |first2=Tsung-Ta |last3=Girit |first3=Caglar |last4=Hao |first4=Zhao |last5=Martin |first5=Michael C. |last6=Zettl |first6=Alex |last7=Crommie |first7=Michael F. |last8=Shen |first8=Y. Ron |last9=Wang |first9=Feng |display-authors=9 }}</ref> The optical response of ] is tunable into the ] regime by an applied magnetic field.<ref>{{Cite journal |doi=10.1063/1.2964093 |journal=Appl Phys Lett |first=Junfeng |last=Liu |first2=A. R. |last2=Wright |first3=Chao |last3=Zhang |first4=Zhongshui |last4=Ma |volume=93 |pages=041106–041110 |date=29 July 2008 |title=Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode=2008ApPhL..93d1106L |issue=4 }}</ref> Graphene/graphene oxide systems exhibit ], allowing tuning of both linear and ultrafast optical properties.<ref name="Kurum2011">{{Cite journal |last=Kurum |first=U. |title=Electrochemically tunable ultrafast optical response of graphene oxide |journal=Applied Physics Letters |volume=98 |page=141103 |year=2011 |bibcode=2011ApPhL..98b1103M |doi=10.1063/1.3540647 |issue=2 |last2=Liu |first2=Bo |last3=Zhang |first3=Kailiang |last4=Liu |first4=Yan |last5=Zhang |first5=Hao }}</ref> | |||
Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as ]s, ]s, and ]. | |||
A graphene-based ] (one-dimensional ]) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633 nm He-Ne laser as the light source.<ref>{{cite journal |first=K.V. |last=Sreekanth |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |pmid=23071901 |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |volume=2 |pages=737 |bibcode=2012NatSR...2E.737S |pmc=3471096 }}</ref> | |||
=== Ambipolar electron and hole transport === | |||
==== Saturable absorption ==== | |||
] | |||
Graphene exhibits high ] at room temperature, with values reported in excess of {{val|15000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name=geim2007/> Hole and electron mobilities are nearly identical.<ref name="E-Phonon" /> The mobility is independent of temperature between {{val|10 |u=K}} and {{val|100 |u=K}},<ref name=novo2005/><ref name="GiantMobility">{{cite journal |last1=Morozov |first1=S.V. |last2=Novoselov |first2=K. |last3=Katsnelson |first3=M. |last4=Schedin |first4=F. |last5=Elias |first5=D. |last6=Jaszczak |first6=J. |last7=Geim |first7=A. |title=Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal=Physical Review Letters |volume=100 |page=016602 |year=2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M |issue=1 |arxiv=0710.5304|s2cid=3543049 }}</ref><ref name="E-ph">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=Chaun |last3=Xiao |first3=Shudong |last4=Ishigami |first4=Masa |last5=Fuhrer |first5=Michael S. |title=Intrinsic and Extrinsic Performance Limits of Graphene Devices on {{chem|SiO|2}} |doi=10.1038/nnano.2008.58 |journal=Nature Nanotechnology |volume=3 |year=2008 |pmid=18654504 |issue=4 |pages=206–9|arxiv=0711.3646 |s2cid=12221376 }}</ref> showing minimal change even at room temperature (300 K),<ref name=geim2007/> suggesting that the dominant scattering mechanism is ]. Scattering by graphene's acoustic ]s intrinsically limits room temperature mobility in freestanding graphene to {{val|200000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}} at a carrier density of {{val |e=12 |u=cm<sup>−2</sup>}}.<ref name="E-ph" /><ref name="GrapheneMC">{{cite journal |last1=Akturk |first1=A. |last2=Goldsman |first2=N. |title=Electron transport and full-band electron-phonon interactions in graphene |doi=10.1063/1.2890147 |journal=Journal of Applied Physics |volume=103 |year=2008 |bibcode=2008JAP...103e3702A |issue=5|pages=053702–053702–8 }}</ref> | |||
Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed ] and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to ] region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of ]s, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast ]. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.<ref name="Kurum2011" /><ref>{{cite journal |last=Bao |first=Qiaoliang |title=Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers |url=http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122454/http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf |archivedate=2011-07-17 |journal=Advanced Functional Materials |volume=19 |page=3077 |year=2009 |doi=10.1002/adfm.200901007 |issue=19 |last2=Zhang |first2=Han |last3=Wang |first3=Yu |last4=Ni |first4=Zhenhua |last5=Yan |first5=Yongli |last6=Shen |first6=Ze Xiang |last7=Loh |first7=Kian Ping |last8=Tang |first8=Ding Yuan }}<br/>{{Cite journal |last=Zhang |first=H. |title=Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene |journal=Optics Express |volume=17 |page=P17630 |url=http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122606/http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf |archivedate=2011-07-17 |bibcode=2009OExpr..1717630Z |last2=Tang |first2=D. Y. |last3=Zhao |first3=L. M. |last4=Bao |first4=Q. L. |last5=Loh |first5=K. P. |year=2009 |doi=10.1364/OE.17.017630 |issue=20 |arxiv=0909.5536 }}<br/>{{Cite journal |last=Zhang |first=H. |last2=Bao |first2=Qiaoliang |last3=Tang |first3=Dingyuan |last4=Zhao |first4=Luming |last5=Loh |first5=Kianping |title=Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker |journal=Applied Physics Letters |volume=95 |page=P141103 |url=http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |format=PDF |archiveurl=http://web.archive.org/web/20110717122745/http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf |format=PDF |archivedate=2011-07-17 |bibcode=2009ApPhL..95n1103Z |year=2009 |doi=10.1063/1.3244206 |issue=14 |arxiv=0909.5540 }}<br/> | |||
{{Cite journal |last=Zhang |first=H. |last2=Tang |first2=Dingyuan |last3=Knize |first3=R. J. |last4=Zhao |first4=Luming |last5=Bao |first5=Qiaoliang |last6=Loh |first6=Kian Ping |title=Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser |journal=Applied Physics Letters |volume=96 |page=111112 |url=http://www.sciencenet.cn/upload/blog/file/2010/3/20103191224576536.pdf |format=PDF |archiveurl=http://www.webcitation.org/5pt6I3oAm |archivedate=2010-05-21 |doi=10.1063/1.3367743 |bibcode=2010ApPhL..96k1112Z |year=2010 |issue=11|arxiv=1003.0154 }}, {{cite journal |last=Zhang |title=Graphene: Mode-locked lasers |journal=NPG Asia Materials |year=2009 |doi=10.1038/asiamat.2009.52 }}</ref> | |||
Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave saturable absorption in graphene demonstrates the possibility of graphene microwave and terahertz photonics devices, such as microwave saturable absorber, modulator, polarizer, microwave signal processing and broad-band wireless access networks.<ref name=Zheng>{{Cite journal |last=Zheng |first=Z. |last2=Zhao |first2=Chujun |last3=Lu |first3=Shunbin |last4=Chen |first4=Yu |last5=Li |first5=Ying |last6=Zhang |first6=Han |last7=Wen |first7=Shuangchun|title=Microwave and optical saturable absorption in graphene |journal=Optics Express |year=2012 |volume=20 |issue=21 |pages=23201–23214 |doi=10.1364/OE.20.023201 |url=http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww.opticsinfobase.org%2FDirectPDFAccess%2FDDD3E2E7-B65E-B0FE-CE508B2B58C39140_242486%2Foe-20-21-23201.pdf%3Fda%3D1%26id%3D242486%26seq%3D0%26mobile%3Dno&org= |format=PDF |pmid=23188285 |bibcode=2012OExpr..2023201Z }}</ref> | |||
The corresponding ] of graphene sheets is {{val |e=-8 |u=Ω⋅m}}, lower than the resistivity of ], which is the lowest known at room temperature.<ref name="UMDnews"> {{webarchive|url=https://web.archive.org/web/20130919083015/https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621|date=19 September 2013}}. Newsdesk.umd.edu (24 March 2008). Retrieved on 2014-01-12.</ref> However, on {{chem|SiO|2}} substrates, electron scattering by optical phonons of the substrate has a more significant effect than scattering by graphene's phonons, limiting mobility to {{val|40000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name="E-ph" /> | |||
==== Nonlinear Kerr effect ==== | |||
Charge transport can be affected by the adsorption of contaminants such as ] and ] molecules, leading to non-repetitive and large hysteresis I-V characteristics. Researchers need to conduct electrical measurements in a vacuum. Coating the graphene surface with materials such as SiN, ] or h-BN has been proposed for protection. In January 2015, the first stable graphene device operation in the air over several weeks was reported for graphene whose surface was protected by ].<ref>{{cite journal |last=Sagade |first=A. A. |s2cid=24846431 |title=Highly Air Stable Passivation of Graphene Based Field Effect Devices |doi=10.1039/c4nr07457b |pmid=25631337 |journal=Nanoscale |volume=7 |issue=8 |pages=3558–3564 |year=2015 |display-authors=etal |bibcode=2015Nanos...7.3558S}}</ref><ref>{{cite web|url=https://spectrum.ieee.org/graphene-devices-stand-the-test-of-time|title=Graphene Devices Stand the Test of Time|date=2015-01-22|access-date=2 February 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801055523/https://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphene-devices-stand-the-test-of-time|url-status=live}}</ref> In 2015, ]-coated graphene exhibited ], a first for graphene.<ref>{{cite web |title=Researchers create superconducting graphene |url=http://www.rdmag.com/news/2015/09/researchers-create-superconducting-graphene |access-date=2015-09-22 |date=2015-09-09 |archive-date=7 September 2017 |archive-url=https://web.archive.org/web/20170907033306/https://www.rdmag.com/news/2015/09/researchers-create-superconducting-graphene |url-status=live }}</ref> | |||
Under more intensive laser illumination, graphene could also possess a nonlinear phase shift due to the optical nonlinear ]. Based on a typical open and close aperture z-scan measurement, graphene possesses a giant non-linear Kerr coefficient of {{val|e=-7|u=cm<sup>2</sup>·W<sup>−1</sup>}}, almost nine orders of magnitude larger than that of bulk dielectrics.<ref name="ZHANGHAN">{{ Cite journal |last=Zhang |first=H. |title=Z-scan measurement of the nonlinear refractive index of graphene |journal=Optics Letters |year=2012 |volume=37 |issue=11 |pages=1856–1858 |doi=10.1364/OL.37.001856 |pmid=22660052 |last2=Virally |first2=Stéphane |last3=Bao |first3=Qiaoliang |last4=Kian Ping |first4=Loh |last5=Massar |first5=Serge |last6=Godbout |first6=Nicolas |last7=Kockaert |first7=Pascal |bibcode=2012OptL...37.1856Z }}</ref> This suggests that graphene may be a nonlinear Kerr medium, paving the way for graphene-based nonlinear Kerr photonics such as a ]. | |||
Electrical resistance in 40-nanometer-wide ]s of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by a factor of 10. The ribbons can function more like ]s or ]s, allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases proportionally with length as electrons encounter impurities.<ref name="k1402">{{cite web |url=http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons |title=New form of graphene allows electrons to behave like photons |work=kurzweilai.net |access-date=27 February 2014 |archive-date=2 March 2014 |archive-url=https://web.archive.org/web/20140302070314/http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons? |url-status=live }}</ref><ref name="doi_12952">{{cite journal |doi=10.1038/nature12952 |pmid=24499819 |title=Exceptional ballistic transport in epitaxial graphene nanoribbons |journal=Nature |volume=506 |issue=7488 |pages=349–354 |year=2014 |last1=Baringhaus |first1=J. |last2=Ruan |first2=M. |last3=Edler |first3=F. |last4=Tejeda |first4=A. |last5=Sicot |first5=M. |last6=Taleb-Ibrahimi |first6=A. |last7=Li |first7=A. P. |last8=Jiang |first8=Z. |last9=Conrad |first9=E. H. |last10=Berger |first10=C. |last11=Tegenkamp |first11=C. |last12=De Heer |first12=W. A. |arxiv=1301.5354 |bibcode=2014Natur.506..349B|s2cid=4445858 }}</ref> | |||
=== Excitonic === | |||
Transport is dominated by two modes: one ballistic and temperature-independent, and the other thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at a specific length—the ballistic mode at 16 micrometers and the thermally activated mode at 160 nanometers (1% of the former length).<ref name="k1402" /> | |||
First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |page=601 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last=Onida |first=Giovanni |last2=Rubio |first2=Angel |last3=Rubio |first3=Angel |issue=2 }}</ref> With GW calculation, the properties of graphene-based materials are accurately investigated, including graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last=Yang |first=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823|arxiv=0906.0969 }}</ref> ],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last=Prezzi |first=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4|arxiv=0706.0916 |bibcode=2008PhRvB..77d1404P }}<br/>{{cite journal |journal=Nano Lett. |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last=Yang |first=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720|arxiv=0707.2983 |bibcode=2007NanoL...7.3112Y }}<br/>{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last=Yang |first=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843 }}</ref> edge and surface functionalized armchair graphene nanoribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |page=17257 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last=Zhu |first=Xi |last2=Su |first2=Haibin |issue=41 }}</ref> hydrogen saturated armchair graphene nanoribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last=Wang |first=Min |last2=Li |first2=Chang Ming |issue=5 |pmid=21503364 |bibcode=2011Nanos...3.2324W }}</ref> ] in graphene SNS junctions with single localized defect<ref>{{Cite journal ||first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |page=2896 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13|arxiv=1006.1391 |bibcode=2010PhyB..405.2896B }}<br/>{{Cite journal |first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=110 |page=613 |year=2010 |doi=10.1134/S1063776110040084 |issue=4|arxiv=1006.1386 |bibcode=2010JETP..110..613B }}</ref> and scaling properties in armchair graphene nanoribbons.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |last=Zhu |first=Xi |last2=Su |first2=Haibin }}</ref> | |||
Graphene electrons can traverse micrometer distances without scattering, even at room temperature.<ref name="Castro" /> | |||
=== Thermal === | |||
==== Electrical conductivity and charge transport ==== | |||
==== Stability ==== | |||
Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon" /> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of the order of <math>4e^2/h</math> or greater<ref name="geim2007" /> and depend on impurity concentration.<ref name="K">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=C. |last3=Adam |first3=S. |last4=Fuhrer |first4=M. S. |last5=Williams |first5=E. D. |last6=Ishigami |first6=M. |title=Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal=Nature Physics |volume=4 |pages=377–381 |year=2008 |bibcode=2008NatPh...4..377C |issue=5 |arxiv=0708.2408|s2cid=53419753 }}</ref> | |||
Near zero carrier density, graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density, governed by the interplay between photoinduced changes of both the Drude weight and the carrier scattering rate.<ref> {{Webarchive|url=https://web.archive.org/web/20181106192035/http://www.kurzweilai.net/light-pulses-control-how-graphene-conducts-electricity |date=6 November 2018 }}. kurzweilai.net. 4 August 2014</ref> | |||
] show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm (“graphene is the least stable structure until about 6000 atoms”) and becomes the most stable ] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=stability>{{Cite journal |first=O. B. |last=Shenderova |first2=V. V. |last2=Zhirnov |first3=D. W. |last3=Brenner |year=2002 |title=Carbon Nanostructures |journal=Critical Reviews in Solid State and Materials Sciences |volume=27 |page=227 |doi=10.1080/10408430208500497 |bibcode=2002CRSSM..27..227S |issue=3–4 }}</ref> | |||
Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in a vacuum.<ref name="K" /><ref name="ChemDoping">{{cite journal |last1=Schedin |first1=F. |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Hill |first4=E. W. |last5=Blake |first5=P. |last6=Katsnelson |first6=M. I. |last7=Novoselov |first7=K. S. |title=Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal=Nature Materials |volume=6 |pages=652–655 |year=2007 |pmid=17660825 |issue=9 |bibcode=2007NatMa...6..652S|arxiv=cond-mat/0610809 |s2cid=3518448 }}</ref> Even for ] concentrations in excess of 10<sup>12</sup> cm<sup>−2</sup>, carrier mobility exhibits no observable change.<ref name="ChemDoping" /> Graphene doped with ] in ] at low temperature can reduce mobility 20-fold.<ref name="K" /><ref name="GrapheneCharge">{{cite journal |last1=Adam |first1=S. |last2=Hwang |first2=E. H. |last3=Galitski |first3=V. M. |last4=Das Sarma |first4=S. |title=A self-consistent theory for graphene transport |journal=Proc. Natl. Acad. Sci. USA |volume=104 |arxiv=0705.1540 |year=2007 |doi=10.1073/pnas.0704772104 |pmid=18003926 |issue=47 |pmc=2141788 |bibcode=2007PNAS..10418392A |pages=18392–7|doi-access=free }}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium. | |||
==== Conductivity ==== | |||
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum)<ref>{{cite journal |first1=Hadar |last1=Steinberg |first2=Gilad |last2=Barak |first3=Amir |last3=Yacoby |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi=10.1038/nphys810 |bibcode=2008NatPh...4..116S |arxiv=0803.0744 |s2cid=14581125 |display-authors=etal}}</ref> is thought to occur. It may therefore be a suitable material for constructing ]s<ref>{{cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |first=Agung |last=Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode=2010arXiv1003.4590T |issue=11–12 |doi=10.26421/QIC12.11-12-7 |s2cid=28441144 |access-date=6 August 2013 |archive-date=6 November 2018 |archive-url=https://web.archive.org/web/20181106210723/https://dl.acm.org/citation.cfm?id=2481569.2481576 |url-status=live }}</ref> using ]ic circuits.<ref>{{cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |first=Jiannis K. |last=Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |pages=375–389 |bibcode=2009ConPh..50..375P |issue=2|s2cid=8825103 }}<br />{{cite web |url=http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf |title=Fractionalization of charge and statistics in graphene and related structures |first=M. |last=Franz |publisher=University of British Columbia |date=5 January 2008 |access-date=2 September 2009 |archive-date=15 November 2010 |archive-url=https://web.archive.org/web/20101115121039/http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf |url-status=dead }}</ref> | |||
The near-room temperature ] of graphene was measured to be between (4.84±0.44) × 10<sup>3</sup> to (5.30±0.48) × 10<sup>3</sup> W·m<sup>−1</sup>·K<sup>−1</sup>. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamonds. The isotopic composition, the ratio of ] to ], has a significant impact on thermal conductivity, where isotopically pure <sup>12</sup>C graphene has higher conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name=chen2012natmat>{{Cite journal |first=Shanshan | |||
|last=Chen |first2=Qingzhi |last2=Wu |first3=Columbia |last3=Mishra |first4=Junyong |last4=Kang |first5=Hengji |last5=Zhang | |||
|first6=Kyeongjae |last6=Cho |first7=Weiwei |last7=Cai |first8=Alexander A. |last8=Balandin |first9=Rodney S. |last9=Ruoff | |||
|publication-date=2012-01-10 |title=Thermal conductivity of isotopically modified graphene |journal=] | |||
|volume=11 |issue=3 |page=203 |pmid= |doi=10.1038/nmat3207 |year=2012 |arxiv=1112.5752 |bibcode=2012NatMa..11..203C |display-authors=9 }}<br />''Lay summary'': {{Cite news |publication-date=2012-01-12 |title=Keeping Electronics Cool | |||
|periodical=] |at=scientificcomputing.com | |||
|publisher=] | |||
|url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |first=Suzanne |last=Tracy |date=12 January 2012 }}</ref> It can be shown by using the ], that the thermal conduction is ]-dominated.<ref name="Balandin">{{Cite journal |last=Balandin |first=A. A. |date=20 February 2008 | |||
|doi=10.1021/nl0731872 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=] | |||
|pmid=18284217 |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B |last2=Ghosh |first2=Suchismita |last3=Bao |first3=Wenzhong |last4=Calizo |first4=Irene |last5=Teweldebrhan |first5=Desalegne |last6=Miao |first6=Feng |last7=Lau |first7=Chun Ning | |||
}}</ref> However, for a gated graphene strip, an applied gate bias causing a ] shift much larger than k<sub>B</sub>T can cause the electronic contribution to increase and dominate over the ] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito">{{Cite journal |journal=] | |||
|last=Saito |first=K. |last2=Nakamura |first2=J. |last3=Natori |first3=A. |title=Ballistic thermal conductance of a graphene sheet | |||
|volume=76 |page=115409 |year=2007 |doi=10.1103/PhysRevB.76.115409 |bibcode=2007PhRvB..76k5409S |issue=11 | |||
}}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |first=Qizhen |last=Liang |first2=Xuxia |last2=Yao |first3=Wei |last3=Wang |first4=Yan |last4=Liu |first5=Ching Ping |last5=Wong |year=2011 |title=A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |journal=ACS Nano |pmid=21384860 |volume=5 |issue=3 |pages=2392–2401 |doi=10.1021/nn200181e }}</ref> | |||
=== Chiral half-integer quantum Hall effect === | |||
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has ] ] of over a {{val|1000|u=W·m<sup>−1</sup>·K<sup>−1</sup>}} (comparable to ]). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger ].<ref>{{Cite book |url=http://books.google.com/?id=7p2pgNOWPbEC |title=Graphite and Precursors |last=Delhaes |first=P. |publisher=CRC Press |year=2001 |isbn=90-5699-228-7 }}</ref> In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{Cite journal |last=Mingo |first=N. |last2=Broido |first2=D.A. |title=Carbon Nanotube Ballistic Thermal Conductance and Its Limits |doi=10.1103/PhysRevLett.95.096105 |journal=Physical Review Letters |volume=95 |page=096105 |year=2005 |bibcode=2005PhRvL..95i6105M |issue=9 }}</ref> | |||
] | |||
==== Quantum hall effect in graphene ==== | |||
Despite its 2-D nature, graphene has 3 ] modes. The two in-plane modes (LA, TA) have a linear ], whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T<sup>2</sup> dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T<sup>1.5</sup> contribution of the out of plane mode.<ref name="mingo"/> Some graphene phonon bands display negative ]s.<ref name="mounet">{{Cite journal |last=Mounet |first=N. |last2=Marzari |first2=N. |title=First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |doi=10.1103/PhysRevB.71.205214 |journal=Physical Review B |volume=71 |page=205214 |year=2005 |arxiv=cond-mat/0412643 |bibcode=2005PhRvB..71t5214M |issue=20 }}</ref> At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and ] (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane ] since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect", was predicted by ] in 1952.<ref name="lifshitz">{{Cite journal |last=Lifshitz |first=I.M. |journal=Journal of Experimental and Theoretical Physics (in Russian) |volume=22 |page=475 |year=1952 }}</ref> | |||
The ] is a quantum mechanical version of the ], which is the production of transverse (perpendicular to the main current) conductivity in the presence of a ]. The quantization of the ] <math>\sigma_{xy}</math> at integer multiples (the "]") of the basic quantity ''e''<sup>2</sup>/''h'' (where ''e'' is the elementary electric charge and ''h'' is the ]). It can usually be observed only in very clean ] or ] solids at temperatures around {{val|3|ul=K}} and very high magnetic fields. | |||
Graphene shows the quantum Hall effect: the conductivity quantization is unusual in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy}=\pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.<ref name="geim2007" /> These anomalies are present not only at extremely low temperatures but also at room temperature, i.e. at roughly {{convert|20|C|K}}.<ref name="novo2005" /> | |||
=== Mechanical === | |||
==== Chiral electrons and anomalies ==== | |||
The flat graphene sheet is unstable with respect to scrolling i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name="nmscrolling">{{Cite journal |first=S. |last=Braga |first2=V. R. |last2=Coluci |first3=S. B. |last3=Legoas |first4=R. |last4=Giro |first5=D. S. |last5=Galvão |first6=R. H. |last6=Baughman |year=2004 |title=Structure and Dynamics of Carbon Nanoscrolls |journal=Nano Letters |volume=4 |page=881 |doi=10.1021/nl0497272 |bibcode=2004NanoL...4..881B |issue=5 }}</ref> | |||
This behavior is a direct result of graphene's chiral, massless Dirac electrons.<ref name="geim2007" /><ref>{{cite journal |last1=Peres |first1=N. M. R. |title=Colloquium : The transport properties of graphene: An introduction |journal=Reviews of Modern Physics |date=15 September 2010 |volume=82 |issue=3 |pages=2673–2700 |doi=10.1103/RevModPhys.82.2673 |arxiv=1007.2849 |bibcode=2010RvMP...82.2673P |s2cid=118585778 }}</ref> In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the ] and is half-filled in neutral graphene,<ref name="Semenoff" /> leading to the "+1/2" in the Hall conductivity.<ref name="gusy2005" /> ] also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy}=\pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at {{nowrap|1=''N'' = 0}} is absent, indicating that bilayer graphene stays metallic at the neutrality point.<ref name="geim2007" /> | |||
] half-integer quantum Hall effect in graphene. Plateaux in transverse conductivity appear at half-integer multiples of 4''e''<sup>2</sup>/''h''.<ref name=geim2007/>]] | |||
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the ], thus the term "''integral'' quantum Hall effect". These oscillations show a phase shift of π, known as ].<ref name=novo2005/><ref name="E-Phonon" /> Berry's phase arises due to chirality or dependence (locking) of the pseudospin quantum number on the momentum of low-energy electrons near the Dirac points.<ref name=zhang2005/> The temperature dependence of the oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass in the Dirac-fermion formalism.<ref name=novo2005/> | |||
==== Experimental observations ==== | |||
As of 2009, graphene appeared to be one of the strongest materials known with a ] over 100 times greater than a hypothetical ] film of the same (thin) thickness,<ref name="nobelprize.org">. nobelprize.org.</ref> with a ] | |||
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of ], show the anomalous effect directly in electrical measurements.<ref name="ByungHeeHong">{{cite journal |last1=Kim |first1=Kuen Soo |title=Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi=10.1038/nature07719 |journal=Nature |volume=457 |pmid=19145232 |issue=7230 |bibcode=2009Natur.457..706K |pages=706–10 |last2=Zhao |first2=Yue |last3=Jang |first3=Houk |last4=Lee |first4=Sang Yoon |last5=Kim |first5=Jong Min |last6=Kim |first6=Kwang S. |last7=Ahn |first7=Jong-Hyun |last8=Kim |first8=Philip |last9=Choi |first9=Jae-Young |last10=Hong |first10=Byung Hee|s2cid=4349731 }}</ref><ref name="0908.1900" /><ref name="ShenAPL" /><ref name="0909.2903" /><ref name="0909.1193" /><ref name="phase1" /> Graphitic layers on the carbon face of silicon carbide show a clear ] in ] experiments, and the effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{cite journal |first=Michael S. |last=Fuhrer |title=A physicist peels back the layers of excitement about graphene |doi=10.1038/4591037e |journal=Nature |volume=459 |page=1037 |year=2009 |pmid=19553953 |issue=7250 |bibcode=2009Natur.459.1037F|s2cid=203913300 |doi-access=free }}</ref> | |||
(stiffness) of {{val|1|u=TPa}} ({{val|fmt=commas|150000000|u=]}}).<ref name=lee>{{Cite journal |last=Lee |first=C. |title=Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene |journal=Science |volume=321 |year=2008 |laysummary=http://web.archive.org/web/20110629131809/http://www.aip.org/isns/reports/2008/027.html |doi=10.1126/science.1157996 |pmid=18635798 |issue=5887 |bibcode=2008Sci...321..385L |pages=385–8 |last2=Wei |first2=X. |last3=Kysar |first3=J. W. |last4=Hone |first4=J. }}</ref> The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4|u=kg}} cat but would weigh only as much as one of the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m<sup>2</sup> of paper).<ref name="nobelprize.org"/> | |||
=== "Massive" electrons === | |||
However, the process of separating it from graphite, where it occurs naturally, requires technological development to be economical enough to be used in industrial processes.<ref name="nypost">{{cite news |url=http://www.nypost.com/seven/08252008/news/regionalnews/toughest_stuff__known_to_man_125993.htm |title=Toughest Stuff Known to Man: Discovery Opens Door to Space Elevator |first=Bill |last=Sanderson |publisher=nypost.com |date=25 August 2008 }}</ref><ref name="ScienceDaily">{{cite web |url=http://www.sciencedaily.com/releases/2010/01/100119111057.htm |title=Breakthrough in Developing Super-Material Graphene |publisher=ScienceDaily |date=20 January 2010 }}</ref> | |||
Graphene's unit cell has two identical carbon atoms and two zero-energy states: one where the electron resides on atom A, and the other on atom B. However, if the unit cell's two atoms are not identical, the situation changes. Research shows that placing ] (h-BN) in contact with graphene can alter the potential felt at atoms A and B sufficiently for the electrons to develop a mass and an accompanying band gap of about 30 meV.<ref name="sci1306">{{cite journal |last1=Fuhrer |first1=M. S. |year=2013 |title=Critical Mass in Graphene |journal=Science |volume=340 |issue=6139 |pages=1413–1414 |bibcode=2013Sci...340.1413F |doi=10.1126/science.1240317 |pmid=23788788 |s2cid=26403885}}</ref> | |||
The ] of suspended graphene sheets has been measured using an ] (AFM). Graphene sheets, held together by van der Waals forces, were suspended over {{chem|SiO|2}} cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was {{val|0.5|u=TPa}}, which differs from that of bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for ] applications such as pressure sensors and resonators.<ref>{{Cite journal |last=Frank |first=I. W. |last2=Tanenbaum |first2=D. M. |last3=Van Der Zande |first3=A.M. |last4=McEuen |first4=P. L. |title=Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal=J. Vac. Sci. Technol. B |volume=25 |pages=2558–2561 |year=2007 |url=http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |format=PDF |bibcode=2007JVSTB..25.2558F |issue=6 }}</ref> | |||
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via ]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a ] and displays much the same physics as topological insulators.<ref name="sci1306" /> | |||
As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the ] shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name=Meyer07/> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.{{sfn|Geim|Novoselov|2007}}<ref name="Carlsson"/><ref name="Fasolino"/><ref>{{Cite journal |first=Dima |last=Bolmatov |first2=Chung-Yu |last2=Mou |title=Graphene-based modulation-doped superlattice structures |journal=Journal of Experimental and Theoretical Physics (JETP) |volume=112 |page=102 |year=2011 |doi=10.1134/S1063776111010043|arxiv=1011.2850 |bibcode=2011JETP..112..102B }}<br/>{{Cite journal |first=Dima |last=Bolmatov |title=Thermodynamic properties of tunneling quasiparticles in graphene-based structures |journal=Physica C |volume=471 |page=1651 |year=2011 |doi=10.1016/j.physc.2011.07.008 |issue=23–24|arxiv=1106.6331 |bibcode=2011PhyC..471.1651B }}</ref> | |||
If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of ]s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against ]ing and could carry currents without dissipation.<ref name="sci1306" /> | |||
== Interactions and phenomena == | |||
=== Strong magnetic fields === | |||
In magnetic fields above 10 ], additional plateaus of the Hall conductivity at {{nowrap |1=''σ''<sub>''xy''</sub> = ''νe''<sup>2</sup>/''h''}} with {{nowrap |1=''ν'' = 0, ±1, ±4}} are observed.<ref name="nu-0-1-4">{{cite journal |last1=Zhang |first1=Y. |last2=Jiang |first2=Z. |last3=Small |first3=J. P. |last4=Purewal |first4=M. S. |last5=Tan |first5=Y.-W. |last6=Fazlollahi |first6=M. |last7=Chudow |first7=J. D. |last8=Jaszczak |first8=J. A. |last9=Stormer |first9=H. L. |last10=Kim |first10=P. |title=Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |pmid=16712020 |journal=Physical Review Letters |volume=96 |page=136806 |year=2006 |bibcode=2006PhRvL..96m6806Z |issue=13 |arxiv=cond-mat/0602649|s2cid=16445720 }}</ref> A plateau at {{nowrap |1=''ν'' = 3}}<ref name="nu-3">{{cite journal |last1=Du |first1=X. |last2=Skachko |first2=Ivan |last3=Duerr |first3=Fabian |last4=Luican |first4=Adina |last5=Andrei |first5=Eva Y. |title=Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal=Nature |volume=462 |pages=192–195 |year=2009 |issue=7270 |pmid=19829294 |arxiv=0910.2532 |bibcode=2009Natur.462..192D|s2cid=2927627 }}</ref> and the ] at {{nowrap |1=''ν'' = {{sfrac|1|3}}}} were also reported.<ref name="nu-3" /><ref name="nu-one3rd">{{cite journal |last1=Bolotin |first1=K. |last2=Ghahari |first2=Fereshte |last3=Shulman |first3=Michael D. |last4=Stormer |first4=Horst L. |last5=Kim |first5=Philip |title=Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal=Nature |volume=462 |pages=196–199 |year=2009 |issue=7270 |pmid=19881489 |arxiv=0910.2763 |bibcode=2009Natur.462..196B|s2cid=4392125 }}</ref> | |||
These observations with {{nowrap |1=''ν'' = 0, ±1, ±3, ±4}} indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. | |||
=== Casimir effect === | |||
The ] is an interaction between disjoint neutral bodies provoked by the fluctuations of the electromagnetic vacuum. Mathematically, it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary conditions on the interacting bodies' surfaces. Due to graphene's strong interaction with the electromagnetic field as a one-atom-thick material, the Casimir effect has garnered significant interest.<ref name="BFGV">{{cite journal |last1=Bordag |first1=M. |last2=Fialkovsky |first2=I. V. |last3=Gitman |first3=D. M. |last4=Vassilevich |first4=D. V. |title=Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal=Physical Review B |volume=80 |year=2009 |page=245406 |doi=10.1103/PhysRevB.80.245406 |bibcode=2009PhRvB..80x5406B |issue=24 |arxiv=0907.3242|s2cid=118398377 }}</ref><ref name="FMD">{{cite journal |last1=Fialkovsky |first1=I. V. |last2=Marachevsky |first2=V.N. |last3=Vassilevich |first3=D. V. |title=Finite temperature Casimir effect for graphene |year=2011 |volume=84 |issue=35446 |journal=Physical Review B |arxiv=1102.1757 |bibcode=2011PhRvB..84c5446F |page=35446 |doi=10.1103/PhysRevB.84.035446|s2cid=118473227 }}</ref> | |||
=== Van der Waals force === | |||
The ] (or dispersion force) is also unusual, obeying an inverse cubic asymptotic ] in contrast to the usual inverse quartic law.<ref name="DWR">{{cite journal |last1=Dobson |first1=J. F. |last2=White |first2=A. |last3=Rubio |first3=A. |title=Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal=Physical Review Letters |volume=96 |year=2006 |page=073201 |doi=10.1103/PhysRevLett.96.073201 |pmid=16606085 |issue=7 |bibcode=2006PhRvL..96g3201D |arxiv=cond-mat/0502422|s2cid=31092090 }}</ref> | |||
=== Permittivity === | |||
Graphene's ] varies with frequency. Over a range from microwave to millimeter wave frequencies, it is approximately 3.3.<ref name="cismaru">{{cite arXiv |last1=Cismaru |first1=Alina |last2=Dragoman |first2=Mircea |last3=Dinescu |first3=Adrian |last4=Dragoman |first4=Daniela |last5=Stavrinidis |first5=G. |last6=Konstantinidis |first6=G. |title=Microwave and Millimeter-wave Electrical Permittivity of Graphene Monolayer |eprint=1309.0990 |year=2013 |class=cond-mat.mes-hall }}</ref> This permittivity, combined with its ability to function as both a conductor and as an insulator, theoretically allows compact ]s made of graphene to store large amounts of electrical energy. | |||
== Optical properties == | |||
Graphene exhibits unique optical properties, showing unexpectedly high ] for an atomic monolayer in vacuum, absorbing approximately {{nowrap|''πα'' ≈ 2.3%}} of ] from visible to infrared wavelengths,<ref name=nair2008/><ref name=zhu2014/><ref>{{cite journal|last1=Kuzmenko|first1=A. B.|last2=Van Heumen|first2=E.|last3=Carbone|first3=F.|last4=Van Der Marel|first4=D.|year=2008|title=Universal infrared conductance of graphite|journal=Physical Review Letters|volume=100|issue=11|page=117401|arxiv=0712.0835|bibcode=2008PhRvL.100k7401K|doi=10.1103/PhysRevLett.100.117401|pmid=18517825|s2cid=17595181}}</ref> where ''α'' is the ]. This is due to the unusual low-energy electronic structure of monolayer graphene, characterized by electron and hole ] meeting at the ], which is qualitatively different from more common quadratic massive bands.<ref name=nair2008/> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, calculations using ] in the thin-film limit account for interatomic distance, hopping values, and frequency, thus assessing optical conductance. | |||
Experimental verification, though confirmed, lacks the precision required to improve upon existing techniques for determining the ].<ref>{{cite web |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |website=ScienceDaily |date=4 April 2008 |access-date=6 April 2008 |archive-date=6 April 2008 |archive-url=https://web.archive.org/web/20080406140754/http://www.sciencedaily.com/releases/2008/04/080403140918.htm |url-status=live }}</ref> | |||
=== Multi-parametric surface plasmon resonance === | |||
] has been utilized to characterize both the thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. At a wavelength of {{convert|670|nm|m|abbr=on|lk=on}}, measured refractive index and extinction coefficient values are 3.135 and 0.897, respectively. Thickness determination yielded 3.7 Å across a 0.5mm area, consistent with the 3.35 Å reported for layer-to-layer carbon atom distance of graphite crystals.<ref>{{cite journal |last1=Jussila |first1=Henri |last2=Yang |first2=He |last3=Granqvist |first3=Niko |last4=Sun |first4=Zhipei |title=Surface plasmon resonance for characterization of large-area atomic-layer graphene film |journal=Optica |date=5 February 2016 |volume=3 |issue=2 |pages=151–158 |doi=10.1364/OPTICA.3.000151|bibcode=2016Optic...3..151J |doi-access=free }}</ref> This method is applicable for real-time label-free interactions of graphene with organic and inorganic substances. The existence of unidirectional surface plasmons in nonreciprocal graphene-based gyrotropic interfaces has been theoretically demonstrated, offering tunability from THz to near-infrared and visible frequencies by controlling graphene's chemical potential.<ref>{{cite journal|last1=Lin|first1=Xiao|last2=Xu|first2=Yang |last3=Zhang|first3=Baile|last4=Hao|first4=Ran|last5=Chen|first5=Hongsheng| last6=Li|first6=Erping|title=Unidirectional surface plasmons in nonreciprocal graphene|journal=New Journal of Physics|volume=15|issue=11|page=113003|date=2013|doi=10.1088/1367-2630/15/11/113003|bibcode=2013NJPh...15k3003L|doi-access=free|hdl=10220/17639|hdl-access=free}}</ref> Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that achievable with metal under similar magnetic field conditions, stemming from graphene's extremely small effective electron mass. | |||
=== Tunable band gap and optical response === | |||
Graphene's ] can be tuned from 0 to {{val|0.25 |u=eV}} (about 5-micrometer wavelength) by applying a voltage to a dual-gate ] ] (FET) at room temperature.<ref>{{cite journal |doi=10.1038/nature08105 |journal=Nature |last1=Zhang |first1=Y. |last2=Tang |first2=Tsung-Ta |last3=Girit |first3=Caglar |last4=Hao |first4=Zhao |last5=Martin |first5=Michael C. |last6=Zettl |first6=Alex |author6-link=Alex Zettl| last7=Crommie |first7=Michael F. |last8=Shen |first8=Y. Ron |last9=Wang |first9=Feng |volume=459 |pages=820–823 |date=11 June 2009|title=Direct observation of a widely tunable bandgap in bilayer graphene|pmid=19516337|issue=7248 |bibcode=2009Natur.459..820Z |osti=974550 |s2cid=205217165 }}</ref> The optical response of ] is tunable into the ] regime by an applied magnetic fields.<ref>{{cite journal |doi=10.1063/1.2964093 |journal=Appl Phys Lett |first1=Junfeng |last1=Liu |first2=A. R. |last2=Wright |first3=Chao |last3=Zhang |first4=Zhongshui |last4=Ma |volume=93 |pages=041106–041110 |date=29 July 2008 |title=Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode=2008ApPhL..93d1106L |issue=4 |url=https://ro.uow.edu.au/engpapers/3322 |access-date=30 August 2019 |archive-date=12 June 2020 |archive-url=https://web.archive.org/web/20200612064434/https://ro.uow.edu.au/engpapers/3322/ |url-status=live }}</ref> Graphene/graphene oxide systems exhibit ] behavior, enabling tuning of both linear and ultrafast optical properties.<ref name="kurum2011" /> | |||
=== Graphene-based Bragg grating === | |||
A graphene-based ] (one-dimensional ]) has been fabricated, demonstrating its capability to excite surface electromagnetic waves in periodic structure using a {{convert|633|nm|m|abbr=on|lk=on}} He–Ne laser as the light source.<ref>{{cite journal |first1=K.V. |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |last1=Sreekanth |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |pmid=23071901 |volume=2 |page=737 |bibcode=2012NatSR...2..737S |pmc=3471096}}</ref> | |||
=== Saturable absorption === | |||
Graphene exhibits unique saturable absorption, which saturates when the input optical intensity exceeds a threshold value. This nonlinear optical behavior, termed ], occurs across the visible to ] spectrum, due to graphene's universal optical absorption and zero band gap. This property has enabled full-band mode-locking in ]s using graphene-based saturable absorbers, contributing significantly to ultrafast ]. Additionally, the optical response of graphene/graphene oxide layers can be electrically tuned.<ref name=kurum2011/><ref name=bao2009/><ref name=zhang2009a/><ref name=zhang2009b/><ref name=zhang2010a/><ref name=zhang2009c/> | |||
Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave-saturable absorption in graphene demonstrates the possibility of graphene microwaves and terahertz photonics devices, such as a microwave-saturable absorber, modulator, polarizer, microwave signal processing, and broadband wireless access networks.<ref name=zheng2012/> | |||
=== Nonlinear Kerr effect === | |||
Under intense laser illumination, graphene exhibits a nonlinear phase shift due to the optical nonlinear ]. Graphene demonstrates a large nonlinear Kerr coefficient of {{val |e=-7 |u=cm<sup>2</sup>⋅W<sup>−1</sup>}}, nearly nine orders of magnitude larger than that of bulk dielectrics,<ref name="ZHANGHAN">{{cite journal |last1=Zhang |first1=H. |last2=Virally |first2=Stéphane |last3=Bao |first3=Qiaoliang |last4=Kian Ping |first4=Loh |last5=Massar |first5=Serge |last6=Godbout |first6=Nicolas |last7=Kockaert |first7=Pascal |title=Z-scan measurement of the nonlinear refractive index of graphene |journal=Optics Letters |year=2012 |volume=37 |issue=11 |pages=1856–1858 |doi=10.1364/OL.37.001856 |pmid=22660052 |bibcode=2012OptL...37.1856Z|arxiv=1203.5527 |s2cid=119237334 }}</ref> suggesting its potential as a powerful nonlinear Kerr medium capable of supporting various nonlinear effects, including ].<ref>{{cite journal |last1=Dong |first1=H |last2=Conti |first2=C |last3=Marini |first3=A |last4=Biancalana |first4=F |year=2013 |title=Terahertz relativistic spatial solitons in doped graphene metamaterials |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=46 |issue= 15|page=15540|doi=10.1088/0953-4075/46/15/155401 |bibcode=2013JPhB...46o5401D |arxiv=1107.5803 |s2cid=118338133 }}</ref> | |||
