The scaling of zero-shear viscosities of semidilute polymer solutions with concentration

To test the universality of the dependence of zero-shear viscosity on concentration for both flexible and locally semiflexible polymers in good solvents, we collected multiple literature data sets and measured the zero shear viscosity of $λ$-phage DNA over a range of semidilute concentrations. We found that all experimental data above a critical concentration $c∕ce>0.5$ fall on a single empirical curve given by $ηp∕ηRouse=(45±2)×(c∕ce)2.95±0.07$ and this scaling law is in good agreement with the theoretical one, $ηp∕ηRouse≈(c∕ce)2.4∕(3ν−1)$ with $ν$ the excluded volume exponent, $ηp=η0−ηs$ the polymer contribution to the zero shear viscosity of the solution with $η0$ the zero-shear viscosity and $ηs$ the solvent viscosity, $ηRouse$ the hypothetical Rouse polymer viscosity, and $ce$ the entanglement concentration of the polymer solution (Menezes and Graessley, 1982; Raspaud et al., 1995; Osaki et al., 2001). This scaling law provides a basis for estimating viscosities for arbitrary semidilute entangled polymer solutions from a knowledge of the solvent viscosity, the entanglement molecular weight in the melt, the excluded volume exponent, the second virial coefficient, and the intrinsic viscosity.