Physics:Inherent viscosity

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

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