== Excitonic properties == | |||
First-principle calculations incorporating quasiparticle corrections and many-body effects have been employed to study the electronic and optical properties of graphene-based materials. The approach was described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |pages=601–659 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last1=Onida |first1=Giovanni |last2=Rubio |first2=Angel |issue=2 |hdl=10261/98472 |url=https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf |hdl-access=free |access-date=23 September 2019 |archive-date=2 February 2021 |archive-url=https://web.archive.org/web/20210202054314/https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf |url-status=live }}</ref> With GW calculation, the properties of graphene-based materials were accurately investigated, including bulk graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last1=Yang |first1=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823 |arxiv=0906.0969|s2cid=36067301 }}</ref> ],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last1=Prezzi |first1=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4 |arxiv=0706.0916 |bibcode=2008PhRvB..77d1404P|s2cid=73518107 }}<br />{{cite journal |journal=Nano Letters |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720 |arxiv=0707.2983 |bibcode=2007NanoL...7.3112Y|s2cid=16943236 }}<br />{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843}}</ref> edge and surface functionalized armchair ribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |pages=17257–17262 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |issue=41 |url=https://figshare.com/articles/Excitons_of_Edge_and_Surface_Functionalized_Graphene_Nanoribbons/2719792 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801070038/https://figshare.com/articles/Excitons_of_Edge_and_Surface_Functionalized_Graphene_Nanoribbons/2719792 |url-status=live }}</ref> hydrogen saturated armchair ribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last1=Wang |first1=Min |last2=Li |first2=Chang Ming |s2cid=31835103 |issue=5 |pmid=21503364 |bibcode=2011Nanos...3.2324W}}</ref> ] in graphene SNS junctions with single localized defect<ref>{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |pages=2896–2899 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13 |arxiv=1006.1391 |bibcode=2010PhyB..405.2896B|s2cid=119226501 }}<br />{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics |volume=110 |pages=613–617 |year=2010 |doi=10.1134/S1063776110040084 |issue=4 |arxiv=1006.1386 |bibcode=2010JETP..110..613B|s2cid=119254414 }}</ref> and armchair ribbon scaling properties.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |pmid=21939213 |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |bibcode=2011JPCA..11511998Z |url=https://figshare.com/articles/Scaling_of_Excitons_in_Graphene_Nanoribbons_with_Armchair_Shaped_Edges/2590648 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801044232/https://figshare.com/articles/Scaling_of_Excitons_in_Graphene_Nanoribbons_with_Armchair_Shaped_Edges/2590648 |url-status=live }}</ref> | |||
=== Spin transport === | === Spin transport === | ||
Graphene is |
Graphene is considered an ideal material for ] due to its minimal ], the near absence of ]s in carbon, and weak ]. Electrical injection and detection of ] have been demonstrated up to room temperature,<ref name="Tombros">{{cite journal |title=Electronic spin transport and spin precession in single graphene layers at room temperature |bibcode=2007Natur.448..571T |last=Tombros |first=Nikolaos |journal=Nature |year=2007 |volume=448 |issue=7153 |pages=571–575 |doi=10.1038/nature06037 |pmid=17632544 |arxiv=0706.1948 |s2cid=4411466 |display-authors=etal}}</ref><ref name="ChoSpin">{{cite journal |first1=Sungjae |last1=Cho |first2=Yung-Fu |last2=Chen |first3=Michael S. |last3=Fuhrer |year=2007 |volume=91 |page=123105 |title=Gate-tunable Graphene Spin Valve |journal=Applied Physics Letters |doi=10.1063/1.2784934 |bibcode=2007ApPhL..91l3105C |issue=12 |arxiv=0706.1597|s2cid=119145153 }}</ref><ref name="Ohishi">{{cite journal |last=Ohishi |first=Megumi |year=2007 |volume=46 |issue=25 |pages=L605–L607 |title=Spin Injection into a Graphene Thin Film at Room Temperature |journal=Jpn J Appl Phys |doi=10.1143/JJAP.46.L605 |bibcode=2007JaJAP..46L.605O |arxiv=0706.1451 |s2cid=119608880 |display-authors=etal}}</ref> with spin coherence length exceeding 1 micrometer observed at this temperature.<ref name="Tombros" /> Control of spin current polarity via electrical gating has been achieved at low temperatures.<ref name="ChoSpin" /> | ||
{{Cite journal |first=Sungjae |last=Cho |first2=Yung-Fu |last2=Chen |first3=Michael S. |last3=Fuhrer |year=2007 |volume=91 |page=123105 |title=Gate-tunable Graphene Spin Valve |journal=Applied Physics Letters |doi=10.1063/1.2784934 | |||
|bibcode=2007ApPhL..91l3105C |issue=12 |arxiv=0706.1597 }}</ref><ref name="Ohishi">{{Cite journal |last=Ohishi |first=Megumi |author2=et al. |year=2007 |volume=46 |pages=L605–L607 |title=Spin Injection into a Graphene Thin Film at Room Temperature |journal=Jpn J Appl Phys |doi=10.1143/JJAP.46.L605 |bibcode=2007JaJAP..46L.605O |arxiv=0706.1451 }}</ref> Spin coherence length above 1 micrometre at room temperature was observed,<ref name="Tombros"/> and control of the spin current polarity with an electrical gate was observed at low temperature.<ref name="ChoSpin"/> | |||
== Magnetic properties == | |||
=== Anomalous quantum Hall effect === | |||
{{jargon|section|date=December 2013}} | |||
=== Strong magnetic fields === | |||
The ] is relevant for accurate measuring of electrical quantities, and in 1985 ] received the ] for its discovery. The effect concerns the dependence of a transverse conductivity on a ], which is perpendicular to a current-carrying stripe. Usually the phenomenon, the quantization of the so-called ] <math>\sigma_{xy}</math> at integer multiples (the "]") of the basic quantity <math>e^2/h</math> (where ''e'' is the elementary electric charge and ''h'' is ]) can be observed only in very clean ] or ] solids at very low temperatures around 3 ] and very high magnetic fields. | |||
Graphene's quantum Hall effect in magnetic fields above approximately 10 ] reveals additional interesting features. Additional plateaus in Hall conductivity at <math>\sigma_{xy}=\nu e^2/h</math> with <math>\nu=0,\pm {1},\pm {4}</math> have been observed,<ref name="nu-0-1-4" /> along with plateau at <math>\nu=3</math><ref name="nu-3" /> and a fractional quantum Hall effect at <math>\nu=1/3</math>.<ref name="nu-3" /><ref name="nu-one3rd" /> | |||
In contrast graphene shows the quantum Hall effect just in the presence of a magnetic field and just with respect to conductivity-quantization: the effect is ''anomalous'' in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy}=\pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.{{sfn|Geim|Novoselov|2007}} Moreover, in graphene these anomalies are present at room temperature, i.e. at roughly {{val|20|u=°C}}.<ref name="2dgasDiracFermions"/> This anomalous behavior is a direct result of graphene's massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the ] and is half-filled in neutral graphene,<ref name="Semenoff"/> leading to the "+1/2" in the Hall conductivity.<ref name="Gusynin">{{Cite journal |last=Gusynin |first=V. P. |last2=Sharapov |first2=S. G. |title=Unconventional Integer Quantum Hall Effect in Graphene |doi=10.1103/PhysRevLett.95.146801 |journal=Physical Review Letters |volume=95 |page=146801 |year=2005 |pmid=16241680 |bibcode=2005PhRvL..95n6801G |arxiv=cond-mat/0506575 |issue=14 }}</ref> Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy}=\pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at ''N=0'' is absent, indicating that bilayer graphene stays metallic at the neutrality point.{{sfn|Geim|Novoselov|2007}} | |||
These observations with <math>\nu=0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis proposes that ] of ] is responsible for this degeneracy lift.{{citation needed|date=December 2013}} | |||
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the ], which show a phase shift of π, known as ].<ref name="2dgasDiracFermions"/><ref name="E-Phonon"/> Berry’s phase arises due to the zero effective carrier mass near the Dirac points.<ref name="Berry'sPhase">{{Cite journal |last=Zhang |first=Y. |last2=Tan |first2=Y. W. |last3=Stormer |first3=H. L. |last4=Kim |first4=P. |title=Experimental observation of the quantum Hall effect and Berry's phase in graphene |doi=10.1038/nature04235 |journal=Nature |volume=438 |pages=201–204 |year=2005 |pmid=16281031 |issue=7065 |arxiv=cond-mat/0509355 |bibcode=2005Natur.438..201Z }}</ref> Study of the temperature dependence of graphene's Shubnikov–de Haas oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E–k relation.<ref name="2dgasDiracFermions"/> | |||
=== Spintronic properties === | |||
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of ], show the ] directly in electrical measurements.<ref name="ByungHeeHong"/><ref name="0908.1900"/><ref name="ShenAPL"/><ref name=0909.2903/><ref name=0909.1193/><ref name=phase1/> Graphitic layers on the carbon face of silicon carbide show a clear ] in ] experiments, and the anomalous quantum Hall effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{Cite journal |first=Michael S. |last=Fuhrer |title=A physicist peels back the layers of excitement about graphene|doi=10.1038/4591037e |journal=Nature |volume=459 |page=1037 |year=2009 |pmid=19553953|issue=7250 |bibcode=2009Natur.459.1037F }}</ref> | |||
Graphene exhibits ] and magnetic properties concurrently.<ref>{{cite journal |last1=Hashimoto |first1=T. |last2=Kamikawa |first2=S. |last3=Yagi |first3=Y. |last4=Haruyama |first4=J. |last5=Yang |first5=H. |last6=Chshiev |first6=M. |title=Graphene edge spins: spintronics and magnetism in graphene nanomeshes |journal=Nanosystems: Physics, Chemistry, Mathematics |date=2014 |volume=5 |issue=1 |pages=25–38 |url=http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/02/NPCM51_P25-38.pdf |access-date=2 May 2019 |archive-date=19 August 2019 |archive-url=https://web.archive.org/web/20190819011954/http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/02/NPCM51_P25-38.pdf |url-status=live }}</ref> Low-defect graphene Nano-meshes, fabricated using a non-lithographic approach, exhibit significant ferromagnetism even at room temperature. Additionally, a spin pumping effect has been observed with fields applied in parallel to the planes of few-layer ferromagnetic nano-meshes, while a ] hysteresis loop is evident under perpendicular fields. Charge-neutral graphene has demonstrated magnetoresistance exceeding 100% in magnetic fields generated by standard permanent magnets (approximately 0.1 tesla), marking a record magneto resistivity ''at room temperature'' among known materials.<ref>{{cite journal |last1=Xin |first1=Na |last2=Lourembam |first2=James |last3=Kumaravadivel |first3=Piranavan |title=Giant magnetoresistance of Dirac plasma in high-mobility graphene |journal=Nature |date=April 2023 |volume=616 |issue=7956 |pages=270–274 |doi=10.1038/s41586-023-05807-0 |pmid=37045919 |pmc=10097601 |arxiv=2302.06863 |bibcode=2023Natur.616..270X }}</ref> | |||
=== Magnetic substrates === | |||
In 2014 researchers magnetized graphene by placing it on an atomically smooth layer of magnetic ], maintaining graphene's electronic properties unaffected. Previous methods involved doping graphene with other substances.<ref>T. Hashimoto, S. Kamikawa, Y. Yagi, J. Haruyama, H. Yang, M. Chshiev, {{Webarchive|url=https://web.archive.org/web/20190505085205/http://nanojournal.ifmo.ru/en/articles-2/volume5/5-1/paper02/ |date=5 May 2019 }}, February 2014, Volume 5, Issue 1, pp 25</ref> The dopant's presence negatively affected its electronic properties.<ref>{{cite news |url=http://www.gizmag.com/magnetized-graphene/35805 |title=Scientists give graphene one more quality – magnetism |first=Ben |last=Coxworth |date=January 27, 2015 |access-date=6 October 2016 |publisher=Gizmag |archive-date=14 July 2016 |archive-url=https://web.archive.org/web/20160714203936/http://www.gizmag.com/magnetized-graphene/35805/? |url-status=live }}</ref> | |||
== Mechanical properties == | |||
Graphene's quantum Hall effect in magnetic fields above 10 ]s or so reveals additional interesting features. Additional plateaus of the Hall conductivity at <math>\sigma_{xy}=\nu e^2/h</math> with <math>\nu=0,\pm {1},\pm {4}</math> are observed.<ref name="nu-0-1-4">{{Cite journal |last=Zhang |first=Y. |title=Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |journal=Physical Review Letters |volume=96 |page=136806 |year=2006 |bibcode=2006PhRvL..96m6806Z |issue=13 |last2=Jiang |first2=Z. |last3=Small |first3=J. P. |last4=Purewal |first4=M. S. |last5=Tan |first5=Y.-W. |last6=Fazlollahi |first6=M. |last7=Chudow |first7=J. D. |last8=Jaszczak |first8=J. A. |last9=Stormer |first9=H. L. |last10=Kim |first10=P. |arxiv=cond-mat/0602649 }}</ref> Also, the observation of a plateau at <math>\nu=3</math><ref name="nu-3">{{Cite journal |last=Du |first=X. |title=Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal=Nature |volume=462 |pages=192–195 |year=2009 |issue=7270 |pmid=19829294 |last2=Skachko |first2=Ivan |last3=Duerr |first3=Fabian |last4=Luican |first4=Adina |last5=Andrei |first5=Eva Y.|arxiv=0910.2532 |bibcode=2009Natur.462..192D }}</ref> and the fractional quantum Hall effect at <math>\nu=1/3</math> were reported.<ref name="nu-3"/><ref name="nu-one3rd">{{Cite journal |last=Bolotin |first=K. |last2=Ghahari |first2=Fereshte |last3=Shulman |first3=Michael D. |last4=Stormer |first4=Horst L. |last5=Kim |first5=Philip |title=Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal=Nature |volume=462 |pages=196–199 |year=2009 |issue=7270 |pmid=19881489 |arxiv=0910.2763 |bibcode=2009Natur.462..196B }}</ref> | |||
The (two-dimensional) density of graphene is 0.763 mg per square meter.{{citation needed|date=July 2020}} | |||
Graphene is the strongest material ever tested,<ref name="lee2008" /><ref name="cao2020" /> with an intrinsic ] of {{convert|130|GPa|abbr=on|lk=on}} (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a ] (stiffness) close to {{convert|1|TPa|abbr=on|lk=on}}. The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4 |u=kg}} cat but would weigh only as much as one of the cat's whiskers, at {{val|0.77 |u=mg}} (about 0.001% of the weight of {{val|1 |u=m<sup>2</sup>}} of paper).<ref name="nobelprize.org">{{cite web |url=http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf |title=Scientific Background on the Nobel Prize in Physics 2010 GRAPHENE |publisher=Nobel Prize |date=5 October 2010 |author=Class for Physics of the Royal Swedish Academy of Sciences |url-status=dead |archive-url= https://web.archive.org/web/20180701222510/https://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf |archive-date= Jul 1, 2018 }}</ref> | |||
These observations with <math>\nu=0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis is that the ] of ] is responsible for lifting the degeneracy.{{citation needed|date=December 2013}} | |||
Large-angle bending of graphene monolayers with minimal strain demonstrates its mechanical robustness. Even under extreme deformation, monolayer graphene maintains excellent carrier mobility.<ref>{{cite journal|last1=Briggs|first1=Benjamin D.|last2=Nagabhirava|first2=Bhaskar|last3=Rao|first3=Gayathri|last4=Deer|first4=Robert|last5=Gao|first5=Haiyuan|last6=Xu|first6=Yang|last7=Yu|first7=Bin|title=Electromechanical robustness of monolayer graphene with extreme bending|journal=Applied Physics Letters |volume=97|issue=22|page=223102|date=2010|doi=10.1063/1.3519982|bibcode=2010ApPhL..97v3102B}}</ref> | |||
== Forms == | |||
The ] of suspended graphene sheets has been measured using an ] (AFM). Graphene sheets were suspended over {{chem|SiO|2}} cavities where an AFM tip was used to apply stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was {{val|0.5 |u=TPa}}, which differs from that of bulk graphite. These intrinsic properties could lead to applications such as ] as pressure sensors and resonators.<ref>{{cite journal |last1=Frank |first1=I. W. |last2=Tanenbaum |first2=D. M. |last3=Van Der Zande |first3=A.M. |last4=McEuen |first4=P. L. |title=Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal=Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures |volume=25 |pages=2558–2561 |year=2007 |url=http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |bibcode=2007JVSTB..25.2558F |issue=6 |access-date=21 April 2009 |archive-date=11 July 2009 |archive-url=https://web.archive.org/web/20090711105102/http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |url-status=live }}</ref> Due to its large surface energy and out of plane ductility, flat graphene sheets are unstable with respect o scrolling, i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name="nmscrolling">{{cite journal |first1=S. |last1=Braga |first2=V. R. |last2=Coluci |first3=S. B. |last3=Legoas |first4=R. |last4=Giro |first5=D. S. |last5=Galvão |first6=R. H. |last6=Baughman |year=2004 |title=Structure and Dynamics of Carbon Nanoscrolls |journal=Nano Letters |volume=4 |pages=881–884 |doi=10.1021/nl0497272 |bibcode=2004NanoL...4..881B |issue=5}}</ref> | |||
=== Nanostripes === | |||
In two-dimensional structures like graphene, thermal and quantum fluctuations cause relative displacement, with fluctuations growing logarithmically with structure size as per the ]. This shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name="meyer2007" /> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.<ref name="geim2007" /><ref name="carl2007" /><ref name="faso2007" /><ref name="bolm2011a" /><ref name="bolm2011b" /> These ripples, when amplified by vacancy defects, induce a negative ] into graphene, resulting in the thinnest ] material known so far.<ref name="grima2014" /> | |||
] ("nanostripes" in the "zig-zag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of ]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{Cite journal |first=A Castro |last=Neto |last2=Peres |first2=N. M. R. |last3=Novoselov |first3=K. S. |last4=Geim |first4=A. K. |last5=Geim |first5=A. K. |title=The electronic properties of graphene |journal=Rev Mod Phys |volume=81 |year=2009 |page=109 |url=http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |format=PDF |bibcode=2009RvMP...81..109C |doi=10.1103/RevModPhys.81.109 |arxiv=0709.1163 }}</ref>) | |||
Graphene-nickel (Ni) composites, created through plating processes, exhibit enhanced mechanical properties due to strong Ni-graphene interactions inhibiting dislocation sliding in the Ni matrix.<ref>{{cite journal|last1=Ren|first1=Zhaodi|last2=Meng|first2=Nan|last3=Shehzad|first3=Khurram|last4=Xu|first4=Yang|last5=Qu|first5=Shaoxing|last6=Yu|first6=Bin|last7=Luo|first7=Jack|title=Mechanical properties of nickel-graphene composites synthesized by electrochemical deposition|journal=Nanotechnology|volume=26|issue=6|page=065706|date=2015|doi=10.1088/0957-4484/26/6/065706|pmid=25605375|bibcode=2015Nanot..26f5706R|s2cid=9501340 |url=http://ubir.bolton.ac.uk/1575/1/Mechanical%20properties%20of%20nickel-graphene%20composites%20synthesized%20by%20electrochemical%20deposition.pdf|access-date=7 January 2020|archive-date=27 October 2020|archive-url=https://web.archive.org/web/20201027171300/http://ubir.bolton.ac.uk/1575/1/Mechanical%20properties%20of%20nickel-graphene%20composites%20synthesized%20by%20electrochemical%20deposition.pdf|url-status=dead}}</ref> | |||
=== Graphene oxide === | |||
{{further2|]}} | |||
Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called ] have a measured ] of 32 ].<ref>{{cite web |url=http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archiveurl=http://web.archive.org/web/20110720013914/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archivedate=2011-07-20 |title=Graphene Oxide Paper |publisher=Northwestern University |accessdate=2011-02-28 }}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes.<ref>{{cite journal |last=Eftekhari |first=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |page=2204 |year=2010 |doi=10.1002/pola.23990 |bibcode=2010JPoSA..48.2204E |issue=10 }}</ref> Graphene oxide flakes in polymers display enhanced photo-conducting properties.<ref>{{cite journal |last=Nalla |first=Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode=2010Nanot..21O5203N }}</ref> Graphene-based membranes are impermeable to all gases and liquids (vacuum-tight). However, water evaporates through them as quickly as if the membrane was not present.<ref name="pmid22282806" /> | |||
=== |
=== Fracture toughness === | ||
{{jargon|section|date=December 2013}} | |||
] Soluble fragments of graphene can be prepared in the laboratory<ref>{{Cite journal |first=Sandip |last=Niyogi |first2=Elena |last2=Bekyarova |first3=Mikhail E. |last3=Itkis |first4=Jared L. |last4=McWilliams |first5=Mark A. |last5=Hamon |first6=Robert C. |last6=Haddon |title=Solution Properties of Graphite and Graphene |journal=] |volume=128 |pages=7720–7721 |year=2006 |doi=10.1021/ja060680r |pmid=16771469 |issue=24 }}</ref> through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and ]. A series of oxidation and exfoliation steps produce small graphene plates with ] groups at their edges. These are converted to ] groups by treatment with ]; next, they are converted to the corresponding graphene ] via treatment with ]. The resulting material (circular graphene layers of 5.3 ] thickness) is soluble in ], ] and ]. | |||
In 2014, researchers from ] and the ] have indicated that despite its strength, graphene is also relatively ], with a ] of about 4 MPa√m.<ref name="ZhangMa2014">{{cite journal |last1=Zhang |first1=Peng |last2=Ma |first2=Lulu |last3=Fan |first3=Feifei |last4=Zeng |first4=Zhi |last5=Peng |first5=Cheng |last6=Loya |first6=Phillip E. |last7=Liu |first7=Zheng |last8=Gong |first8=Yongji |last9=Zhang |first9=Jiangnan |last10=Zhang |first10=Xingxiang |last11=Ajayan |first11=Pulickel M. |last12=Zhu |first12=Ting |last13=Lou |first13=Jun |title=Fracture toughness of graphene |journal=Nature Communications |volume=5 |page=3782 |year=2014 |doi=10.1038/ncomms4782 |pmid=24777167 |bibcode=2014NatCo...5.3782Z |doi-access=free }}</ref> This indicates that imperfect graphene is likely to crack in a brittle manner like ], as opposed to many ] which tend to have fracture toughness in the range of 15–50 MPa√m. Later in 2014, the Rice team announced that graphene showed a greater ability to distribute force from an impact than any known material, ten times that of steel per unit weight.<ref>{{Cite news |url=http://singularityhub.com/2014/12/04/graphene-armor-would-be-light-flexible-and-far-stronger-than-steel/ |title=Graphene Armor Would Be Light, Flexible and Far Stronger Than Steel |last=Dorrieron |first=Jason |date=4 December 2014 |work=Singularity Hub |access-date=6 October 2016 |archive-date=30 August 2016 |archive-url=https://web.archive.org/web/20160830142957/http://singularityhub.com/2014/12/04/graphene-armor-would-be-light-flexible-and-far-stronger-than-steel/ |url-status=live }}</ref> The force was transmitted at {{convert|22.2|km/s}}.<ref>{{cite news |url=http://www.gizmag.com/graphene-bulletproof-armor/35004 |title=Graphene could find use in lightweight ballistic body armor |first=Ben |last=Coxworth |date=1 December 2014 |work=Gizmag |access-date=6 October 2016 |archive-date=23 July 2016 |archive-url=https://web.archive.org/web/20160723233608/http://www.gizmag.com/graphene-bulletproof-armor/35004/ |url-status=live }}</ref> | |||
Refluxing single-layer graphene oxide (SLGO) in ]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependant on their preparation methodology. When using thionyl chloride, ] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%. | |||
] | |||
=== Polycrystalline graphene === | |||
] reflux is commonly used for reducing SLGO to SLG(R), but ]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with ]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (ca. 3–5% conversion of the intermediate to the final amide).<ref>{{Cite journal |first=Raymond L.D. |last=Whitby |first2=Alina |last2=Korobeinyk |first3=Katya V. |last3=Glevatska |title=Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal=] |volume=49 |issue=2 |pages=722–725 |year=2011 |doi=10.1016/j.carbon.2010.09.049 }}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reactions types have been explored. SLGO has also been grafted with ], cross-linked through ] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{Cite journal |first=Sungjin |last=Park, |first2=Dmitriy A. |last2=Dikin |first3=SonBinh T. |last3=Nguyen |first4=Rodney S. |last4=Ruoff |title=Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal=] |volume=113 |pages=15801–15804 |year=2009 |doi=10.1021/jp907613s |issue=36 }}</ref> | |||
Various methods – most notably, ] (CVD), as discussed in the section below – have been developed to produce large-scale graphene needed for device applications. Such methods often synthesize polycrystalline graphene.<ref name=":5">{{cite journal |last1=Papageorgiou |first1=Dimitrios G. |last2=Kinloch |first2=Ian A. |last3=Young |first3=Robert J. |title=Mechanical properties of graphene and graphene-based nanocomposites |journal=Progress in Materials Science |date=October 2017 |volume=90 |pages=75–127 |doi=10.1016/j.pmatsci.2017.07.004 |doi-access=free }}</ref> The mechanical properties of polycrystalline graphene are affected by the nature of the defects, such as ] and ], present in the system and the average grain-size. | |||
Full ] from both sides of graphene sheet results in ], but partial hydrogenation leads to hydrogenated graphene.<ref>{{Cite journal |first=D. C. |last=Elias |last2=Nair |first2=R. R. |last3=Mohiuddin |first3=T. M. G. |last4=Morozov |first4=S. V. |last5=Blake |first5=P. |last6=Halsall |first6=M. P. |last7=Ferrari |first7=A. C. |last8=Boukhvalov |first8=D. W. |last9=Katsnelson |first9=M. I. |last10=Geim |first10=A. K. |last11=Novoselov |first11=K. S. |title=Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane |journal=Science |year=2009 |volume=323 |doi=10.1126/science.1167130 |pmid=19179524 |issue=5914 |bibcode=2009Sci...323..610E |pages=610–3 |arxiv=0810.4706 }}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to ] (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene. | |||
Graphene grain boundaries typically contain heptagon-pentagon pairs. The arrangement of such defects depends on whether the GB is in a zig-zag or armchair direction. It further depends on the tilt-angle of the GB.<ref>{{cite journal |last1=Li |first1=J.C.M. |title=Disclination model of high angle grain boundaries |journal=Surface Science |date=June 1972 |volume=31 |pages=12–26 |doi=10.1016/0039-6028(72)90251-8 |bibcode=1972SurSc..31...12L }}</ref> In 2010, researchers from ] computationally predicted that as the tilt-angle increases, the grain boundary strength also increases. They showed that the weakest link in the grain boundary is at the critical bonds of the heptagon rings. As the grain boundary angle increases, the strain in these heptagon rings decreases, causing the grain boundary to be stronger than lower-angle GBs. They proposed that, in fact, for sufficiently large angle GB, the strength of the GB is similar to pristine graphene.<ref>{{cite journal |last1=Grantab |first1=R. |last2=Shenoy |first2=V. B. |last3=Ruoff |first3=R. S. |title=Anomalous Strength Characteristics of Tilt Grain Boundaries in Graphene |journal=Science |date=12 November 2010 |volume=330 |issue=6006 |pages=946–948 |doi=10.1126/science.1196893 |pmid=21071664 |bibcode=2010Sci...330..946G |arxiv=1007.4985 |s2cid=12301209 }}</ref> In 2012, it was further shown that the strength can increase or decrease, depending on the detailed arrangements of the defects.<ref>{{cite journal |last1=Wei |first1=Yujie |last2=Wu |first2=Jiangtao |last3=Yin |first3=Hanqing |last4=Shi |first4=Xinghua |last5=Yang |first5=Ronggui |last6=Dresselhaus |first6=Mildred |title=The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene |journal=Nature Materials |date=September 2012 |volume=11 |issue=9 |pages=759–763 |doi=10.1038/nmat3370 |pmid=22751178 |bibcode=2012NatMa..11..759W |url=http://dspace.imech.ac.cn/handle/311007/46051 |access-date=30 August 2019 |archive-date=22 November 2019 |archive-url=https://web.archive.org/web/20191122205832/http://dspace.imech.ac.cn/handle/311007/46051 |url-status=live }}</ref> These predictions have since been supported by experimental evidence. In a 2013 study led by James Hone's group, researchers probed the elastic ] and ] of CVD-grown graphene by combining nano-indentation and high-resolution ]. They found that the elastic stiffness is identical and strength is only slightly lower than those in pristine graphene.<ref>{{cite journal |last1=Lee |first1=G.-H. |last2=Cooper |first2=R. C. |last3=An |first3=S. J. |last4=Lee |first4=S. |last5=van der Zande |first5=A. |last6=Petrone |first6=N. |last7=Hammerberg |first7=A. G. |last8=Lee |first8=C. |last9=Crawford |first9=B. |last10=Oliver |first10=W. |last11=Kysar |first11=J. W. |last12=Hone |first12=J. |title=High-Strength Chemical-Vapor-Deposited Graphene and Grain Boundaries |journal=Science |date=31 May 2013 |volume=340 |issue=6136 |pages=1073–1076 |doi=10.1126/science.1235126 |pmid=23723231 |bibcode=2013Sci...340.1073L |s2cid=35277622 }}</ref> In the same year, researchers from ] and ] probed bi-crystalline graphene with ] and ]. They found that the strength of grain boundaries indeed tends to increase with the tilt angle.<ref>{{cite journal |last1=Rasool |first1=Haider I. |last2=Ophus |first2=Colin |last3=Klug |first3=William S. |last4=Zettl |first4=A. |last5=Gimzewski |first5=James K. |title=Measurement of the intrinsic strength of crystalline and polycrystalline graphene |journal=Nature Communications |date=December 2013 |volume=4 |issue=1 |page=2811 |doi=10.1038/ncomms3811 |bibcode=2013NatCo...4.2811R |doi-access=free }}</ref> | |||
=== Casimir effect and dispersion === | |||
While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The consensus is that the strength decreases along with increasing densities of vacancies. Various studies have shown that for graphene with a sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, a high density of vacancies can severely reduce the strength of graphene.<ref name=":7">{{cite journal |last1=Zhang |first1=Teng |last2=Li |first2=Xiaoyan |last3=Gao |first3=Huajian |title=Fracture of graphene: a review |journal=International Journal of Fracture |date=November 2015 |volume=196 |issue=1–2 |pages=1–31 |doi=10.1007/s10704-015-0039-9 |s2cid=135899138 }}</ref> | |||
The ] is an interaction between any disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the surfaces of the interacting bodies. Since the interaction of graphene with an electromagnetic field is surprisingly strong for a one-atom-thick material, the Casimir effect is of growing interest.<ref name=BFGV>{{Cite journal |last=Bordag |first=M. |last2=Fialkovsky |first2=I. V. |last3=Gitman |first3=D. M. |last4=Vassilevich |first4=D. V. |title=Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal=Physical Review B |volume=80 |year=2009 |page=245406 |doi=10.1103/PhysRevB.80.245406 |bibcode=2009PhRvB..80x5406B |issue=24 |arxiv=0907.3242 }}</ref><ref name=FMD>{{cite journal |last=Fialkovsky |first=I. V. |last2=Marachevsky |first2=V.N. |last3=Vassilevich |first3=D. V. |title=Finite temperature Casimir effect for graphene |year=2011 |volume=84 |issue=35446 |journal=Physical Review B |arxiv=1102.1757 |bibcode=2011PhRvB..84c5446F |page=35446 |doi=10.1103/PhysRevB.84.035446 }}</ref> | |||
Compared to the fairly well-understood nature of the effect that grain boundary and vacancies have on the mechanical properties of graphene, there is no clear consensus on the general effect that the average grain size has on the strength of polycrystalline graphene.<ref name=":6">{{cite journal |last1=Akinwande |first1=Deji |last2=Brennan |first2=Christopher J. |last3=Bunch |first3=J. Scott |last4=Egberts |first4=Philip |last5=Felts |first5=Jonathan R. |last6=Gao |first6=Huajian |last7=Huang |first7=Rui |last8=Kim |first8=Joon-Seok |last9=Li |first9=Teng |last10=Li |first10=Yao |last11=Liechti |first11=Kenneth M. |last12=Lu |first12=Nanshu |last13=Park |first13=Harold S. |last14=Reed |first14=Evan J. |last15=Wang |first15=Peng |last16=Yakobson |first16=Boris I. |last17=Zhang |first17=Teng |last18=Zhang |first18=Yong-Wei |last19=Zhou |first19=Yao |last20=Zhu |first20=Yong |title=A review on mechanics and mechanical properties of 2D materials—Graphene and beyond |journal=Extreme Mechanics Letters |date=May 2017 |volume=13 |pages=42–77 |doi=10.1016/j.eml.2017.01.008 |arxiv=1611.01555 |bibcode=2017ExML...13...42A |s2cid=286118 }}</ref><ref name=":7" /><ref name=":8">{{cite journal |last1=Isacsson |first1=Andreas |last2=Cummings |first2=Aron W |last3=Colombo |first3=Luciano |last4=Colombo |first4=Luigi |last5=Kinaret |first5=Jari M |last6=Roche |first6=Stephan |title=Scaling properties of polycrystalline graphene: a review |journal=2D Materials |date=19 December 2016 |volume=4 |issue=1 |page=012002 |doi=10.1088/2053-1583/aa5147 |arxiv=1612.01727 |s2cid=118840850 }}</ref> In fact, three notable theoretical or computational studies on this topic have led to three different conclusions.<ref name=":9">{{Cite journal|last1=Kotakoski|first1=Jani|last2=Meyer|first2=Jannik C.|date=2012-05-24|title=Mechanical properties of polycrystalline graphene based on a realistic atomistic model|journal=Physical Review B|volume=85|issue=19|page=195447|doi=10.1103/PhysRevB.85.195447|bibcode=2012PhRvB..85s5447K|arxiv=1203.4196|s2cid=118835225}}</ref><ref name=":10">{{cite journal |last1=Song |first1=Zhigong |last2=Artyukhov |first2=Vasilii I. |last3=Yakobson |first3=Boris I. |last4=Xu |first4=Zhiping |title=Pseudo Hall–Petch Strength Reduction in Polycrystalline Graphene |journal=Nano Letters |date=10 April 2013 |volume=13 |issue=4 |pages=1829–1833 |doi=10.1021/nl400542n |pmid=23528068 |bibcode=2013NanoL..13.1829S }}</ref><ref name=":11">{{cite journal |last1=Sha |first1=Z. D. |last2=Quek |first2=S. S. |last3=Pei |first3=Q. X. |last4=Liu |first4=Z. S. |last5=Wang |first5=T. J. |last6=Shenoy |first6=V. B. |last7=Zhang |first7=Y. W. |title=Inverse Pseudo Hall-Petch Relation in Polycrystalline Graphene |journal=Scientific Reports |date=May 2015 |volume=4 |issue=1 |page=5991 |doi=10.1038/srep05991 |pmid=25103818 |pmc=4125985 |bibcode=2014NatSR...4.5991S }}</ref> First, in 2012, Kolakowski and Myer studied the mechanical properties of polycrystalline graphene with "realistic atomistic model", using ] (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected ] sites that are at least 5A (arbitrarily chosen) apart from other sites. Polycrystalline graphene was generated from these nucleation sites and was subsequently annealed at 3000K, and then quenched. Based on this model, they found that cracks are initiated at grain-boundary junctions, but the grain size does not significantly affect the strength.<ref name=":9" /> Second, in 2013, Z. Song et al. used MD simulations to study the mechanical properties of polycrystalline graphene with uniform-sized hexagon-shaped grains. The hexagon grains were oriented in various lattice directions and the GBs consisted of only heptagon, pentagon, and hexagonal carbon rings. The motivation behind such a model was that similar systems had been experimentally observed in graphene flakes grown on the surface of liquid copper. While they also noted that crack is typically initiated at the triple junctions, they found that as the grain size decreases, the yield strength of graphene increases. Based on this finding, they proposed that polycrystalline follows pseudo ].<ref name=":10" /> Third, in 2013, Z. D. Sha et al. studied the effect of grain size on the properties of polycrystalline graphene, by modeling the grain patches using ]. The GBs in this model consisted of heptagons, pentagons, and hexagons, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the aforementioned study, they found an inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases.<ref name=":11" /> Experimental observations and other theoretical predictions also gave differing conclusions, similar to the three given above.<ref name=":8" /> Such discrepancies show the complexity of the effects that grain size, arrangements of defects, and the nature of defects have on the mechanical properties of polycrystalline graphene. | |||
The related van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.<ref name=DWR>{{Cite journal |last=Dobson |first=J. F. |last2=White |first=A. |last2=Rubio |first2=A. |title=Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal=Physical Review Letters |volume=96 |year=2006 |page=073201 |doi=10.1103/PhysRevLett.96.073201 |issue=7 |bibcode=2006PhRvL..96g3201D|arxiv=cond-mat/0502422 }}</ref> | |||
== Other properties == | |||
{{main|Bilayer graphene}} | |||
Bilayer graphene displays the ], a tunable ]<ref name="PRB75.155115">{{Cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last=Min |first=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15|pages=155115 |arxiv=cond-mat/0612236 |bibcode=2007PhRvB..75o5115M }}</ref> and potential for ]<ref name="PRL104.096802">{{Cite journal |doi=10.1103/PhysRevLett.104.096802 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last=Barlas |first=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |pages=96802 |bibcode=2010PhRvL.104i6802B|arxiv=0909.1502 }}</ref> –making them promising candidates for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene. | |||
=== Thermal conductivity === | |||
One way to synthesize bilayer graphene is via ], and can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v">{{Cite journal |doi=10.1021/nl204547v |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last=Min |first=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=NanoLetters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |page=1609|bibcode=2012NanoL..12.1609B }}</ref> | |||
Thermal transport in graphene is a burgeoning area of research, particularly for its potential applications in thermal management. Most experimental measurements have posted large uncertainties in the results of thermal conductivity due to the limitations of the instruments used. Following predictions for graphene and related ],<ref name="DT130">{{cite journal |last1=Berber |first1=Savas |last2=Kwon |first2=Young-Kyun |last3=Tománek |first3=David |author-link3=David Tománek |date=2000 |title=Unusually High Thermal Conductivity of Carbon Nanotubes |journal=Phys. Rev. Lett. |volume=84 |issue=20 |pages=4613–6 |arxiv=cond-mat/0002414 |bibcode=2000PhRvL..84.4613B |doi=10.1103/PhysRevLett.84.4613 |pmid=10990753 |s2cid=9006722}}</ref> early measurements of the ] of suspended graphene reported an exceptionally large thermal conductivity up to {{val|5300|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}},<ref name="Balandin">{{cite journal |last1=Balandin |first1=A. A. |last2=Ghosh |first2=Suchismita |last3=Bao |first3=Wenzhong |last4=Calizo |first4=Irene |last5=Teweldebrhan |first5=Desalegne |last6=Miao |first6=Feng |last7=Lau |first7=Chun Ning |date=20 February 2008 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=Nano Letters |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B |doi=10.1021/nl0731872 |pmid=18284217 |s2cid=9310741}}</ref> compared with the thermal conductivity of pyrolytic ] of approximately {{val|2,000|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature.<ref name="Touloukian1970">{{cite book |author=Y S. Touloukian |url={{google books |plainurl=y |id=31sqAAAAYAAJ}} |title=Thermophysical Properties of Matter: Thermal conductivity: nonmetallic solids |publisher=IFI/Plenum |year=1970 |isbn=978-0-306-67020-6}}</ref> However, later studies primarily on more scalable but more defected graphene derived by Chemical Vapor Deposition have been unable to reproduce such high thermal conductivity measurements, producing a wide range of thermal conductivities between {{val|1,500}} – {{val|2,500|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} for suspended single-layer graphene.<ref name="CaiMoore2010">{{cite journal |last1=Cai |first1=Weiwei |last2=Moore |first2=Arden L. |last3=Zhu |first3=Yanwu |last4=Li |first4=Xuesong |last5=Chen |first5=Shanshan |last6=Shi |first6=Li |last7=Ruoff |first7=Rodney S. |year=2010 |title=Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition |journal=Nano Letters |volume=10 |issue=5 |pages=1645–1651 |bibcode=2010NanoL..10.1645C |doi=10.1021/nl9041966 |pmid=20405895 |s2cid=207664146}}</ref><ref name="FaugerasFaugeras2010">{{cite journal |last1=Faugeras |first1=Clement |last2=Faugeras |first2=Blaise |last3=Orlita |first3=Milan |last4=Potemski |first4=M. |last5=Nair |first5=Rahul R. |last6=Geim |first6=A. K. |year=2010 |title=Thermal Conductivity of Graphene in Corbino Membrane Geometry |journal=ACS Nano |volume=4 |issue=4 |pages=1889–1892 |arxiv=1003.3579 |bibcode=2010arXiv1003.3579F |doi=10.1021/nn9016229 |pmid=20218666 |s2cid=207558462}}</ref><ref name="XuPereira2014">{{cite journal |last1=Xu |first1=Xiangfan |last2=Pereira |first2=Luiz F. C. |last3=Wang |first3=Yu |last4=Wu |first4=Jing |last5=Zhang |first5=Kaiwen |last6=Zhao |first6=Xiangming |last7=Bae |first7=Sukang |last8=Tinh Bui |first8=Cong |last9=Xie |first9=Rongguo |last10=Thong |first10=John T. L. |last11=Hong |first11=Byung Hee |last12=Loh |first12=Kian Ping |last13=Donadio |first13=Davide |last14=Li |first14=Baowen |last15=Özyilmaz |first15=Barbaros |year=2014 |title=Length-dependent thermal conductivity in suspended single-layer graphene |journal=Nature Communications |volume=5 |page=3689 |arxiv=1404.5379 |bibcode=2014NatCo...5.3689X |doi=10.1038/ncomms4689 |pmid=24736666 |s2cid=10617464}}</ref><ref name="LeeYoon2011">{{cite journal |last1=Lee |first1=Jae-Ung |last2=Yoon |first2=Duhee |last3=Kim |first3=Hakseong |last4=Lee |first4=Sang Wook |last5=Cheong |first5=Hyeonsik |year=2011 |title=Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy |journal=Physical Review B |volume=83 |issue=8 |page=081419 |arxiv=1103.3337 |bibcode=2011PhRvB..83h1419L |doi=10.1103/PhysRevB.83.081419 |s2cid=118664500}}</ref> The large range in the reported thermal conductivity can be caused by large measurement uncertainties as well as variations in the graphene quality and processing conditions. In addition, it is known that when single-layer graphene is supported on an amorphous material, the thermal conductivity is reduced to about {{val|500}} – {{val|600|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature as a result of scattering of graphene lattice waves by the substrate,<ref name="SeolJo2010">{{cite journal |last1=Seol |first1=J. H. |last2=Jo |first2=I. |last3=Moore |first3=A. L. |last4=Lindsay |first4=L. |last5=Aitken |first5=Z. H. |last6=Pettes |first6=M. T. |last7=Li |first7=X. |last8=Yao |first8=Z. |last9=Huang |first9=R. |last10=Broido |first10=D. |last11=Mingo |first11=N. |last12=Ruoff |first12=R. S. |last13=Shi |first13=L. |year=2010 |title=Two-Dimensional Phonon Transport in Supported Graphene |url=https://hal-cea.archives-ouvertes.fr/cea-00818281 |url-status=live |journal=Science |volume=328 |issue=5975 |pages=213–216 |bibcode=2010Sci...328..213S |doi=10.1126/science.1184014 |pmid=20378814 |s2cid=213783 |archive-url=https://web.archive.org/web/20230204015608/https://hal-cea.archives-ouvertes.fr/cea-00818281 |archive-date=4 February 2023 |access-date=28 January 2023}}</ref><ref name="Klemens2001">{{cite journal |last1=Klemens |first1=P. G. |year=2001 |title=Theory of Thermal Conduction in Thin Ceramic Films |journal=International Journal of Thermophysics |volume=22 |issue=1 |pages=265–275 |doi=10.1023/A:1006776107140 |s2cid=115849714}}</ref> and can be even lower for few-layer graphene encased in amorphous oxide.<ref name="JangChen2010">{{cite journal |last1=Jang |first1=Wanyoung |last2=Chen |first2=Zhen |last3=Bao |first3=Wenzhong |last4=Lau |first4=Chun Ning |last5=Dames |first5=Chris |year=2010 |title=Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite |journal=Nano Letters |volume=10 |issue=10 |pages=3909–3913 |bibcode=2010NanoL..10.3909J |doi=10.1021/nl101613u |pmid=20836537 |s2cid=45253497}}</ref> Likewise, polymeric residue can contribute to a similar decrease in the thermal conductivity of suspended graphene to approximately {{val|500}} – {{val|600|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} for bilayer graphene.<ref name="PettesJo2011">{{cite journal |last1=Pettes |first1=Michael Thompson |last2=Jo |first2=Insun |last3=Yao |first3=Zhen |last4=Shi |first4=Li |year=2011 |title=Influence of Polymeric Residue on the Thermal Conductivity of Suspended Bilayer Graphene |journal=Nano Letters |volume=11 |issue=3 |pages=1195–1200 |bibcode=2011NanoL..11.1195P |doi=10.1021/nl104156y |pmid=21314164}}</ref> | |||
