Journal of Rheology, Vol.49, No.5, 1117-1128, 2005
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 lambda-phage DNA over a range of semidilute concentrations. We found that all experimental data above a critical concentration c/c(e)>0.5 fall on a single empirical curve given by eta(p)/eta(Rouse)=(45 +/- 2) x (c/c(e))(2.95 +/- 0.07) and this scaling law is in good agreement with the theoretical one, eta(p)/eta(Rouse)approximate to(c/c(e))(2.4/(3 nu-1)) with v the excluded volume exponent, eta(p)=eta(0)-eta(s) the polymer contribution to the zero shear viscosity of the solution with eta(0) the zero-shear viscosity and eta(s) the solvent viscosity, eta(Rouse) the hypothetical Rouse polymer viscosity, and c(e) 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. (C) 2005 The Society of Rheology.