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

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Abstract
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 ∕ c e > 0.5 fall on a single empirical curve given by η p ∕ η Rouse = ( 45 ± 2 ) × ( c ∕ c e ) 2.95 ± 0.07 and this scaling law is in good agreement with the theoretical one, η p ∕ η Rouse ≈ ( c ∕ c e ) 2.4 ∕ ( 3 ν − 1 ) with ν the excluded volume exponent, η p = η 0 − η s the polymer contribution to the zero shear viscosity of the solution with η 0 the zero-shear viscosity and η s the solventviscosity, η Rouse the hypothetical Rouse polymerviscosity, 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 solventviscosity, the entanglement molecular weight in the melt, the excluded volume exponent, the second virial coefficient, and the intrinsic viscosity.