=== Graphene Fiber === | |||
In 2011, Xinming Li and Hongwei Zhu from Tsinghua University reported a novel yet simple approach to fabricate graphene fibers from chemical vapor deposition grown graphene films.<ref>{{Cite journal|doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages=12164–71 |date=29 August 2011 |last=Li |first=Xinming |last2=Zhao |first2=Tianshuo |last3=Wang |first3=Kunlin |last4=Yang |first4=Ying |last5=Wei |first5=Jinquan |last6=Kang |first6=Feiyu |last7=Wu |first7=Dehai |last8=Zhu |first8=Hongwei }}</ref> The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable surface tension. Flexible all-solid-state supercapacitors based on this graphene fibers were demonstrated in 2013.<ref>{{cite web|url=http://pubs.rsc.org/en/content/articlelanding/2013/cp/c3cp52908h#!divAbstract |title=Flexible all solid-state supercapacitors based on chemical vapor deposition derived graphene fibers |date=3 September 2013 }}</ref> | |||
Isotopic composition, specifically the ratio of ] to ], significantly affects graphene's thermal conductivity. Isotopically pure <sup>12</sup>C graphene exhibits higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name="chen2012natmat">{{cite journal |last1=Chen |first1=Shanshan |last2=Wu |first2=Qingzhi |last3=Mishra |first3=Columbia |last4=Kang |first4=Junyong |last5=Zhang |first5=Hengji |last6=Cho |first6=Kyeongjae |last7=Cai |first7=Weiwei |last8=Balandin |first8=Alexander A. |last9=Ruoff |first9=Rodney S. |year=2012 |title=Thermal conductivity of isotopically modified graphene |journal=] |publication-date=10 January 2012 |volume=11 |issue=3 |pages=203–207 |arxiv=1112.5752 |bibcode=2012NatMa..11..203C |doi=10.1038/nmat3207 |pmid=22231598 |s2cid=119228971}}<br />''Lay summary'': {{cite news |last=Tracy |first=Suzanne |date=12 January 2012 |title=Keeping Electronics Cool |url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |periodical=Scientific Computing |publisher=] |at=scientificcomputing.com |publication-date=12 January 2012}}</ref> It can be shown by using the ], that the thermal conduction is ]-dominated.<ref name="Balandin" /> However, for a gated graphene strip, an applied gate bias causing a ] shift much larger than ''k''<sub>B</sub>''T'' can cause the electronic contribution to increase and dominate over the ] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito2">{{cite journal |last1=Saito |first1=K. |last2=Nakamura |first2=J. |last3=Natori |first3=A. |year=2007 |title=Ballistic thermal conductance of a graphene sheet |journal=] |volume=76 |issue=11 |page=115409 |bibcode=2007PhRvB..76k5409S |doi=10.1103/PhysRevB.76.115409}}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |last1=Liang |first1=Qizhen |last2=Yao |first2=Xuxia |last3=Wang |first3=Wei |last4=Liu |first4=Yan |last5=Wong |first5=Ching Ping |year=2011 |title=A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |url=https://figshare.com/articles/A_Three_Dimensional_Vertically_Aligned_Functionalized_Multilayer_Graphene_Architecture_An_Approach_for_Graphene_Based_Thermal_Interfacial_Materials/2680561 |url-status=live |journal=ACS Nano |volume=5 |issue=3 |pages=2392–2401 |doi=10.1021/nn200181e |pmid=21384860 |archive-url=https://web.archive.org/web/20200801041807/https://figshare.com/articles/A_Three_Dimensional_Vertically_Aligned_Functionalized_Multilayer_Graphene_Architecture_An_Approach_for_Graphene_Based_Thermal_Interfacial_Materials/2680561 |archive-date=1 August 2020 |access-date=1 December 2019}}</ref> | |||
=== 3D graphene === | |||
Graphite, a 3D counterpart to graphene, exhibits a ] ] exceeding {{val|1,000|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} (similar to ]), In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger ].<ref>{{cite book |last=Delhaes |first=P. |url={{google books |plainurl=y |id=7p2pgNOWPbEC}} |title=Graphite and Precursors |publisher=CRC Press |year=2001 |isbn=978-90-5699-228-6}}</ref> In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductance, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{cite journal |last1=Mingo |first1=N. |last2=Broido |first2=D.A. |year=2005 |title=Carbon Nanotube Ballistic Thermal Conductance and Its Limits |journal=Physical Review Letters |volume=95 |issue=9 |page=096105 |bibcode=2005PhRvL..95i6105M |doi=10.1103/PhysRevLett.95.096105 |pmid=16197233}}</ref> | |||
In 2013, a three-dimensional ] of hexagonally arranged carbon was termed 3D graphene, although self-supporting 3D graphene has not yet been produced.<ref>{{Cite doi|10.1002/ange.201303497}}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |date= |accessdate=2013-08-24 |last=Wang |first=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |page=9380 |doi=10.1002/ange.201303497 }}</ref> | |||
Graphene's thermal conductivity is influenced by its three ] modes: two linear ] dispersion relation in-plane modes (LA, TA) and one quadratic dispersion relation out-of-plane mode (ZA). At low temperatures, the dominance of the T<sup>1.5</sup> thermal conductivity contribution of the out-of-plane mode supersedes the ''T''<sup>2</sup> dependence of the linear modes.<ref name="mingo" /> Some graphene phonon bands exhibit negative ]s,<ref name="mounet">{{cite journal |last1=Mounet |first1=N. |last2=Marzari |first2=N. |year=2005 |title=First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |journal=Physical Review B |volume=71 |issue=20 |page=205214 |arxiv=cond-mat/0412643 |bibcode=2005PhRvB..71t5214M |doi=10.1103/PhysRevB.71.205214 |s2cid=119461729}}</ref> resulting in negative ] at low temperatures. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes, whose frequencies increase with in-plane ], akin to a stretched string with higher frequency vibrations.<ref name="lifshitz">{{cite book |last=Lifshitz |first=I.M. |title=Journal of Experimental and Theoretical Physics |year=1952 |volume=22 |page=475 |language=ru}}</ref> | |||
== Production techniques == | |||
=== Chemical properties === | |||
True isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle. However, other routes to 2d materials exist: | |||
{{quote|Fundamental forces place seemingly insurmountable barriers in the way of creating ... The nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich variety of stable 3D structures that occur in soot. | |||
Graphene has a theoretical ] (SSA) of {{val|2630 |ul=m2 |up=g}}. This is much larger than that reported to date for carbon black (typically smaller than {{val|900 |ul=m2 |up=g}}) or for carbon nanotubes (CNTs), from ≈100 to {{val|1000 |ul=m2 |up=g}} and is similar to ].<ref name="bonaccorso2015">{{cite journal |doi=10.1126/science.1246501 |pmid=25554791 |title=Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage |journal=Science |volume=347 |issue=6217 |page=1246501 |year=2015 |last1=Bonaccorso |first1=F. |last2=Colombo |first2=L. |last3=Yu |first3=G. |last4=Stoller |first4=M. |last5=Tozzini |first5=V. |last6=Ferrari |first6=A. C. |last7=Ruoff |first7=R. S. |last8=Pellegrini |first8=V. |bibcode=2015Sci...347...41B|s2cid=6655234 }}</ref> | |||
But there is a way around the problem. Interactions with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists within graphite... One can then hope to fool Nature and extract single-atom-thick crystallites at a low enough temperature that they remain in the quenched state prescribed by the original higher-temperature 3D growth.<ref name="PhysTod"/>}} | |||
Graphene is the only form of carbon (or solid material) in which every atom is available for chemical reaction from two sides (due to the 2D structure). Atoms at the edges of a graphene sheet have special chemical reactivity. Graphene has the highest ratio of edge atoms of any ]. Defects within a sheet increase its chemical reactivity.<ref name="denis2013"/> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below {{convert|260|C|K|sigfig=2}}.<ref name="Yamada3"/> Graphene burns at very low temperatures (e.g., {{convert|350|C|K|sigfig=2}}).<ref name="Eftekhari"/> Graphene is commonly modified with oxygen- and nitrogen-containing ] and analyzed by ] and ]. However, the determination of structures of graphene with oxygen-<ref name="Yamada1"/> and nitrogen-<ref name="Yamada2"/> functional groups require the structures to be well controlled. | |||
In 2013, ] physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker multilayer sheets.<ref>{{cite news |url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected |work=Phys.org |date=1 February 2013 |access-date=14 December 2013 |archive-date=24 September 2018 |archive-url=https://web.archive.org/web/20180924213239/https://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |url-status=live }}</ref> | |||
Graphene planes become better separated in ] graphite compounds. | |||
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as ]s. Bombarded with pure carbon atoms, the atoms perfectly align into ]s, filling the holes.<ref name=zan2012/><ref name=puiu2012/> | |||
Graphene fragments are produced (along with other debris) whenever graphite is abraded, such as when drawing with a pencil.<ref name=SciAm>{{Cite news |last=Geim |first=A. K. |last2=Kim |first2=P. |date=April 2008 |title=Carbon Wonderland |url=http://www.scientificamerican.com/article.cfm?id=carbon-wonderland |work=] |quote=... bits of graphene are undoubtedly present in every pencil mark }}</ref> | |||
=== Biological properties === | |||
In 2011 the Institute of Electronic Materials Technology and Department of Physics at ] announced Sicilicon-based epitaxy technology for producing large pieces of graphene with the best quality to date.<ref> | |||
{{cite web |date=22 April 2011 |title=Polish scientists hope to patent graphene mass-production technology |url=http://www.wbj.pl/article-54247-polish-scientists-to-patent-graphene-mass-production-technology.html |work=] | |||
}}<br/>{{cite web |last=Waszak |first=S. |date=April 2011 |title=Polish team claims leap for wonder material graphene |url=http://www.physorg.com/news/2011-04-team-material-graphene.html |work=] }}</ref> | |||
Despite the promising results in different cell studies and proof of concept studies, there is still incomplete understanding of the full biocompatibility of graphene-based materials.<ref>{{cite journal |last1=Bullock |first1=Christopher J. |last2=Bussy |first2=Cyrill |title=Biocompatibility Considerations in the Design of Graphene Biomedical Materials |journal=Advanced Materials Interfaces |date=18 April 2019 |volume=6 |issue=11 |page=1900229 |doi=10.1002/admi.201900229 |doi-access=free }}</ref> Different cell lines react differently when exposed to graphene, and it has been shown that the lateral size of the graphene flakes, the form and surface chemistry can elicit different biological responses on the same cell line.<ref>{{cite journal |last1=Liao |first1=Ken-Hsuan |last2=Lin |first2=Yu-Shen |last3=Macosko |first3=Christopher W. |last4=Haynes |first4=Christy L. |title=Cytotoxicity of Graphene Oxide and Graphene in Human Erythrocytes and Skin Fibroblasts |journal=ACS Applied Materials & Interfaces |date=27 July 2011 |volume=3 |issue=7 |pages=2607–2615 |doi=10.1021/am200428v |pmid=21650218 }}</ref> | |||
=== Mechanical exfoliation === | |||
There are indications that graphene has promise as a useful material for interacting with neural cells; studies on cultured neural cells show limited success.<ref>{{cite journal |last1=Fabbro |first1=Alessandra |last2=Scaini |first2=Denis |last3=León |first3=Verónica |last4=Vázquez |first4=Ester |last5=Cellot |first5=Giada |last6=Privitera |first6=Giulia |last7=Lombardi |first7=Lucia |last8=Torrisi |first8=Felice |last9=Tomarchio |first9=Flavia |last10=Bonaccorso |first10=Francesco |last11=Bosi |first11=Susanna |last12=Ferrari |first12=Andrea C. |last13=Ballerini |first13=Laura |last14=Prato |first14=Maurizio |title=Graphene-Based Interfaces Do Not Alter Target Nerve Cells |journal=ACS Nano |date=26 January 2016 |volume=10 |issue=1 |pages=615–623 |doi=10.1021/acsnano.5b05647 |pmid=26700626 |hdl=11368/2860012 |hdl-access=free }}</ref><ref>{{cite web |title=Graphene shown to safely interact with neurons in the brain |url=https://www.cam.ac.uk/research/news/graphene-shown-to-safely-interact-with-neurons-in-the-brain |website=University of Cambridge |date=2016-01-29 |access-date=2016-02-16 |archive-date=23 February 2016 |archive-url=https://web.archive.org/web/20160223124743/https://www.cam.ac.uk/research/news/graphene-shown-to-safely-interact-with-neurons-in-the-brain |url-status=live }}</ref> | |||
This involves splitting single layers of graphene from multi-layered graphite. Achieving single layers typically requires multiple exfoliation steps, each producing a slice with fewer layers, until only one remains. Geim and Novosolev used adhesive tape to split the layers. | |||
Graphene also has some utility in ]s. Researchers at the Graphene Research Centre at the ] (NUS) discovered in 2011 the ability of graphene to accelerate the osteogenic differentiation of human ] without the use of biochemical inducers.<ref>{{cite journal |last1=Nayak |first1=Tapas R. |last2=Andersen |first2=Henrik |last3=Makam |first3=Venkata S. |last4=Khaw |first4=Clement |last5=Bae |first5=Sukang |last6=Xu |first6=Xiangfan |last7=Ee |first7=Pui-Lai R. |last8=Ahn |first8=Jong-Hyun |last9=Hong |first9=Byung Hee |last10=Pastorin |first10=Giorgia |last11=Özyilmaz |first11=Barbaros |title=Graphene for Controlled and Accelerated Osteogenic Differentiation of Human Mesenchymal Stem Cells |journal=ACS Nano |date=28 June 2011 |volume=5 |issue=6 |pages=4670–4678 |doi=10.1021/nn200500h |pmid=21528849 |bibcode=2011arXiv1104.5120N |arxiv=1104.5120 |s2cid=20794090 }}</ref> | |||
After exfoliation the flakes are deposited on a silicon wafer using "dry deposition". Individual atomic planes can be viewed with an optical microscope. Crystallites larger than 1 mm and visible to the naked eye can be obtained with the technique. It is often referred to as a "]" or "drawing" method. The latter name appeared because the dry deposition resembles drawing with a piece of graphite.<ref name="PhysTod">{{Cite journal |last=Geim |first=A. K. |last2=MacDonald |first2=A. H. |title=Graphene: Exploring carbon flatland |journal=Physics Today |volume=60 |pages=35–41 |year=2007 |doi=10.1063/1.2774096 |bibcode=2007PhT....60h..35G |issue=8 }}</ref> | |||
Graphene can be used in biosensors; in 2015, researchers demonstrated that a graphene-based sensor can be used to detect a cancer risk biomarker. In particular, by using epitaxial graphene on silicon carbide, they were repeatedly able to detect 8-hydroxydeoxyguanosine (8-OHdG), a DNA damage biomarker.<ref>{{Cite journal |title=Generic epitaxial graphene biosensors for ultrasensitive detection of cancer risk biomarker |last=Tehrani |first=Z. |date=2014-09-01 |journal=2D Materials |doi=10.1088/2053-1583/1/2/025004 |bibcode=2014TDM.....1b5004T |volume=1 |issue=2 |page=025004 |s2cid=55035225 |url=https://cronfa.swan.ac.uk/Record/cronfa19735/Download/0019735-07052015130054.pdf |access-date=7 January 2020 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801050028/https://cronfa.swan.ac.uk/Record/cronfa19735/Download/0019735-07052015130054.pdf |url-status=live }}</ref> | |||
=== Epitaxy === | |||
=== Support substrate === | |||
] refers to the deposition of a crystalline overlayer on a crystalline substrate, where there is registry between the two. In some cases epitaxial graphene layers are coupled to surfaces weakly enough (by ]s) to retain the two dimensional ] of isolated graphene.<ref name=Gall1> | |||
{{cite journal | |||
|last=Gall |first=N. R. | |||
|last2=Rut'Kov |first2=E. V. | |||
|last3=Tontegode |first3=A. Ya. | |||
|year=1997 | |||
|title=Two Dimensional Graphite Films on Metals and Their Intercalation | |||
|journal=] | |||
|volume=11 |issue=16 |page=1865 | |||
|bibcode=1997IJMPB..11.1865G | |||
|doi=10.1142/S0217979297000976 | |||
}}</ref><ref name=Gall2> | |||
{{cite journal | |||
|last=Gall |first=N. R. | |||
|last2=Rut'Kov |first2=E. V. | |||
|last3=Tontegode |first3=A. Ya. | |||
|year=1995 | |||
|title=Influence of surface carbon on the formation of silicon-refractory metal interfaces | |||
|journal=] | |||
|volume=266 |issue=2 |page=229 | |||
|bibcode=1995TSF...266..229G | |||
|doi=10.1016/0040-6090(95)06572-5 | |||
}}</ref> An example of weakly coupled epitaxial graphene is the one grown on SiC.<ref name="Nov 04"> | |||
{{cite journal | |||
|last=Novoselov |first=K. S. | |||
|last2=Geim |first2=A. K. | |||
|last3=Morozov |first3=S. V. | |||
|last4=Jiang |first4=D. | |||
|last5=Zhang |first5=Y. | |||
|last6=Dubonos |first6=S. V. | |||
|last7=Grigorieva |first7=I. V. | |||
|last8=Firsov |first8=A. A. | |||
|year=2004 | |||
|title=Electric Field Effect in Atomically Thin Carbon Films | |||
|url=http://onnes.ph.man.ac.uk/nano/Publications/Science_2004.pdf |format=PDF | |||
|journal=] | |||
|volume=306 |issue=5696 |pages=666–669 | |||
|arxiv=cond-mat/0410550 | |||
|bibcode=2004Sci...306..666N | |||
|doi=10.1126/science.1102896 | |||
|pmid=15499015 | |||
}}</ref> | |||
The electronic property of graphene can be significantly influenced by the supporting substrate. Studies of graphene monolayers on clean and hydrogen(H)-passivated silicon (100) (Si(100)/H) surfaces have been performed.<ref>{{cite journal|last1=Xu|first1=Yang|last2=He|first2=K. T.|last3=Schmucker|first3=S. W.|last4=Guo|first4=Z.|last5=Koepke|first5=J. C.|last6=Wood|first6=J. D.|last7=Lyding|first7=J. W.|last8=Aluru|first8=N. R.|s2cid=207573621|title=Inducing Electronic Changes in Graphene through Silicon (100) Substrate Modification|journal=Nano Letters|volume=11|issue=7|pages=2735–2742|date=2011|doi=10.1021/nl201022t|pmid=21661740|bibcode=2011NanoL..11.2735X}}</ref> The Si(100)/H surface does not perturb the electronic properties of graphene, whereas the interaction between the clean Si(100) surface and graphene changes the electronic states of graphene significantly. This effect results from the covalent bonding between C and surface Si atoms, modifying the π-orbital network of the graphene layer. The local density of states shows that the bonded C and Si surface states are highly disturbed near the Fermi energy. | |||
Graphene monolayers grown on SiC and Ir are weakly coupled to these substrates (how weakly remains debated) and the graphene–substrate interaction can be further passivated.<ref name=SiCplusH2/> | |||
== Graphene layers and structural variants == | |||
==== Silicon carbide ==== | |||
=== Monolayer sheets === | |||
{{Main|Tunable nanoporous carbon|l1=Carbide-derived Carbon}} | |||
In 2013 a group of Polish scientists presented a production unit that allows the manufacture of continuous monolayer sheets.<ref>{{cite journal |title=Single and Multilayer Growth of Graphene from the Liquid Phase |journal=Applied Mechanics and Materials |volume=510 |pages=8–12 |doi=10.4028/www.scientific.net/AMM.510.8 |year=2014 |last1=Kula |first1=Piotr |last2=Pietrasik |first2=Robert |last3=Dybowski |first3=Konrad |last4=Atraszkiewicz |first4=Radomir |last5=Szymanski |first5=Witold |last6=Kolodziejczyk |first6=Lukasz |last7=Niedzielski |first7=Piotr |last8=Nowak |first8=Dorota |s2cid=93345920 }}</ref> The process is based on graphene growth on a liquid metal matrix.<ref>{{cite web |title=Polish scientists find way to make super-strong graphene sheets {{!}} Graphene-Info |url=http://www.graphene-info.com/polish-scientists-find-way-make-super-strong-graphene-sheets |website=www.graphene-info.com |access-date=2015-07-01 |archive-date=1 July 2015 |archive-url=https://web.archive.org/web/20150701184231/http://www.graphene-info.com/polish-scientists-find-way-make-super-strong-graphene-sheets |url-status=live }}</ref> The product of this process was called ]. In a new study published in Nature, the researchers have used a single-layer graphene electrode and a novel surface-sensitive non-linear spectroscopy technique to investigate the top-most water layer at the electrochemically charged surface. They found that the interfacial water response to the applied electric field is asymmetric concerning the nature of the applied field.<ref>{{cite journal |last1=Montenegro |first1=Angelo |last2=Dutta |first2=Chayan |last3=Mammetkuliev |first3=Muhammet |last4=Shi |first4=Haotian |last5=Hou |first5=Bingya |last6=Bhattacharyya |first6=Dhritiman |last7=Zhao |first7=Bofan |last8=Cronin |first8=Stephen B. |last9=Benderskii |first9=Alexander V. |title=Asymmetric response of interfacial water to applied electric fields |journal=Nature |date=3 June 2021 |volume=594 |issue=7861 |pages=62–65 |doi=10.1038/s41586-021-03504-4 |pmid=34079138 |bibcode=2021Natur.594...62M |s2cid=235321882 }}</ref> | |||
Heating ] (SiC) to high temperatures (>{{val|1100|u=°C}}) under low pressures (~10<sup>−6</sup> torr) reduces it to graphene.<ref>{{Cite journal |last=Sutter |first=P. |title=Epitaxial graphene: How silicon leaves the scene |journal=Nature Materials |volume=8 |year=2009 |pmid=19229263 |doi=10.1038/nmat2392 |issue=3 |bibcode=2009NatMa...8..171S |pages=171–2 }}</ref> This process produces epitaxial graphene with dimensions dependent upon the size of the wafer. The face of the SiC used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the resulting graphene. | |||
=== Bilayer graphene === | |||
The electronic band-structure (so-called Dirac cone structure) was first visualized in this material.<ref name=ohta1>{{Cite journal |last=Ohta, |first=T. |year=2007 |title=Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy |journal=Physical Review Letters |volume=98 |page=206802 |doi=10.1103/PhysRevLett.98.206802 |pmid=17677726 |bibcode=2007PhRvL..98t6802O |issue=20 |last2=Bostwick |first2=Aaron |last3=McChesney |first3=J. |last4=Seyller |first4=Thomas |last5=Horn |first5=Karsten |last6=Rotenberg |first6=Eli }}</ref><ref name=ohta2>{{Cite journal |last=Bostwick |first=A. |year=2007 |title=Symmetry breaking in few layer graphene films |journal=New Journal of Physics |volume=9 |page=385 |doi=10.1088/1367-2630/9/10/385 |bibcode=2007NJPh....9..385B |issue=10 |last2=Ohta |first2=Taisuke |last3=McChesney |first3=Jessica L |last4=Emtsev |first4=Konstantin V |last5=Seyller |first5=Thomas |last6=Horn |first6=Karsten |last7=Rotenberg |first7=Eli |arxiv=0705.3705 }}</ref><ref name="Lanzara06">{{Cite journal |last=Zhou |first=S.Y. |last2=Gweon |first2=G.-H. |last3=Graf |first3=J. |last4=Fedorov |first4=A. V. |last5=Spataru |first5=C. D. |last6=Diehl |first6=R. D. |last7=Kopelevich |first7=Y. |last8=Lee |first8=D.-H. |last9=Louie |first9=Steven G. |last10=Lanzara |first10=A. |title=First direct observation of Dirac fermions in graphite |doi=10.1038/nphys393 |journal=Nature Physics |volume=2 |pages=595–599 |year=2006 |arxiv=cond-mat/0608069 |bibcode=2006NatPh...2..595Z |issue=9 }}</ref> Weak anti-localization is observed in this material, but not in exfoliated graphene produced by the pencil-trace method.<ref name=exf>{{Cite journal |last=Morozov |first=S.V. |title=Strong Suppression of Weak Localization in Graphene |doi=10.1103/PhysRevLett.97.016801 |journal=Physical Review Letters |volume=97 |page=016801 |year=2006 |pmid=16907394 |issue=1 |bibcode=2006PhRvL..97a6801M |arxiv=cond-mat/0603826 |last2=Novoselov |first2=K. S. |last3=Katsnelson |first3=M. I. |last4=Schedin |first4=F. |last5=Ponomarenko |first5=L. A. |last6=Jiang |first6=D. |last7=Geim |first7=A. K. }}</ref> Large, temperature-independent mobilities have been observed, approaching those in exfoliated graphene placed on silicon oxide, but lower than mobilities in suspended graphene produced by the drawing method. Even without transfer, graphene on SiC exhibits massless Dirac fermions.<ref name="ByungHeeHong"/><ref name="0908.1900">{{cite journal |first=Johannes |last=Jobst |first2=Daniel |last2=Waldmann |first3=Florian |last3=Speck |first4=Roland |last4=Hirner |first5=Duncan K. |last5=Maude |first6=Thomas |last6=Seyller |first7=Heiko B. |last7=Weber |title=How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year=2009 |doi=10.1103/PhysRevB.81.195434 |journal=Physical Review B |volume=81 |issue=19 |pages=195434 |arxiv=0908.1900|bibcode=2010PhRvB..81s5434J }}</ref><ref name="ShenAPL">{{Cite journal |first=T. |last=Shen |first2=J.J. |last2=Gu |first3=M |last3=Xu |first4=Y.Q. |last4=Wu |first5=M.L. |last5=Bolen |first6=M.A. |last6=Capano |first7=L.W. |last7=Engel |first8=P.D. |last8=Ye |title=Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal=Applied Physics Letters |bibcode=2009ApPhL..95q2105S |year=2009 |volume=95 |issue=17 |page=172105 |arxiv=0908.3822 }}</ref><ref name=0909.2903>{{cite journal |first=Xiaosong |last=Wu, |first2=Yike |last2=Hu |first3=Ming |last3=Ruan |first4=Nerasoa K |last4=Madiomanana |first5=John |last5=Hankinson |first6=Mike |last6=Sprinkle |first7=Claire |last7=Berger |first8=Walt A. |last8=de Heer |year=2009 |title=Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi=10.1063/1.3266524 |journal=Applied Physics Letters |volume=95 |issue=22 |page=223108 |arxiv=0909.2903|bibcode=2009ApPhL..95v3108W }}</ref><ref name=0909.1193>{{cite journal |first=Samuel |last=Lara-Avila |first2=Alexei |last2=Kalaboukhov |first3=Sara |last3=Paolillo |first4=Mikael |last4=Syväjärvi |first5=Rositza |last5=Yakimova |first6=Vladimir |last6=Fal'ko |first7=Alexander |last7=Tzalenchuk |first8=Sergey |last8=Kubatkin |year=2009 |title=SiC Graphene Suitable For Quantum Hall Resistance Metrology |doi=10.1038/nnano.2009.474 |journal=Nature Nanotechnology |volume=5 |issue=3 |pages=186–9 |pmid=20081845 |arxiv=0909.1193 |bibcode=2010NatNa...5..186T }}<!-- sources differ --></ref><ref name=phase1>{{cite journal |first=J.A. |last=Alexander-Webber |first2=A.M.R. |last2=Baker |first3=T.J.B.M. |last3=Janssen |first4=A. |last4=Tzalenchuk |first5=S. |last5=Lara-Avila |first6=S. |last6=Kubatkin |first7=R. |last7=Yakimova |first8=B. A. |last8=Piot |first9=D. K. |last9=Maude |first10=R.J. |last10=Nicholas |year=2013 |title=Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi=10.1103/PhysRevLett.111.096601 |journal=Physical Review Letters |volume=111 |issue=9 |page=096601 |pmid=24033057 |arxiv=1304.4897|bibcode=2013PhRvL.111i6601A }}</ref> | |||
{{main|Bilayer graphene}} | |||
Bilayer graphene displays the ], a tunable ]<ref name="PRB75.155115">{{cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last1=Min |first1=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15 |page=155115 |arxiv=cond-mat/0612236 |bibcode=2007PhRvB..75o5115M|s2cid=119443126 }}</ref> and potential for ]<ref name="PRL104.096802">{{cite journal |doi=10.1103/PhysRevLett.104.096802 |pmid=20367001 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last1=Barlas |first1=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |page=96802 |bibcode=2010PhRvL.104i6802B |arxiv=0909.1502|s2cid=33249360 }}</ref> –making it a promising candidate for ] and ] applications. Bilayer graphene typically can be found either in ] configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other.<ref name="nl204547v">{{cite journal |doi=10.1021/nl204547v |pmid=22329410 |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last1=Min |first1=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=Nano Letters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |s2cid=896422 |pages=1609–1615 |bibcode=2012NanoL..12.1609B}}</ref> Stacking order and orientation govern the optical and electronic properties of bilayer graphene. | |||
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single layer,<ref name="Hass1">{{Cite journal |last=Hass |first=J. |year=2008 |title=Why multilayer graphene on 4H-SiC(000(1)over-bar) behaves like a single sheet of graphene |journal=Physical Review Letters |volume=100 |page=125504 |doi=10.1103/PhysRevLett.100.125504 |bibcode=2008PhRvL.100l5504H |issue=12 |last2=Varchon |first2=F. |last3=Millán-Otoya |first3=J. |last4=Sprinkle |first4=M. |last5=Sharma |first5=N. |last6=De Heer |first6=W. |last7=Berger |first7=C. |last8=First |first8=P. |last9=Magaud |first9=L. |last10=Conrad |first10=E. }}</ref> in other cases the properties are affected,<ref name=ohta1/><ref name=ohta2/> as they are in bulk graphite. This effect is well understood theoretically and is related to the symmetry of the interlayer interactions.<ref name="Hass1"/> | |||
One way to synthesize bilayer graphene is via ], which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v" /> | |||
Epitaxial graphene on SiC can be patterned using standard microelectronics methods. The band gap can be tuned by laser irradiation.<ref>{{cite journal |doi=10.1021/nn201757j |title=Laser Patterning of Epitaxial Graphene for Schottky Junction Photodetectors |year=2011 |last=Singh |first=Ram Sevak |last2=Nalla |first2=Venkatram |last3=Chen |first3=Wei |last4=Wee |first4=Andrew Thye Shen |last5=Ji |first5=Wei |journal=ACS Nano |volume=5 |issue=7 |pages=5969–75 |pmid=21702443 }}</ref> | |||
It has been shown that the two graphene layers can withstand important strain or doping mismatch<ref>{{cite journal |last1=Forestier |first1=Alexis |last2=Balima |first2=Félix |last3=Bousige |first3=Colin |last4=de Sousa Pinheiro |first4=Gardênia |last5=Fulcrand |first5=Rémy |last6=Kalbác |first6=Martin |last7=San-Miguel |first7=Alfonso |title=Strain and Piezo-Doping Mismatch between Graphene Layers |journal=J. Phys. Chem. C |date=April 28, 2020 |volume=124 |issue=20 |page=11193 |doi=10.1021/acs.jpcc.0c01898 |s2cid=219011027 |url=https://hal.archives-ouvertes.fr/hal-02651267/document |access-date=21 December 2020 |archive-date=29 April 2021 |archive-url=https://web.archive.org/web/20210429043452/https://hal.archives-ouvertes.fr/hal-02651267/document |url-status=live }}</ref> which ultimately should lead to their exfoliation. | |||
==== Metal substrates ==== | |||
=== Turbostratic === | |||
The atomic structure of a metal substrate can seed the growth of graphene. Graphene grown on ] does not typically produce uniform layer thickness. Bonding between the bottom graphene layer and the substrate may affect layer properties.<ref name="PhysOrg.com">{{Cite news |title=A smarter way to grow graphene |url=http://www.physorg.com/news129980833.html |publisher=PhysOrg.com |date=May 2008 }}</ref> | |||
Turbostratic graphene exhibits weak interlayer coupling, and the spacing is increased with respect to Bernal-stacked multilayer graphene. Rotational misalignment preserves the 2D electronic structure, as confirmed by ]. The D peak is very weak, whereas the 2D and G peaks remain prominent. A rather peculiar feature is that the I<sub>2D</sub>/I<sub>G</sub> ratio can exceed 10. However, most importantly, the M peak, which originates from AB stacking, is absent, whereas the TS<sub>1</sub> and TS<sub>2</sub> modes are visible in the ].<ref name="Luong 647–651">{{Cite journal|last1=Luong|first1=Duy X.|last2=Bets|first2=Ksenia V.|last3=Algozeeb|first3=Wala Ali|last4=Stanford|first4=Michael G.|last5=Kittrell|first5=Carter|last6=Chen|first6=Weiyin|last7=Salvatierra|first7=Rodrigo V.|last8=Ren|first8=Muqing|last9=McHugh|first9=Emily A.|last10=Advincula|first10=Paul A.|last11=Wang|first11=Zhe|date=January 2020|title=Gram-scale bottom-up flash graphene synthesis|url=https://www.nature.com/articles/s41586-020-1938-0|journal=Nature|language=en|volume=577|issue=7792|pages=647–651|doi=10.1038/s41586-020-1938-0|pmid=31988511|bibcode=2020Natur.577..647L|s2cid=210926149|issn=1476-4687|access-date=16 October 2021|archive-date=20 October 2021|archive-url=https://web.archive.org/web/20211020123054/https://www.nature.com/articles/s41586-020-1938-0|url-status=live}}</ref><ref>{{Cite journal|last1=Stanford|first1=Michael G.|last2=Bets|first2=Ksenia V.|last3=Luong|first3=Duy X.|last4=Advincula|first4=Paul A.|last5=Chen|first5=Weiyin|last6=Li|first6=John Tianci|last7=Wang|first7=Zhe|last8=McHugh|first8=Emily A.|last9=Algozeeb|first9=Wala A.|last10=Yakobson|first10=Boris I.|last11=Tour|first11=James M.|date=2020-10-27|title=Flash Graphene Morphologies|url=https://doi.org/10.1021/acsnano.0c05900|journal=ACS Nano|volume=14|issue=10|pages=13691–13699|doi=10.1021/acsnano.0c05900|pmid=32909736|osti=1798502 |s2cid=221623214|issn=1936-0851}}</ref> The material is formed through conversion of non-graphenic carbon into graphenic carbon without providing sufficient energy to allow for the reorganization through annealing of adjacent graphene layers into crystalline graphitic structures. | |||
Graphene grown on ] is very weakly bonded, uniform in thickness and can be highly ordered. As on many other substrates, graphene on iridium is slightly rippled. Due to the long-range order of these ripples, minigaps in the electronic band-structure (Dirac cone) become visible.<ref name="grIr111">{{Cite journal |last=Pletikosić |first=I. |year=2009 |title=Dirac Cones and Minigaps for Graphene on Ir(111) |journal=Physical Review Letters |volume=102 |page=056808 |doi=10.1103/PhysRevLett.102.056808 |bibcode=2009PhRvL.102e6808P |issue=5 |last2=Kralj |first2=M. |last3=Pervan |first3=P. |last4=Brako |first4=R. |last5=Coraux |first5=J. |last6=n’Diaye |first6=A. |last7=Busse |first7=C. |last8=Michely |first8=T. |arxiv=0807.2770 }}</ref> | |||
High-quality sheets of few-layer graphene exceeding {{convert|1|cm2|abbr=on|sigfig=1}} in area have been synthesized via ] on thin ] films with ] as a carbon source. These sheets have been successfully transferred to various substrates.<ref name="ByungHeeHong">{{Cite journal |last=Kim |first=Kuen Soo |author2=''et al.'' |title=Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi=10.1038/nature07719 |journal=Nature |volume=457 |pmid=19145232 |issue=7230 |bibcode=2009Natur.457..706K |pages=706–10 }}</ref><ref name="hongR" /><ref>{{cite journal |first=J. |last=Rafiee |first2=X. |last2=Mi |first3=H. |last3=Gullapalli |first4=A.V. |last4=Thomas |first5=F. |last5=Yavari |first6=Y. |last6=Shi |first7=P.M. |last7=Ajayan |first8=N.A. |last8=Koratkar |title=Wetting transparency of graphene |journal=Nature Materials |issue=11 |year=2012 |pages=217-222 }}</ref> | |||
=== Graphene superlattices === | |||
An improvement of this technique employs ] foil; at very low pressure, the growth of graphene automatically stops after a single graphene layer forms. Arbitrarily large films can be created.<ref name=hongR/><ref name="CopperGraphene">{{Cite journal |last=Li |first=Xuesong |author2=''et al.'' |title=Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils |year=2009 |pmid=19423775 |doi=10.1126/science.1171245 |journal=Science |volume=324 |issue=5932 |bibcode=2009Sci...324.1312L |pages=1312–4 |arxiv=0905.1712 }}</ref> The single layer growth is also due to low concentration of carbon in methane. Larger ]s such as ] and ] produce bilayer graphene.<ref>{{cite journal |last=Wassei |first=Jonathan K. |last2=Mecklenburg |first2=Matthew |last3=Torres |first3=Jaime A.|last4=Fowler |first4=Jesse D. |last5=Regan |first5=B. C. |last6=Kaner |first6=Richard B. |last7=Weiller |first7=Bruce H. |title=Chemical Vapor Deposition of Graphene on Copper from Methane, Ethane and Propane: Evidence for Bilayer Selectivity |journal=Small |date=12 May 2012 |volume=8 |issue=9 |pages=1415–1422 |doi=10.1002/smll.201102276 |pmid=22351509 }}</ref> Atmospheric pressure CVD growth produces multilayer graphene on copper (similar to that grown on nickel films).<ref name=lenski>{{cite journal |last=Lenski |first=Daniel R. |last2=Fuhrer |first2=Michael S. |title=Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition |year=2011 |doi=10.1063/1.3605545 |journal=Journal of Applied Physics |volume=110 |page=013720 |arxiv=1011.1683 |bibcode=2011JAP...110a3720L }}</ref> Graphene has been demonstrated at temperatures compatible with conventional ] processing, using a nickel-based alloy with gold as catalyst.<ref name="cmosgraphene">{{Cite journal |last=Weatherup |first=R.S. |year=2011 |title=In Situ Characterization of Alloy Catalysts for Low-Temperature Graphene Growth |journal=Nano Letters |doi=10.1021/nl202036y |volume=11 |issue=10 |pages=4154–60 |pmid=21905732 |last2=Bayer |first2=Bernhard C. |last3=Blume |first3=Raoul |last4=Ducati |first4=Caterina |last5=Baehtz |first5=Carsten |last6=Schlögl |first6=Robert |last7=Hofmann |first7=Stephan |bibcode=2011NanoL..11.4154W }}</ref> | |||
Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities for designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms.<ref>{{cite journal|last1=Xu|first1=Yang|last2=Liu|first2=Yunlong|last3=Chen|first3=Huabin|last4=Lin|first4=Xiao|last5=Lin|first5=Shisheng|last6=Yu|first6=Bin|last7=Luo|first7=Jikui|title=Ab initio study of energy-band modulation in graphene-based two-dimensional layered superlattices|journal=Journal of Materials Chemistry|volume=22|issue=45|pages=23821|date=2012|doi=10.1039/C2JM35652J}}</ref> The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction. | |||
=== Reduction of graphite oxide === | |||
A superlattice corresponds to a periodic or quasi-periodic arrangement of different materials and can be described by a superlattice period which confers a new translational symmetry to the system, impacting their phonon dispersions and subsequently their thermal transport properties. Recently, uniform monolayer graphene-hBN structures have been successfully synthesized via lithography patterning coupled with chemical vapor deposition (CVD).<ref>{{cite journal |last1=Liu |first1=Zheng |last2=Ma |first2=Lulu |last3=Shi |first3=Gang |last4=Zhou |first4=Wu |last5=Gong |first5=Yongji |last6=Lei |first6=Sidong |last7=Yang |first7=Xuebei |last8=Zhang |first8=Jiangnan |last9=Yu |first9=Jingjiang |last10=Hackenberg |first10=Ken P. |last11=Babakhani |first11=Aydin |last12=Idrobo |first12=Juan-Carlos |last13=Vajtai |first13=Robert |last14=Lou |first14=Jun |last15=Ajayan |first15=Pulickel M. |title=In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes |url=https://www.nature.com/articles/nnano.2012.256 |journal=Nature Nanotechnology |pages=119–124 |language=en |doi=10.1038/nnano.2012.256 |date=February 2013 |volume=8 |issue=2 |pmid=23353677 |bibcode=2013NatNa...8..119L |access-date=1 December 2020 |archive-date=7 April 2023 |archive-url=https://web.archive.org/web/20230407181357/https://www.nature.com/articles/nnano.2012.256 |url-status=live }}</ref> Furthermore, superlattices of graphene-HBN are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport.<ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Thermal Conductivity of Graphene-hBN Superlattice Ribbons |url= |journal=Scientific Reports |pages=2737 |language=en |doi=10.1038/s41598-018-20997-8 |date=9 February 2018|volume=8 |issue=1 |pmid=29426893 |pmc=5807325 |bibcode=2018NatSR...8.2737F }}</ref><ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Suppression of coherent thermal transport in quasiperiodic graphene-hBN superlattice ribbons |url=https://doi.org/10.1016/j.carbon.2019.12.090 |journal=Carbon |pages=335–341 |doi=10.1016/j.carbon.2019.12.090 |date=April 2020|volume=160 |arxiv=2001.03072 |bibcode=2020Carbo.160..335F |s2cid=210116531 }}</ref><ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Thermal conductivity of Thue–Morse and double-period quasiperiodic graphene-hBN superlattices |url=https://www.sciencedirect.com/science/article/abs/pii/S0017931021015623 |journal=International Journal of Heat and Mass Transfer |pages=122464 |language=en |doi=10.1016/j.ijheatmasstransfer.2021.122464 |date=1 May 2022 |volume=186 |bibcode=2022IJHMT.18622464F |s2cid=245712349 |access-date=6 January 2022 |archive-date=6 January 2022 |archive-url=https://web.archive.org/web/20220106140014/https://www.sciencedirect.com/science/article/abs/pii/S0017931021015623 |url-status=live }}</ref><ref>{{cite thesis |last1=Félix |first1=Isaac de Macêdo |title=Transporte térmico em nanofitas de grafeno-nitreto de boro |date=29 March 2016 |publisher=Brasil |url=https://repositorio.ufrn.br/jspui/handle/123456789/21498 |type=masterThesis |access-date=6 January 2022 |archive-date=5 March 2022 |archive-url=https://web.archive.org/web/20220305094427/https://repositorio.ufrn.br/jspui/handle/123456789/21498 |url-status=live }}</ref><ref>{{cite thesis |last1=Félix |first1=Isaac de Macêdo |title=Condução de calor em nanofitas quase-periódicas de grafeno-hBN |url=https://repositorio.ufrn.br/handle/123456789/30749 |language=pt-BR |date=4 August 2020 |publisher=Universidade Federal do Rio Grande do Norte |type=doctoralThesis |access-date=1 December 2020 |archive-date=2 February 2021 |archive-url=https://web.archive.org/web/20210202054317/https://repositorio.ufrn.br/handle/123456789/30749 |url-status=live }} ] Text was copied from this source, which is available under a {{Webarchive|url=https://web.archive.org/web/20171016050101/https://creativecommons.org/licenses/by/4.0/ |date=16 October 2017 }}.</ref> | |||
] reduction was probably the first method of graphene synthesis. P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name="Boehm">. Graphene Times (2009-12-07). Retrieved on 2010-12-10.</ref> Geim acknowledged Boehm's contribution.<ref>. Aps.org. January 2010.</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Reduction of graphite oxide monolayer films, e.g. by ], ] in ]/], was reported to yield graphene films. However, the quality is lower compared to scotch-tape graphene, due to incomplete removal of functional groups. Furthermore, the ] protocol introduces permanent defects due to over-oxidation. Recently, the oxidation protocol was enhanced to yield ] with an almost intact carbon framework that allows highly efficient removal of functional groups. The measured ] mobility exceeded {{convert|1000|cm|2}}/Vs.<ref name="Eigler2013">{{cite journal |first=S. |last=Eigler |first2=M. |last2=Enzelberger-Heim |first3=S. |last3=Grimm |first4=P. |last=Hofmann |first=W. |last=Kroener |first=A. |last=Geworski |first=C. |last=Dotzer |first4=M. |last5=Röckert |first5=J. |last5=Xiao |first6=C. |last6=Papp |first7=O. |last7=Lytken |first8=H.-P. |last8=Steinrück |first9=P. |last9=Müller |first10=A. |last10=Hirsch |title=Wet Chemical Synthesis of Graphene |journal=Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 |doi=10.1002/adma.201300155 |pmid=23703794 }}</ref> ] analysis of reduced graphene oxide has been conducted.<ref name="Yamada">{{cite doi|10.1007/s10853-013-7630-0 }}</ref><ref>{{cite doi|10.1039/C2CP40790F }}</ref> | |||
