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In polymer science, inherent viscosity is the ratio of the natural logarithm of the relative viscosity of a polymer to its mass concentration. Inherent viscosity scales inversely to mass density, and a common unit is dL/g.

Inherent viscosity is defined as $${\displaystyle \eta _{inh}={\frac {\ln \eta _{rel}}{c}}}$$ where ${\textstyle c}$ is the mass concentration of the polymer and ${\textstyle \eta _{rel}}$ is the relative viscosity, which is defined as $${\displaystyle \eta _{rel}={\frac {\eta }{\eta _{s}}}}$$ where ${\textstyle \eta }$ is the viscosity of the solution and ${\textstyle \eta _{s}}$ is the viscosity of the solvent.

The definition of ${\textstyle \eta _{\text{inh}}}$ is a finite difference approximation to the derivative $${\displaystyle \left.{\frac {d(\ln(\eta ))}{dc}}\right|_{c=0}}$$ That ideal limiting value is the intrinsic viscosity, which is a good measure of the polymerization degree.

References

1. "Dilute Solution Viscosity of Polymers".
2. "IUPAC". doi:10.1351/goldbook.I03033.
3. Hester, Roger (2001). "Molecular Weight Determination By Dilute Solution Viscosity Measurements". Macrolab. University of Southern Mississippi.
4. Osuji 2009, §1.3: Intrinsic viscosity determination.
5. Osuji, Chinedum (February 5, 2009). "Size and Mass Characterization - Non Scattering (notes for ENAS 606: Polymer Physics)". Osuji lab. Yale University. §1.2.1: Intrinsic viscosity. Note that there are several typos in Osuji's displays, including an extra "c" in equation (7; §1.3); and a missing logarithm in the initial definition of inherent viscosity (§1.1).
6. "Reference: Polymer Properties" (PDF). Sigma-Aldrich. p. 51.

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