== Nanostructured graphene forms == | |||
Applying a layer of graphite oxide film to a ] and burning it in a DVD writer produced a thin graphene film with high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram), and was highly resistant and malleable.<ref>{{cite web |url=http://www.sciencemag.org/content/335/6074/1326 |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |publisher=Sciencemag.org |date=16 March 2012 }}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=15 March 2012 }}</ref> | |||
=== Graphene nanoribbons === | |||
] | |||
] Electronic band structure of graphene strips of varying widths in zig-zag orientation. Tight-binding calculations show that they are all metallic.]] | |||
] Electronic band structure of graphene strips of various widths in the armchair orientation. Tight-binding calculations show that they are semiconducting or metallic depending on width (chirality).]] | |||
] ("nanostripes" in the "zig-zag"/"zigzag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of ]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{cite journal |first1=A Castro |last1=Neto |last2=Peres |first2=N. M. R. |last3=Novoselov |first3=K. S. |last4=Geim |first4=A. K. |last5=Geim |first5=A. K. |title=The electronic properties of graphene |journal=Rev Mod Phys |volume=81 |issue=1 |year=2009 |pages=109–162 |url=http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |archive-url=https://web.archive.org/web/20101115121052/http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |url-status=dead |archive-date=2010-11-15 |bibcode=2009RvMP...81..109C |doi=10.1103/RevModPhys.81.109 |arxiv=0709.1163|hdl=10261/18097 |s2cid=5650871 }}</ref>) | |||
=== Metal-carbon melts === | |||
=== Graphene quantum dots === | |||
This process dissolves carbon atoms inside a ] melt at a certain temperature and then precipitates the dissolved carbon at lower temperatures as single layer graphene (SLG).<ref name="shaahin">{{Cite journal |first=Shaahin |last=Amini |first2=Javier |last2=Garay |first3=Guanxiong |last3=Liu |first4=Alexander A. |last4=Balandin |first5=Reza |last5=Abbaschian |title=Growth of Large-Area Graphene Films from Metal-Carbon Melts |journal=Journal of Applied Physics |volume=108 |issue=9 |page=094321 |year=2010 |doi=10.1063/1.3498815 |bibcode=2010JAP...108i4321A |arxiv=1011.4081 }}</ref> | |||
A ] (GQD) is a graphene fragment with a size lesser than 100 nm. The properties of GQDs are different from bulk graphene due to the quantum confinement effects which only become apparent when the size is smaller than 100 nm.<ref name=tang2014/><ref name=tang2012/><ref name=tang2013/> | |||
The metal is first melted in contact with a carbon source, possibly a graphite crucible inside which the melt is carried out or graphite powder or chunks that are placed in the melt. Keeping the melt in contact with the carbon at a specific temperature dissolves the carbon atoms, saturating the melt based on the ] of metal-carbon. Upon lowering the temperature, carbon's solubility decreases and the excess carbon precipitates atop the melt. The floating layer can be either skimmed or frozen for later removal. Using different morphology, including thick graphite, few layer graphene (FLG) and SLG were observed on metal substrate. ] proved that SLG had grown on ] substrate. The SLG Raman spectrum featured no D and D′ band, indicating its pristine nature. Among transition metals, nickel provides the best substrate for growing SLG. Since nickel is not Raman active, direct Raman spectroscopy of graphene layers on top of the nickel is achievable.<ref name="shaahin"/> | |||
== Modified and functionalized graphene == | |||
=== Sodium ethoxide pyrolysis === | |||
{{Main|Graphene chemistry}} | |||
=== Graphene oxide === | |||
Gram-quantities of graphene were produced by the reduction of ] by ] metal, followed by ] of the ] product and washing with water to remove sodium salts.<ref>{{Cite journal |doi=10.1038/nnano.2008.365 |title=Gram-scale production of graphene based on solvothermal synthesis and sonication |year=2008 |last=Choucair |first=M. |journal=Nature Nanotechnology |pmid=19119279 |volume=4 |issue=1 |pages=30–3 |last2=Thordarson |first2=P |last3=Stride |first3=JA |bibcode=2009NatNa...4...30C }}</ref> | |||
{{further|Graphite oxide}} | |||
Graphene oxide is usually produced through chemical exfoliation of graphite. A particularly popular technique is the improved ].<ref>{{Cite journal|last1=Marcano|first1=Daniela C.|last2=Kosynkin|first2=Dmitry V.|last3=Berlin|first3=Jacob M.|last4=Sinitskii|first4=Alexander|last5=Sun|first5=Zhengzong|last6=Slesarev|first6=Alexander|last7=Alemany|first7=Lawrence B.|last8=Lu|first8=Wei|last9=Tour|first9=James M.|date=2010-08-24|title=Improved Synthesis of Graphene Oxide|url=https://doi.org/10.1021/nn1006368|journal=ACS Nano|volume=4|issue=8|pages=4806–4814|doi=10.1021/nn1006368|pmid=20731455|issn=1936-0851}}</ref> Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called ], have a measured ] of 32 ].<ref>{{cite web |url=http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archive-url=https://web.archive.org/web/20160602213039/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archive-date=2 June 2016 |title=Graphene Oxide Paper |publisher=Northwestern University |access-date=28 February 2011}}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the ] pathway and similar chemical processes.<ref>{{cite journal |last1=Eftekhari |first1=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |pages=2204–2213 |year=2010 |doi=10.1002/pola.23990 |bibcode=2010JPoSA..48.2204E |issue=10}}</ref> Graphene oxide flakes in ]s display enhanced photo-conducting properties.<ref>{{cite journal |last1=Nalla |first1=Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode=2010Nanot..21O5203N|s2cid=24385952 }}</ref> Graphene is normally ] and impermeable to all gases and liquids (vacuum-tight). However, when formed into a graphene oxide-based capillary membrane, both liquid water and water vapor flow through as quickly as if the membrane were not present.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last1=Nair |first1=R. R. |last2=Wu |first2=H. A. |last3=Jayaram |first3=P. N. |last4=Grigorieva |first4=I. V. |last5=Geim |first5=A. K. |bibcode=2012Sci...335..442N|s2cid=15204080 }}</ref> | |||
=== Nanotube slicing === | |||
In 2022, researchers evaluated the biological effects of low doses on graphene oxide on larvae and imago of '']''. Results show that oral administration of graphene oxide at concentrations of 0.02-1% has a beneficial effect on the developmental rate and hatching ability of larvae. Long-term administration of a low dose of graphene oxide extends the lifespan of Drosophila and significantly enhances resistance to environmental stresses. These suggest that graphene oxide affects carbohydrate and lipid metabolism in adult Drosophila. These findings might provide a useful reference to assess the biological effects of graphene oxide, which could play an important role in a variety of graphene-based biomedical applications.<ref name="Evaluation of biological effects of graphene oxide using Drosophila">{{cite journal |last1=Strilbytska |first1=Olha |last2=Semaniuk |first2=Uliana |last3=Burdyliuk |first3=Nadia |last4=Lushchak |first4=Oleh |title=Evaluation of biological effects of graphene oxide using Drosophila |url=https://journals.pnu.edu.ua/index.php/pcss/article/view/5751 |journal=Physics and Chemistry of Solid State |year=2022 |volume=2 |issue=23 |pages=242–248 |doi=10.15330/pcss.23.2.242-248 |s2cid=248823106 |doi-access=free |access-date=6 February 2023 |archive-date=6 February 2023 |archive-url=https://web.archive.org/web/20230206095248/https://journals.pnu.edu.ua/index.php/pcss/article/view/5751 |url-status=live }}</ref> | |||
Graphene can be created by cutting open ]s.<ref>{{cite journal |title=Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons |last=Brumfiel |first=G. |journal=Nature |year=2009 |doi=10.1038/news.2009.367 }}</ref> In one such method ] are cut open in solution by action of ] and ].<ref>{{Cite journal |title=Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons |last=Kosynkin |first=D. V. |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07872 |pmid=19370030 |issue=7240 |bibcode=2009Natur.458..872K |pages=872–6 |last2=Higginbotham |first2=Amanda L. |last3=Sinitskii |first3=Alexander |last4=Lomeda |first4=Jay R. |last5=Dimiev |first5=Ayrat |last6=Price |first6=B. Katherine |last7=Tour |first7=James M. }}</ref> In another method graphene nanoribbons were produced by ] of nanotubes partly embedded in a ] film.<ref>{{Cite journal |title=Narrow graphene nanoribbons from carbon nanotubes |last=Liying |first=Jiao |first2=Li |last2=Zhang |first3=Xinran |last3=Wang |first4=Georgi |last4=Diankov |first5=Hongjie |last5=Dai |authorlink5=Hongjie Dai |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07919 |pmid=19370031 |issue=7240 |bibcode=2009Natur.458..877J |pages=877–80 }}</ref> | |||
=== |
=== Chemical modification === | ||
] Soluble fragments of graphene can be prepared in the laboratory through chemical modification of graphite.<ref>{{cite journal |last1=Niyogi |first1=Sandip |last2=Bekyarova |first2=Elena |last3=Itkis |first3=Mikhail E. |last4=McWilliams |first4=Jared L. |last5=Hamon |first5=Mark A. |last6=Haddon |first6=Robert C. |year=2006 |title=Solution Properties of Graphite and Graphene |journal=] |volume=128 |issue=24 |pages=7720–7721 |doi=10.1021/ja060680r |pmid=16771469|bibcode=2006JAChS.128.7720N }}</ref> First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and ]. A series of oxidation and exfoliation steps produce small graphene plates with ] groups at their edges. These are converted to ] groups by treatment with ]; next, they are converted to the corresponding graphene ] via treatment with octadecyl amine. The resulting material (circular graphene layers of {{convert|5.3|angstrom|m|abbr=on|lk=on|disp=or}} thickness) is soluble in ], ] and ]. | |||
Dispersing graphite in a proper liquid medium can produce graphene by ]. Non-exfoliated graphite is separated from graphene by ],<ref>{{cite doi|10.1038/nnano.2008.215 }}</ref> producing graphene concentrations initially up to {{val|0.01|u=mg/ml}} in ] (NMP) and later to {{val|2.1|u=mg/ml}} in NMP,.<ref>{{cite doi|10.1039/C1JM11076D }}</ref> Using a suitable ] as the dispersing liquid medium for graphite exfoliation<ref>{{cite doi|10.1039/C0JM02461A }}</ref> produced concentrations of {{val|5.33|u=mg/ml}}. The concentration of graphene sheets produced by this method is very low because there is nothing preventing the sheets from restacking due to the van der Waals forces pulling them back together. the maximum concentrations achieved are the points at which the van der Waals forces overcome the interactive forces between the graphene sheets and the solvent molecules. | |||
Refluxing single-layer graphene oxide (SLGO) in ]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependent on their preparation methodology. When using thionyl chloride, ] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%. | |||
=== Surfactant-aided exfoliation === | |||
] | |||
Similar to solvent exfoliation, graphite is sonicated in a suitable solvent. In this case, however, surfactant molecules are added which prevent the restacking of the graphene sheets by adsorbing to the surface of the graphene. The concentration of graphene achieved by this method is higher than solvent exfoliation, but the removal of the surfactant molecules is often necessary and usually requires chemical treatments. | |||
] reflux is commonly used for reducing SLGO to SLG(R), but ]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with ] (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with ]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (c. 3–5% conversion of the intermediate to the final amide).<ref>{{cite journal |first1=Raymond L.D. |last1=Whitby |first2=Alina |last2=Korobeinyk |first3=Katya V. |last3=Glevatska |title=Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal=] |volume=49 |issue=2 |pages=722–725 |year=2011 |doi=10.1016/j.carbon.2010.09.049|bibcode=2011Carbo..49..722W }}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reaction types have been explored. SLGO has also been grafted with ], cross-linked through ] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{cite journal |first1=Sungjin |last1=Park |first2=Dmitriy A. |last2=Dikin |first3=SonBinh T. |last3=Nguyen |first4=Rodney S. |last4=Ruoff |s2cid=55033112 |title=Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal=] |volume=113 |pages=15801–15804 |year=2009 |doi=10.1021/jp907613s |issue=36}}</ref> | |||
=== Interface trapping === | |||
Full ] from both sides of the graphene sheet results in ], but partial hydrogenation leads to hydrogenated graphene.<ref>{{cite journal |first1=D. C. |last1=Elias |last2=Nair |first2=R. R. |last3=Mohiuddin |first3=T. M. G. |last4=Morozov |first4=S. V. |last5=Blake |first5=P. |last6=Halsall |first6=M. P. |last7=Ferrari |first7=A. C. |last8=Boukhvalov |first8=D. W. |last9=Katsnelson |first9=M. I. |last10=Geim |first10=A. K. |last11=Novoselov |first11=K. S. |title=Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane |journal=Science |year=2009 |volume=323 |doi=10.1126/science.1167130 |pmid=19179524 |issue=5914 |bibcode=2009Sci...323..610E |pages=610–3 |arxiv=0810.4706|s2cid=3536592 }}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to ] (graphene fluoride),<ref>{{cite journal |last1=Garcia |first1=J. C. |last2=de Lima |first2=D. B. |last3=Assali |first3=L. V. C. |last4=Justo |first4=J. F. |title=Group IV graphene- and graphane-like nanosheets |journal=J. Phys. Chem. C |date=2011 |volume=115 |issue=27 |pages=13242–13246 |doi=10.1021/jp203657w|arxiv=1204.2875 |s2cid=98682200 }}</ref> while partial fluorination (generally ]) provides fluorinated (halogenated) graphene. | |||
Macro-scale graphene films can be created by sonicating graphite while at the interface of two immiscible liquids, most notably heptane and water. The graphene sheets are exfoliated because of the sonication and then adsorbed to the high energy interface between the heptane and the water, where they are kept from restacking. The force holding the graphene at the interface is very strong, withstanding forces in excess of 300,000 g. The solvents may then be evaporated, leaving behind the graphene film. Films created using the interface trapping method are very transparent (up to ~95 %T) and conductive.<ref>Woltornist, S. J., Oyer, A. J., Carrillo, J.-M. Y., Dobrynin, A. V, & Adamson, D. H. (2013). Conductive thin films of pristine graphene by solvent interface trapping. ACS nano, 7(8), 7062–6. {{DOI|10.1021/nn402371c }}</ref> | |||
=== |
=== Graphene ligand/complex === | ||
Graphene can be a ] to ] metals and metal ions by introducing functional groups. Structures of graphene ligands are similar to e.g. metal-] complex, metal-] complex, and metal-] complex. Copper and nickel ions can be coordinated with graphene ligands.<ref>{{cite journal |doi=10.1016/j.carbon.2011.03.056 |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |volume=49 |issue=10 |pages=3375–3378 |year=2011 |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Kim |first3=J. |last4=Hirose-Takai |first4=K. |last5=Sato |first5=Y. |last6=Suenaga |first6=K. |last7=Ohba |first7=T. |last8=Sodesawa |first8=T. |last9=Sato |first9=S.|bibcode=2011Carbo..49.3375Y }}<br/>{{cite journal |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Jungpil |first3=K. |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |doi=10.1016/j.carbon.2011.03.056 |volume=49 |issue=10 |pages=3375–3378 |display-authors=etal|year=2011 |bibcode=2011Carbo..49.3375Y }}</ref><ref>{{cite journal |doi=10.1016/j.carbon.2014.03.036 |title=Functionalized graphene sheets coordinating metal cations |journal=Carbon |volume=75 |pages=81–94 |year=2014 |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |last4=Uchizawa |first4=S. |last5=Hirose-Takai |first5=K. |last6=Sato |first6=Y. |last7=Suenaga |first7=K. |last8=Sato |first8=S.|bibcode=2014Carbo..75...81Y }}<br/>{{cite journal |title=Functionalized graphene sheets coordinating metal cations |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |journal=Carbon |doi=10.1016/j.carbon.2014.03.036 |volume=75 |pages=81–94 |display-authors=etal|year=2014 |bibcode=2014Carbo..75...81Y }}</ref> | |||
A highly exothermic reaction combusts ] in an oxidation-reduction reaction with carbon dioxide, producing a variety of carbon nanoparticles including graphene and ]s. The carbon dioxide reactant may be either solid (dry-ice) or gaseous. The products of this reaction are carbon and ]. {{cite patent|US|8377408|status=patent}} was issued for this process.<ref>{{cite doi|10.1039/C1JM11227A }}</ref> | |||
== Advanced graphene structures == | |||
== Potential applications == | |||
=== Graphene fiber === | |||
In 2011, researchers reported a novel yet simple approach to fabricating graphene fibers from chemical vapor deposition-grown graphene films.<ref>{{cite journal |doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages=12164–71 |date=29 August 2011 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Wang |first3=Kunlin |last4=Yang |first4=Ying |last5=Wei |first5=Jinquan |last6=Kang |first6=Feiyu |last7=Wu |first7=Dehai |last8=Zhu |first8=Hongwei |url=https://figshare.com/articles/Directly_Drawing_Self_Assembled_Porous_and_Monolithic_Graphene_Fiber_from_Chemical_Vapor_Deposition_Grown_Graphene_Film_and_Its_Electrochemical_Properties/2608015 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801053549/https://figshare.com/articles/Directly_Drawing_Self_Assembled_Porous_and_Monolithic_Graphene_Fiber_from_Chemical_Vapor_Deposition_Grown_Graphene_Film_and_Its_Electrochemical_Properties/2608015 |url-status=live }}</ref> The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable ]. Flexible all-solid-state supercapacitors based on these graphene fibers were demonstrated in 2013.<ref>{{cite journal |title=Flexible all-solid-state supercapacitors based on chemical vapor deposition derived graphene fibers |journal=Physical Chemistry Chemical Physics |volume=15 |issue=41 |pages=17752–7 |date=3 September 2013|doi=10.1039/C3CP52908H |pmid=24045695 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Chen |first3=Qiao |last4=Li |first4=Peixu |last5=Wang |first5=Kunlin |last6=Zhong |first6=Minlin |last7=Wei |first7=Jinquan |last8=Wu |first8=Dehai |last9=Wei |first9=Bingqing |last10=Zhu |first10=Hongwei |s2cid=22426420 |bibcode=2013PCCP...1517752L }}</ref> | |||
In 2015, intercalating small graphene fragments into the gaps formed by larger, coiled graphene sheets, after annealing provided pathways for conduction, while the fragments helped reinforce the fibers.{{sentence fragment |date=May 2016}} The resulting fibers offered better thermal and electrical conductivity and mechanical strength. Thermal conductivity reached {{convert|1290|W/m/K|W/m/K|abbr=in|lk=on}}, while tensile strength reached {{convert|1080|MPa|abbr=on|lk=on}}.<ref>{{Cite journal |title=Highly thermally conductive and mechanically strong graphene fibers |first1=Guoqing |last1=Xin |first2=Tiankai |last2=Yao |first3=Hongtao |last3=Sun |first4=Spencer Michael |last4=Scott |first5=Dali |last5=Shao |first6=Gongkai |last6=Wang |first7=Jie |last7=Lian |date=September 4, 2015 |journal=Science |doi=10.1126/science.aaa6502 |pmid= 26339027|volume=349 |issue=6252 |pages=1083–1087 |bibcode=2015Sci...349.1083X|doi-access=free }}</ref> | |||
Potential applications include lightweight, thin, flexible, yet durable display screens, electric circuits, and solar cells, as well as various medical, chemical and industrial processes enhanced or enabled by the use of new graphene materials.<ref>{{cite web |last=Monie |first=Sanjay |title=Developments in Conductive Inks |url=http://industrial-printing.net/content/developments-conductive-inks?page=0%2C3 |publisher=Industrial & Specialty Printing |accessdate=2010-04-26 }}</ref> | |||
In 2016, kilometer-scale continuous graphene fibers with outstanding mechanical properties and excellent electrical conductivity were produced by high-throughput wet-spinning of graphene oxide liquid crystals followed by ] through a full-scale synergetic defect-engineering strategy.<ref>{{cite journal|last1= Xu|first1=Zhen|last2=Liu|first2=Yingjun|last3=Zhao|first3=Xiaoli|last4=Li|first4=Peng|last5=Sun|first5=Haiyan|last6=Xu|first6=Yang|last7=Ren|first7=Xibiao|last8=Jin|first8=Chuanhong|last9=Xu|first9=Peng|last10=Wang|first10=Miao|last11=Gao|first11=Chao|title=Ultrastiff and Strong Graphene Fibers via Full-Scale Synergetic Defect Engineering|journal= Advanced Materials|volume=28|issue=30|pages=6449–6456|date=2016|doi=10.1002/adma.201506426|pmid=27184960|bibcode=2016AdM....28.6449X |s2cid=31988847 }}</ref> The graphene fibers with superior performances promise wide applications in functional textiles, lightweight motors, microelectronic devices, etc. | |||
In 2008, graphene produced by exfoliation was one of the most expensive materials on Earth, with a sample with the area of the cross section of a human hair costing more than $1,000 as of April 2008 (about $100,000,000/cm<sup>2</sup>).<ref name=SciAm/> Since then, exfoliation procedures have been scaled up, and now companies sell graphene in large quantities.<ref> | |||
{{cite journal | |||
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}}</ref> The price of epitaxial graphene on SiC is dominated by the substrate price, which was approximately $100/cm<sup>2</sup> as of 2009.{{update|date=December 2013}} Hong and his team in South Korea pioneered the synthesis of large-scale graphene films using ] (CVD) on thin ] layers, which triggered research on practical applications,<ref> | |||
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|pmid=20562870 | |||
}}</ref> | |||
] in Beijing, led by Wei Fei of the Department of Chemical Engineering, claims to be able to create a carbon nanotube fiber that has a tensile strength of {{convert|80|GPa|abbr=on|lk=on}}.<ref>{{cite journal|last1=Bai|first1=Yunxiang|last2=Zhang|first2=Rufan|last3=Ye|first3=Xuan|last4=Zhu|first4=Zhenxing|last5=Xie|first5=Huanhuan|last6=Shen|first6=Boyuan|last7=Cai|first7=Dali|last8=Liu|first8=Bofei|last9=Zhang|first9=Chenxi|last10=Jia|first10=Zhao|last11=Zhang|first11=Shenli|last12=Li|first12=Xide|last13=Wei|first13=Fei|date=2018|title=Carbon nanotube bundles with tensile strength over 80 GPa.|journal=Nature Nanotechnology|volume=13|issue=7|pages=589–595|doi=10.1038/s41565-018-0141-z|pmid=29760522|bibcode=2018NatNa..13..589B|s2cid=46890587}}</ref> | |||
In 2013, the European Union made a €1 billion grant to be used for research into potential graphene applications.<ref>{{cite web |url=http://europa.eu/rapid/press-release_IP-13-54_en.htm |title=EUROPA - PRESS RELEASES - Press Release - Graphene and Human Brain Project win largest research excellence award in history, as battle for sustained science funding continues |publisher=Europa.eu |date=28 January 2013 }}</ref> In 2013 the ] consortium formed, including ] and seven other European universities and research centers, along with ].<ref>{{cite web |last=Thomson |first=Iain |title=Nokia shares $1.35bn EU graphene research grant |url=http://www.theregister.co.uk/2013/02/01/nokia_eu_graphene_grant/ |publisher=The Register}}<br/>{{cite web |url=http://www.graphene-flagship.eu/GF/consortium.php |title=FET Graphene Flagship |publisher=Graphene-flagship.eu |date= |accessdate=2013-08-24 }}</ref> ] has also been working on graphene technology for several years.<ref>{{cite web |last=Sherriff |first=Lucy |url=http://www.zdnet.com/nokia-dials-into-graphene-in-photo-sensor-patent-move-7000003759/ |title=Nokia dials into graphene in photo-sensor patent move |publisher=ZDNet |date=5 September 2012 }}</ref> | |||
=== |
=== 3D graphene === | ||
In 2013, a three-dimensional ] of hexagonally arranged carbon was termed 3D graphene, and self-supporting 3D graphene was also produced.<ref>{{cite journal |last1=Wang |first1=H. |last2=Sun |first2=K. |last3=Tao |first3=F. |last4=Stacchiola |first4=D. J. |last5=Hu |first5=Y. H. |title=3D Honeycomb-Like Structured Graphene and Its High Efficiency as a Counter-Electrode Catalyst for Dye-Sensitized Solar Cells |doi=10.1002/ange.201303497 |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |year=2013 |pmid= 23897636|bibcode=2013AngCh.125.9380W |hdl=2027.42/99684 |hdl-access=free }}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |access-date=24 August 2013 |last1=Wang |first1=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |doi=10.1002/ange.201303497 |year=2013 |bibcode=2013AngCh.125.9380W |hdl=2027.42/99684 |hdl-access=free |archive-date=25 August 2013 |archive-url=https://web.archive.org/web/20130825023850/http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells? |url-status=live }}</ref> 3D structures of graphene can be fabricated by using either CVD or solution-based methods. A 2016 review by Khurram and Xu et al. provided a summary of then-state-of-the-art techniques for fabrication of the 3D structure of graphene and other related two-dimensional materials.<ref name="auto">{{cite journal |last1=Shehzad |first1=Khurram |last2=Xu |first2=Yang |last3=Gao |first3=Chao |last4=Xianfeng |first4=Duan |title=Three-dimensional macro-structures of two-dimensional nanomaterials |journal=Chemical Society Reviews |volume=45 |issue=20 |pages=5541–5588 |date=2016 |doi=10.1039/C6CS00218H |pmid=27459895 }}</ref> In 2013, researchers at ] reported a novel radical-initiated crosslinking method to fabricate porous 3D free-standing architectures of graphene and carbon nanotubes using nanomaterials as building blocks without any polymer matrix as support.<ref name="PMID 23436939">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Trinward Kwaczala |first2=Andrea |last3=Kanakia |first3=Shruti |last4=Patel |first4=Sunny C. |last5=Judex |first5=Stefan |last6=Sitharaman |first6=Balaji |year=2013 |title=Fabrication and characterization of three-dimensional macroscopic all-carbon scaffolds. |journal=Carbon |volume=53 |pages=90–100 |doi=10.1016/j.carbon.2012.10.035 |pmid=23436939 |pmc=3578711}}</ref> These 3D graphenes (all-carbon) scaffolds/foams have applications in several fields such as energy storage, filtration, thermal management, and biomedical devices and implants.<ref name="auto"/><ref name="PMID 25788440">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Gopalan |first2=Anu Gopalan |last3=D'Agati |first3=Michael |last4=Srinivas Sankaran |first4=Jeyantt |last5=Judex |first5=Stefan |last6=Qin |first6=Yi-Xian |last7=Sitharaman |first7=Balaji |year=2015 |title=Porous three-dimensional carbon nanotube scaffolds for tissue engineering |journal=Journal of Biomedical Materials Research Part A |volume=103 |issue=10 |pages=3212–3225 |doi=10.1002/jbm.a.35449 |pmid=25788440|pmc=4552611 }}</ref> | |||
Graphene is reported to have enhanced ] by increasing the yield of ] product.<ref name="doi10.1088/0957-4484/23/45/455106">{{cite doi|10.1088/0957-4484/23/45/455106 }}</ref> Experiments revealed that graphene's ] could be the main factor behind this result. Graphene yields DNA product equivalent to positive control with up to 65% reduction in PCR cycles. | |||
Box-shaped graphene (BSG) ] appearing after mechanical cleavage of ] was reported in 2016.<ref name="stm2016">{{cite journal |last1=Lapshin |first1=Rostislav V. |title=STM observation of a box-shaped graphene nanostructure appeared after mechanical cleavage of pyrolytic graphite |journal=Applied Surface Science |date=January 2016 |volume=360 |pages=451–460 |doi=10.1016/j.apsusc.2015.09.222 |bibcode=2016ApSS..360..451L |arxiv=1611.04379 |s2cid=119369379 }}</ref> The discovered nanostructure is a multilayer system of parallel hollow nanochannels located along the surface and having quadrangular cross-section. The thickness of the channel walls is approximately equal to 1 nm. Potential fields of BSG application include ultra-sensitive ]s, high-performance catalytic cells, nanochannels for ] ] and manipulation, high-performance heat sinking surfaces, ] of enhanced performance, ]s, electron multiplication channels in emission ] devices, high-capacity ]s for safe ]. | |||
=== Integrated circuits === | |||
Three dimensional bilayer graphene has also been reported.<ref>{{cite journal |author=Harris PJF |title=Hollow structures with bilayer graphene walls |journal=Carbon |volume=50 |issue=9 |pages=3195–3199 |year=2012 |doi=10.1016/j.carbon.2011.10.050 |bibcode=2012Carbo..50.3195H |url=https://zenodo.org/record/896080 |access-date=30 August 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801051738/https://zenodo.org/record/896080 |url-status=live }}</ref><ref>{{cite journal |vauthors=Harris PJ, Slater TJ, Haigh SJ, Hage FS, Kepaptsoglou DM, Ramasse QM, Brydson R |title=Bilayer graphene formed by passage of current through graphite: evidence for a three dimensional structure |journal=Nanotechnology |volume=25 |issue=46 |pages=465601 |year=2014 |doi=10.1088/0957-4484/25/46/465601 |pmid=25354780 |bibcode=2014Nanot..25.5601H |s2cid=12995375 |url=http://centaur.reading.ac.uk/38041/1/3D%20FOR%20NANOTECHNOLOGY%20SUBMITTED%20REVISED%20with%20figs.pdf |access-date=30 August 2019 |archive-date=3 November 2018 |archive-url=https://web.archive.org/web/20181103103228/http://centaur.reading.ac.uk/38041/1/3D%20FOR%20NANOTECHNOLOGY%20SUBMITTED%20REVISED%20with%20figs.pdf |url-status=live }}</ref> | |||
For ], graphene has a high ], as well as low noise, allowing it to be used as the channel in a ]. Single sheets of graphene are hard to produce and even harder to make on an appropriate substrate.<ref>{{Cite journal |last=Chen |first=J. |last2=Ishigami |first2=M. |last3=Jang |first3=C. |last4=Hines |first4=D. R. |last5=Fuhrer |first5=M. S. |last6=Williams |first6=E. D. |title=Printed graphene circuits |journal=Advanced Materials |volume=19 |pages=3623–3627 |year=2007 |doi=10.1002/adma.200701059 |issue=21 }}</ref> | |||
=== Pillared graphene === | |||
In 2008, the smallest transistor so far, one atom thick, 10 atoms wide was made of graphene.<ref name="Ponomarenko_2008_356" /> IBM announced in December 2008 that they had fabricated and characterized graphene transistors operating at GHz frequencies.<ref>{{cite web |url=http://arxivblog.com/?p=755 |title=Graphene transistors clocked at 26 GHz Arxiv article |publisher=Arxivblog.com |date=11 December 2008 }}</ref> In May 2009, an n-type transistor was announced meaning that both n and p-type graphene transistors had been created.<ref>{{Cite journal |laysummary=http://news.ufl.edu/2009/05/07/graphene/ |journal=Science |volume=324 |issue=5928 |year=2009 |pmid=19423822 |doi=10.1126/science.1170335 |title=N-Doping of Graphene Through Electrothermal Reactions with Ammonia |bibcode=2009Sci...324..768W |pages=768–71 |author-separator=; |last=Wang |first=X. |last2=Li |first2=X. |last3=Zhang |first3=L. |last4=Yoon |first4=Y. |last5=Weber |first5=P. K. |last6=Wang |first6=H. |last7=Guo |first7=J. |last8=Dai |first8=H. |authorlink8=Hongjie Dai }}</ref><ref name="americanelements">{{cite web |title=Nanotechnology Information Center: Properties, Applications, Research, and Safety Guidelines |url=http://www.americanelements.com/nanotech.htm |publisher=] }}</ref> A functional graphene integrated circuit was demonstrated – a complementary ] consisting of one p- and one n-type graphene transistor.<ref>{{Cite journal |laysummary=http://physicsworld.com/cws/article/news/38924 |last=Traversi |first=F. |last2=Russo |first2=V. |last3=Sordan |first3=R. |journal=Appl. Phys. Lett. |volume=94 |page=223312 |year=2009 |doi=10.1063/1.3148342 |title=Integrated complementary graphene inverter |bibcode=2009ApPhL..94v3312T |issue=22 |arxiv=0904.2745 }}</ref> However, this inverter suffered from a very low voltage gain. | |||
{{main|Pillared graphene}} | |||
Pillared graphene is a hybrid carbon, structure consisting of an oriented array of carbon nanotubes connected at each end to a sheet of graphene. It was first described theoretically by George Froudakis and colleagues at the ] in Greece in 2008. Pillared graphene has not yet been synthesized in the laboratory, but it has been suggested that it may have useful electronic properties, or as a hydrogen storage material. | |||
According to a January 2010 report,<ref name="UK's NPL">{{cite web |url=http://www.npl.co.uk/news/european-collaboration-breakthrough-in-developing-graphene |title=European collaboration breakthrough in developing graphene |publisher=NPL |date=19 January 2010 }}</ref> graphene was epitaxially grown on SiC in a quantity and with quality suitable for mass production of integrated circuits. At high temperatures, the quantum Hall effect could be measured in these samples. IBM built 'processors' using 100 GHz transistors on {{convert|2|in|mm|adj=on}} graphene sheets.<ref name="LinDimitrakopoulos2010">{{cite journal |last=Lin |first=Y.-M. |last2=Dimitrakopoulos |first2=C. |last3=Jenkins |first3=K. A. |last4=Farmer |first4=D. B. |last5=Chiu |first5=H.-Y. |last6=Grill |first6=A. |last7=Avouris |first7=Ph. |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |journal=Science |volume=327 |issue=5966 |year=2010 |pages=662–662 |issn=0036-8075 |doi=10.1126/science.1184289 |pmid=20133565|arxiv=1002.3845 |bibcode=2010Sci...327..662L }}</ref> | |||
=== Reinforced graphene === | |||
In June 2011, IBM researchers announced that they had succeeded in creating the first graphene-based integrated circuit, a broadband radio mixer.<ref name="LinValdes-Garcia2011">{{cite journal |last=Lin |first=Y.-M. |last2=Valdes-Garcia |first2=A. |last3=Han |first3=S.-J. |last4=Farmer |first4=D. B. |last5=Meric |first5=I. |last6=Sun |first6=Y. |last7=Wu |first7=Y. |last8=Dimitrakopoulos |first8=C. |last9=Grill |first9=A. |last10=Avouris |first10=P. |last11=Jenkins |first11=K. A. |title=Wafer-Scale Graphene Integrated Circuit |journal=Science |volume=332 |issue=6035 |year=2011 |pages=1294–1297 |issn=0036-8075 |doi=10.1126/science.1204428 |pmid=21659599|bibcode=2011Sci...332.1294L }}</ref> The circuit handled frequencies up to 10 GHz. Its performance was unaffected by temperatures up to 127 C. | |||
Graphene reinforced with embedded ] reinforcing bars ("]") is easier to manipulate, while improving the electrical and mechanical qualities of both materials.<ref name="kurz5011">{{cite web|url=http://www.kurzweilai.net/carbon-nanotubes-as-reinforcing-bars-to-strengthen-graphene-and-increase-conductivity|title=Carbon nanotubes as reinforcing bars to strengthen graphene and increase conductivity|date=9 April 2014|publisher=Kurzweil Library|access-date=23 April 2014|archive-date=12 April 2014|archive-url=https://web.archive.org/web/20140412021444/http://www.kurzweilai.net/carbon-nanotubes-as-reinforcing-bars-to-strengthen-graphene-and-increase-conductivity|url-status=live}}</ref><ref>{{cite journal |doi=10.1021/nn501132n |pmid=24694285 |pmc=4046778 |title=Rebar Graphene |journal=ACS Nano |year=2014 |last1=Yan |first1=Z. |last2=Peng |first2=Z. |last3=Casillas |first3=G. |last4=Lin |first4=J. |last5=Xiang |first5=C. |last6=Zhou |first6=H. |last7=Yang |first7=Y. |last8=Ruan |first8=G. |last9=Raji |first9=A. R. O. |last10=Samuel |first10=E. L. G. |last11=Hauge |first11=R. H. |last12=Yacaman |first12=M. J. |last13=Tour |first13=J. M. |volume=8|issue=5 |pages=5061–8 }}</ref> | |||
In June 2013 an 8 transistor 1.28 GHz ring oscillator circuit was described.<ref>{{cite web |url=http://physicsworld.com/cws/article/news/2013/jun/17/graphene-circuit-breaks-the-gigahertz-barrier |title=Graphene circuit breaks the gigahertz barrier |year=2013 }}</ref> | |||
Functionalized single- or multi-walled carbon nanotubes are spin-coated on copper foils and then heated and cooled, using the nanotubes themselves as the carbon source. Under heating, the functional ]s decompose into graphene, while the nanotubes partially split and form in-plane ]s with the graphene, adding strength. ] domains add more strength. The nanotubes can overlap, making the material a better conductor than standard CVD-grown graphene. The nanotubes effectively bridge the ] found in conventional graphene. The technique eliminates the traces of substrate on which later-separated sheets were deposited using epitaxy.<ref name=kurz5011/> | |||
==== Transistors ==== | |||
Stacks of a few layers have been proposed as a cost-effective and physically flexible replacement for ] (ITO) used in displays and ]s.<ref name=kurz5011/> | |||
Graphene exhibits a pronounced response to perpendicular external electric fields, potentially forming ]s (FET). A 2004 paper documented FETs with an on-off ratio of ~30 at room temperature.{{citation needed|date=May 2013}} A 2006 paper announced an all-graphene planar FET with side gates.<ref> March 14, 2006</ref> Their devices showed changes of 2% at cryogenic temperatures. The first top-gated FET (on–off ratio of <2) was demonstrated in 2007.<ref>{{Cite journal |last=Lemme |first=M. C. |author2=et al. |title=A graphene field-effect device |journal=IEEE Electron Device Letters |volume=28 |page=282 |year=2007 |doi=10.1109/LED.2007.891668 |arxiv=cond-mat/0703208 |bibcode=2007IEDL...28..282L |issue=4 }}</ref> Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor.<ref name="MIT1">{{Cite news |last=Bullis |first=K. |title=Graphene Transistors |publisher=] Technology Review, Inc |location=Cambridge |date=28 January 2008 |url=http://www.technologyreview.com/Nanotech/20119/ }}</ref> | |||
=== Molded graphene === | |||
{{cite patent|US|7015142|status=patent}} for graphene-based electronics was issued in 2006. In 2008, researchers at ] produced hundreds of transistors on a single chip<ref name="Kedzierski">{{Cite journal |last=Kedzierski |first=J. |title=Epitaxial Graphene Transistors on SiC Substrates |doi=10.1109/TED.2008.926593 |journal=IEEE Transactions on Electron Devices |volume=55 |pages=2078–2085 |year=2008 |bibcode=2008ITED...55.2078K |issue=8 |last2=Hsu |first2=Pei-Lan |last3=Healey |first3=Paul |last4=Wyatt |first4=Peter W. |last5=Keast |first5=Craig L. |last6=Sprinkle |first6=Mike |last7=Berger |first7=Claire |last8=De Heer |first8=Walt A. |arxiv=0801.2744 }}</ref> and in 2009, very high frequency transistors were produced at ].<ref name="HRL">{{Cite journal |last=Moon |first=J.S. |title=Epitaxial-Graphene RF Field-Effect Transistors on Si-Face 6H-SiC Substrates |doi=10.1109/LED.2009.2020699 |journal=IEEE Electron Device Letters |volume=30 |pages=650–652 |year=2009 |bibcode=2009IEDL...30..650M |issue=6 |last2=Curtis |first2=D. |last3=Hu |first3=M. |last4=Wong |first4=D. |last5=McGuire |first5=C. |last6=Campbell |first6=P.M. |last7=Jernigan |first7=G. |last8=Tedesco |first8=J.L. |last9=Vanmil |first9=B. |last10=Myers-Ward |first10=R. |last11=Eddy |first11=C. |last12=Gaskill |first12=D.K. }}</ref> | |||
In 2015, researchers from the ] (UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene.<ref>{{Cite web|title=Robust new process forms 3D shapes from flat sheets of graphene|url=https://grainger.illinois.edu/news/11255|date=2015-06-23|website=grainger.illinois.edu|language=en|access-date=2020-05-31|archive-date=12 May 2020|archive-url=https://web.archive.org/web/20200512144924/https://grainger.illinois.edu/news/11255|url-status=dead}}</ref> A film of graphene that had been soaked in solvent to make it swell and become malleable was overlaid on an underlying substrate "former". The solvent evaporated over time, leaving behind a layer of graphene that had taken on the shape of the underlying structure. In this way, they were able to produce a range of relatively intricate micro-structured shapes.<ref>{{cite web|url=https://newatlas.com/3d-shapes-graphene-uiuc/38164/|title=Graphene takes on a new dimension|last=Jeffrey|first=Colin|date=June 28, 2015|website=New Atlas|access-date=2019-11-10|archive-date=10 November 2019|archive-url=https://web.archive.org/web/20191110190051/https://newatlas.com/3d-shapes-graphene-uiuc/38164/|url-status=live}}</ref> Features vary from 3.5 to 50 μm. Pure graphene and gold-decorated graphene were each successfully integrated with the substrate.<ref>{{cite web|url=http://www.kurzweilai.net/how-to-form-3-d-shapes-from-flat-sheets-of-graphene|title=How to form 3-D shapes from flat sheets of graphene|date=June 30, 2015|website=Kurzweil Library|access-date=2019-11-10|archive-date=6 October 2015|archive-url=https://web.archive.org/web/20151006014133/http://www.kurzweilai.net/how-to-form-3-d-shapes-from-flat-sheets-of-graphene|url-status=live}}</ref> | |||
A 2008 paper demonstrated a switching effect based on a reversible chemical modification of the graphene layer that gives an on–off ratio of greater than six orders of magnitude. These reversible switches could potentially be employed in nonvolatile memories.<ref>{{Cite journal |last=Echtermeyer |first=Tim. J. |author2=et al. |journal=IEEE Electron Device Letters |volume=29 |page=952 |year=2008 |doi=10.1109/LED.2008.2001179 |title=Nonvolatile Switching in Graphene Field-Effect Devices |bibcode=2008IEDL...29..952E |issue=8 |arxiv=0805.4095 }}</ref> | |||
== Specialized graphene configurations == | |||
In 2009, researchers demonstrated four different types of ], each composed of a single graphene transistor.<ref>{{Cite journal |last=Sordan |first=R. |last2=Traversi |first2=F. |last3=Russo |first3=V. |journal=Appl. Phys. Lett. |volume=94 |page=073305 |year=2009 |doi=10.1063/1.3079663 |title=Logic gates with a single graphene transistor |bibcode=2009ApPhL..94g3305S |issue=7 }}</ref> | |||
=== Graphene aerogel === | |||
An ] made of graphene layers separated by carbon nanotubes was measured at 0.16 milligrams per cubic centimeter. A solution of graphene and carbon nanotubes in a mold is freeze-dried to dehydrate the solution, leaving the aerogel. The material has superior elasticity and absorption. It can recover completely after more than 90% compression, and absorb up to 900 times its weight in oil, at a rate of 68.8 grams per second.<ref>{{cite news |title=Graphene aerogel is seven times lighter than air, can balance on a blade of grass - Slideshow {{!}} ExtremeTech |url=http://www.extremetech.com/extreme/153063-graphene-aerogel-is-seven-times-lighter-than-air-can-balance-on-a-blade-of-grass |website=ExtremeTech |access-date=2015-10-11 |date=April 10, 2013 |first=Sebastian |last=Anthony |archive-date=8 October 2015 |archive-url=https://web.archive.org/web/20151008024745/http://www.extremetech.com/extreme/153063-graphene-aerogel-is-seven-times-lighter-than-air-can-balance-on-a-blade-of-grass |url-status=live }}</ref> | |||
Practical uses for these circuits are limited by the very small ] they exhibit. Typically, the amplitude of the output signal is about 40 times less than that of the input signal. Moreover, none of these circuits operated at frequencies higher than 25 kHz. | |||
=== Graphene nanocoil === | |||
In the same year, tight-binding numerical simulations<ref name="fiori2">Fiori G., Iannaccone G., "On the possibility of tunable-gap bilayer graphene FET", IEEE Electr. Dev. Lett., 30, 261 (2009)</ref> demonstrated that the band-gap induced in graphene bilayer field effect transistors is not sufficiently large for high-performance transistors for digital applications, but can be sufficient for ultra-low voltage applications, when exploiting a tunnel-FET architecture.<ref name="fiori3">Fiori G., Iannaccone G., "Ultralow-Voltage Bilayer graphene tunnel FET", IEEE Electr. Dev. Lett., 30, 1096 (2009)</ref> | |||
In 2015, a coiled form of graphene was discovered in graphitic carbon (coal). The spiraling effect is produced by defects in the material's hexagonal grid that causes it to spiral along its edge, mimicking a ], with the graphene surface approximately perpendicular to the axis. When voltage is applied to such a coil, current flows around the spiral, producing a magnetic field. The phenomenon applies to spirals with either zigzag or armchair patterns, although with different current distributions. Computer simulations indicated that a conventional spiral inductor of 205 microns in diameter could be matched by a nanocoil just 70 nanometers wide, with a field strength reaching as much as 1 ].<ref name=":0">{{cite web|url=http://www.kurzweilai.net/graphene-nano-coils-discovered-to-be-powerful-natural-electromagnets|title=Graphene nano-coils discovered to be powerful natural electromagnets|date=October 16, 2015|website=Kurzweil Library|access-date=2019-11-10|archive-date=19 October 2015|archive-url=https://web.archive.org/web/20151019232000/http://www.kurzweilai.net/graphene-nano-coils-discovered-to-be-powerful-natural-electromagnets?|url-status=live}}</ref> | |||
In February 2010, researchers announced transistors with an on/off rate of 100 gigahertz, far exceeding the rates of previous attempts, and exceeding the speed of silicon transistors with an equal gate length. The {{val|240|u=nm}} devices were made with conventional silicon-manufacturing equipment.<ref name=Bourzac2010>{{Cite news | |||
|last=Bourzac |first=Katherine |title=Graphene Transistors that Can Work at Blistering Speeds |work=MIT Technology Review |date=5 February 2010 |url=http://www.technologyreview.com/computing/24482/?a=f }}</ref><ref name=TW2010>. News.techworld.com. Retrieved on 2010-12-10.</ref><ref>{{Cite journal |journal=Science |title=100-GHz Transistors from Wafer-Scale Epitaxial Graphene |first7=P |last7=Avouris |first6=A |last6=Grill |first5=HY |last5=Chiu |first4=DB |last4=Farmer |first3=KA |last3=Jenkins |first2=C |last2=Dimitrakopoulos |author=Lin <!-- check this -->|volume=327 |issue=5966 |year=2010 |page=662 |pmid=20133565 |publisher=Science |doi=10.1126/science.1184289 |bibcode=2010Sci...327..662L |arxiv=1002.3845 }}</ref> | |||
The nano-solenoids analyzed through computer models at ] should be capable of producing powerful magnetic fields of about 1 tesla, about the same as the coils found in typical loudspeakers, according to Yakobson and his team – and about the same field strength as some MRI machines. They found the magnetic field would be strongest in the hollow, nanometer-wide cavity at the spiral's center.<ref name=":0" /> | |||
In November 2011, researchers used 3d printing (]) as a method for fabricating graphene devices.<ref>. Cornell University Library. Retrieved on 2011-29-11.</ref> | |||
A ] made with such a coil behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear ].<ref>{{Cite journal |title=Riemann Surfaces of Carbon as Graphene Nanosolenoids |journal=Nano Letters |volume=16 |issue=1 |pages=34–9 |date=2015-10-14 |doi=10.1021/acs.nanolett.5b02430 |pmid=26452145 |first1=Fangbo |last1=Xu |first2=Henry |last2=Yu |first3=Arta |last3=Sadrzadeh |first4=Boris I. |last4=Yakobson |bibcode=2016NanoL..16...34X}}</ref> | |||
In 2013, researchers demonstrated graphene's high mobility in a detector that allows broad band frequency selectivity ranging from the THz to IR region (0.76-33THz)<ref>{{cite journal |last=Kawano |first=Yukio |title=Wide-band frequency-tunable terahertz and infrared detection with graphene |journal=Nanotechnology |year=2013 |volume=24 |issue=21 |doi=10.1088/0957-4484/24/21/214004|page=214004 |pmid=23618878 |bibcode=2013Nanot..24u4004K }}</ref> A separate group created a terahertz-speed transistor with bistable characteristics, which means that the device can spontaneously switch between two electronic states. The device consists of two layers of graphene separated by an insulating layer of ] a few atomic layers thick. Electrons move through this barrier by ]. These new transistors exhibit “negative differential conductance,” whereby the same electrical current flows at two different applied voltages.<ref>{{cite journal |url=http://www.kurzweilai.net/radical-new-graphene-design-operates-at-terahertz-speed |title=Radical new graphene design operates at terahertz speed |doi=10.1038/ncomms2817 |publisher=KurzweilAI |date= |accessdate=2013-05-02|arxiv=1303.6864 |bibcode=2013NatCo...4E1794B |last=Britnell |first=L. |last2=Gorbachev |first2=R. V. |last3=Geim |first3=A. K. |last4=Ponomarenko |first4=L. A. |last5=Mishchenko |first5=A. |last6=Greenaway |first6=M. T. |last7=Fromhold |first7=T. M. |last8=Novoselov |first8=K. S. |last9=Eaves |first9=L. |journal=Nature Communications |volume=4 |pages=1794– |pmid=23653206 |pmc=3644101 |issue=4 |year=2013|display-authors=9 }}<br/>{{cite DOI|10.1038/ncomms2817 }}</ref> | |||
=== Crumpled graphene === | |||
Graphene does not have an energy band-gap, which presents a hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. The negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gap-less graphene. The negative differential resistance — observed under certain biasing schemes — is an intrinsic property of graphene resulting from its symmetric band structure. The results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.<ref>{{cite journal |first=Guanxiong |last=Liu |first2=Sonia |last2=Ahsan |last3=Khitun |first3=Alexander G. |last4=Lake |first4=Roger K. |last5=Balandin |first5=Alexander A. |title=Graphene-Based Non-Boolean Logic Circuits |year=2013 |volume=114 |issue=10 |journal=Journal of Applied Physics |arxiv=1308.2931 |bibcode=2013JAP...114o4310L |page=4310 |doi=10.1063/1.4824828 }}</ref> | |||
In 2016, ] introduced a method for "crumpling" graphene, adding wrinkles to the material on a nanoscale. This was achieved by depositing layers of graphene oxide onto a shrink film, then shrunken, with the film dissolved before being shrunken again on another sheet of film. The crumpled graphene became ], and when used as a battery electrode, the material was shown to have as much as a 400% increase in ] ].<ref>{{cite web |last1=Stacey |first1=Kevin |title=Wrinkles and crumples make graphene better {{!}} News from Brown |url=https://news.brown.edu/articles/2016/03/wrinkles |website=news.brown.edu |publisher=Brown University |access-date=23 June 2016 |archive-url=https://web.archive.org/web/20160408041658/https://news.brown.edu/articles/2016/03/wrinkles |archive-date=8 April 2016 |language=en |date=21 March 2016}}</ref><ref>{{cite journal |last1=Chen |first1=Po-Yen |last2=Sodhi |first2=Jaskiranjeet |last3=Qiu |first3=Yang |last4=Valentin |first4=Thomas M. |last5=Steinberg |first5=Ruben Spitz |last6=Wang |first6=Zhongying |last7=Hurt |first7=Robert H. |last8=Wong |first8=Ian Y. |title=Multiscale Graphene Topographies Programmed by Sequential Mechanical Deformation |journal=Advanced Materials |volume=28 |issue=18 |publisher=John Wiley & Sons, Inc. |pages=3564–3571 |doi=10.1002/adma.201506194 |pmid=26996525 |date=6 May 2016|bibcode=2016AdM....28.3564C |s2cid=19544549 }}</ref> | |||
In 2013 researchers reported the creation of transistors printed on flexible plastic that operate at 25-gigahertz, sufficient for communications circuits and that can be fabricated at scale. The researchers first fabricate the non-graphene-containing structures—the electrodes and gates—on plastic sheets. Separately, they grow large graphene sheets on metal, then peel it off and transfer it to the plastic. Finally, they top the sheet with a waterproof layer. The devices work after being soaked in water, and are flexible enough to be folded.<ref>{{cite web |last=Bourzac |first=Katherine |url=http://www.technologyreview.com/news/518606/printed-graphene-transistors-promise-a-flexible-electronic-future/ |title=Superfast, Bendable Electronic Switches Made from Graphene | MIT Technology Review |publisher=Technologyreview.com |date= |accessdate=2013-08-24 }}</ref> | |||
== Mechanical synthesis == | |||
{{Main|Graphene production techniques}} | |||
A rapidly increasing list of production techniques have been developed to enable graphene's use in commercial applications.<ref>{{cite journal|last1=Backes|first1=Claudia|display-authors=etal|title=Production and processing of graphene and related materials|journal=2D Materials|volume=7|pages= 022001|date=2020|issue=2|doi=10.1088/2053-1583/ab1e0a|bibcode=2020TDM.....7b2001B|doi-access=free|hdl=2262/91730|hdl-access=free}}</ref> | |||
] can be reversibly reduced and oxidized using electrical stimulus. Controlled reduction and oxidation in two-terminal devices containing multilayer graphene oxide films are shown to result in switching between partially reduced graphene oxide and graphene, a process that modifies the electronic and optical properties. Oxidation and reduction are related to resistive switching.<ref>{{Cite journal |last=Ekiz |first=O.O. |author2=et al. |title=Reversible Electrical Reduction and Oxidation of Graphene Oxide |journal=ACS Nano |year=2011 |doi=10.1021/nn1014215 |volume=5 |issue=4 |pages=2475–2482 |pmid=21391707}}<br/>{{Cite journal |last=Ekiz |first=O.O. |author2=et al. |title=Supporting information for Reversible Electrical Reduction and Oxidation of Graphene Oxide |journal=ACS Nano |year=2011 |doi=10.1021/nn1014215 |volume=5 |issue=4 |pages=2475–2482 |pmid=21391707 }}</ref> | |||
Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of ] density with increasing lateral size forces 2D crystallites to bend into the third dimension. In all cases, graphene must bond to a substrate to retain its two-dimensional shape.<ref name=geim2009a/> | |||
=== Transparent conducting electrodes === | |||
=== Bottom-up and top-down methods === | |||
Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, required for such applications as ]s, ]s, ], and ]s. In particular, graphene's mechanical strength and flexibility are advantageous compared to ], which is brittle. Graphene films may be deposited from solution over large areas.<ref name="MPI">{{Cite journal |last=Wang |first=X. |author2=et al. |year=2007 |title=Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells |journal=Nano Letters |doi=10.1021/nl072838r |volume=8 |pmid=18069877 |issue=1 |bibcode=2008NanoL...8..323W |pages=323–7 }}</ref><ref name="Eda">{{Cite journal |last=Eda |first=G |last2=Fanchini |first2=G |last3=Chhowalla |first3=M |title=Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material |journal=Nat Nanotechnol |volume=3 |issue=5 |pages=270–4 |year=2008 |pmid=18654522 |doi=10.1038/nnano.2008.83 }}</ref> | |||
Small graphene structures, such as graphene quantum dots and nanoribbons, can be produced by "bottom-up" methods that assemble the lattice from organic molecule monomers (e. g. citric acid, glucose). "Top-down" methods, on the other hand, cut bulk graphite and graphene materials with strong chemicals (e. g. mixed acids).<ref name=":1">{{Cite journal |last1=Whitener |first1=Keith E. |last2=Sheehan |first2=Paul E. |date=2014-06-01 |title=Graphene synthesis |url=https://linkinghub.elsevier.com/retrieve/pii/S0925963514000983 |journal=Diamond and Related Materials |volume=46 |pages=25–34 |doi=10.1016/j.diamond.2014.04.006 |bibcode=2014DRM....46...25W |issn=0925-9635}}</ref> | |||
=== Micro-mechanical cleavage === | |||
Large-area, continuous, transparent and highly conducting few-layered graphene films were produced by chemical vapor deposition and used as ]s for application in ] devices. A power conversion efficiency (PCE) up to 1.71% was demonstrated, which is 55.2% of the PCE of a control device based on indium tin oxide.<ref>{{Cite journal |title=Large area, continuous, few-layered graphene as anodes in organic photovoltaic devices |journal=Applied Physics Letters |volume=95 |page=063302 |year=2009 |doi=10.1063/1.3204698 |last=Wang |first=Yu |last2=Chen |first2=Xiaohong |last3=Zhong |first3=Yulin |last4=Zhu |first4=Furong |last5=Loh |first5=Kian Ping |bibcode=2009ApPhL..95f3302W |issue=6 }}</ref> | |||
The most famous, clean and rather straight-forward method of isolating graphene sheets, called micro-mechanical cleavage or more colloquially called the scotch tape method, was introduced by Novoselov et al. in 2004, which uses ] to mechanically cleave high-quality ] ] into successively thinner platelets. Other methods do exist like exfoliation.<ref name=":1" /> | |||
=== Exfoliation techniques === | |||
]s (OLEDs) with graphene anodes have been demonstrated.<ref>{{Cite journal |last=Wu |first=J.B. |author2=et al. |year=2010 |title=Organic Light-Emitting Diodes on Solution-Processed Graphene Transparent Electrodes |journal=ACS Nano |volume=4 |page=43 |doi=10.1021/nn900728d }}</ref> The electronic and optical performance of graphene-based devices are similar to devices made with indium tin oxide. | |||
==== Mechanical exfoliation ==== | |||
A carbon-based device called a ] (LEC) was demonstrated with chemically-derived graphene as the ] and the ] ] as the anode.<ref>{{Cite journal |last=Matyba |first=P. |author2=et al. |year=2010 |title=Graphene and Mobile Ions: The Key to All-Plastic, Solution-Processed Light-Emitting Devices |journal=ACS Nano |volume=4 |doi=10.1021/nn9018569 |pmid=20131906 |issue=2 |pages=637–42 }}</ref> Unlike its predecessors, this device contains only carbon-based electrodes, with no metal. | |||
Geim and Novoselov initially used ] to pull graphene sheets away from graphite. Achieving single layers typically requires multiple exfoliation steps. After exfoliation, the flakes are deposited on a silicon wafer. Crystallites larger than 1 mm and visible to the naked eye can be obtained.<ref name="PhysTod">{{cite journal |last1=Geim |first1=A. K. |last2=MacDonald |first2=A. H. |title=Graphene: Exploring carbon flatland |journal=Physics Today |volume=60 |pages=35–41 |year=2007 |doi=10.1063/1.2774096 |bibcode=2007PhT....60h..35G |issue=8|s2cid=123480416 |doi-access=free }}</ref> | |||
As of 2014, exfoliation produced graphene with the lowest number of defects and highest electron mobility. Alternatively, a ] can penetrate onto the graphite source to cleave layers. In the same year, defect-free, unoxidized graphene-containing liquids were made from graphite using mixers that produce local shear rates greater than {{val|10|e=4}}.<ref name="arx1406">{{cite arXiv |eprint=1406.0809 |class=cond-mat.mtrl-sci |first1=F. V. |last1=Kusmartsev |first2=W. M. |last2=Wu |title=Application of Graphene within Optoelectronic Devices and Transistors |last3=Pierpoint |first3=M. P. |last4=Yung |first4=K. C. |year=2014}}</ref><ref name="Jayasena2011">{{cite journal |last=Jayasena |first=Buddhika |author2=Subbiah Sathyan |date=2011 |title=A novel mechanical cleavage method for synthesizing few-layer graphenes |journal=Nanoscale Research Letters |volume=6 |issue=95 |pages=95 |bibcode=2011NRL.....6...95J |doi=10.1186/1556-276X-6-95 |pmc=3212245 |pmid=21711598 |doi-access=free}}</ref><ref>{{cite web |url=http://www.kurzweilai.net/a-new-method-of-producing-large-volumes-of-high-quality-graphene |title=A new method of producing large volumes of high-quality graphene |publisher=KurzweilAI |date=2 May 2014 |access-date=3 August 2014 |archive-date=10 August 2014 |archive-url=https://web.archive.org/web/20140810200204/http://www.kurzweilai.net/a-new-method-of-producing-large-volumes-of-high-quality-graphene |url-status=live }}</ref><ref>{{cite journal |doi=10.1038/nmat3944 |pmid=24747780 |title=Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids |journal=Nature Materials |date=2014 |volume=13 |issue=6 |pages=624–630 |first=Keith R. |last=Paton |bibcode=2014NatMa..13..624P |hdl=2262/73941 |s2cid=43256835 |url=http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |access-date=30 August 2019 |archive-date=7 March 2020 |archive-url=https://web.archive.org/web/20200307194908/http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |url-status=live }}</ref> | |||
=== Ethanol distillation === | |||
Shear exfoliation is another method in which by using a rotor-stator mixer the scalable production of defect-free graphene has become possible. It has been shown that, as ] is not necessary for mechanical exfoliation, ResonantAcoustic mixing or low speed ]ing is effective in the production of high-yield and water-soluble graphene.<ref>{{cite journal |last1=ROUZAFZAY |first1=F. |last2=SHIDPOUR |first2=R. |year=2020 |title=Graphene@ZnO nanocompound for short-time water treatment under sun-simulated irradiation: Effect of shear exfoliation of graphene using kitchen blender on photocatalytic degradation |journal=Alloys and Compounds |volume=829 |pages=154614 |doi=10.1016/J.JALLCOM.2020.154614 |s2cid=216233251}}</ref><ref>{{cite journal |last1=Paton |first1=Keith R. |last2=Varrla |first2=Eswaraiah |last3=Backes |first3=Claudia |last4=Smith |first4=Ronan J. |last5=Khan |first5=Umar |last6=O'Neill |first6=Arlene |last7=Boland |first7=Conor |last8=Lotya |first8=Mustafa |last9=Istrate |first9=Oana M. |last10=King |first10=Paul |last11=Higgins |first11=Tom |last12=Barwich |first12=Sebastian |last13=May |first13=Peter |last14=Puczkarski |first14=Pawel |last15=Ahmed |first15=Iftikhar |date=June 2014 |title=Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids |url=http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |url-status=live |journal=Nature Materials |volume=13 |issue=6 |pages=624–630 |bibcode=2014NatMa..13..624P |doi=10.1038/nmat3944 |pmid=24747780 |s2cid=43256835 |archive-url=https://web.archive.org/web/20200307194908/http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |archive-date=7 March 2020 |access-date=30 August 2019 |hdl-access=free |last16=Moebius |first16=Matthias |last17=Pettersson |first17=Henrik |last18=Long |first18=Edmund |last19=Coelho |first19=João |last20=O'Brien |first20=Sean E. |last21=McGuire |first21=Eva K. |last22=Sanchez |first22=Beatriz Mendoza |last23=Duesberg |first23=Georg S. |last24=McEvoy |first24=Niall |last25=Pennycook |first25=Timothy J. |last26=Downing |first26=Clive |last27=Crossley |first27=Alison |last28=Nicolosi |first28=Valeria |last29=Coleman |first29=Jonathan N. |hdl=2262/73941}}</ref><ref>{{cite patent |country=USA |number=US11038172B2 |inventor=Bor Z. Jang |status=Active |title=Environmentally benign process for producing graphene-protected anode particles for lithium batteries |pubdate=2020-09-10 |gdate=2021-06-15 |fdate=2019-03-08 |pridate=2019-03-08 |assign1=Nanotek Instruments, Inc |assign2=Global Graphene Group, Inc |url=https://patents.google.com/patent/US11038172B2/en}}</ref> | |||
Graphene oxide membranes allow water vapor to pass through, but are impermeable to other liquids and gases.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last=Nair |first=R. R. |last2=Wu |first2=H. A. |last3=Jayaram |first3=P. N. |last4=Grigorieva |first4=I. V. |last5=Geim |first5=A. K. |bibcode=2012Sci...335..442N }}</ref> This phenomenon has been used for further distilling of ] to higher alcohol concentrations, in a room-temperature laboratory, without the application of heat or vacuum as used in traditional ] methods.<ref>{{cite news |url=http://www.dailymail.co.uk/sciencetech/article-2092321/Hi-tech-wonder-material-graphene-unexpected-use--distill-vodka-room-temperature.html |location=London |work=Daily Mail |first=Rob |last=Waugh |title=Hi-tech 'wonder material' graphene has an unexpected use – it can distill vodka at room temperature }}</ref> Further development and commercialization of such membranes could revolutionize the economics of ] production and the ] industry. | |||
==== Liquid phase exfoliation ==== | |||
=== Desalination === | |||
] (LPE) is a relatively simple method that involves dispersing graphite in a liquid medium to produce graphene by ] or high shear mixing, followed by ]. Restacking is an issue with this technique unless solvents with appropriate surface energy are used (e.g. NMP). Adding a ] to a solvent prior to sonication prevents restacking by adsorbing to the graphene's surface. This produces a higher graphene concentration, but removing the surfactant requires chemical treatments.<ref name="PhysTod" /><ref>{{cite journal |last1=Lotya |first1=Mustafa |last2=Hernandez |first2=Yenny |last3=King |first3=Paul J. |last4=Smith |first4=Ronan J. |last5=Nicolosi |first5=Valeria |last6=Karlsson |first6=Lisa S. |last7=Blighe |first7=Fiona M. |last8=De |first8=Sukanta |last9=Wang |first9=Zhiming |last10=McGovern |first10=I. T. |last11=Duesberg |first11=Georg S. |last12=Coleman |first12=Jonathan N. |date=18 March 2009 |title=Liquid Phase Production of Graphene by Exfoliation of Graphite in Surfactant/Water Solutions |journal=Journal of the American Chemical Society |volume=131 |issue=10 |pages=3611–3620 |arxiv=0809.2690 |doi=10.1021/ja807449u |pmid=19227978 |bibcode=2009JAChS.131.3611L |s2cid=16624132}}</ref> | |||
LPE results in nanosheets with a broad size distribution and thicknesses roughly in the range of 1-10 monolayers. However, liquid cascade centrifugation can be used to size-select the suspensions and achieve monolayer enrichment.<ref>{{cite journal |last1=Backes |first1=Claudia |last2=Campi |first2=Davide |last3=Szydlowska |first3=Beata M. |last4=Synnatschke |first4=Kevin |last5=Ojala |first5=Ezgi |last6=Rashvand |first6=Farnia |last7=Harvey |first7=Andrew |last8=Griffin |first8=Aideen |last9=Sofer |first9=Zdenek |last10=Marzari |first10=Nicola |last11=Coleman |first11=Jonathan N. |last12=O’Regan |first12=David D. |title=Equipartition of Energy Defines the Size–Thickness Relationship in Liquid-Exfoliated Nanosheets |journal=ACS Nano |date=25 June 2019 |volume=13 |issue=6 |pages=7050–7061 |doi=10.1021/acsnano.9b02234|pmid=31199123 |arxiv=2006.14909 |s2cid=189813507 }}</ref> | |||
Research suggests that graphene filters could outperform other techniques of ] by a significant margin.<ref name="Cohen-TanugiGrossman2012">{{cite journal |last=Cohen-Tanugi |first=David |last2=Grossman |first2=Jeffrey C. |title=Water Desalination across Nanoporous Graphene |journal=Nano Letters |volume=12 |issue=7 |year=2012 |pages=3602–3608 |issn=1530-6984 |doi=10.1021/nl3012853 |pmid=22668008 |bibcode=2012NanoL..12.3602C }}</ref> | |||
Sonicating graphite at the interface of two ] liquids, most notably ] and water, produced macro-scale graphene films. The graphene sheets are adsorbed to the high-energy interface between the materials and are kept from restacking. The sheets are up to about 95% transparent and conductive.<ref>{{cite journal |last1=Woltornist |first1=S. J. |last2=Oyer |first2=A. J. |last3=Carrillo |first3=J.-M. Y. |last4=Dobrynin |first4=A. V |last5=Adamson |first5=D. H. |s2cid=27816586 |year=2013 |title=Conductive thin films of pristine graphene by solvent interface trapping |journal=ACS Nano |volume=7 |issue=8 |pages=7062–6 |doi=10.1021/nn402371c|pmid=23879536 }}</ref> | |||
=== Solar cells === | |||
With definite cleavage parameters, the box-shaped graphene (BSG) ] can be prepared on ] ].<ref name="stm2016" /> A major advantage of LPE is that it can be used to exfoliate many inorganic 2D materials beyond graphene, e.g. BN, MoS2, WS2.<ref>{{cite journal |last1=Coleman |first1=Jonathan N. |last2=Lotya |first2=Mustafa |last3=O’Neill |first3=Arlene |last4=Bergin |first4=Shane D. |last5=King |first5=Paul J. |last6=Khan |first6=Umar |last7=Young |first7=Karen |last8=Gaucher |first8=Alexandre |last9=De |first9=Sukanta |last10=Smith |first10=Ronan J. |last11=Shvets |first11=Igor V. |last12=Arora |first12=Sunil K. |last13=Stanton |first13=George |last14=Kim |first14=Hye-Young |last15=Lee |first15=Kangho |last16=Kim |first16=Gyu Tae |last17=Duesberg |first17=Georg S. |last18=Hallam |first18=Toby |last19=Boland |first19=John J. |last20=Wang |first20=Jing Jing |last21=Donegan |first21=John F. |last22=Grunlan |first22=Jaime C. |last23=Moriarty |first23=Gregory |last24=Shmeliov |first24=Aleksey |last25=Nicholls |first25=Rebecca J. |last26=Perkins |first26=James M. |last27=Grieveson |first27=Eleanor M. |last28=Theuwissen |first28=Koenraad |last29=McComb |first29=David W. |last30=Nellist |first30=Peter D. |last31=Nicolosi |first31=Valeria |title=Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials |journal=Science |date=4 February 2011 |volume=331 |issue=6017 |pages=568–571 |doi=10.1126/science.1194975|pmid=21292974 |bibcode=2011Sci...331..568C |hdl=2262/66458 |s2cid=23576676 |hdl-access=free }}</ref> | |||
Graphene has a unique combination of high electrical conductivity and optical transparency, which make it a candidate for use in solar cells. A single sheet of graphene is a zero-bandgap semiconductor whose charge carriers are delocalized over large areas, implying that carrier scattering does not occur. Because this material only absorbs 2.3% of visible light, it is a candidate for applications requiring a transparent conductor. Graphene can be assembled into a film electrode with low roughness. However, graphene films produced via solution processing contain lattice defects and grain boundaries that act as recombination centers and decrease the material's electrical conductivity. Thus, these films must be made thicker than one atomic layer to obtain useful sheet resistances. This added resistance can be combatted by incorporating conductive filler materials, such as a ] matrix. Reduced graphene film's electrical conductivity can be improved by attaching large ] such as ]-1-sulfonic acid sodium salt (PyS) and the disodium salt of 3,4,9,10-perylenetetracarboxylic diimide bisbenzenesulfonic acid (PDI). These molecules, under high temperatures, facilitate better π-conjugation of the graphene basal plane. Graphene films have high transparency in the visible and near-] regions and are chemically and thermally stable.<ref name="Mukhopadhyay 2013 202-213">{{cite book |last=Mukhopadhyay|first=Prithu |title=Graphite, Graphene and their Polymer Nanocomposites |year=2013 |publisher=Taylor & Francis Group |location=Boca Raton, Florida |isbn=978-1-4398-2779-6 |pages=202–213 }}</ref> | |||
==== Exfoliation with supercritical carbon dioxide ==== | |||
For graphene to be used in commercial solar cells, large-scale production are required. However, no scalable process for producing graphene is available, including the peeling of pyrolytic graphene or thermal decomposition of silicon carbide.<ref name="Mukhopadhyay 2013 202-213"/> | |||
Liquid-phase exfoliation can also be done by a less-known process of intercalating ] (scCO2) into the interstitial spaces in the graphite lattice, followed by rapid depressurization. The scCO2 intercalates easily inside the graphite lattice at a pressure of roughly 100 ]. Carbon dioxide turns gaseous as soon as the vessel is depressurized and makes the graphite explode into few-layered graphene.<ref name=":1" /> | |||
This method may have multiple advantages: being non-toxic, the graphite does not have to be chemically treated in any way before the process, and the whole process can be completed in a single step as opposed to other exfoliation methods.<ref name=":1" /> | |||
Graphene's high charge mobilities recommend it for use as a charge collector and transporter in ]s (PV). Using graphene as a photoactive material requires its bandgap to be 1.4-1.9eV. In 2010, single cell efficiencies of nanostructured graphene-based PVs of over 12% were achieved. According to P. Mukhopadhyay and R. K. Gupta ] could be "devices in which semiconducting graphene is used as the photoactive material and metallic graphene is used as the conductive electrodes".<ref name="Mukhopadhyay 2013 202-213"/> | |||
=== Splitting monolayer carbon allotropes === | |||
In 2010,Xinming Li and Hongwei Zhu from Tsinghua University first reported graphene-silicon heterojunction solar cell,where graphene served as a transparent electrode and introduced a built-in electric field near the interface between the graphene and n-type silicon to help collect photo-generated carriers.More studies promote this new type of photovoltaic device.<ref>{{cite web|doi=10.1002/adma.200904383/abstract |title=Graphene-On-Silicon Schottky Junction Solar Cells |date=9 April 2010 |doi_brokendate=2014-03-24 }}</ref> For example,in 2012 researchers from the University of Florida reported efficiency of 8.6% for a prototype cell consisting of a wafer of silicon coated with a layer of graphene doped with trifluoromethanesulfonyl-amide (TFSA). Furthermore,Xinming Li found chemical doping could improve the graphene characteristics and significantly enhance the efficiency of graphene-silicon solar cell to 9.6% in 2013.<ref>{{cite web|doi=10.1002/aenm.201300052/abstract |title=Anomalous Behaviors of Graphene Transparent Conductors in Graphene–Silicon Heterojunction Solar Cells |date=19 April 2013 |doi_brokendate=2014-03-24 }}</ref><ref>{{cite web|url=http://pubs.rsc.org/en/Content/ArticleLanding/2013/NR/c2nr33795a#!divAbstract |title=Ion doping of graphene for high-efficiency heterojunction solar cells |date=3 January 2013 }}</ref> | |||
Graphene can be created by opening ]s by cutting or etching.<ref>{{cite journal |title=Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons |last=Brumfiel |first=G. |journal=Nature |year=2009 |doi=10.1038/news.2009.367}}</ref> In one such method, ] were cut open in solution by action of ] and ].<ref>{{cite journal |title=Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons |last1=Kosynkin |first1=D. V. |last2=Higginbotham |first2=Amanda L. |last3=Sinitskii |first3=Alexander |last4=Lomeda |first4=Jay R. |last5=Dimiev |first5=Ayrat |last6=Price |first6=B. Katherine |last7=Tour |first7=James M. |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07872 |pmid=19370030 |issue=7240 |bibcode=2009Natur.458..872K |pages=872–6|hdl=10044/1/4321 |s2cid=2920478 |hdl-access=free }}</ref><ref>{{cite journal |title=Narrow graphene nanoribbons from carbon nanotubes |last1=Liying |first1=Jiao |first2=Li |last2=Zhang |first3=Xinran |last3=Wang |first4=Georgi |last4=Diankov |first5=Hongjie |last5=Dai |author-link5=Hongjie Dai |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07919 |pmid=19370031 |issue=7240 |bibcode=2009Natur.458..877J |pages=877–80|s2cid=205216466 }}</ref> In 2014, carbon nanotube-reinforced graphene was made via spin coating and annealing functionalized carbon nanotubes.<ref name="kurz5011" /> | |||
Another approach sprays ] at supersonic speeds onto a substrate. The balls cracked open upon impact, and the resulting unzipped cages then bond together to form a graphene film.<ref>{{cite web |title=How to Make Graphene Using Supersonic Buckyballs {{!}} MIT Technology Review |url=http://www.technologyreview.com/view/539911/how-to-make-graphene-using-supersonic-buckyballs |website=MIT Technology Review |access-date=2015-10-11 |date=August 13, 2015 |archive-date=17 December 2015 |archive-url=https://web.archive.org/web/20151217235401/http://www.technologyreview.com/view/539911/how-to-make-graphene-using-supersonic-buckyballs/ |url-status=live }}</ref> | |||
In 2013 another team claimed to have reached 15.6% percent using a combination of ]e and graphene as a charge collector and ] as a sunlight absorber. The device is manufacturable at temperatures under {{convert|150|C|F}} using solution-based deposition. This lowers production costs and offers the potential using flexible plastics.<ref>{{cite web|url=http://www.gizmag.com/graphene-solar-cell-record-efficiency/30466 |title=Graphene-based solar cell hits record 15.6 percent efficiency |publisher=Gizmag.com |date= |accessdate=2014-01-23 }}</ref><ref>{{cite doi|10.1021/nl403997a }}</ref> | |||
== Chemical synthesis == | |||
Large scale production of highly transparent graphene films by ] was achieved in 2008. In this process, ultra-thin graphene sheets are created by first depositing carbon atoms in the form of graphene films on a nickel plate from ] gas. A protective layer of ] is laid over the graphene layer and the nickel underneath is dissolved in an acid bath. The final step is to attach the plastic-protected graphene to a flexible ] sheet, which can then be incorporated into an OPV cell. Graphene/polymer sheets range in size up to 150 square centimeters and can be used to create dense arrays of flexible OPV cells. It may eventually be possible to run printing presses covering extensive areas with inexpensive solar cells, much like newspaper presses print newspapers (]).<ref>{{Cite news |url=http://www.sciencedaily.com/releases/2010/07/100723095430.htm |title=Graphene organic photovoltaics: Flexible material only a few atoms thick may offer cheap solar power |work=ScienceDaily |date=24 July 2010}}<br/>Walker, Sohia. (2010-08-04) . Comptalks.com. Retrieved on 2010-12-10.</ref> | |||
=== Graphite oxide reduction === | |||
Silicon generates only one current-driving electron for each photon it absorbs, while graphene can produce multiple electrons. Solar cells made with graphene could offer 60% conversion efficiency – double the widely-accepted maximum efficiency of silicon cells.<ref>inhabitat.com cooperating with ICFO (Institute of Photonic Sciences)</ref> | |||
P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name=grtim2009/><ref>{{cite web|url=http://www.aps.org/publications/apsnews/201001/letters.cfm|title=Many Pioneers in Graphene Discovery|last=Geim|first=Andre|date=January 2010|work=Letters to the Editor|publisher=American Physical Society|access-date=2019-11-10|archive-date=2 November 2021|archive-url=https://web.archive.org/web/20211102053634/https://www.aps.org/publications/apsnews/201001/letters.cfm|url-status=live}}</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. | |||
Another method is the reduction of graphite oxide monolayer films, e.g. by ] with ] in ]/] with an almost intact carbon framework that allows efficient removal of functional groups. Measured ] mobility exceeded 1,000 cm/Vs (10 m/Vs).<ref name="Eigler2013">{{cite journal |first1=S. |last1=Eigler |first2=M. |last2=Enzelberger-Heim |first3=S. |last3=Grimm |first4=P. |last4=Hofmann |first5=W. |last5=Kroener |first6=A. |last6=Geworski |first7=C. |last7=Dotzer |first8=M. |last8=Röckert |first9=J. |last9=Xiao |first10=C. |last10=Papp |first11=O. |last11=Lytken |first12=H.-P. |last12=Steinrück |first13=P. |last13=Müller |first14=A. |last14=Hirsch |title=Wet Chemical Synthesis of Graphene |journal=Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 |doi=10.1002/adma.201300155 |pmid=23703794|bibcode=2013AdM....25.3583E |s2cid=26172029 }}</ref> | |||
=== Single-molecule gas detection === | |||
Burning a graphite oxide coated ] produced a conductive graphene film (1,738 siemens per meter) and specific surface area (1,520 square meters per gram) that was highly resistant and malleable.<ref>{{cite journal |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |journal=Science |volume=335 |issue=6074 |pages=1326–1330 |date=16 March 2012 |doi=10.1126/science.1216744 |pmid=22422977 |last1=El-Kady |first1=M. F. |last2=Strong |first2=V. |last3=Dubin |first3=S. |last4=Kaner |first4=R. B. |s2cid=18958488 |bibcode=2012Sci...335.1326E }}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=15 March 2012 |access-date=20 March 2012 |archive-url=https://www.webcitation.org/6HPJaTQQj?url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |archive-date=16 June 2013 |url-status=dead }}</ref> | |||
Theoretically graphene makes an excellent sensor due to its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect ] molecules. However, similar to carbon nanotubes, graphene has no dangling bonds on its surface. Gaseous molecules cannot be readily adsorbed onto graphene surfaces, so intrinsically graphene is insensitive.<ref>{{cite journal |last=Dan |first=Yaping |title=Intrinsic Response of Graphene Vapor Sensors |journal=Nano Letters |date=April 2009 |volume=9 |issue=4 |pages=1472–1475 |doi=10.1021/nl8033637 |last2=Lu |first2=Ye |last3=Kybert |first3=Nicholas J. |last4=Luo |first4=Zhengtang |last5=Johnson |first5=A. T. Charlie |pmid=19267449 |arxiv=0811.3091 |bibcode=2009NanoL...9.1472D }}</ref> The sensitivity of graphene chemical gas sensors can be dramatically enhanced by functionalization, for example, coating the film with a thin layer of certain polymers. The thin polymer layer acts like a concentrator that absorbs gaseous molecules. The molecule absorption introduces a local change in ] of graphene sensors. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise, which makes this change in resistance detectable.<ref name=ChemDoping/> | |||
A dispersed reduced graphene oxide suspension was synthesized in water by a hydrothermal dehydration method without using any surfactant. The approach is facile, industrially applicable, environmentally friendly, and cost-effective. Viscosity measurements confirmed that the graphene colloidal suspension (graphene nanofluid) exhibits Newtonian behavior, with the viscosity showing a close resemblance to that of water.<ref>{{cite journal |last1=Sadri |first1=R. |s2cid=53349683 |title=Experimental study on thermo-physical and rheological properties of stable and green reduced graphene oxide nanofluids: Hydrothermal assisted technique |journal=Journal of Dispersion Science and Technology |date=15 Feb 2017 |volume=38 |issue=9 |pages=1302–1310 |doi=10.1080/01932691.2016.1234387 }}</ref> | |||
=== Quantum dots === | |||
=== Molten salts === | |||
Graphene ]s (GQDs) keep all dimensions less than 10 nm. Their size and edge ] govern their electrical, magnetic, optical and chemical properties. GQDs can be produced via graphite nanotomy<ref name="GQD">{{Cite journal |first=Nihar |last=Mohanty |first2=David |last2=Moore |first3=Zhiping |last3=Xu |first4=T. S. |last4=Sreeprasad |first5=Ashvin |last5=Nagaraja |first6=Alfredo A. |last6=Rodriguez |first7=Vikas |last7=Berry |title=Nanotomy Based Production of Transferrable and Dispersible Graphene-Nanostructures of Controlled Shape and Size |doi=10.1038/ncomms1834 |journal=Nature Communications |volume=3 |page=844 |year=2012 |issue=5 |bibcode=2012NatCo...3E.844M }}</ref> or via bottom-up, solution-based routes (]).<ref name="GQD1">{{Cite journal |last=Jinming |first=Cai |title=Atomically precise bottom-up fabrication of graphene nanoribbons |doi=10.1038/nature09211 |journal=Nature |volume=466 |page=470 |year=2010 |issue=7305|bibcode=2010Natur.466..470C |first2=Pascal |last2=Ruffieux |first=Rached |last3=Jaafar |first=Marco |last4=Bieri |first=Thomas |last5=Braun |first=Stephan |last6=Blankenburg |first=Matthias |last7=Muoth |first=Ari P. |last8=Seitsonen |first=Moussa |last9=Saleh |first=Xinliang |last10=Feng |first=Klaus |last11=Müllen |first=Roman |last12=Fasel }}</ref> GQDs with controlled structure can be incorporated into applications in electronics, optoelectronics and electromagnetics. ] can be created by changing the width of graphene nanoribbons (GNRs) at selected points along the ribbon.<ref name="Ponomarenko_2008_356">{{Cite journal |laysummary=http://news.bbc.co.uk/2/hi/technology/7352464.stm |last=Ponomarenko |first=L. A. |title=Chaotic Dirac Billiard in Graphene Quantum Dots |journal=Science |volume=320 |year=2008 |doi=10.1126/science.1154663 |pmid=18420930 |issue=5874 |bibcode=2008Sci...320..356P |pages=356–8 |last2=Schedin |first2=F. |last3=Katsnelson |first3=M. I. |last4=Yang |first4=R. |last5=Hill |first5=E. W. |last6=Novoselov |first6=K. S. |last7=Geim |first7=A. K. |arxiv=0801.0160 }}</ref><ref>{{Cite journal |last=Wang |first=Z. F. |last2=Shi |first2=Q. W. |last3=Li |first3=Q. |last4=Wang |first4=X. |last5=Hou |first5=J. G. |last6=Zheng |first6=H. |author7=et al. |title=Z-shaped graphene nanoribbon quantum dot device |doi=10.1063/1.2761266 |journal=Applied Physics Letters |volume=91 |page=053109 |year=2007 |bibcode=2007ApPhL..91e3109W |issue=5 |arxiv=0705.0023 }}</ref> | |||
Graphite particles can be corroded in molten salts to form a variety of carbon nanostructures including graphene.<ref>{{cite journal |first1=A.R. |last1=Kamali |first2=D.J. |last2=Fray |journal=Carbon |volume=56 |pages=121–131 |doi=10.1016/j.carbon.2012.12.076 |title=Molten salt corrosion of graphite as a possible way to make carbon nanostructures|year=2013 |bibcode=2013Carbo..56..121K }}</ref> Hydrogen cations, dissolved in molten lithium chloride, can be discharged on cathodically-polarized graphite rods, which then intercalate, peeling graphene sheets. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability.<ref>{{cite journal |last1=Kamali |first1=D.J.Fray |year= 2015|title=Large-scale preparation of graphene by high temperature insertion of hydrogen into graphite |journal=Nanoscale |volume=7 |issue= 26|pages=11310–11320 |doi=10.1039/C5NR01132A|pmid=26053881 |doi-access=free }}</ref> | |||
=== |
=== Electrochemical synthesis === | ||
Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, and number of defects and affects its properties. The process begins by bathing the graphite in a solvent for intercalation. The process can be tracked by monitoring the solution's transparency with an LED and photodiode.<ref>{{cite web |title=How to tune graphene properties by introducing defects {{!}} KurzweilAI |url=http://www.kurzweilai.net/how-to-tune-graphene-properties-by-introducing-defects |website=www.kurzweilai.net |access-date=2015-10-11 |date=July 30, 2015 |archive-date=5 September 2015 |archive-url=https://web.archive.org/web/20150905200802/http://www.kurzweilai.net/how-to-tune-graphene-properties-by-introducing-defects |url-status=live }}</ref><ref>{{Cite journal |title=Controlling the properties of graphene produced by electrochemical exfoliation - IOPscience |date=2015-08-21 |doi=10.1088/0957-4484/26/33/335607 |pmid=26221914 |first1=Mario |last1=Hofmann |first2=Wan-Yu |last2=Chiang |first3=Tuân D |last3=Nguyễn |first4=Ya-Ping |last4=Hsieh |s2cid=206072084 |volume=26 |issue=33 |journal=Nanotechnology |page=335607 |bibcode=2015Nanot..26G5607H}}</ref> | |||
=== Hydrothermal self-assembly === | |||
In 2009, researchers built experimental graphene ]s that take an incoming signal of a certain frequency and output a signal at a multiple of that frequency.<ref>{{Cite journal |laysummary=http://www.physorg.com/news156698836.html |last=Wang |first=H. |last2=Nezich |first2=D. |last3=Kong |first3=J. |last4=Palacios |first4=T. |journal=IEEE Electr. Device. L. |volume=30 |page=547 |year=2009 |doi=10.1109/LED.2009.2016443 |title=Graphene Frequency Multipliers |issue=5}}<br/>{{Cite journal |first=D. |last=Cricchio |first2=P. P. |last2=Corso |first3=E. |last3=Fiordilino |first4=G. |last4=Orlando |first5=F. |last5=Persico |journal=J. Phys. B |year=2009 |volume=42 |page=085404 |doi=10.1088/0953-4075/42/8/085404 |title=A paradigm of fullerene |issue=8 |bibcode=2009JPhB...42h5404C }}</ref> | |||
Graphene has been prepared by using a sugar like ], ], etc. This substrate-free "bottom-up" synthesis is safer, simpler and more environmentally friendly than exfoliation. The method can control the thickness, ranging from monolayer to multilayer, which is known as the "Tang-Lau Method".<ref name="r1">{{cite journal |last1=Tang |first1=L. |last2=Li |first2=X. |last3=Ji |first3=R. |last4=Teng |first4=K. S. |last5=Tai |first5=G. |last6=Ye |first6=J. |last7=Wei |first7=C. |last8=Lau |first8=S. P. |doi=10.1039/C2JM15944A |title=Bottom-up synthesis of large-scale graphene oxide nanosheets |journal=Journal of Materials Chemistry |volume=22 |issue=12 |page=5676 |year=2012 |hdl=10397/15682 |hdl-access=free }}</ref><ref name=lixu2013/><ref name=lili2013b/><ref name=lixu2014/> | |||
=== |
=== Sodium ethoxide pyrolysis === | ||
Gram-quantities were produced by the reaction of ] with ] metal, followed by ] and washing with water.<ref>{{cite journal |doi=10.1038/nnano.2008.365 |title=Gram-scale production of graphene based on solvothermal synthesis and sonication |year=2008 |last1=Choucair |first1=M. |last2=Thordarson |first2=P |last3=Stride |first3=JA |journal=Nature Nanotechnology |pmid=19119279 |volume=4 |issue=1 |pages=30–3 |bibcode=2009NatNa...4...30C}}</ref> | |||
=== Microwave-assisted oxidation === | |||
When the ] of graphene is tuned, its optical absorption can be changed. In 2011, researchers reported the first graphene-based optical modulator. Operating at {{val|1.2|u=GHz}} without a temperature controller, this modulator has a broad bandwidth (from 1.3 to 1.6 μm) and small footprint (~{{val|25|u=μm<sup>2</sup>}}).<ref>{{cite journal |last=Liu |first=Ming |last2=Yin |last3=Xiaobo |last4=Ulin-Avila |last5=Erick |last6=Geng |last7=Baisong |last8=Zentgraf |last9=Thomas |last10=Ju |last11=Long |last12=Wang |last13=Feng |last14=Zhang |last15=Xiang |title=A graphene-based broadband optical modulator |journal=Nature |date=8 May 2011 |volume=474 |issue=7349 |pages=64–67 |doi=10.1038/nature10067 |pmid=21552277 |bibcode=2011Natur.474...64L }}</ref> | |||
In 2012, microwave energy was reported to directly synthesize graphene in one step.<ref>{{cite journal |last1=Chiu |first1=Pui Lam |last2=Mastrogiovanni |first2=Daniel D. T. |last3=Wei |first3=Dongguang |last4=Louis |first4=Cassandre |last5=Jeong |first5=Min |last6=Yu |first6=Guo |last7=Saad |first7=Peter |last8=Flach |first8=Carol R. |last9=Mendelsohn |first9=Richard |last10=Garfunkel |first10=Eric |last11=He |first11=Huixin |title=Microwave- and Nitronium Ion-Enabled Rapid and Direct Production of Highly Conductive Low-Oxygen Graphene |journal=Journal of the American Chemical Society |date=4 April 2012 |volume=134 |issue=13 |pages=5850–5856 |doi=10.1021/ja210725p |pmid=22385480 |bibcode=2012JAChS.134.5850C |s2cid=11991071 }}</ref> This approach avoids use of potassium permanganate in the reaction mixture. It was also reported that by microwave radiation assistance, graphene oxide with or without holes can be synthesized by controlling microwave time.<ref>{{cite journal |doi=10.1002/smll.201403402 |pmid=25683019 |title=Microwave Enabled One-Pot, One-Step Fabrication and Nitrogen Doping of Holey Graphene Oxide for Catalytic Applications |journal=Small |volume=11 |issue=27 |pages=3358–68 |year=2015 |last1=Patel |first1=Mehulkumar |last2=Feng |first2=Wenchun |last3=Savaram |first3=Keerthi |last4=Khoshi |first4=M. Reza |last5=Huang |first5=Ruiming |last6=Sun |first6=Jing |last7=Rabie |first7=Emann |last8=Flach |first8=Carol |last9=Mendelsohn |first9=Richard |last10=Garfunkel |first10=Eric |last11=He |first11=Huixin|s2cid=14567874 |hdl=2027.42/112245 |hdl-access=free }}</ref> Microwave heating can dramatically shorten the reaction time from days to seconds. | |||
Graphene can also be made by ] assisted hydrothermal pyrolysis.<ref name=tang2014/><ref name=tang2012/> | |||
=== Coolant additive === | |||
=== Thermal decomposition of silicon carbide === | |||
Graphene's high thermal conductivity suggests that it could be used as an additive in coolants. Preliminary research work showed that 5% graphene by volume can enhance the thermal conductivity of a base fluid by 86%.<ref>{{cite doi|10.1016/j.physleta.2011.01.040 }}</ref> Another application due to graphene's enhanced thermal conductivity was found in PCR.<ref name="doi10.1088/0957-4484/23/45/455106"/> | |||
Heating ] (SiC) to high temperatures ({{val|1100 |u=°C}}) under low pressures (c. 10<sup>−6</sup> torr, or 10<sup>−4</sup> Pa) reduces it to graphene.<ref name="0908.1900">{{cite journal |first1=Johannes |last1=Jobst |first2=Daniel |last2=Waldmann |first3=Florian |last3=Speck |first4=Roland |last4=Hirner |first5=Duncan K. |last5=Maude |first6=Thomas |last6=Seyller |first7=Heiko B. |last7=Weber |title=How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year=2009 |doi=10.1103/PhysRevB.81.195434 |journal=Physical Review B |volume=81 |issue=19 |page=195434 |arxiv=0908.1900 |bibcode=2010PhRvB..81s5434J|s2cid=118710923 }}</ref><ref name="ShenAPL">{{cite journal |first1=T. |last1=Shen |first2=J.J. |last2=Gu |first3=M |last3=Xu |first4=Y.Q. |last4=Wu |first5=M.L. |last5=Bolen |first6=M.A. |last6=Capano |first7=L.W. |last7=Engel |first8=P.D. |last8=Ye |title=Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal=Applied Physics Letters |bibcode=2009ApPhL..95q2105S |year=2009 |volume=95 |issue=17 |page=172105 |arxiv=0908.3822|s2cid=9546283 }}</ref><ref name="0909.2903">{{cite journal |first1=Xiaosong |last1=Wu |first2=Yike |last2=Hu |first3=Ming |last3=Ruan |first4=Nerasoa K |last4=Madiomanana |first5=John |last5=Hankinson |first6=Mike |last6=Sprinkle |first7=Claire |last7=Berger |first8=Walt A. |last8=de Heer |year=2009 |title=Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi=10.1063/1.3266524 |journal=Applied Physics Letters |volume=95 |issue=22 |page=223108 |arxiv=0909.2903 |bibcode=2009ApPhL..95v3108W|s2cid=118422866 }}</ref><ref name="0909.1193">{{cite journal |first1=Samuel |last1=Lara-Avila |first2=Alexei |last2=Kalaboukhov |first3=Sara |last3=Paolillo |first4=Mikael |last4=Syväjärvi |first5=Rositza |last5=Yakimova |first6=Vladimir |last6=Fal'ko |first7=Alexander |last7=Tzalenchuk |first8=Sergey |last8=Kubatkin |title=SiC Graphene Suitable For Quantum Hall Resistance Metrology |journal=Science Brevia |date=7 July 2009 |arxiv=0909.1193 |doi=<!-- none --> |bibcode=2009arXiv0909.1193L |pmid=<!-- none -->}}</ref><ref name="phase1">{{cite journal |first1=J.A. |last1=Alexander-Webber |first2=A.M.R. |last2=Baker |first3=T.J.B.M. |last3=Janssen |first4=A. |last4=Tzalenchuk |first5=S. |last5=Lara-Avila |first6=S. |last6=Kubatkin |first7=R. |last7=Yakimova |first8=B. A. |last8=Piot |first9=D. K. |last9=Maude |first10=R.J. |last10=Nicholas |year=2013 |title=Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi=10.1103/PhysRevLett.111.096601 |journal=Physical Review Letters |volume=111 |issue=9 |page=096601 |pmid=24033057 |arxiv=1304.4897 |bibcode=2013PhRvL.111i6601A|s2cid=118388086 }}</ref><ref>{{cite journal |last=Sutter |first=P. |title=Epitaxial graphene: How silicon leaves the scene |journal=Nature Materials |volume=8 |year=2009 |pmid=19229263 |doi=10.1038/nmat2392 |issue=3 |bibcode=2009NatMa...8..171S |pages=171–2 |url=https://zenodo.org/record/1233465 |access-date=12 April 2020 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801050128/https://zenodo.org/record/1233465 |url-status=live }}</ref> | |||
== Vapor deposition and growth techniques == | |||
=== Reference material === | |||
=== Chemical vapor deposition === | |||
Graphene's properties suggest it as a ] for characterizing electroconductive and transparent materials. One layer of graphene absorbs 2.3% of white light.<ref>{{Cite journal |first=R. R. |last=Nair |year=2008 |title=Fine Structure Constant Defines Visual Transparency of Graphene |journal=Science |pmid=18388259 |volume=320 |issue=5881 |page=1308 |doi=10.1126/science.1156965 |bibcode=2008Sci...320.1308N |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. }}</ref> | |||
==== Epitaxy ==== | |||
] is a wafer-scale technique to produce graphene. ] graphene may be coupled to surfaces weakly enough (by the active valence electrons that create ]s) to retain the two-dimensional ] of isolated graphene.<ref name=Gall1>{{cite journal |last1=Gall |first1=N. R. |last2=Rut'Kov |first2=E. V. |last3=Tontegode |first3=A. Ya. |year=1997 |title=Two Dimensional Graphite Films on Metals and Their Intercalation |journal=] |volume=11 |issue=16 |pages=1865–1911 |bibcode=1997IJMPB..11.1865G |doi=10.1142/S0217979297000976}}</ref> | |||
A normal ] coated with a layer of ] (Ge) dipped in dilute ] strips the naturally forming ] groups, creating hydrogen-terminated germanium. CVD can coat that with graphene.<ref>{{cite news |url=http://www.extremetech.com/extreme/179874-samsungs-graphene-breakthrough-could-finally-put-the-wonder-material-into-real-world-devices |title=Samsung's graphene breakthrough could finally put the wonder material into real-world devices |newspaper=ExtremeTech |date=7 April 2014 |access-date=13 April 2014 |archive-date=14 April 2014 |archive-url=https://web.archive.org/web/20140414080057/http://www.extremetech.com/extreme/179874-samsungs-graphene-breakthrough-could-finally-put-the-wonder-material-into-real-world-devices |url-status=live }}</ref><ref>{{cite journal |doi=10.1126/science.1252268 |pmid=24700471 |title=Wafer-Scale Growth of Single-Crystal Monolayer Graphene on Reusable Hydrogen-Terminated Germanium |journal=Science |volume=344 |issue=6181 |pages=286–9 |year=2014 |last1=Lee |first1=J.-H. |last2=Lee |first2=E. K. |last3=Joo |first3=W.-J. |last4=Jang |first4=Y. |last5=Kim |first5=B.-S. |last6=Lim |first6=J. Y. |last7=Choi |first7=S.-H. |last8=Ahn |first8=S. J. |last9=Ahn |first9=J. R. |last10=Park |first10=M.-H. |last11=Yang |first11=C.-W. |last12=Choi |first12=B. L. |last13=Hwang |first13=S.-W. |last14=Whang |first14=D. |bibcode=2014Sci...344..286L|s2cid=206556123 }}</ref> | |||
This property was used to define the '']'' that combines ] and ]. This parameter was used to compare materials without the use of two independent parameters.<ref>{{Cite journal |first=S. |last=Eigler |year=2009 |title=A new parameter based on graphene for characterizing transparent, conductive materials |journal=Carbon |volume=47 |pages=2936–2939 |doi=10.1016/j.carbon.2009.06.047 |issue=12 }}</ref> | |||
The direct synthesis of graphene on insulator TiO<sub>2</sub> with high-dielectric-constant (high-κ). A two-step CVD process is shown to grow graphene directly on TiO<sub>2</sub> crystals or exfoliated TiO<sub>2</sub> nanosheets without using any metal catalyst.<ref>{{cite journal|last1=Bansal|first1=Tanesh|last2=Durcan|first2=Christopher A. |last3=Jain|first3=Nikhil|last4=Jacobs-Gedrim|first4=Robin B.|last5=Xu|first5=Yang|last6=Yu|first6=Bin|title=Synthesis of few-to-monolayer graphene on rutile titanium dioxide|journal=Carbon|volume=55|pages=168–175|date=2013|doi=10.1016/j.carbon.2012.12.023|bibcode=2013Carbo..55..168B }}</ref> | |||
=== Thermal management === | |||
==== Metal substrates ==== | |||
In 2011, researchers reported that a three-dimensional, vertically aligned, functionalized multilayer graphene architecture can be an approach for graphene-based ] (]) with superior thermal conductivity and ultra-low ] between graphene and metal.<ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401"/> | |||
CVD graphene can be grown on metal substrates including ],<ref name="PhysOrg.com">{{cite news |title=A smarter way to grow graphene |url=http://www.physorg.com/news129980833.html |publisher=PhysOrg.com |date=May 2008 |access-date=11 November 2008 |archive-date=28 January 2012 |archive-url=https://web.archive.org/web/20120128134607/http://www.physorg.com/news129980833.html |url-status=live }}</ref> ],<ref name="grIr111">{{cite journal |last1=Pletikosić |first1=I. |last2=Kralj |first2=M. |last3=Pervan |first3=P. |last4=Brako |first4=R. |last5=Coraux |first5=J. |last6=n'Diaye |first6=A. |last7=Busse |first7=C. |last8=Michely |first8=T. |year=2009 |title=Dirac Cones and Minigaps for Graphene on Ir(111) |journal=Physical Review Letters |volume=102 |page=056808 |doi=10.1103/PhysRevLett.102.056808 |pmid=19257540 |bibcode=2009PhRvL.102e6808P |issue=5 |arxiv=0807.2770|s2cid=43507175 }}</ref> ]<ref>{{cite web |url=http://www.gizmag.com/graphene-glass-substrate-deposition/32271 |title=New process could lead to more widespread use of graphene |publisher=Gizmag.com |date=28 May 2014 |access-date=14 June 2014 |archive-date=5 September 2015 |archive-url=https://web.archive.org/web/20150905152750/http://www.gizmag.com/graphene-glass-substrate-deposition/32271/ |url-status=live }}</ref> and ].<ref>{{Cite journal|last1=Liu|first1=W.|last2=Li|first2=H.|last3=Xu|first3=C.|last4=Khatami|first4=Y.|last5=Banerjee|first5=K.|year=2011|title=Synthesis of high-quality monolayer and bilayer graphene on copper using chemical vapor deposition|url=https://www.sciencedirect.com/science/article/abs/pii/S0008622311004106|journal=Carbon|volume=49|issue=13|pages=4122–4130|doi=10.1016/j.carbon.2011.05.047|bibcode=2011Carbo..49.4122L|access-date=8 April 2020|archive-date=4 February 2021|archive-url=https://web.archive.org/web/20210204133312/https://www.sciencedirect.com/science/article/abs/pii/S0008622311004106|url-status=live}}</ref><ref>{{cite journal |last1=Mattevi |first1=Cecilia |last2=Kim |first2=Hokwon |last3=Chhowalla |first3=Manish |s2cid=213144 |title=A review of chemical vapour deposition of graphene on copper |journal=Journal of Materials Chemistry |date=2011 |volume=21 |issue=10 |pages=3324–3334 |doi=10.1039/C0JM02126A}}</ref> | |||
Graphene-metal composites can be utilized in thermal interface materials.<ref name="shaahin"/> | |||
=== |
==== Roll-to-roll ==== | ||
In 2014, a two-step roll-to-roll manufacturing process was announced. The first roll-to-roll step produces the graphene via chemical vapor deposition. The second step binds the graphene to a substrate.<ref>{{cite web |url=http://www.purdue.edu/newsroom/releases/2014/Q3/purdue-based-startup-scales-up-graphene-production,-develops-biosensors-and-supercapacitors.html |title=Purdue-based startup scales up graphene production, develops biosensors and supercapacitors |date=18 September 2014 |access-date=4 October 2014 |publisher=Purdue University |last=Martin |first=Steve |archive-date=3 October 2014 |archive-url=https://web.archive.org/web/20141003052536/http://www.purdue.edu/newsroom/releases/2014/Q3/purdue-based-startup-scales-up-graphene-production,-develops-biosensors-and-supercapacitors.html |url-status=live }}</ref><ref>{{Cite news |url=http://www.rdmag.com/videos/2014/09/startup-scales-graphene-production-develops-biosensors-and-supercapacitors |title=Startup scales up graphene production, develops biosensors and supercapacitors |date=19 September 2014 |work=R&D Magazine |access-date=4 October 2014 |archive-date=6 October 2014 |archive-url=https://web.archive.org/web/20141006071239/http://www.rdmag.com/videos/2014/09/startup-scales-graphene-production-develops-biosensors-and-supercapacitors |url-status=live }}</ref> | |||
==== Supercapacitor ==== | |||
] | |||
==== Cold wall ==== | |||
Due to graphene's high surface area to mass ratio, one potential application is in the conductive plates of ]s.<ref name="Stoller"> | |||
{{Cite journal |last=Stoller |first=Meryl D. |first2=Sungjin |last2=Park |first3=Yanwu |last3=Zhu |first4=Jinho |last4=An |first5=Rodney S. |last5=Ruoff |year=2008 |url=http://bucky-central.me.utexas.edu/RuoffsPDFs/179.pdf |format=PDF |doi=10.1021/nl802558y |title=Graphene-Based Ultracapacitors |journal=Nano Lett |volume=8 |pmid=18788793 |issue=10 |bibcode=2008NanoL...8.3498S |pages=3498–502 }}</ref> | |||
Growing graphene in an industrial resistive-heating cold wall CVD system was claimed to produce graphene 100 times faster than conventional CVD systems, cut costs by 99%, and produce material with enhanced electronic qualities.<ref>{{cite web |title=New process could usher in "graphene-driven industrial revolution" |url=http://www.gizmag.com/graphene-low-cost-nanocvd/38195 |website=www.gizmag.com |access-date=2015-10-05 |first=Darren |last=Quick |date=June 26, 2015 |archive-date=6 September 2015 |archive-url=https://web.archive.org/web/20150906024257/http://www.gizmag.com/graphene-low-cost-nanocvd/38195/ |url-status=live }}</ref><ref>{{cite journal |last1=Bointon |first1=Thomas H. |last2=Barnes |first2=Matthew D. |last3=Russo |first3=Saverio |last4=Craciun |first4=Monica F. |author-link4=Monica Craciun |date=July 2015 |title=High Quality Monolayer Graphene Synthesized by Resistive Heating Cold Wall Chemical Vapor Deposition |journal=Advanced Materials |volume=27 |issue=28 |pages=4200–4206 |arxiv=1506.08569 |bibcode=2015AdM....27.4200B |doi=10.1002/adma.201501600 |pmc=4744682 |pmid=26053564}}</ref> | |||
In February 2013 researchers announced a novel technique to produce graphene ]s based on the DVD burner reduction approach.<ref>{{cite web |last=Malasarn |first=Davin |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-technique-243553.aspx |title=UCLA researchers develop new technique to scale up production of graphene micro-supercapacitors / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=19 February 2013 }}</ref> | |||
==== |
==== Wafer scale CVD graphene ==== | ||
CVD graphene is scalable and has been grown on deposited Cu thin film catalyst on 100 to 300 mm standard Si/SiO<sub>2</sub> wafers<ref>{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Chou |first3=Harry |last4=Holt |first4=Milo |last5=Ruoff |first5=Rodney S. |last6=Akinwande |first6=Deji |s2cid=30130350 |date=2012-03-27 |title=Synthesis of High Quality Monolayer Graphene at Reduced Temperature on Hydrogen-Enriched Evaporated Copper (111) Films |journal=ACS Nano |volume=6 |issue=3 |pages=2319–2325 |doi=10.1021/nn205068n |pmid=22314052 }}</ref><ref name=":3">{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Holt |first3=Milo |last4=Chou |first4=Harry |last5=McDonnell |first5=Stephen J. |last6=Ferrer |first6=Domingo A. |last7=Babenco |first7=Matías G. |last8=Wallace |first8=Robert M. |last9=Banerjee |first9=Sanjay K. |s2cid=55726071 |date=2012-11-15 |title=Uniform Wafer-Scale Chemical Vapor Deposition of Graphene on Evaporated Cu (111) Film with Quality Comparable to Exfoliated Monolayer |journal=The Journal of Physical Chemistry C |volume=116 |issue=45 |pages=24068–24074 |doi=10.1021/jp3068848 }}</ref><ref name=":4">{{Cite journal |last1=Rahimi |first1=Somayyeh |last2=Tao |first2=Li |last3=Chowdhury |first3=Sk. Fahad |last4=Park |first4=Saungeun |last5=Jouvray |first5=Alex |last6=Buttress |first6=Simon |last7=Rupesinghe |first7=Nalin |last8=Teo |first8=Ken |last9=Akinwande |first9=Deji |date=2014-10-28 |title=Toward 300 mm Wafer-Scalable High-Performance Polycrystalline Chemical Vapor Deposited Graphene Transistors |journal=ACS Nano |volume=8 |issue=10 |pages=10471–10479 |doi=10.1021/nn5038493 |pmid=25198884 |s2cid=5077855 }}</ref> on an Axitron Black Magic system. Monolayer graphene coverage of >95% is achieved on 100 to 300 mm wafer substrates with negligible defects, confirmed by extensive Raman mapping.<ref name=":3" /><ref name=":4" /> | |||
Stable ] cycling has recently been demonstrated in bi- and few layer graphene films grown on ] ],<ref>{{cite doi|10.1021/am301782h}}<br/>{{cite web |url=http://jes.ecsdl.org/content/159/6/A752.abstract |title=Fabrication and Electrochemical Characterization of Single and Multi-Layer Graphene Anodes for Lithium-Ion Batteries |publisher=Jes.ecsdl.org |date= |accessdate=2013-06-24 }}</ref> while single layer graphene films have been demonstrated as a protective layer against corrosion in battery components such as the battery case.<ref>{{cite doi|10.1021/ja301586m }}</ref> This creates possibilities for flexible electrodes for microscale Li-ion batteries where the anode acts as the active material as well as the current collector.<ref>{{cite web |last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/faster-and-cheaper-process-for-graphene-in-liion-batteries |title=Faster and Cheaper Process for Graphene in Li-ion Batteries - IEEE Spectrum |publisher=Spectrum.ieee.org |date=17 January 2013 }}</ref> | |||
=== Solvent interface trapping method (SITM) === | |||
There are also ] Li-ion batteries.<ref>{{cite web|last=Johnson |first=Dexter |url=http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphenesilicon-anodes-for-liion-batteries-go-commercial |title=Graphene-Silicon Anodes for Li-ion Batteries Go Commercial - IEEE Spectrum |publisher=Spectrum.ieee.org |date=21 March 2012 }}</ref><ref>{{cite web|url=http://phys.org/news/2013-04-xgs-silicon-graphene-anode-materials-lithium-ion.html |title=XGS presents new silicon-graphene anode materials for lithium-ion batteries |publisher=Phys.org |date= |accessdate=2014-02-26 }}</ref> | |||
As reported by a group led by D. H. Adamson, graphene can be produced from natural graphite while preserving the integrity of the sheets using the solvent interface trapping method (SITM). SITM uses a high-energy interface, such as oil and water, to exfoliate graphite to graphene. Stacked graphite delaminates, or spreads, at the oil/water interface to produce few-layer graphene in a thermodynamically favorable process in much the same way as small molecule surfactants spread to minimize the interfacial energy. In this way, graphene behaves like a 2D surfactant.<ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Alamer |first2=Fahad Alhashmi |last3=McDannald |first3=Austin |last4=Jain |first4=Menka |last5=Sotzing |first5=Gregory A. |last6=Adamson |first6=Douglas H. |date=2015-01-01 |title=Preparation of conductive graphene/graphite infused fabrics using an interface trapping method |url=https://www.sciencedirect.com/science/article/pii/S0008622314008719 |journal=Carbon |language=en |volume=81 |pages=38–42 |doi=10.1016/j.carbon.2014.09.020 |bibcode=2015Carbo..81...38W |issn=0008-6223}}</ref><ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Carrillo |first2=Jan-Michael Y. |last3=Xu |first3=Thomas O. |last4=Dobrynin |first4=Andrey V. |last5=Adamson |first5=Douglas H. |date=2015-02-10 |title=Polymer/Pristine Graphene Based Composites: From Emulsions to Strong, Electrically Conducting Foams |url=https://pubs.acs.org/doi/10.1021/ma5024236 |journal=Macromolecules |language=en |volume=48 |issue=3 |pages=687–693 |doi=10.1021/ma5024236 |bibcode=2015MaMol..48..687W |osti=1265313 |issn=0024-9297 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200603/https://pubs.acs.org/doi/10.1021/ma5024236 |url-status=live }}</ref><ref>{{Cite journal |last1=Ward |first1=Shawn P. |last2=Abeykoon |first2=Prabodha G. |last3=McDermott |first3=Sean T. |last4=Adamson |first4=Douglas H. |date=2020-09-08 |title=Effect of Aqueous Anions on Graphene Exfoliation |url=https://pubs.acs.org/doi/10.1021/acs.langmuir.0c01569 |journal=Langmuir |language=en |volume=36 |issue=35 |pages=10421–10428 |doi=10.1021/acs.langmuir.0c01569 |pmid=32794716 |s2cid=225385130 |issn=0743-7463 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200601/https://pubs.acs.org/doi/10.1021/acs.langmuir.0c01569 |url-status=live }}</ref> SITM has been reported for a variety of applications such conductive polymer-graphene foams,<ref>{{Cite journal |last1=Bento |first1=Jennifer L. |last2=Brown |first2=Elizabeth |last3=Woltornist |first3=Steven J. |last4=Adamson |first4=Douglas H. |date=January 2017 |title=Thermal and Electrical Properties of Nanocomposites Based on Self-Assembled Pristine Graphene |journal=Advanced Functional Materials |language=en |volume=27 |issue=1 |pages=1604277 |doi=10.1002/adfm.201604277 |s2cid=102395615 |issn=1616-301X|doi-access=free }}</ref><ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Varghese |first2=Deepthi |last3=Massucci |first3=Daniel |last4=Cao |first4=Zhen |last5=Dobrynin |first5=Andrey V. |last6=Adamson |first6=Douglas H. |date=May 2017 |title=Controlled 3D Assembly of Graphene Sheets to Build Conductive, Chemically Selective and Shape-Responsive Materials |url=https://onlinelibrary.wiley.com/doi/10.1002/adma.201604947 |journal=Advanced Materials |language=en |volume=29 |issue=18 |pages=1604947 |doi=10.1002/adma.201604947 |pmid=28262992 |bibcode=2017AdM....2904947W |s2cid=205274548 |issn=0935-9648 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200600/https://onlinelibrary.wiley.com/doi/10.1002/adma.201604947 |url-status=live }}</ref><ref>{{Cite journal |last1=Varghese |first1=Deepthi |last2=Bento |first2=Jennifer L. |last3=Ward |first3=Shawn P. |last4=Adamson |first4=Douglas H. |date=2020-06-16 |title=Self-Assembled Graphene Composites for Flow-Through Filtration |url=https://pubs.acs.org/doi/10.1021/acsami.0c05831 |journal=ACS Applied Materials & Interfaces |volume=12 |issue=26 |language=en |pages=29692–29699 |doi=10.1021/acsami.0c05831 |pmid=32492330 |s2cid=219316507 |issn=1944-8244 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200604/https://pubs.acs.org/doi/10.1021/acsami.0c05831 |url-status=live }}</ref><ref>{{Cite journal |last1=Brown |first1=Elizabeth E. B. |last2=Woltornist |first2=Steven J. |last3=Adamson |first3=Douglas H. |date=2020-11-15 |title=PolyHIPE foams from pristine graphene: Strong, porous, and electrically conductive materials templated by a 2D surfactant |url=https://www.sciencedirect.com/science/article/pii/S0021979720309048 |journal=Journal of Colloid and Interface Science |language=en |volume=580 |pages=700–708 |doi=10.1016/j.jcis.2020.07.026 |pmid=32712476 |bibcode=2020JCIS..580..700B |s2cid=220798190 |issn=0021-9797}}</ref> conductive polymer-graphene microspheres,<ref>{{Cite journal |last1=Liyanage |first1=Chinthani D. |last2=Varghese |first2=Deepthi |last3=Brown |first3=Elizabeth E. B. |last4=Adamson |first4=Douglas H. |date=2019-11-05 |title=Pristine Graphene Microspheres by the Spreading and Trapping of Graphene at an Interface |url=https://pubs.acs.org/doi/10.1021/acs.langmuir.9b02650 |journal=Langmuir |language=en |volume=35 |issue=44 |pages=14310–14315 |doi=10.1021/acs.langmuir.9b02650 |pmid=31647673 |s2cid=204883163 |issn=0743-7463 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200601/https://pubs.acs.org/doi/10.1021/acs.langmuir.9b02650 |url-status=live }}</ref> conductive thin films<ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Oyer |first2=Andrew J. |last3=Carrillo |first3=Jan-Michael Y. |last4=Dobrynin |first4=Andrey V. |last5=Adamson |first5=Douglas H. |date=2013-08-27 |title=Conductive Thin Films of Pristine Graphene by Solvent Interface Trapping |url=https://pubs.acs.org/doi/10.1021/nn402371c |journal=ACS Nano |language=en |volume=7 |issue=8 |pages=7062–7066 |doi=10.1021/nn402371c |pmid=23879536 |issn=1936-0851 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200605/https://pubs.acs.org/doi/10.1021/nn402371c |url-status=live }}</ref> and conductive inks.<ref>{{Cite journal |last1=Chen |first1=Feiyang |last2=Varghese |first2=Deepthi |last3=McDermott |first3=Sean T. |last4=George |first4=Ian |last5=Geng |first5=Lijiang |last6=Adamson |first6=Douglas H. |date=2020-10-22 |title=Interface-exfoliated graphene-based conductive screen-printing inks: low-loading, low-cost, and additive-free |journal=Scientific Reports |language=en |volume=10 |issue=1 |pages=18047 |doi=10.1038/s41598-020-74821-3 |pmid=33093555 |pmc=7583245 |bibcode=2020NatSR..1018047C |issn=2045-2322}}</ref> | |||
=== Engineered piezoelectricity === | |||
=== Carbon dioxide reduction === | |||
] simulations predict that depositing certain ]s on graphene can render it ] responsive to an electric field applied in the out-of-plane direction. This type of locally engineered piezoelectricity is similar in magnitude to that of bulk piezoelectric materials and makes graphene a candidate for control and sensing in nanoscale devices.<ref name="stanford_2012">{{cite web |title=Straintronics: Stanford engineers create piezoelectric graphene |url=http://news.stanford.edu/news/2012/april/straintronics-piezoelectric-graphene-040312.html |publisher=Stanford University |date=3 April 2012}}<br/>{{cite journal |last=Ong |first=M. |last=Reed |first=E.J. |title=Engineered Piezoelectricity in Graphene |journal=ACS Nano |year=2012 |doi=10.1021/nn204198g |volume=6 |issue=2 |pages=1387–94 |pmid=22196055 }}</ref> | |||
A highly exothermic reaction combusts ] in an oxidation-reduction reaction with carbon dioxide, producing carbon nanoparticles including graphene and ]s.<ref>{{Cite journal |last1=Chakrabarti |first1=A. |last2=Lu |first2=J. |last3=Skrabutenas |first3=J. C. |last4=Xu |first4=T. |last5=Xiao |first5=Z. |last6=Maguire |first6=J. A. |last7=Hosmane |first7=N. S. |s2cid=96850993 |doi=10.1039/C1JM11227A |title=Conversion of carbon dioxide to few-layer graphene |journal=Journal of Materials Chemistry |volume=21 |issue=26 |page=9491 |year=2011 }}</ref> | |||
=== Biodevice === | |||
=== Supersonic spray === | |||
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.<ref name="Berry">{{Cite journal |first=Nihar |last=Mohanty |first=Vikas |last=Berry |year=2008 |doi=10.1021/nl802412n |title=Graphene-based Single-Bacterium Resolution Biodevice and DNA-Transistor – Interfacing Graphene-Derivatives with Nano and Micro Scale Biocomponents |journal=Nano Letters |volume=8 |pages=4469–76 |pmid=18983201 |bibcode=2008NanoL...8.4469M |issue=12 }}</ref> | |||
Supersonic acceleration of droplets through a ] was used to deposit reduced graphene oxide on a substrate. The energy of the impact rearranges those carbon atoms into flawless graphene.<ref>{{Cite journal |doi=10.1002/adfm.201400732 |title=Self-Healing Reduced Graphene Oxide Films by Supersonic Kinetic Spraying |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |year=2014 |last1=Kim |first1=D. Y. |last2=Sinha-Ray |first2=S. |last3=Park |first3=J. J. |last4=Lee |first4=J. G. |last5=Cha |first5=Y. H. |last6=Bae |first6=S. H. |last7=Ahn |first7=J. H. |last8=Jung |first8=Y. C. |last9=Kim |first9=S. M. |last10=Yarin |first10=A. L. |last11=Yoon |first11=S. S.|s2cid=96283118 }}</ref><ref>{{cite journal |url=http://www.kurzweilai.net/supersonic-spray-creates-high-quality-graphene-layer |title=Supersonic spray creates high-quality graphene layer |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |doi=10.1002/adfm.201400732 |publisher=KurzweilAI |access-date=14 June 2014 |year=2014 |last1=Kim |first1=Do-Yeon |last2=Sinha-Ray |first2=Suman |last3=Park |first3=Jung-Jae |last4=Lee |first4=Jong-Gun |last5=Cha |first5=You-Hong |last6=Bae |first6=Sang-Hoon |last7=Ahn |first7=Jong-Hyun |last8=Jung |first8=Yong Chae |last9=Kim |first9=Soo Min |last10=Yarin |first10=Alexander L. |last11=Yoon |first11=Sam S. |s2cid=96283118 |archive-date=4 June 2014 |archive-url=https://web.archive.org/web/20140604000811/http://www.kurzweilai.net/supersonic-spray-creates-high-quality-graphene-layer |url-status=live }}</ref> | |||
]-approximation. The unoccupied (occupied) states, colored in blue–red (yellow–green), touch each other without ] exactly at the above-mentioned six k-vectors.]] | |||
=== Laser === | |||
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of {{val|0.34|u=nm}}) layers as nanoelectrodes into a nanopore<ref name="small_5_23">{{Cite journal | |||
|last=Xu |first=M. S. Xu |first2=D. |last2=Fujita |first3=N. |last3=Hanagata |year=2009 |pmid=19904762 |doi=10.1002/smll.200900976 |title=Perspectives and Challenges of Emerging Single-Molecule DNA Sequencing Technologies |journal=Small |volume=5 |issue=23 |pages=2638–49 }}</ref> can solve a bottleneck for nanopore-based single-molecule DNA sequencing. | |||
In 2014, a {{chem|CO|2}} ] was used to produce patterned porous three-dimensional laser-induced graphene (LIG) film networks from commercial polymer films. The resulting material exhibits high electrical conductivity and surface area. The laser induction process is compatible with roll-to-roll manufacturing processes.<ref>{{Cite journal |doi=10.1038/ncomms6714 |pmid=25493446 |pmc=4264682 |title=Laser-induced porous graphene films from commercial polymers |journal=Nature Communications |volume=5 |page=5714 |year=2014 |last1=Lin |first1=J. |last2=Peng |first2=Z. |last3=Liu |first3=Y. |last4=Ruiz-Zepeda |first4=F. |last5=Ye |first5=R. |last6=Samuel |first6=E. L. G. |last7=Yacaman |first7=M. J. |last8=Yakobson |first8=B. I. |last9=Tour |first9=J. M. |bibcode=2014NatCo...5.5714L}}</ref> A similar material, laser-induced graphene fibers (LIGF), was reported in 2018.<ref>{{Cite journal|last1=Duy|first1=Luong Xuan|last2=Peng|first2=Zhiwei|last3=Li|first3=Yilun|last4=Zhang|first4=Jibo|last5=Ji|first5=Yongsung|last6=Tour|first6=James M.|date=2018-01-01|title=Laser-induced graphene fibers|url=https://www.sciencedirect.com/science/article/pii/S0008622317310370|journal=Carbon|language=en|volume=126|pages=472–479|doi=10.1016/j.carbon.2017.10.036|bibcode=2018Carbo.126..472D |issn=0008-6223}}</ref> | |||
On November 20, 2013 the ] awarded $100,000 to 'to develop new elastic composite materials for condoms containing nanomaterials like graphene'.<ref name="bbc_25016994">{{cite news |title=Bill Gates condom challenge 'to be met' by graphene scientists |url=http://www.bbc.co.uk/news/uk-england-manchester-25016994 |work=BBC News |date=20 November 2013 }}</ref> | |||
=== |
=== Flash Joule heating === | ||
In 2019, flash Joule heating (transient high-temperature electrothermal heating) was discovered to be a method to synthesize turbostratic graphene in bulk powder form. The method involves electrothermally converting various carbon sources, such as carbon black, coal, and food waste into micron-scale flakes of graphene.<ref name="Luong 647–651"/><ref>{{Cite journal|last1=Stanford|first1=Michael G.|last2=Bets|first2=Ksenia V.|last3=Luong|first3=Duy X.|last4=Advincula|first4=Paul A.|last5=Chen|first5=Weiyin|last6=Li|first6=John Tianci|last7=Wang|first7=Zhe|last8=McHugh|first8=Emily A.|last9=Algozeeb|first9=Wala A.|last10=Yakobson|first10=Boris I.|last11=Tour|first11=James M.|date=2020-10-27|title=Flash Graphene Morphologies|url=https://pubs.acs.org/doi/10.1021/acsnano.0c05900|journal=ACS Nano|language=en|volume=14|issue=10|pages=13691–13699|doi=10.1021/acsnano.0c05900|pmid=32909736|osti=1798502|s2cid=221623214|issn=1936-0851|access-date=16 October 2021|archive-date=4 August 2022|archive-url=https://web.archive.org/web/20220804211511/https://pubs.acs.org/doi/10.1021/acsnano.0c05900|url-status=live}}</ref> More recent works demonstrated the use of mixed ], waste rubber tires, and pyrolysis ash as carbon feedstocks.<ref>{{Cite journal|last1=Algozeeb|first1=Wala A.|last2=Savas|first2=Paul E.|last3=Luong|first3=Duy Xuan|last4=Chen|first4=Weiyin|last5=Kittrell|first5=Carter|last6=Bhat|first6=Mahesh|last7=Shahsavari|first7=Rouzbeh|last8=Tour|first8=James M.|date=2020-11-24|title=Flash Graphene from Plastic Waste|url=https://pubs.acs.org/doi/10.1021/acsnano.0c06328|journal=ACS Nano|language=en|volume=14|issue=11|pages=15595–15604|doi=10.1021/acsnano.0c06328|pmid=33119255|osti=1798504|s2cid=226203667|issn=1936-0851|access-date=16 October 2021|archive-date=16 October 2021|archive-url=https://web.archive.org/web/20211016050155/https://pubs.acs.org/doi/10.1021/acsnano.0c06328|url-status=live}}</ref><ref>{{Cite journal|last1=Wyss|first1=Kevin M.|last2=Beckham|first2=Jacob L.|last3=Chen|first3=Weiyin|last4=Luong|first4=Duy Xuan|last5=Hundi|first5=Prabhas|last6=Raghuraman|first6=Shivaranjan|last7=Shahsavari|first7=Rouzbeh|last8=Tour|first8=James M.|date=2021-04-15|title=Converting plastic waste pyrolysis ash into flash graphene|journal=Carbon|language=en|volume=174|pages=430–438|doi=10.1016/j.carbon.2020.12.063|s2cid=232864412|issn=0008-6223|doi-access=free|bibcode=2021Carbo.174..430W }}</ref><ref>{{Cite journal|last1=Advincula|first1=Paul A.|last2=Luong|first2=Duy Xuan|last3=Chen|first3=Weiyin|last4=Raghuraman|first4=Shivaranjan|last5=Shahsavari|first5=Rouzbeh|last6=Tour|first6=James M.|date=June 2021|title=Flash graphene from rubber waste|journal=Carbon|language=en|volume=178|pages=649–656|doi=10.1016/j.carbon.2021.03.020|s2cid=233573678|issn=0008-6223|doi-access=free|bibcode=2021Carbo.178..649A }}</ref> The graphenization process is kinetically controlled, and the energy dose is chosen to preserve the carbon in its graphenic state (excessive energy input leads to subsequent graphitization through annealing). | |||
Stacked graphene layers on a quartz substrate increased the absorption of millimeter (radio) waves by 90 per cent over 125 – 165 GHz bandwidth, extensible to microwave and low-terahertz frequencies, while remaining transparent to visible light. For example, graphene could be used as a coating for buildings or windows to block radio waves. Absorption is a result of mutually coupled ]s represented by each graphene-quartz substrate. A repeated transfer-and-etch process was used to control surface resistivity.<ref name="kurz_radio">{{cite web |url=http://www.kurzweilai.net/graphene-found-to-efficiently-absorb-radio-waves |title=Graphene found to efficiently absorb radio waves |publisher=KurzweilAI |date= |accessdate=2014-02-26 }}</ref><ref name="doi_srep04130">{{cite doi|10.1038/srep04130 }}</ref> | |||
=== Ion implantation === | |||
== Pseudo-relativistic theory{{anchor|pseudorel|reason=linked from ]}} == | |||
Accelerating carbon ions inside an electrical field into a semiconductor made of thin nickel films on a substrate of SiO<sub>2</sub>/Si, creates a wafer-scale ({{Convert|4|in}}) wrinkle/tear/residue-free graphene layer at a relatively low temperature of 500 °C.<ref>{{cite web |title=Korean researchers grow wafer-scale graphene on a silicon substrate {{!}} KurzweilAI |url=http://www.kurzweilai.net/korean-researchers-grow-wafer-scale-graphene-on-a-silicon-substrate |website=www.kurzweilai.net |access-date=2015-10-11 |date=July 21, 2015 |archive-date=7 August 2020 |archive-url=https://web.archive.org/web/20200807051259/https://www.kurzweilai.net/korean-researchers-grow-wafer-scale-graphene-on-a-silicon-substrate |url-status=live }}</ref><ref>{{cite journal |last1=Kim |first1=Janghyuk |last2=Lee |first2=Geonyeop |last3=Kim |first3=Jihyun |title=Wafer-scale synthesis of multi-layer graphene by high-temperature carbon ion implantation |journal=Applied Physics Letters |date=20 July 2015 |volume=107 |issue=3 |pages=033104 |doi=10.1063/1.4926605 |bibcode=2015ApPhL.107c3104K }}</ref> | |||
Graphene's electrical properties can be described by a conventional ] model; in this model the energy of the electrons with wave vector '''k''' is<ref name="Semenoff" /><ref name="Wallace">{{Cite journal |last=Wallace |first=P.R. |title=The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume=71 |year=1947 |page=622 |bibcode=1947PhRv...71..622W |issue=9 }}</ref> | |||
=== CMOS-compatible graphene === | |||
: <math>E=\pm\sqrt{\gamma_0^2\left(1+4\cos^2{\frac{k_ya}{2}}+4\cos{\frac{k_ya}{2}} \cdot \cos{\frac{k_x\sqrt{3}a}{2}}\right)}</math> | |||
Integration of graphene in the widely employed ] demands its transfer-free direct synthesis on ] substrates at temperatures below 500 °C. At the ] 2018, researchers from ], demonstrated a novel CMOS-compatible graphene synthesis process at 300 °C suitable for back-end-of-line (]) applications.<ref>{{Cite journal|last=Thomas|first=Stuart|date=2018|title=CMOS-compatible graphene|journal=Nature Electronics|volume=1|issue=12|pages=612|doi=10.1038/s41928-018-0178-x|s2cid=116643404|doi-access=free}}</ref><ref>{{cite book |doi=10.1109/IEDM.2018.8614535 |chapter=CMOS-Compatible Doped-Multilayer-Graphene Interconnects for Next-Generation VLSI |title=2018 IEEE International Electron Devices Meeting (IEDM) |year=2018 |last1=Jiang |first1=Junkai |last2=Chu |first2=Jae Hwan |last3=Banerjee |first3=Kaustav |author3-link=Kaustav Banerjee |pages=34.5.1–34.5.4 |isbn=978-1-7281-1987-8 |s2cid=58675631 }}</ref><ref>{{Cite news|url=https://www.news.ucsb.edu/2019/019563/graphene-goes-mainstream|title=Graphene goes mainstream|date=July 23, 2019|work=The Current, UC Santa Barbara|access-date=9 April 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801101103/https://www.news.ucsb.edu/2019/019563/graphene-goes-mainstream|url-status=live}}</ref> The process involves pressure-assisted solid-state ] of ] through a ] of metal catalyst. The synthesized large-area graphene films were shown to exhibit high quality (via ] characterization) and similar ] values when compared with high-temperature CVD synthesized graphene films of the same cross-section down to widths of 20 ]. | |||
with the nearest-neighbor hopping energy γ<sub>0</sub> ≈ {{val|2.8|u=eV}} and the ] a ≈ {{val|2.46|u=Å}}. The ] and ], respectively, correspond to the different signs in the above ]; they touch each other at six points, the "K-values". However, only two of these six points are independent, while the rest are equivalent by symmetry. In the vicinity of the K-points the energy depends ''linearly'' on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the ] even has an effective ]. | |||
== Simulation == | |||
As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless ]. This pseudo-relativistic description is restricted to the ], i.e., to vanishing rest mass ''M''<sub>0</sub>, which leads to interesting additional features:<ref name="Semenoff" /><ref name="cabra2">{{cite journal |last=Lamas |first=C.A. |first2=D.C. |last2=Cabra |first3=N. |last3=Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |pages=75108 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406|bibcode=2009PhRvB..80g5108L }}</ref> | |||
In addition to experimental investigation of graphene and graphene-based devices, numerical modeling and simulation of graphene has also been an important research topic. The ] provides an analytic expression for the graphene's conductivity and shows that it is a function of several physical parameters including wavelength, temperature, and chemical potential.<ref>{{cite journal |last1=Gusynin |first1=V P |last2=Sharapov |first2=S G |last3=Carbotte |first3=J P |title=Magneto-optical conductivity in graphene |journal=Journal of Physics: Condensed Matter |date=17 January 2007 |volume=19 |issue=2 |pages=026222 |doi=10.1088/0953-8984/19/2/026222|arxiv=0705.3783 |bibcode=2007JPCM...19b6222G |s2cid=119638159 }}</ref> Moreover, a surface conductivity model, which describes graphene as an infinitesimally thin (two-sided) sheet with a local and isotropic conductivity, has been proposed. This model permits the derivation of analytical expressions for the electromagnetic field in the presence of a graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current.<ref>{{cite journal |last1=Hanson |first1=George W. |title=Dyadic Green's Functions for an Anisotropic, Non-Local Model of Biased Graphene |journal=IEEE Transactions on Antennas and Propagation |date=March 2008 |volume=56 |issue=3 |pages=747–757 |doi=10.1109/TAP.2008.917005|bibcode=2008ITAP...56..747H |s2cid=32535262 }}</ref> | |||
: <math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math> | |||
Even though these analytical models and methods can provide results for several canonical problems for benchmarking purposes, many practical problems involving graphene, such as the design of arbitrarily shaped electromagnetic devices, are analytically intractable. With the recent advances in the field of ], various accurate and efficient numerical methods have become available for analysis of electromagnetic field/wave interactions on graphene sheets and/or graphene-based devices. A comprehensive summary of computational tools developed for analyzing graphene-based devices/systems is proposed.<ref>{{cite journal |last1=Niu |first1=Kaikun |last2=Li |first2=Ping |last3=Huang |first3=Zhixiang |last4=Jiang |first4=Li Jun |last5=Bagci |first5=Hakan |title=Numerical Methods for Electromagnetic Modeling of Graphene: A Review |journal=] |date=2020 |volume=5 |pages=44–58 |doi=10.1109/JMMCT.2020.2983336 |bibcode=2020IJMMC...5...44N |hdl=10754/662399 |s2cid=216262889 |hdl-access=free }}</ref> | |||
Here ''v<sub>F</sub>'' ~ {{val|e=6}} is the ] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the ], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro" /> | |||
== |
== Graphene analogs == | ||
Graphene analogs<ref>{{cite journal |last1=Polini |first1=Marco |last2=Guinea |first2=Francisco |last3=Lewenstein |first3=Maciej |last4=Manoharan |first4=Hari C. |last5=Pellegrini |first5=Vittorio |title=Artificial honeycomb lattices for electrons, atoms and photons |journal=Nature Nanotechnology |date=September 2013 |volume=8 |issue=9 |pages=625–633 |doi=10.1038/nnano.2013.161 |pmid=24002076 |arxiv=1304.0750 |bibcode=2013NatNa...8..625P }}</ref> (also referred to as "artificial graphene") are two-dimensional systems which exhibit similar properties to graphene. Graphene analogs have been studied intensively since the discovery of graphene in 2004. People try to develop systems in which the physics is easier to observe and manipulate than in graphene. In those systems, electrons are not always the particles that are used. They might be optical photons,<ref>{{cite journal |last1=Plotnik |first1=Yonatan |last2=Rechtsman |first2=Mikael C. |last3=Song |first3=Daohong |last4=Heinrich |first4=Matthias |last5=Zeuner |first5=Julia M. |last6=Nolte |first6=Stefan |last7=Lumer |first7=Yaakov |last8=Malkova |first8=Natalia |last9=Xu |first9=Jingjun |last10=Szameit |first10=Alexander |last11=Chen |first11=Zhigang |last12=Segev |first12=Mordechai |title=Observation of unconventional edge states in 'photonic graphene' |journal=Nature Materials |date=January 2014 |volume=13 |issue=1 |pages=57–62 |doi=10.1038/nmat3783 |pmid=24193661 |bibcode=2014NatMa..13...57P |arxiv=1210.5361 |s2cid=26962706 }}</ref> microwave photons,<ref>{{Cite journal |title=Topological Transition of Dirac Points in a Microwave Experiment |journal=Physical Review Letters |date=2013-01-14 |page=033902 |volume=110 |issue=3 |doi=10.1103/PhysRevLett.110.033902 |pmid=23373925 |first1=Matthieu |last1=Bellec |first2=Ulrich |last2=Kuhl |first3=Gilles |last3=Montambaux |first4=Fabrice |last4=Mortessagne |arxiv=1210.4642 |bibcode=2013PhRvL.110c3902B|s2cid=8335461 }}</ref> plasmons,<ref>{{cite journal |last1=Scheeler |first1=Sebastian P. |last2=Mühlig |first2=Stefan |last3=Rockstuhl |first3=Carsten |last4=Hasan |first4=Shakeeb Bin |last5=Ullrich |first5=Simon |last6=Neubrech |first6=Frank |last7=Kudera |first7=Stefan |last8=Pacholski |first8=Claudia |title=Plasmon Coupling in Self-Assembled Gold Nanoparticle-Based Honeycomb Islands |journal=The Journal of Physical Chemistry C |date=12 September 2013 |volume=117 |issue=36 |pages=18634–18641 |doi=10.1021/jp405560t }}</ref> microcavity polaritons,<ref>{{Cite journal |title=Direct Observation of Dirac Cones and a Flatband in a Honeycomb Lattice for Polaritons |journal=Physical Review Letters |date=2014-03-18 |page=116402 |volume=112 |issue=11 |doi=10.1103/PhysRevLett.112.116402 |pmid=24702392 |first1=T. |last1=Jacqmin |first2=I. |last2=Carusotto |first3=I. |last3=Sagnes |first4=M. |last4=Abbarchi |first5=D. D. |last5=Solnyshkov |first6=G. |last6=Malpuech |first7=E. |last7=Galopin |first8=A. |last8=Lemaître |first9=J. |last9=Bloch |arxiv=1310.8105 |bibcode=2014PhRvL.112k6402J|s2cid=31526933 }}</ref> or even atoms.<ref>{{cite journal |title= Multi-component quantum gases in spin-dependent hexagonal lattices|issue=5 |pages=434–440 |journal=Nature Physics |volume=7 |doi=10.1038/nphys1916 |date=May 2011 |last1=Sengstock |first1=K. |last2=Lewenstein |first2=M. |last3=Windpassinger |first3=P. |last4=Becker |first4=C. |last5=Meineke |first5=G. |last6=Plenkers |first6=W. |last7=Bick |first7=A. |last8=Hauke |first8=P. |last9=Struck |first9=J. |last10=Soltan-Panahi |first10=P. |bibcode=2011NatPh...7..434S |arxiv=1005.1276 |s2cid=118519844 }}</ref> Also, the honeycomb structure in which those particles evolve can be of a different nature than carbon atoms in graphene. It can be, respectively, a ], an array of metallic rods, metallic ]s, a lattice of coupled microcavities, or an ]. | |||
{{columns-list|3| | |||
== Applications == | |||
* ] | |||
{{main|Potential applications of graphene}} | |||
* ] | |||
* ] | |||
* ] | |||
* ] | |||
* ] | |||
* ] | |||
* ] | |||
Graphene is a transparent and flexible conductor that holds great promise for various material/device applications, including solar cells,<ref>{{cite journal |last1=Zhong |first1=Mengyao |last2=Xu |first2=Dikai |last3=Yu |first3=Xuegong |last4=Huang |first4=Kun |last5=Liu |first5=Xuemei |last6=Qu |first6=Yiming |last7=Xu |first7=Yang |last8=Yang |first8=Deren |title=Interface coupling in graphene/fluorographene heterostructure for high-performance graphene/silicon solar cells |journal=Nano Energy |date=October 2016 |volume=28 |pages=12–18 |doi=10.1016/j.nanoen.2016.08.031 |bibcode=2016NEne...28...12Z }}</ref> light-emitting diodes (LED), integrated photonic circuit devices,<ref>{{Cite journal |last1=Phare |first1=Christopher T. |last2=Daniel Lee |first2=Yoon-Ho |last3=Cardenas |first3=Jaime |last4=Lipson |first4=Michal |year=2015 |title=Graphene electro-optic modulator with 30 GHz bandwidth |url=https://www.nature.com/articles/nphoton.2015.122 |journal=Nature Photonics |language=en |volume=9 |issue=8 |pages=511–514 |doi=10.1038/nphoton.2015.122 |bibcode=2015NaPho...9..511P |s2cid=117786282 |issn=1749-4893 |access-date=19 September 2022 |archive-date=24 September 2022 |archive-url=https://web.archive.org/web/20220924083922/https://www.nature.com/articles/nphoton.2015.122 |url-status=live }}</ref><ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Ye |first2=Shengwei |last3=Shen |first3=Yijie |last4=Xiao |first4=Qirong |last5=Fu |first5=Xing |last6=Lu |first6=Rongguo |last7=Liu |first7=Yong |last8=Gong |first8=Mali |year=2018 |title=Waveguide Engineering of Graphene Optoelectronics—Modulators and Polarizers |journal=IEEE Photonics Journal |volume=10 |issue=1 |pages=1–17 |doi=10.1109/JPHOT.2018.2789894 |bibcode=2018IPhoJ..1089894M |s2cid=25707442 |issn=1943-0655|doi-access=free }}</ref> touch panels, and smart windows or phones.<ref>{{Cite journal |last1=Akinwande |first1=D. |last2=Tao |first2=L. |last3=Yu |first3=Q. |last4=Lou |first4=X. |last5=Peng |first5=P. |last6=Kuzum |first6=D. |author-link6=Duygu Kuzum |date=2015-09-01 |title=Large-Area Graphene Electrodes: Using CVD to facilitate applications in commercial touchscreens, flexible nanoelectronics, and neural interfaces. |journal=IEEE Nanotechnology Magazine |volume=9 |issue=3 |pages=6–14 |doi=10.1109/MNANO.2015.2441105 |s2cid=26541191}}</ref> Smartphone products with graphene touch screens are already on the market.<ref>{{Cite journal |last1=Kong |first1=Wei |last2=Kum |first2=Hyun |last3=Bae |first3=Sang-Hoon |last4=Shim |first4=Jaewoo |last5=Kim |first5=Hyunseok |last6=Kong |first6=Lingping |last7=Meng |first7=Yuan |last8=Wang |first8=Kejia |last9=Kim |first9=Chansoo |last10=Kim |first10=Jeehwan |year=2019 |title=Path towards graphene commercialization from lab to market |url=https://www.nature.com/articles/s41565-019-0555-2 |journal=Nature Nanotechnology |language=en |volume=14 |issue=10 |pages=927–938 |doi=10.1038/s41565-019-0555-2 |pmid=31582831 |bibcode=2019NatNa..14..927K |s2cid=203653990 |issn=1748-3395 |access-date=17 September 2022 |archive-date=22 September 2022 |archive-url=https://web.archive.org/web/20220922232818/https://www.nature.com/articles/s41565-019-0555-2 |url-status=live }}</ref> | |||
}} | |||
In 2013, Head announced their new range of graphene tennis racquets.<ref>{{Cite news|url=http://www.tennis.com/gear/2015/02/racquet-review-head-graphene-xt-speed-pro/53947/|title=Racquet Review: Head Graphene XT Speed Pro|newspaper=Tennis.com|access-date=2016-10-15|archive-date=2 May 2019|archive-url=https://web.archive.org/web/20190502064716/http://www.tennis.com/gear/2015/02/racquet-review-head-graphene-xt-speed-pro/53947/|url-status=live}}</ref> | |||
== References == | |||
{{Reflist|colwidth=30em}} | |||
As of 2015, there is one product available for commercial use: a graphene-infused printer powder.<ref>{{cite web |url=https://www.noble3dprinters.com/product/graphenite-graphene-infused-3d-printer-powder-30-lbs-499-95 |title=GRAPHENITE – GRAPHENE INFUSED 3D PRINTER POWDER – 30 Lbs – $499.95 |publisher=Noble3DPrinters |work=noble3dprinters.com |access-date=16 July 2015 }}{{Dead link|date=January 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> Many other uses for graphene have been proposed or are under development, in areas including electronics, ], ], lightweight/strong ], ]s and ].<ref name="auto"/><ref>{{cite web |url=http://www.graphenea.com/pages/graphene-uses-applications |title=Graphene Uses & Applications |publisher=Graphenea |access-date=13 April 2014 |archive-date=11 February 2014 |archive-url=https://web.archive.org/web/20140211025208/http://www.graphenea.com/pages/graphene-uses-applications |url-status=live }}</ref> Graphene is often produced as a powder and as a dispersion in a polymer matrix. This dispersion is supposedly suitable for advanced composites,<ref>{{cite journal |pmid=23405887 |pmc=3601907 |year=2013 |last1=Lalwani |first1=G |title=Two-dimensional nanostructure-reinforced biodegradable polymeric nanocomposites for bone tissue engineering |journal=Biomacromolecules |volume=14 |issue=3 |pages=900–9 |last2=Henslee |first2=A. M. |last3=Farshid |first3=B |last4=Lin |first4=L |last5=Kasper |first5=F. K. |last6=Qin |first6=Y. X. |last7=Mikos |first7=A. G. |last8=Sitharaman |first8=B |doi=10.1021/bm301995s}}</ref><ref>{{cite journal |first1=M.A. |last1=Rafiee |first2=J. |last2=Rafiee |first3=Z. |last3=Wang |first4=H. |last4=Song |first5=Z.Z. |last5=Yu |first6=N. |last6=Koratkar |s2cid=18266151 |title=Enhanced mechanical properties of nanocomposites at low graphene content |journal=ACS Nano |volume=3 |issue=12 |year=2009 |pages=3884–3890 |doi=10.1021/nn9010472|pmid=19957928 }}</ref> paints and coatings, lubricants, oils and functional fluids, capacitors and batteries, thermal management applications, display materials and packaging, solar cells, inks and 3D-printer materials, and barriers and films.<ref>{{cite web |url=http://www.appliedgraphenematerials.com/products/graphene-dispersions/ |title=Applied Graphene Materials plc :: Graphene dispersions |work=appliedgraphenematerials.com |access-date=26 May 2014 |archive-date=27 May 2014 |archive-url=https://web.archive.org/web/20140527212601/http://www.appliedgraphenematerials.com/products/graphene-dispersions/ |url-status=dead }}</ref> | |||
== Sources == | |||
On August 2, 2016, ] new Mono model is said to be made out of graphene as the first of both a street-legal track car and a production car.<ref>{{Cite web |url=http://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/ |title=BAC Debuts First Ever Graphene Constructed Vehicle |date=2016-08-02 |access-date=2016-08-04 |archive-date=4 August 2016 |archive-url=https://web.archive.org/web/20160804224120/http://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/ |url-status=live }}</ref> | |||
* {{cite journal | |||
In January 2018, graphene-based spiral ]s exploiting ] at room temperature were first demonstrated at the ], led by ]. These inductors were predicted to allow significant miniaturization in ] ] applications.<ref>{{Cite journal| doi=10.1038/s41928-017-0010-z| title=On-chip intercalated-graphene inductors for next-generation radio frequency electronics| year=2018| last1=Kang| first1=Jiahao| last2=Matsumoto| first2=Yuji| last3=Li| first3=Xiang| last4=Jiang| first4=Junkai| last5=Xie| first5=Xuejun| last6=Kawamoto| first6=Keisuke| last7=Kenmoku| first7=Munehiro| last8=Chu| first8=Jae Hwan| last9=Liu| first9=Wei| last10=Mao| first10=Junfa| last11=Ueno| first11=Kazuyoshi| last12=Banerjee| first12=Kaustav| author12-link=Kaustav Banerjee| journal=Nature Electronics| volume=1| pages=46–51| s2cid=139420526| url=https://escholarship.org/uc/item/2fb2f7h1| access-date=25 August 2020| archive-date=8 June 2020| archive-url=https://web.archive.org/web/20200608230020/https://escholarship.org/uc/item/2fb2f7h1| url-status=live}}</ref><ref>{{Cite web|url=https://www.forbes.com/sites/startswithabang/2018/03/08/breakthrough-in-miniaturized-inductors-to-revolutionize-electronics/#55414a40779e|title=The Last Barrier to Ultra-Miniaturized Electronics is Broken, Thanks To A New Type Of Inductor|last=Siegel|first=E.|year=2018|website=Forbes.com|access-date=8 April 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801040010/https://www.forbes.com/sites/startswithabang/2018/03/08/breakthrough-in-miniaturized-inductors-to-revolutionize-electronics/#55414a40779e|url-status=live}}</ref><ref>{{Cite web|url=https://physicsworld.com/a/engineers-reinvent-the-inductor-after-two-centuries/|title=Engineers reinvent the inductor after two centuries|year=2018|website=physicsworld|access-date=8 April 2020|archive-date=8 April 2020|archive-url=https://web.archive.org/web/20200408043458/https://physicsworld.com/a/engineers-reinvent-the-inductor-after-two-centuries/|url-status=live}}</ref> | |||
|last=Geim |first=A. K. | |||
|last2=Novoselov |first2=K. S. | |||
The potential of epitaxial graphene on ] for ] has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in the encapsulation and doping of epitaxial graphene have led to the commercialization of epitaxial graphene quantum resistance standards.<ref>{{cite journal |last1=Reiss |first1=T. |last2=Hjelt |first2=K. |last3=Ferrari |first3=A.C. |title=Graphene is on track to deliver on its promises |journal=Nature Nanotechnology |date=2019 |volume=14 |issue=907 |pages=907–910 |doi=10.1038/s41565-019-0557-0|pmid=31582830 |bibcode=2019NatNa..14..907R |s2cid=203653976 }}</ref> | |||
|year=2007 | |||
|title=The rise of graphene | |||
Novel uses for graphene continue to be researched and explored. One such use is in combination with water-based epoxy resins to produce anticorrosive coatings.<ref>{{Cite journal |last1=Monetta |first1=T. |last2=Acquesta |first2=A. |last3=Carangelo |first3=A. |last4=Bellucci |first4=F. |date=2018-09-01 |title=Considering the effect of graphene loading in water-based epoxy coatings |url=https://doi.org/10.1007/s11998-018-0045-8 |journal=Journal of Coatings Technology and Research |language=en |volume=15 |issue=5 |pages=923–931 |doi=10.1007/s11998-018-0045-8 |s2cid=139956928 |issn=1935-3804}}</ref> The van der Waals nature of graphene and other two-dimensional (2D) materials also permits van der Waals heterostructures<ref>{{Cite journal |last1=Castellanos-Gomez |first1=Andres |last2=Duan |first2=Xiangfeng |last3=Fei |first3=Zhe |last4=Gutierrez |first4=Humberto Rodriguez |last5=Huang |first5=Yuan |last6=Huang |first6=Xinyu |last7=Quereda |first7=Jorge |last8=Qian |first8=Qi |last9=Sutter |first9=Eli |last10=Sutter |first10=Peter |date=2022-07-28 |title=Van der Waals heterostructures |url=https://www.nature.com/articles/s43586-022-00139-1 |journal=Nature Reviews Methods Primers |language=en |volume=2 |issue=1 |pages=1–19 |doi=10.1038/s43586-022-00139-1 |osti=1891442 |s2cid=251175507 |issn=2662-8449 |access-date=21 April 2023 |archive-date=21 April 2023 |archive-url=https://web.archive.org/web/20230421224309/https://www.nature.com/articles/s43586-022-00139-1 |url-status=live }}</ref> and integrated circuits based on ] of 2D materials.<ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Feng |first2=Jiangang |last3=Han |first3=Sangmoon |last4=Xu |first4=Zhihao |last5=Mao |first5=Wenbo |last6=Zhang |first6=Tan |last7=Kim |first7=Justin S. |last8=Roh |first8=Ilpyo |last9=Zhao |first9=Yepin |last10=Kim |first10=Dong-Hwan |last11=Yang |first11=Yang |last12=Lee |first12=Jin-Wook |last13=Yang |first13=Lan |last14=Qiu |first14=Cheng-Wei |last15=Bae |first15=Sang-Hoon |date=2023-04-21 |title=Photonic van der Waals integration from 2D materials to 3D nanomembranes |url=https://www.nature.com/articles/s41578-023-00558-w |journal=Nature Reviews Materials |volume=8 |issue=8 |language=en |pages=498–517 |doi=10.1038/s41578-023-00558-w |bibcode=2023NatRM...8..498M |s2cid=258279195 |issn=2058-8437 |access-date=21 April 2023 |archive-date=21 April 2023 |archive-url=https://web.archive.org/web/20230421223403/https://www.nature.com/articles/s41578-023-00558-w |url-status=live }}</ref><ref>{{Cite journal |last1=Liu |first1=Yuan |last2=Huang |first2=Yu |last3=Duan |first3=Xiangfeng |date=March 2019 |title=Van der Waals integration before and beyond two-dimensional materials |journal=Nature |language=en |volume=567 |issue=7748 |pages=323–333 |doi=10.1038/s41586-019-1013-x |pmid=30894723 |bibcode=2019Natur.567..323L |s2cid=256768556 |issn=1476-4687|doi-access=free }}</ref> | |||
|journal=] | |||
|volume=6 |issue=3 |pages=183–91 | |||
Graphene is utilized in detecting gasses and chemicals in environmental monitoring, developing highly sensitive biosensors for medical diagnostics, and creating flexible, wearable sensors for health monitoring.<ref>{{cite book |last1=Shahdeo |first1=Deepshikha |last2=Roberts |first2=Akanksha |year=2020 |title=Comprehensive Analytical Chemistry |chapter=Graphene based sensors |editor=Chaudhery Mustansar Hussain |volume=91 |pages=175–199 |doi=10.1016/bs.coac.2020.08.007 |doi-access=free|isbn=978-0-323-85371-2 }}</ref><ref>{{cite journal |last1=Liu |first1=Jihong |last2=Bao |first2=Siyu |year=2022 |title=Applications of Graphene-Based Materials in Sensors: A Review |journal=Micromachines |volume=13 |issue=2 |page=184 |doi=10.3390/mi13020184 |doi-access=free |pmc=8880160 |pmid=35208308}}</ref> Graphene's transparency also enhances optical sensors, making them more effective in imaging and spectroscopy.<ref>{{cite journal |last1=Li |first1=Zongwen |last2=Zhang |first2=Wenfei |year=2019 |title=Graphene Optical Biosensors |journal=Int J Mol Sci |volume=20 |issue=10 |page=2461 |doi=10.3390/ijms20102461 |doi-access=free |pmc=6567174 |pmid=31109057}}</ref> | |||
|bibcode=2007NatMa...6..183G | |||
|doi=10.1038/nmat1849 | |||
== Toxicity == | |||
|pmid=17330084 |ref=harv | |||
}} | |||
One review on graphene toxicity published in 2016 by Lalwani et al. summarizes the ], ], antimicrobial and environmental effects and highlights the various mechanisms of graphene toxicity.<ref name=lalwani16>{{cite journal |pmid=27154267 |pmc=5039077 |year=2016 |last1=Lalwani |first1=Gaurav |title=Toxicology of graphene-based nanomaterials |journal=Advanced Drug Delivery Reviews |volume=105 |issue=Pt B |pages=109–144 |last2=D'Agati |first2=Michael |last3=Mahmud Khan |first3=Amit |last4=Sitharaman |first4=Balaji |doi=10.1016/j.addr.2016.04.028 }}</ref> Another review published in 2016 by Ou et al. focused on graphene-family nanomaterials (GFNs) and revealed several typical mechanisms such as physical destruction, ], ] damage, inflammatory response, ], ], and ].<ref name="ou16">{{cite journal |doi=10.1186/s12989-016-0168-y|pmc=5088662| title = Toxicity of graphene-family nanoparticles: A general review of the origins and mechanisms | year = 2016 | last1 = Ou | first1 = Lingling | last2 = Song | first2 = Bin | last3 = Liang | first3 = Huimin | last4 = Liu | first4 = Jia | last5 = Feng | first5=Xiaoli|last6=Deng|first6=Bin|last7=Sun|first7=Ting|last8=Shao|first8=Longquan|journal=Particle and Fibre Toxicology|volume=13|issue=1|page=57|pmid=27799056 |doi-access=free |bibcode=2016PFTox..13...57O }}</ref> | |||
A 2020 study showed that the toxicity of graphene is dependent on several factors such as shape, size, purity, post-production processing steps, oxidative state, functional groups, dispersion state, synthesis methods, route and dose of administration, and exposure times.<ref>{{cite journal|pmc=7287048|year=2020|last1=Joshi |first1= Shubhi |title=Green synthesis of peptide-functionalized reduced graphene oxide (rGO) nano bioconjugate with enhanced antibacterial activity|journal= Scientific Reports |volume=10 |issue=9441|last2=Siddiqui |first2=Ruby |last3=Sharma |first3=Pratibha |last4=Kumar |first4=Rajesh |last5=Verma |first5=Gaurav |last6=Saini |first6=Avneet|page=9441|doi=10.1038/s41598-020-66230-3 |pmid=32523022|bibcode=2020NatSR..10.9441J}}</ref> | |||
In 2014, research at ] showed that ]s, graphene nanoplatelets, and graphene nano–onions are non-toxic at concentrations up to 50 μg/ml. These nanoparticles do not alter the differentiation of human bone marrow ] towards ] (bone) or ] (fat), suggesting that at low doses, graphene nanoparticles are safe for biomedical applications.<ref>{{cite journal |pmid=24674462 |pmc=3995421 |year=2014 |last1=Talukdar |first1=Y |title=The effects of graphene nanostructures on mesenchymal stem cells |journal=Biomaterials |volume=35 |issue=18 |pages=4863–77 |last2=Rashkow |first2=J. T. |last3=Lalwani |first3=G |last4=Kanakia |first4=S |last5=Sitharaman |first5=B |doi=10.1016/j.biomaterials.2014.02.054 }}</ref> In 2013, research at ] found that 10 μm few-layered graphene flakes can pierce ] in solution. They were observed to enter initially via sharp and jagged points, allowing graphene to be internalized in the cell. The physiological effects of this remain unknown, and this remains a relatively unexplored field.<ref name=brownedu>{{cite web |first=Kevin |last=Stacey |date=10 July 2013 |url=https://news.brown.edu/articles/2013/07/graphene |title=Jagged graphene edges can slice and dice cell membranes - News from Brown |work=brown.edu |access-date=9 March 2015 |archive-date=25 March 2015 |archive-url=https://web.archive.org/web/20150325093234/https://news.brown.edu/articles/2013/07/graphene |url-status=live }}</ref><ref name=li13>{{Cite journal |doi=10.1073/pnas.1222276110 |pmid=23840061 |pmc=3725082 |title=Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites |journal=Proceedings of the National Academy of Sciences |volume=110 |issue=30 |pages=12295–12300 |year=2013 |last1=Li |first1=Y. |last2=Yuan |first2=H. |last3=von Dem Bussche |first3=A. |last4=Creighton |first4=M. |last5=Hurt |first5=R. H. |last6=Kane |first6=A. B. |last7=Gao |first7=H. |bibcode=2013PNAS..11012295L|doi-access=free }}</ref> | |||
== See also == | |||
* {{annotated link|Borophene}} | |||
* {{annotated link|Carbon fiber}} | |||
* {{annotated link|Penta-graphene}} | |||
* {{annotated link|Phagraphene}} | |||
* {{annotated link|Plumbene}} | |||
* {{annotated link|Silicene}} | |||
==References== | |||
<references> | |||
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<ref name="zdet2015">{{cite journal |last1=Zdetsis |first1=Aristides D. |last2=Economou |first2=E. N. |title=A Pedestrian Approach to the Aromaticity of Graphene and Nanographene: Significance of Huckel's (4 n +2)π Electron Rule |journal=The Journal of Physical Chemistry C |date=23 July 2015 |volume=119 |issue=29 |pages=16991–17003 |doi=10.1021/acs.jpcc.5b04311 }}</ref> | |||
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</references> | |||
== External links == | == External links == | ||
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* at '']'' (University of Nottingham) | * at '']'' (University of Nottingham) | ||
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* National Science Foundation, March 27, 2008 | |||
* {{cite web |url=http://www.nanohub.org/resource_files/2005/12/00723/2004.10.20-l21-ece453.pdf |format=PDF |title=Band structure of graphene |format=PDF |accessdate=2009-08-15}} | |||
* | |||
* {{cite web |url=http://physics.aps.org/articles/v2/30 |title=Pauling's dreams for graphene |first=Antonio H. |last=Castro Neto |date=12 May 2009}} | |||
* {{Cite journal |first=N M R |last=Peres |first2=R M |last2=Ribeiro |year=2009 |title=Focus on Graphene |journal=] |volume=11 |page=095002 |doi=10.1088/1367-2630/11/9/095002 |bibcode=2009NJPh...11i5002P |issue=9 }} | |||
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* , 15 September 2010, BBC Radio program Discovery | |||
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Latest revision as of 12:57, 7 December 2024
Hexagonal lattice made of carbon atoms Not to be confused with Graphite or Grapheme.Graphene | |
---|---|
Graphene is an atomic-scale honeycomb structure made of carbon atoms | |
Material type | Allotrope of carbon |
Chemical properties | |
Chemical formula | C |
Mechanical properties | |
Young's modulus (E) | ≈1 TPa |
Tensile strength (σt) | 130 GPa |
Thermal properties | |
Thermal conductivity (k) | 5300 W⋅m⋅K |
Graphene (/ˈɡræfiːn/) is a carbon allotrope consisting of a single layer of atoms arranged in a honeycomb planar nanostructure. The name "graphene" is derived from "graphite" and the suffix -ene, indicating the presence of double bonds within the carbon structure.
Graphene is known for its exceptionally high tensile strength, electrical conductivity, transparency, and being the thinnest two-dimensional material in the world. Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths. On a microscopic scale, graphene is the strongest material ever measured.
The existence of graphene was first theorized in 1947 by Philip R. Wallace during his research on graphite's electronic properties. In 2004, the material was isolated and characterized by Andre Geim and Konstantin Novoselov at the University of Manchester using a piece of graphite and adhesive tape. In 2010, Geim and Novoselov were awarded the Nobel Prize in Physics for their "groundbreaking experiments regarding the two-dimensional material graphene". While small amounts of graphene are easy to produce using the method by which it was originally isolated, attempts to scale and automate the manufacturing process for mass production have had limited success due to cost-effectiveness and quality control concerns. The global graphene market was $9 million in 2012, with most of the demand from research and development in semiconductors, electronics, electric batteries, and composites.
The IUPAC (International Union of Pure and Applied Chemistry) advises using the term "graphite" for the three-dimensional material and reserving "graphene" for discussions about the properties or reactions of single-atom layers. A narrower definition, of "isolated or free-standing graphene", requires that the layer be sufficiently isolated from its environment, but would include layers suspended or transferred to silicon dioxide or silicon carbide.
History
Main article: Discovery of grapheneStructure of graphite and its intercalation compounds
In 1859, Benjamin Brodie noted the highly lamellar structure of thermally reduced graphite oxide. Pioneers in X-ray crystallography attempted to determine the structure of graphite. The lack of large single crystal graphite specimens contributed to the independent development of X-ray powder diffraction by Peter Debye and Paul Scherrer in 1915, and Albert Hull in 1916. However, neither of their proposed structures was correct. In 1918, Volkmar Kohlschütter and P. Haenni described the properties of graphite oxide paper. The structure of graphite was successfully determined from single-crystal X-ray diffraction by J. D. Bernal in 1924, although subsequent research has made small modifications to the unit cell parameters.
The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was separately pointed out in 1984 by Gordon Walter Semenoff, and by David P. Vincenzo and Eugene J. Mele. Semenoff emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.
Observations of thin graphite layers and related structures
Transmission electron microscopy (TEM) images of thin graphite samples consisting of a few graphene layers were published by G. Ruess and F. Vogt in 1948. Eventually, single layers were also observed directly. Single layers of graphite were also observed by transmission electron microscopy within bulk materials, particularly inside soot obtained by chemical exfoliation.
From 1961 to 1962, Hanns-Peter Boehm published a study of extremely thin flakes of graphite. The study measured flakes as small as ~0.4 nm, which is around 3 atomic layers of amorphous carbon. This was the best possible resolution for TEMs in the 1960s. However, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known method is to analyze the relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are likely given in references 24 and 26 of Geim and Novoselov's 2007 review.
In 1975, van Bommel et al. epitaxially grew a single layer of graphite on top of silicon carbide. Others grew single layers of carbon atoms on other materials. This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials and, in some cases, hybridization between the d-orbitals of the substrate atoms and π orbitals of graphene, which significantly alter the electronic structure compared to that of free-standing graphene.
Boehm et al. coined the term "graphene" for the hypothetical single-layer structure in 1986. The term was used again in 1987 to describe single sheets of graphite as a constituent of graphite intercalation compounds, which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of carbon nanotubes by R. Saito and Mildred and Gene Dresselhaus in 1992, and in the description of polycyclic aromatic hydrocarbons in 2000 by S. Wang and others.
Efforts to make thin films of graphite by mechanical exfoliation started in 1990. Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.
In 2002, Robert B. Rutherford and Richard L. Dudman filed for a patent in the US on a method to produce graphene by repeatedly peeling off layers from a graphite flake adhered to a substrate, achieving a graphite thickness of 0.00001 inches (0.00025 millimetres). The key to success was the ability to quickly and efficiently identify graphene flakes on the substrate using optical microscopy, which provided a small but visible contrast between the graphene and the substrate.
Another U.S. patent was filed in the same year by Bor Z. Jang and Wen C. Huang for a method to produce graphene-based on exfoliation followed by attrition.
In 2014, inventor Larry Fullerton patented a process for producing single-layer graphene sheets.
Full isolation and characterization
Graphene was properly isolated and characterized in 2004 by Andre Geim and Konstantin Novoselov at the University of Manchester. They pulled graphene layers from graphite with a common adhesive tape in a process called micro-mechanical cleavage, colloquially referred to as the Scotch tape technique. The graphene flakes were then transferred onto a thin silicon dioxide layer on a silicon plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the SiO
2 could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range.
This work resulted in the two winning the Nobel Prize in Physics in 2010 for their groundbreaking experiments with graphene. Their publication and the surprisingly easy preparation method that they described, sparked a "graphene gold rush". Research expanded and split off into many different subfields, exploring different exceptional properties of the material—quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc.
Exploring commercial applications
Since the early 2000s, several companies and research laboratories have been working to develop commercial applications of graphene. In 2014, a National Graphene Institute was established with that purpose at the University of Manchester, with a £60 million initial funding. In North East England two commercial manufacturers, Applied Graphene Materials and Thomas Swan Limited have begun manufacturing. Cambridge Nanosystems is a large-scale graphene powder production facility in East Anglia.
Structure
Graphene is a single layer of carbon atoms tightly bound in a hexagonal honeycomb lattice. It is an allotrope of carbon in the form of a plane of sp-bonded atoms with a molecular bond length of 0.142 nm (1.42 Å). In a graphene sheet, each atom is connected to its three nearest carbon neighbors by σ-bonds, and a delocalized π-bond, which contributes to a valence band that extends over the whole sheet. This type of bonding is also seen in polycyclic aromatic hydrocarbons. The valence band is touched by a conduction band, making graphene a semimetal with unusual electronic properties that are best described by theories for massless relativistic particles. Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport is ballistic over long distances; the material exhibits large quantum oscillations and large nonlinear diamagnetism.
Bonding
Three of the four outer-shell electrons of each atom in a graphene sheet occupy three sp hybrid orbitals – a combination of orbitals s, px and py — that are shared with the three nearest atoms, forming σ-bonds. The length of these bonds is about 0.142 nanometers.
The remaining outer-shell electron occupies a pz orbital that is oriented perpendicularly to the plane. These orbitals hybridize together to form two half-filled bands of free-moving electrons, π, and π∗, which are responsible for most of graphene's notable electronic properties. Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of hydrogenation (ΔHhydro) agree well with the literature reports.
Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm (3.35 Å).
Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures. However, unlayered graphene displaying only (hk0) rings have been observed in the core of presolar graphite onions. TEM studies show faceting at defects in flat graphene sheets and suggest a role for two-dimensional crystallization from a melt.
Geometry
The hexagonal lattice structure of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of a metallic grid. Some of these images showed a "rippling" of the flat sheet, with an amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals, or may originate from the ubiquitous dirt seen in all TEM images of graphene. Photoresist residue, which must be removed to obtain atomic-resolution images, may be the "adsorbates" observed in TEM images, and may explain the observed rippling.
The hexagonal structure is also seen in scanning tunneling microscope (STM) images of graphene supported on silicon dioxide substrates The rippling seen in these images is caused by the conformation of graphene to the substrates' lattice and is not intrinsic.
Stability
Ab initio calculations show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm and becomes the most stable fullerene (as within graphite) only for molecules larger than 24,000 atoms.
Electronic properties
Main article: Electronic properties of grapheneGraphene is a zero-gap semiconductor because its conduction and valence bands meet at the Dirac points. The Dirac points are six locations in momentum space on the edge of the Brillouin zone, divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene a valley degeneracy of . In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero.
If the in-plane direction is confined rather than infinite, its electronic structure changes. These confined structures are referred to as graphene nanoribbons. If the nanoribbon has a "zig-zag" edge, the bandgap remains zero. If it has an "armchair" edge, the bandgap is non-zero.
Graphene's honeycomb structure can be viewed as two interleaving triangular lattices. This perspective has been used to calculate the band structure for a single graphite layer using a tight-binding approximation.
Electronic spectrum
Electrons propagating through the graphene honeycomb lattice effectively lose their mass, producing quasi-particles described by a 2D analogue of the Dirac equation rather than the Schrödinger equation for spin-1/2 particles.
Dispersion relation
The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by Philip Kim and Yuanbo Zhang. This effect provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions and proof of the Dirac fermion nature of electrons. These effects were previously observed in bulk graphite by Yakov Kopelevich, Igor A. Luk'yanchuk, and others, in 2003–2004.
When atoms are placed onto the graphene hexagonal lattice, the overlap between the pz(π) orbitals and the s or the px and py orbitals is zero by symmetry. Therefore, pz electrons forming the π bands in graphene can be treated independently. Within this π-band approximation, using a conventional tight-binding model, the dispersion relation (restricted to first-nearest-neighbor interactions only) that produces the energy of the electrons with wave vector k is:
with the nearest-neighbor (π orbitals) hopping energy γ0 ≈ 2.8 eV and the lattice constant a ≈ 2.46 Å. The conduction and valence bands correspond to the different signs. With one pz electron per atom in this model, the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the K point in the Brillouin zone), where there is a zero density of states but no band gap. Thus, graphene exhibits a semi-metallic (or zero-gap semiconductor) character, although this is not true for a graphene sheet rolled into a carbon nanotube due to its curvature. Two of the six Dirac points are independent, while the rest are equivalent by symmetry. Near the K-points, the energy depends linearly on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the wave function has an effective 2-spinor structure.
Consequently, at low energies even neglecting the true spin, electrons can be described by an equation formally equivalent to the massless Dirac equation. Hence, the electrons and holes are called Dirac fermions. This pseudo-relativistic description is restricted to the chiral limit, i.e., to vanishing rest mass M0, leading to interesting additional features:
Here vF ~ 10 m/s (.003 c) is the Fermi velocity in graphene, which replaces the velocity of light in the Dirac theory; is the vector of the Pauli matrices, is the two-component wave function of the electrons, and E is their energy.
The equation describing the electrons' linear dispersion relation is:
where the wavevector q is measured from the Brillouin zone vertex K, , and the zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice.
Single-atom wave propagation
Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as high-κ dielectrics, superconductors, and ferromagnetic.
Ambipolar electron and hole transport
Graphene exhibits high electron mobility at room temperature, with values reported in excess of 15000 cm⋅V⋅s. Hole and electron mobilities are nearly identical. The mobility is independent of temperature between 10 K and 100 K, showing minimal change even at room temperature (300 K), suggesting that the dominant scattering mechanism is defect scattering. Scattering by graphene's acoustic phonons intrinsically limits room temperature mobility in freestanding graphene to 200000 cm⋅V⋅s at a carrier density of 10 cm.
The corresponding resistivity of graphene sheets is 10 Ω⋅m, lower than the resistivity of silver, which is the lowest known at room temperature. However, on SiO
2 substrates, electron scattering by optical phonons of the substrate has a more significant effect than scattering by graphene's phonons, limiting mobility to 40000 cm⋅V⋅s.
Charge transport can be affected by the adsorption of contaminants such as water and oxygen molecules, leading to non-repetitive and large hysteresis I-V characteristics. Researchers need to conduct electrical measurements in a vacuum. Coating the graphene surface with materials such as SiN, PMMA or h-BN has been proposed for protection. In January 2015, the first stable graphene device operation in the air over several weeks was reported for graphene whose surface was protected by aluminum oxide. In 2015, lithium-coated graphene exhibited superconductivity, a first for graphene.
Electrical resistance in 40-nanometer-wide nanoribbons of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by a factor of 10. The ribbons can function more like optical waveguides or quantum dots, allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases proportionally with length as electrons encounter impurities.
Transport is dominated by two modes: one ballistic and temperature-independent, and the other thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at a specific length—the ballistic mode at 16 micrometers and the thermally activated mode at 160 nanometers (1% of the former length).
Graphene electrons can traverse micrometer distances without scattering, even at room temperature.
Electrical conductivity and charge transport
Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of . The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO
2 substrate may lead to local puddles of carriers that allow conduction. Several theories suggest that the minimum conductivity should be ; however, most measurements are of the order of or greater and depend on impurity concentration.
Near zero carrier density, graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density, governed by the interplay between photoinduced changes of both the Drude weight and the carrier scattering rate.
Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in a vacuum. Even for dopant concentrations in excess of 10 cm, carrier mobility exhibits no observable change. Graphene doped with potassium in ultra-high vacuum at low temperature can reduce mobility 20-fold. The mobility reduction is reversible on heating the graphene to remove the potassium.
Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum) is thought to occur. It may therefore be a suitable material for constructing quantum computers using anyonic circuits.
Chiral half-integer quantum Hall effect
Quantum hall effect in graphene
The quantum Hall effect is a quantum mechanical version of the Hall effect, which is the production of transverse (perpendicular to the main current) conductivity in the presence of a magnetic field. The quantization of the Hall effect at integer multiples (the "Landau level") of the basic quantity e/h (where e is the elementary electric charge and h is the Planck constant). It can usually be observed only in very clean silicon or gallium arsenide solids at temperatures around 3 K and very high magnetic fields.
Graphene shows the quantum Hall effect: the conductivity quantization is unusual in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is , where N is the Landau level and the double valley and double spin degeneracies give the factor of 4. These anomalies are present not only at extremely low temperatures but also at room temperature, i.e. at roughly 20 °C (293 K).
Chiral electrons and anomalies
This behavior is a direct result of graphene's chiral, massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the Atiyah–Singer index theorem and is half-filled in neutral graphene, leading to the "+1/2" in the Hall conductivity. Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. ). In the second anomaly, the first plateau at N = 0 is absent, indicating that bilayer graphene stays metallic at the neutrality point.
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the Shubnikov–de Haas oscillations, thus the term "integral quantum Hall effect". These oscillations show a phase shift of π, known as Berry's phase. Berry's phase arises due to chirality or dependence (locking) of the pseudospin quantum number on the momentum of low-energy electrons near the Dirac points. The temperature dependence of the oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass in the Dirac-fermion formalism.
Experimental observations
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of silicon carbide, show the anomalous effect directly in electrical measurements. Graphitic layers on the carbon face of silicon carbide show a clear Dirac spectrum in angle-resolved photoemission experiments, and the effect is observed in cyclotron resonance and tunneling experiments.
"Massive" electrons
Graphene's unit cell has two identical carbon atoms and two zero-energy states: one where the electron resides on atom A, and the other on atom B. However, if the unit cell's two atoms are not identical, the situation changes. Research shows that placing hexagonal boron nitride (h-BN) in contact with graphene can alter the potential felt at atoms A and B sufficiently for the electrons to develop a mass and an accompanying band gap of about 30 meV.
The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via optical spectroscopy. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and displays much the same physics as topological insulators.
If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of quantum dots, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against backscattering and could carry currents without dissipation.
Interactions and phenomena
Strong magnetic fields
In magnetic fields above 10 tesla, additional plateaus of the Hall conductivity at σxy = νe/h with ν = 0, ±1, ±4 are observed. A plateau at ν = 3 and the fractional quantum Hall effect at ν = 1/3 were also reported.
These observations with ν = 0, ±1, ±3, ±4 indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted.
Casimir effect
The Casimir effect is an interaction between disjoint neutral bodies provoked by the fluctuations of the electromagnetic vacuum. Mathematically, it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary conditions on the interacting bodies' surfaces. Due to graphene's strong interaction with the electromagnetic field as a one-atom-thick material, the Casimir effect has garnered significant interest.
Van der Waals force
The Van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic asymptotic power law in contrast to the usual inverse quartic law.
Permittivity
Graphene's permittivity varies with frequency. Over a range from microwave to millimeter wave frequencies, it is approximately 3.3. This permittivity, combined with its ability to function as both a conductor and as an insulator, theoretically allows compact capacitors made of graphene to store large amounts of electrical energy.
Optical properties
Graphene exhibits unique optical properties, showing unexpectedly high opacity for an atomic monolayer in vacuum, absorbing approximately πα ≈ 2.3% of light from visible to infrared wavelengths, where α is the fine-structure constant. This is due to the unusual low-energy electronic structure of monolayer graphene, characterized by electron and hole conical bands meeting at the Dirac point, which is qualitatively different from more common quadratic massive bands. Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, calculations using Fresnel equations in the thin-film limit account for interatomic distance, hopping values, and frequency, thus assessing optical conductance.
Experimental verification, though confirmed, lacks the precision required to improve upon existing techniques for determining the fine-structure constant.
Multi-parametric surface plasmon resonance
Multi-parametric surface plasmon resonance has been utilized to characterize both the thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. At a wavelength of 670 nm (6.7×10 m), measured refractive index and extinction coefficient values are 3.135 and 0.897, respectively. Thickness determination yielded 3.7 Å across a 0.5mm area, consistent with the 3.35 Å reported for layer-to-layer carbon atom distance of graphite crystals. This method is applicable for real-time label-free interactions of graphene with organic and inorganic substances. The existence of unidirectional surface plasmons in nonreciprocal graphene-based gyrotropic interfaces has been theoretically demonstrated, offering tunability from THz to near-infrared and visible frequencies by controlling graphene's chemical potential. Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that achievable with metal under similar magnetic field conditions, stemming from graphene's extremely small effective electron mass.
Tunable band gap and optical response
Graphene's band gap can be tuned from 0 to 0.25 eV (about 5-micrometer wavelength) by applying a voltage to a dual-gate bilayer graphene field-effect transistor (FET) at room temperature. The optical response of graphene nanoribbons is tunable into the terahertz regime by an applied magnetic fields. Graphene/graphene oxide systems exhibit electrochromic behavior, enabling tuning of both linear and ultrafast optical properties.
Graphene-based Bragg grating
A graphene-based Bragg grating (one-dimensional photonic crystal) has been fabricated, demonstrating its capability to excite surface electromagnetic waves in periodic structure using a 633 nm (6.33×10 m) He–Ne laser as the light source.
Saturable absorption
Graphene exhibits unique saturable absorption, which saturates when the input optical intensity exceeds a threshold value. This nonlinear optical behavior, termed saturable absorption, occurs across the visible to near-infrared spectrum, due to graphene's universal optical absorption and zero band gap. This property has enabled full-band mode-locking in fiber lasers using graphene-based saturable absorbers, contributing significantly to ultrafast photonics. Additionally, the optical response of graphene/graphene oxide layers can be electrically tuned.
Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave-saturable absorption in graphene demonstrates the possibility of graphene microwaves and terahertz photonics devices, such as a microwave-saturable absorber, modulator, polarizer, microwave signal processing, and broadband wireless access networks.
Nonlinear Kerr effect
Under intense laser illumination, graphene exhibits a nonlinear phase shift due to the optical nonlinear Kerr effect. Graphene demonstrates a large nonlinear Kerr coefficient of 10 cm⋅W, nearly nine orders of magnitude larger than that of bulk dielectrics, suggesting its potential as a powerful nonlinear Kerr medium capable of supporting various nonlinear effects, including solitons.
Excitonic properties
First-principle calculations incorporating quasiparticle corrections and many-body effects have been employed to study the electronic and optical properties of graphene-based materials. The approach was described as three stages. With GW calculation, the properties of graphene-based materials were accurately investigated, including bulk graphene, nanoribbons, edge and surface functionalized armchair ribbons, hydrogen saturated armchair ribbons, Josephson effect in graphene SNS junctions with single localized defect and armchair ribbon scaling properties.
Spin transport
Graphene is considered an ideal material for spintronics due to its minimal spin–orbit interaction, the near absence of nuclear magnetic moments in carbon, and weak hyperfine interaction. Electrical injection and detection of spin current have been demonstrated up to room temperature, with spin coherence length exceeding 1 micrometer observed at this temperature. Control of spin current polarity via electrical gating has been achieved at low temperatures.
Magnetic properties
Strong magnetic fields
Graphene's quantum Hall effect in magnetic fields above approximately 10 tesla reveals additional interesting features. Additional plateaus in Hall conductivity at with have been observed, along with plateau at and a fractional quantum Hall effect at .
These observations with indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis proposes that magnetic catalysis of symmetry breaking is responsible for this degeneracy lift.
Spintronic properties
Graphene exhibits spintronic and magnetic properties concurrently. Low-defect graphene Nano-meshes, fabricated using a non-lithographic approach, exhibit significant ferromagnetism even at room temperature. Additionally, a spin pumping effect has been observed with fields applied in parallel to the planes of few-layer ferromagnetic nano-meshes, while a magnetoresistance hysteresis loop is evident under perpendicular fields. Charge-neutral graphene has demonstrated magnetoresistance exceeding 100% in magnetic fields generated by standard permanent magnets (approximately 0.1 tesla), marking a record magneto resistivity at room temperature among known materials.
Magnetic substrates
In 2014 researchers magnetized graphene by placing it on an atomically smooth layer of magnetic yttrium iron garnet, maintaining graphene's electronic properties unaffected. Previous methods involved doping graphene with other substances. The dopant's presence negatively affected its electronic properties.
Mechanical properties
The (two-dimensional) density of graphene is 0.763 mg per square meter.
Graphene is the strongest material ever tested, with an intrinsic tensile strength of 130 GPa (19,000,000 psi) (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a Young's modulus (stiffness) close to 1 TPa (150,000,000 psi). The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a 4 kg cat but would weigh only as much as one of the cat's whiskers, at 0.77 mg (about 0.001% of the weight of 1 m of paper).
Large-angle bending of graphene monolayers with minimal strain demonstrates its mechanical robustness. Even under extreme deformation, monolayer graphene maintains excellent carrier mobility.
The spring constant of suspended graphene sheets has been measured using an atomic force microscope (AFM). Graphene sheets were suspended over SiO
2 cavities where an AFM tip was used to apply stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was 0.5 TPa, which differs from that of bulk graphite. These intrinsic properties could lead to applications such as NEMS as pressure sensors and resonators. Due to its large surface energy and out of plane ductility, flat graphene sheets are unstable with respect o scrolling, i.e. bending into a cylindrical shape, which is its lower-energy state.
In two-dimensional structures like graphene, thermal and quantum fluctuations cause relative displacement, with fluctuations growing logarithmically with structure size as per the Mermin–Wagner theorem. This shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene, and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure. These ripples, when amplified by vacancy defects, induce a negative Poisson's ratio into graphene, resulting in the thinnest auxetic material known so far.
Graphene-nickel (Ni) composites, created through plating processes, exhibit enhanced mechanical properties due to strong Ni-graphene interactions inhibiting dislocation sliding in the Ni matrix.
Fracture toughness
In 2014, researchers from Rice University and the Georgia Institute of Technology have indicated that despite its strength, graphene is also relatively brittle, with a fracture toughness of about 4 MPa√m. This indicates that imperfect graphene is likely to crack in a brittle manner like ceramic materials, as opposed to many metallic materials which tend to have fracture toughness in the range of 15–50 MPa√m. Later in 2014, the Rice team announced that graphene showed a greater ability to distribute force from an impact than any known material, ten times that of steel per unit weight. The force was transmitted at 22.2 kilometres per second (13.8 mi/s).
Polycrystalline graphene
Various methods – most notably, chemical vapor deposition (CVD), as discussed in the section below – have been developed to produce large-scale graphene needed for device applications. Such methods often synthesize polycrystalline graphene. The mechanical properties of polycrystalline graphene are affected by the nature of the defects, such as grain-boundaries (GB) and vacancies, present in the system and the average grain-size.
Graphene grain boundaries typically contain heptagon-pentagon pairs. The arrangement of such defects depends on whether the GB is in a zig-zag or armchair direction. It further depends on the tilt-angle of the GB. In 2010, researchers from Brown University computationally predicted that as the tilt-angle increases, the grain boundary strength also increases. They showed that the weakest link in the grain boundary is at the critical bonds of the heptagon rings. As the grain boundary angle increases, the strain in these heptagon rings decreases, causing the grain boundary to be stronger than lower-angle GBs. They proposed that, in fact, for sufficiently large angle GB, the strength of the GB is similar to pristine graphene. In 2012, it was further shown that the strength can increase or decrease, depending on the detailed arrangements of the defects. These predictions have since been supported by experimental evidence. In a 2013 study led by James Hone's group, researchers probed the elastic stiffness and strength of CVD-grown graphene by combining nano-indentation and high-resolution TEM. They found that the elastic stiffness is identical and strength is only slightly lower than those in pristine graphene. In the same year, researchers from University of California, Berkeley and University of California, Los Angeles probed bi-crystalline graphene with TEM and AFM. They found that the strength of grain boundaries indeed tends to increase with the tilt angle.
While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The consensus is that the strength decreases along with increasing densities of vacancies. Various studies have shown that for graphene with a sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, a high density of vacancies can severely reduce the strength of graphene.
Compared to the fairly well-understood nature of the effect that grain boundary and vacancies have on the mechanical properties of graphene, there is no clear consensus on the general effect that the average grain size has on the strength of polycrystalline graphene. In fact, three notable theoretical or computational studies on this topic have led to three different conclusions. First, in 2012, Kolakowski and Myer studied the mechanical properties of polycrystalline graphene with "realistic atomistic model", using molecular-dynamics (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected nucleation sites that are at least 5A (arbitrarily chosen) apart from other sites. Polycrystalline graphene was generated from these nucleation sites and was subsequently annealed at 3000K, and then quenched. Based on this model, they found that cracks are initiated at grain-boundary junctions, but the grain size does not significantly affect the strength. Second, in 2013, Z. Song et al. used MD simulations to study the mechanical properties of polycrystalline graphene with uniform-sized hexagon-shaped grains. The hexagon grains were oriented in various lattice directions and the GBs consisted of only heptagon, pentagon, and hexagonal carbon rings. The motivation behind such a model was that similar systems had been experimentally observed in graphene flakes grown on the surface of liquid copper. While they also noted that crack is typically initiated at the triple junctions, they found that as the grain size decreases, the yield strength of graphene increases. Based on this finding, they proposed that polycrystalline follows pseudo Hall-Petch relationship. Third, in 2013, Z. D. Sha et al. studied the effect of grain size on the properties of polycrystalline graphene, by modeling the grain patches using Voronoi construction. The GBs in this model consisted of heptagons, pentagons, and hexagons, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the aforementioned study, they found an inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases. Experimental observations and other theoretical predictions also gave differing conclusions, similar to the three given above. Such discrepancies show the complexity of the effects that grain size, arrangements of defects, and the nature of defects have on the mechanical properties of polycrystalline graphene.
Other properties
Thermal conductivity
Thermal transport in graphene is a burgeoning area of research, particularly for its potential applications in thermal management. Most experimental measurements have posted large uncertainties in the results of thermal conductivity due to the limitations of the instruments used. Following predictions for graphene and related carbon nanotubes, early measurements of the thermal conductivity of suspended graphene reported an exceptionally large thermal conductivity up to 5300 W⋅m⋅K, compared with the thermal conductivity of pyrolytic graphite of approximately 2000 W⋅m⋅K at room temperature. However, later studies primarily on more scalable but more defected graphene derived by Chemical Vapor Deposition have been unable to reproduce such high thermal conductivity measurements, producing a wide range of thermal conductivities between 1500 – 2500 W⋅m⋅K for suspended single-layer graphene. The large range in the reported thermal conductivity can be caused by large measurement uncertainties as well as variations in the graphene quality and processing conditions. In addition, it is known that when single-layer graphene is supported on an amorphous material, the thermal conductivity is reduced to about 500 – 600 W⋅m⋅K at room temperature as a result of scattering of graphene lattice waves by the substrate, and can be even lower for few-layer graphene encased in amorphous oxide. Likewise, polymeric residue can contribute to a similar decrease in the thermal conductivity of suspended graphene to approximately 500 – 600 W⋅m⋅K for bilayer graphene.
Isotopic composition, specifically the ratio of C to C, significantly affects graphene's thermal conductivity. Isotopically pure C graphene exhibits higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio. It can be shown by using the Wiedemann–Franz law, that the thermal conduction is phonon-dominated. However, for a gated graphene strip, an applied gate bias causing a Fermi energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.
Graphite, a 3D counterpart to graphene, exhibits a basal plane thermal conductivity exceeding 1000 W⋅m⋅K (similar to diamond), In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger lattice spacing. In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductance, per unit circumference, length of carbon nanotubes.
Graphene's thermal conductivity is influenced by its three acoustic phonon modes: two linear dispersion relation dispersion relation in-plane modes (LA, TA) and one quadratic dispersion relation out-of-plane mode (ZA). At low temperatures, the dominance of the T thermal conductivity contribution of the out-of-plane mode supersedes the T dependence of the linear modes. Some graphene phonon bands exhibit negative Grüneisen parameters, resulting in negative thermal expansion coefficient at low temperatures. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes, whose frequencies increase with in-plane lattice parameter, akin to a stretched string with higher frequency vibrations.
Chemical properties
Graphene has a theoretical specific surface area (SSA) of 2630 m/g. This is much larger than that reported to date for carbon black (typically smaller than 900 m/g) or for carbon nanotubes (CNTs), from ≈100 to 1000 m/g and is similar to activated carbon. Graphene is the only form of carbon (or solid material) in which every atom is available for chemical reaction from two sides (due to the 2D structure). Atoms at the edges of a graphene sheet have special chemical reactivity. Graphene has the highest ratio of edge atoms of any allotrope. Defects within a sheet increase its chemical reactivity. The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below 260 °C (530 K). Graphene burns at very low temperatures (e.g., 350 °C (620 K)). Graphene is commonly modified with oxygen- and nitrogen-containing functional groups and analyzed by infrared spectroscopy and X-ray photoelectron spectroscopy. However, the determination of structures of graphene with oxygen- and nitrogen- functional groups require the structures to be well controlled.
In 2013, Stanford University physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker multilayer sheets.
Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as hydrocarbons. Bombarded with pure carbon atoms, the atoms perfectly align into hexagons, filling the holes.
Biological properties
Despite the promising results in different cell studies and proof of concept studies, there is still incomplete understanding of the full biocompatibility of graphene-based materials. Different cell lines react differently when exposed to graphene, and it has been shown that the lateral size of the graphene flakes, the form and surface chemistry can elicit different biological responses on the same cell line.
There are indications that graphene has promise as a useful material for interacting with neural cells; studies on cultured neural cells show limited success.
Graphene also has some utility in osteogenesis. Researchers at the Graphene Research Centre at the National University of Singapore (NUS) discovered in 2011 the ability of graphene to accelerate the osteogenic differentiation of human mesenchymal stem cells without the use of biochemical inducers.
Graphene can be used in biosensors; in 2015, researchers demonstrated that a graphene-based sensor can be used to detect a cancer risk biomarker. In particular, by using epitaxial graphene on silicon carbide, they were repeatedly able to detect 8-hydroxydeoxyguanosine (8-OHdG), a DNA damage biomarker.
Support substrate
The electronic property of graphene can be significantly influenced by the supporting substrate. Studies of graphene monolayers on clean and hydrogen(H)-passivated silicon (100) (Si(100)/H) surfaces have been performed. The Si(100)/H surface does not perturb the electronic properties of graphene, whereas the interaction between the clean Si(100) surface and graphene changes the electronic states of graphene significantly. This effect results from the covalent bonding between C and surface Si atoms, modifying the π-orbital network of the graphene layer. The local density of states shows that the bonded C and Si surface states are highly disturbed near the Fermi energy.
Graphene layers and structural variants
Monolayer sheets
In 2013 a group of Polish scientists presented a production unit that allows the manufacture of continuous monolayer sheets. The process is based on graphene growth on a liquid metal matrix. The product of this process was called High Strength Metallurgical Graphene. In a new study published in Nature, the researchers have used a single-layer graphene electrode and a novel surface-sensitive non-linear spectroscopy technique to investigate the top-most water layer at the electrochemically charged surface. They found that the interfacial water response to the applied electric field is asymmetric concerning the nature of the applied field.
Bilayer graphene
Main article: Bilayer grapheneBilayer graphene displays the anomalous quantum Hall effect, a tunable band gap and potential for excitonic condensation –making it a promising candidate for optoelectronic and nanoelectronic applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene.
One way to synthesize bilayer graphene is via chemical vapor deposition, which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.
It has been shown that the two graphene layers can withstand important strain or doping mismatch which ultimately should lead to their exfoliation.
Turbostratic
Turbostratic graphene exhibits weak interlayer coupling, and the spacing is increased with respect to Bernal-stacked multilayer graphene. Rotational misalignment preserves the 2D electronic structure, as confirmed by Raman spectroscopy. The D peak is very weak, whereas the 2D and G peaks remain prominent. A rather peculiar feature is that the I2D/IG ratio can exceed 10. However, most importantly, the M peak, which originates from AB stacking, is absent, whereas the TS1 and TS2 modes are visible in the Raman spectrum. The material is formed through conversion of non-graphenic carbon into graphenic carbon without providing sufficient energy to allow for the reorganization through annealing of adjacent graphene layers into crystalline graphitic structures.
Graphene superlattices
Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities for designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms. The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction.
A superlattice corresponds to a periodic or quasi-periodic arrangement of different materials and can be described by a superlattice period which confers a new translational symmetry to the system, impacting their phonon dispersions and subsequently their thermal transport properties. Recently, uniform monolayer graphene-hBN structures have been successfully synthesized via lithography patterning coupled with chemical vapor deposition (CVD). Furthermore, superlattices of graphene-HBN are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport.
Nanostructured graphene forms
Graphene nanoribbons
Graphene nanoribbons ("nanostripes" in the "zig-zag"/"zigzag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of spintronics. (In the "armchair" orientation, the edges behave like semiconductors.)
Graphene quantum dots
A graphene quantum dot (GQD) is a graphene fragment with a size lesser than 100 nm. The properties of GQDs are different from bulk graphene due to the quantum confinement effects which only become apparent when the size is smaller than 100 nm.
Modified and functionalized graphene
Main article: Graphene chemistryGraphene oxide
Further information: Graphite oxideGraphene oxide is usually produced through chemical exfoliation of graphite. A particularly popular technique is the improved Hummers' method. Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called graphene oxide paper, have a measured tensile modulus of 32 GPa. The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the polymerization pathway and similar chemical processes. Graphene oxide flakes in polymerss display enhanced photo-conducting properties. Graphene is normally hydrophobic and impermeable to all gases and liquids (vacuum-tight). However, when formed into a graphene oxide-based capillary membrane, both liquid water and water vapor flow through as quickly as if the membrane were not present.
In 2022, researchers evaluated the biological effects of low doses on graphene oxide on larvae and imago of Drosophila melanogaster. Results show that oral administration of graphene oxide at concentrations of 0.02-1% has a beneficial effect on the developmental rate and hatching ability of larvae. Long-term administration of a low dose of graphene oxide extends the lifespan of Drosophila and significantly enhances resistance to environmental stresses. These suggest that graphene oxide affects carbohydrate and lipid metabolism in adult Drosophila. These findings might provide a useful reference to assess the biological effects of graphene oxide, which could play an important role in a variety of graphene-based biomedical applications.
Chemical modification
Soluble fragments of graphene can be prepared in the laboratory through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and nitric acid. A series of oxidation and exfoliation steps produce small graphene plates with carboxyl groups at their edges. These are converted to acid chloride groups by treatment with thionyl chloride; next, they are converted to the corresponding graphene amide via treatment with octadecyl amine. The resulting material (circular graphene layers of 5.3 Å or 5.3×10 m thickness) is soluble in tetrahydrofuran, tetrachloromethane and dichloroethane.
Refluxing single-layer graphene oxide (SLGO) in solvents leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependent on their preparation methodology. When using thionyl chloride, acyl chloride groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.
Hydrazine reflux is commonly used for reducing SLGO to SLG(R), but titrations show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with hydrochloric acid (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with carbodiimides leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (c. 3–5% conversion of the intermediate to the final amide). It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reaction types have been explored. SLGO has also been grafted with polyallylamine, cross-linked through epoxy groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.
Full hydrogenation from both sides of the graphene sheet results in Graphane, but partial hydrogenation leads to hydrogenated graphene. Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to fluorographene (graphene fluoride), while partial fluorination (generally halogenation) provides fluorinated (halogenated) graphene.
Graphene ligand/complex
Graphene can be a ligand to coordinate metals and metal ions by introducing functional groups. Structures of graphene ligands are similar to e.g. metal-porphyrin complex, metal-phthalocyanine complex, and metal-phenanthroline complex. Copper and nickel ions can be coordinated with graphene ligands.
Advanced graphene structures
Graphene fiber
In 2011, researchers reported a novel yet simple approach to fabricating graphene fibers from chemical vapor deposition-grown graphene films. The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable surface tension. Flexible all-solid-state supercapacitors based on these graphene fibers were demonstrated in 2013.
In 2015, intercalating small graphene fragments into the gaps formed by larger, coiled graphene sheets, after annealing provided pathways for conduction, while the fragments helped reinforce the fibers. The resulting fibers offered better thermal and electrical conductivity and mechanical strength. Thermal conductivity reached 1,290 W/m/K (1,290 watts per metre per kelvin), while tensile strength reached 1,080 MPa (157,000 psi).
In 2016, kilometer-scale continuous graphene fibers with outstanding mechanical properties and excellent electrical conductivity were produced by high-throughput wet-spinning of graphene oxide liquid crystals followed by graphitization through a full-scale synergetic defect-engineering strategy. The graphene fibers with superior performances promise wide applications in functional textiles, lightweight motors, microelectronic devices, etc.
Tsinghua University in Beijing, led by Wei Fei of the Department of Chemical Engineering, claims to be able to create a carbon nanotube fiber that has a tensile strength of 80 GPa (12,000,000 psi).
3D graphene
In 2013, a three-dimensional honeycomb of hexagonally arranged carbon was termed 3D graphene, and self-supporting 3D graphene was also produced. 3D structures of graphene can be fabricated by using either CVD or solution-based methods. A 2016 review by Khurram and Xu et al. provided a summary of then-state-of-the-art techniques for fabrication of the 3D structure of graphene and other related two-dimensional materials. In 2013, researchers at Stony Brook University reported a novel radical-initiated crosslinking method to fabricate porous 3D free-standing architectures of graphene and carbon nanotubes using nanomaterials as building blocks without any polymer matrix as support. These 3D graphenes (all-carbon) scaffolds/foams have applications in several fields such as energy storage, filtration, thermal management, and biomedical devices and implants.
Box-shaped graphene (BSG) nanostructure appearing after mechanical cleavage of pyrolytic graphite was reported in 2016. The discovered nanostructure is a multilayer system of parallel hollow nanochannels located along the surface and having quadrangular cross-section. The thickness of the channel walls is approximately equal to 1 nm. Potential fields of BSG application include ultra-sensitive detectors, high-performance catalytic cells, nanochannels for DNA sequencing and manipulation, high-performance heat sinking surfaces, rechargeable batteries of enhanced performance, nanomechanical resonators, electron multiplication channels in emission Nano-electronic devices, high-capacity sorbents for safe hydrogen storage.
Three dimensional bilayer graphene has also been reported.
Pillared graphene
Main article: Pillared graphenePillared graphene is a hybrid carbon, structure consisting of an oriented array of carbon nanotubes connected at each end to a sheet of graphene. It was first described theoretically by George Froudakis and colleagues at the University of Crete in Greece in 2008. Pillared graphene has not yet been synthesized in the laboratory, but it has been suggested that it may have useful electronic properties, or as a hydrogen storage material.
Reinforced graphene
Graphene reinforced with embedded carbon nanotube reinforcing bars ("rebar") is easier to manipulate, while improving the electrical and mechanical qualities of both materials.
Functionalized single- or multi-walled carbon nanotubes are spin-coated on copper foils and then heated and cooled, using the nanotubes themselves as the carbon source. Under heating, the functional carbon groups decompose into graphene, while the nanotubes partially split and form in-plane covalent bonds with the graphene, adding strength. π–π stacking domains add more strength. The nanotubes can overlap, making the material a better conductor than standard CVD-grown graphene. The nanotubes effectively bridge the grain boundaries found in conventional graphene. The technique eliminates the traces of substrate on which later-separated sheets were deposited using epitaxy.
Stacks of a few layers have been proposed as a cost-effective and physically flexible replacement for indium tin oxide (ITO) used in displays and photovoltaic cells.
Molded graphene
In 2015, researchers from the University of Illinois at Urbana-Champaign (UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene. A film of graphene that had been soaked in solvent to make it swell and become malleable was overlaid on an underlying substrate "former". The solvent evaporated over time, leaving behind a layer of graphene that had taken on the shape of the underlying structure. In this way, they were able to produce a range of relatively intricate micro-structured shapes. Features vary from 3.5 to 50 μm. Pure graphene and gold-decorated graphene were each successfully integrated with the substrate.
Specialized graphene configurations
Graphene aerogel
An aerogel made of graphene layers separated by carbon nanotubes was measured at 0.16 milligrams per cubic centimeter. A solution of graphene and carbon nanotubes in a mold is freeze-dried to dehydrate the solution, leaving the aerogel. The material has superior elasticity and absorption. It can recover completely after more than 90% compression, and absorb up to 900 times its weight in oil, at a rate of 68.8 grams per second.
Graphene nanocoil
In 2015, a coiled form of graphene was discovered in graphitic carbon (coal). The spiraling effect is produced by defects in the material's hexagonal grid that causes it to spiral along its edge, mimicking a Riemann surface, with the graphene surface approximately perpendicular to the axis. When voltage is applied to such a coil, current flows around the spiral, producing a magnetic field. The phenomenon applies to spirals with either zigzag or armchair patterns, although with different current distributions. Computer simulations indicated that a conventional spiral inductor of 205 microns in diameter could be matched by a nanocoil just 70 nanometers wide, with a field strength reaching as much as 1 tesla.
The nano-solenoids analyzed through computer models at Rice University should be capable of producing powerful magnetic fields of about 1 tesla, about the same as the coils found in typical loudspeakers, according to Yakobson and his team – and about the same field strength as some MRI machines. They found the magnetic field would be strongest in the hollow, nanometer-wide cavity at the spiral's center.
A solenoid made with such a coil behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear inductance.
Crumpled graphene
In 2016, Brown University introduced a method for "crumpling" graphene, adding wrinkles to the material on a nanoscale. This was achieved by depositing layers of graphene oxide onto a shrink film, then shrunken, with the film dissolved before being shrunken again on another sheet of film. The crumpled graphene became superhydrophobic, and when used as a battery electrode, the material was shown to have as much as a 400% increase in electrochemical current density.
Mechanical synthesis
Main article: Graphene production techniquesA rapidly increasing list of production techniques have been developed to enable graphene's use in commercial applications.
Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of phonon density with increasing lateral size forces 2D crystallites to bend into the third dimension. In all cases, graphene must bond to a substrate to retain its two-dimensional shape.
Bottom-up and top-down methods
Small graphene structures, such as graphene quantum dots and nanoribbons, can be produced by "bottom-up" methods that assemble the lattice from organic molecule monomers (e. g. citric acid, glucose). "Top-down" methods, on the other hand, cut bulk graphite and graphene materials with strong chemicals (e. g. mixed acids).
Micro-mechanical cleavage
The most famous, clean and rather straight-forward method of isolating graphene sheets, called micro-mechanical cleavage or more colloquially called the scotch tape method, was introduced by Novoselov et al. in 2004, which uses adhesive tape to mechanically cleave high-quality graphite crystals into successively thinner platelets. Other methods do exist like exfoliation.
Exfoliation techniques
Mechanical exfoliation
Geim and Novoselov initially used adhesive tape to pull graphene sheets away from graphite. Achieving single layers typically requires multiple exfoliation steps. After exfoliation, the flakes are deposited on a silicon wafer. Crystallites larger than 1 mm and visible to the naked eye can be obtained.
As of 2014, exfoliation produced graphene with the lowest number of defects and highest electron mobility. Alternatively, a sharp single-crystal diamond wedge can penetrate onto the graphite source to cleave layers. In the same year, defect-free, unoxidized graphene-containing liquids were made from graphite using mixers that produce local shear rates greater than 10×10.
Shear exfoliation is another method in which by using a rotor-stator mixer the scalable production of defect-free graphene has become possible. It has been shown that, as turbulence is not necessary for mechanical exfoliation, ResonantAcoustic mixing or low speed ball milling is effective in the production of high-yield and water-soluble graphene.
Liquid phase exfoliation
Liquid phase exfoliation (LPE) is a relatively simple method that involves dispersing graphite in a liquid medium to produce graphene by sonication or high shear mixing, followed by centrifugation. Restacking is an issue with this technique unless solvents with appropriate surface energy are used (e.g. NMP). Adding a surfactant to a solvent prior to sonication prevents restacking by adsorbing to the graphene's surface. This produces a higher graphene concentration, but removing the surfactant requires chemical treatments.
LPE results in nanosheets with a broad size distribution and thicknesses roughly in the range of 1-10 monolayers. However, liquid cascade centrifugation can be used to size-select the suspensions and achieve monolayer enrichment.
Sonicating graphite at the interface of two immiscible liquids, most notably heptane and water, produced macro-scale graphene films. The graphene sheets are adsorbed to the high-energy interface between the materials and are kept from restacking. The sheets are up to about 95% transparent and conductive.
With definite cleavage parameters, the box-shaped graphene (BSG) nanostructure can be prepared on graphite crystal. A major advantage of LPE is that it can be used to exfoliate many inorganic 2D materials beyond graphene, e.g. BN, MoS2, WS2.
Exfoliation with supercritical carbon dioxide
Liquid-phase exfoliation can also be done by a less-known process of intercalating supercritical carbon dioxide (scCO2) into the interstitial spaces in the graphite lattice, followed by rapid depressurization. The scCO2 intercalates easily inside the graphite lattice at a pressure of roughly 100 atm. Carbon dioxide turns gaseous as soon as the vessel is depressurized and makes the graphite explode into few-layered graphene.
This method may have multiple advantages: being non-toxic, the graphite does not have to be chemically treated in any way before the process, and the whole process can be completed in a single step as opposed to other exfoliation methods.
Splitting monolayer carbon allotropes
Graphene can be created by opening carbon nanotubes by cutting or etching. In one such method, multi-walled carbon nanotubes were cut open in solution by action of potassium permanganate and sulfuric acid. In 2014, carbon nanotube-reinforced graphene was made via spin coating and annealing functionalized carbon nanotubes.
Another approach sprays buckyballs at supersonic speeds onto a substrate. The balls cracked open upon impact, and the resulting unzipped cages then bond together to form a graphene film.
Chemical synthesis
Graphite oxide reduction
P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962. Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes.
Another method is the reduction of graphite oxide monolayer films, e.g. by hydrazine with annealing in argon/hydrogen with an almost intact carbon framework that allows efficient removal of functional groups. Measured charge carrier mobility exceeded 1,000 cm/Vs (10 m/Vs).
Burning a graphite oxide coated DVD produced a conductive graphene film (1,738 siemens per meter) and specific surface area (1,520 square meters per gram) that was highly resistant and malleable.
A dispersed reduced graphene oxide suspension was synthesized in water by a hydrothermal dehydration method without using any surfactant. The approach is facile, industrially applicable, environmentally friendly, and cost-effective. Viscosity measurements confirmed that the graphene colloidal suspension (graphene nanofluid) exhibits Newtonian behavior, with the viscosity showing a close resemblance to that of water.
Molten salts
Graphite particles can be corroded in molten salts to form a variety of carbon nanostructures including graphene. Hydrogen cations, dissolved in molten lithium chloride, can be discharged on cathodically-polarized graphite rods, which then intercalate, peeling graphene sheets. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability.
Electrochemical synthesis
Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, and number of defects and affects its properties. The process begins by bathing the graphite in a solvent for intercalation. The process can be tracked by monitoring the solution's transparency with an LED and photodiode.
Hydrothermal self-assembly
Graphene has been prepared by using a sugar like glucose, fructose, etc. This substrate-free "bottom-up" synthesis is safer, simpler and more environmentally friendly than exfoliation. The method can control the thickness, ranging from monolayer to multilayer, which is known as the "Tang-Lau Method".
Sodium ethoxide pyrolysis
Gram-quantities were produced by the reaction of ethanol with sodium metal, followed by pyrolysis and washing with water.
Microwave-assisted oxidation
In 2012, microwave energy was reported to directly synthesize graphene in one step. This approach avoids use of potassium permanganate in the reaction mixture. It was also reported that by microwave radiation assistance, graphene oxide with or without holes can be synthesized by controlling microwave time. Microwave heating can dramatically shorten the reaction time from days to seconds.
Graphene can also be made by microwave assisted hydrothermal pyrolysis.
Thermal decomposition of silicon carbide
Heating silicon carbide (SiC) to high temperatures (1100 °C) under low pressures (c. 10 torr, or 10 Pa) reduces it to graphene.
Vapor deposition and growth techniques
Chemical vapor deposition
Epitaxy
Epitaxial graphene growth on silicon carbide is a wafer-scale technique to produce graphene. Epitaxial graphene may be coupled to surfaces weakly enough (by the active valence electrons that create Van der Waals forces) to retain the two-dimensional electronic band structure of isolated graphene.
A normal silicon wafer coated with a layer of germanium (Ge) dipped in dilute hydrofluoric acid strips the naturally forming germanium oxide groups, creating hydrogen-terminated germanium. CVD can coat that with graphene.
The direct synthesis of graphene on insulator TiO2 with high-dielectric-constant (high-κ). A two-step CVD process is shown to grow graphene directly on TiO2 crystals or exfoliated TiO2 nanosheets without using any metal catalyst.
Metal substrates
CVD graphene can be grown on metal substrates including ruthenium, iridium, nickel and copper.
Roll-to-roll
In 2014, a two-step roll-to-roll manufacturing process was announced. The first roll-to-roll step produces the graphene via chemical vapor deposition. The second step binds the graphene to a substrate.
Cold wall
Growing graphene in an industrial resistive-heating cold wall CVD system was claimed to produce graphene 100 times faster than conventional CVD systems, cut costs by 99%, and produce material with enhanced electronic qualities.
Wafer scale CVD graphene
CVD graphene is scalable and has been grown on deposited Cu thin film catalyst on 100 to 300 mm standard Si/SiO2 wafers on an Axitron Black Magic system. Monolayer graphene coverage of >95% is achieved on 100 to 300 mm wafer substrates with negligible defects, confirmed by extensive Raman mapping.
Solvent interface trapping method (SITM)
As reported by a group led by D. H. Adamson, graphene can be produced from natural graphite while preserving the integrity of the sheets using the solvent interface trapping method (SITM). SITM uses a high-energy interface, such as oil and water, to exfoliate graphite to graphene. Stacked graphite delaminates, or spreads, at the oil/water interface to produce few-layer graphene in a thermodynamically favorable process in much the same way as small molecule surfactants spread to minimize the interfacial energy. In this way, graphene behaves like a 2D surfactant. SITM has been reported for a variety of applications such conductive polymer-graphene foams, conductive polymer-graphene microspheres, conductive thin films and conductive inks.
Carbon dioxide reduction
A highly exothermic reaction combusts magnesium in an oxidation-reduction reaction with carbon dioxide, producing carbon nanoparticles including graphene and fullerenes.
Supersonic spray
Supersonic acceleration of droplets through a Laval nozzle was used to deposit reduced graphene oxide on a substrate. The energy of the impact rearranges those carbon atoms into flawless graphene.
Laser
In 2014, a CO
2 infrared laser was used to produce patterned porous three-dimensional laser-induced graphene (LIG) film networks from commercial polymer films. The resulting material exhibits high electrical conductivity and surface area. The laser induction process is compatible with roll-to-roll manufacturing processes. A similar material, laser-induced graphene fibers (LIGF), was reported in 2018.
Flash Joule heating
In 2019, flash Joule heating (transient high-temperature electrothermal heating) was discovered to be a method to synthesize turbostratic graphene in bulk powder form. The method involves electrothermally converting various carbon sources, such as carbon black, coal, and food waste into micron-scale flakes of graphene. More recent works demonstrated the use of mixed plastic waste, waste rubber tires, and pyrolysis ash as carbon feedstocks. The graphenization process is kinetically controlled, and the energy dose is chosen to preserve the carbon in its graphenic state (excessive energy input leads to subsequent graphitization through annealing).
Ion implantation
Accelerating carbon ions inside an electrical field into a semiconductor made of thin nickel films on a substrate of SiO2/Si, creates a wafer-scale (4 inches (100 mm)) wrinkle/tear/residue-free graphene layer at a relatively low temperature of 500 °C.
CMOS-compatible graphene
Integration of graphene in the widely employed CMOS fabrication process demands its transfer-free direct synthesis on dielectric substrates at temperatures below 500 °C. At the IEDM 2018, researchers from University of California, Santa Barbara, demonstrated a novel CMOS-compatible graphene synthesis process at 300 °C suitable for back-end-of-line (BEOL) applications. The process involves pressure-assisted solid-state diffusion of carbon through a thin-film of metal catalyst. The synthesized large-area graphene films were shown to exhibit high quality (via Raman characterization) and similar resistivity values when compared with high-temperature CVD synthesized graphene films of the same cross-section down to widths of 20 nm.
Simulation
In addition to experimental investigation of graphene and graphene-based devices, numerical modeling and simulation of graphene has also been an important research topic. The Kubo formula provides an analytic expression for the graphene's conductivity and shows that it is a function of several physical parameters including wavelength, temperature, and chemical potential. Moreover, a surface conductivity model, which describes graphene as an infinitesimally thin (two-sided) sheet with a local and isotropic conductivity, has been proposed. This model permits the derivation of analytical expressions for the electromagnetic field in the presence of a graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current.
Even though these analytical models and methods can provide results for several canonical problems for benchmarking purposes, many practical problems involving graphene, such as the design of arbitrarily shaped electromagnetic devices, are analytically intractable. With the recent advances in the field of computational electromagnetics (CEM), various accurate and efficient numerical methods have become available for analysis of electromagnetic field/wave interactions on graphene sheets and/or graphene-based devices. A comprehensive summary of computational tools developed for analyzing graphene-based devices/systems is proposed.
Graphene analogs
Graphene analogs (also referred to as "artificial graphene") are two-dimensional systems which exhibit similar properties to graphene. Graphene analogs have been studied intensively since the discovery of graphene in 2004. People try to develop systems in which the physics is easier to observe and manipulate than in graphene. In those systems, electrons are not always the particles that are used. They might be optical photons, microwave photons, plasmons, microcavity polaritons, or even atoms. Also, the honeycomb structure in which those particles evolve can be of a different nature than carbon atoms in graphene. It can be, respectively, a photonic crystal, an array of metallic rods, metallic nanoparticles, a lattice of coupled microcavities, or an optical lattice.
Applications
Main article: Potential applications of grapheneGraphene is a transparent and flexible conductor that holds great promise for various material/device applications, including solar cells, light-emitting diodes (LED), integrated photonic circuit devices, touch panels, and smart windows or phones. Smartphone products with graphene touch screens are already on the market.
In 2013, Head announced their new range of graphene tennis racquets.
As of 2015, there is one product available for commercial use: a graphene-infused printer powder. Many other uses for graphene have been proposed or are under development, in areas including electronics, biological engineering, filtration, lightweight/strong composite materials, photovoltaics and energy storage. Graphene is often produced as a powder and as a dispersion in a polymer matrix. This dispersion is supposedly suitable for advanced composites, paints and coatings, lubricants, oils and functional fluids, capacitors and batteries, thermal management applications, display materials and packaging, solar cells, inks and 3D-printer materials, and barriers and films.
On August 2, 2016, Briggs Automative Company's new Mono model is said to be made out of graphene as the first of both a street-legal track car and a production car.
In January 2018, graphene-based spiral inductors exploiting kinetic inductance at room temperature were first demonstrated at the University of California, Santa Barbara, led by Kaustav Banerjee. These inductors were predicted to allow significant miniaturization in radio-frequency integrated circuit applications.
The potential of epitaxial graphene on SiC for metrology has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in the encapsulation and doping of epitaxial graphene have led to the commercialization of epitaxial graphene quantum resistance standards.
Novel uses for graphene continue to be researched and explored. One such use is in combination with water-based epoxy resins to produce anticorrosive coatings. The van der Waals nature of graphene and other two-dimensional (2D) materials also permits van der Waals heterostructures and integrated circuits based on Van der Waals integration of 2D materials.
Graphene is utilized in detecting gasses and chemicals in environmental monitoring, developing highly sensitive biosensors for medical diagnostics, and creating flexible, wearable sensors for health monitoring. Graphene's transparency also enhances optical sensors, making them more effective in imaging and spectroscopy.
Toxicity
One review on graphene toxicity published in 2016 by Lalwani et al. summarizes the in vitro, in vivo, antimicrobial and environmental effects and highlights the various mechanisms of graphene toxicity. Another review published in 2016 by Ou et al. focused on graphene-family nanomaterials (GFNs) and revealed several typical mechanisms such as physical destruction, oxidative stress, DNA damage, inflammatory response, apoptosis, autophagy, and necrosis.
A 2020 study showed that the toxicity of graphene is dependent on several factors such as shape, size, purity, post-production processing steps, oxidative state, functional groups, dispersion state, synthesis methods, route and dose of administration, and exposure times.
In 2014, research at Stony Brook University showed that graphene nanoribbons, graphene nanoplatelets, and graphene nano–onions are non-toxic at concentrations up to 50 μg/ml. These nanoparticles do not alter the differentiation of human bone marrow stem cells towards osteoblasts (bone) or adipocytes (fat), suggesting that at low doses, graphene nanoparticles are safe for biomedical applications. In 2013, research at Brown University found that 10 μm few-layered graphene flakes can pierce cell membranes in solution. They were observed to enter initially via sharp and jagged points, allowing graphene to be internalized in the cell. The physiological effects of this remain unknown, and this remains a relatively unexplored field.
See also
- Borophene – Allotrope of boron
- Carbon fiber – Light, strong and rigid composite materialPages displaying short descriptions of redirect targets
- Penta-graphene – allotrope of carbonPages displaying wikidata descriptions as a fallback
- Phagraphene – proposed graphene allotropePages displaying wikidata descriptions as a fallback
- Plumbene – Material made up of a single layer of lead atoms
- Silicene – Two-dimensional allotrope of silicon
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External links
- Manchester's Revolutionary 2D Material at The University of Manchester
- Graphene at The Periodic Table of Videos (University of Nottingham)
- Graphene: Patent surge reveals global race
- 'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes' (PDF)
- Band structure of graphene (PDF).
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Molecules detected in outer space | ||||||||||||||||||||
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Molecules |
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Deuterated molecules | ||||||||||||||||||||
Unconfirmed | ||||||||||||||||||||
Related |
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