Concentration dependence of the translational friction coefficient for polymer solutions

Abstract

A theory of the concentration dependence of the polymer translational friction coefficient f (and the sedimentation coefficient) is presented in terms of a multiple scattering representation of fluid scattering by the polymers in solution. The translational friction coefficient emerges as the the average T matrix for scattering of the fluid by the polymers, and the results of the Kirkwood–Riseman theory are recovered for the case of infinite dilution. The translational friction coefficient is evaluated under Θ conditions for concentrations equal to, or greater than, that of the semidilute region and for low but finite concentrations c, where f can be represented as a linear function of c via f=f₀(1+k_sc). The results obtained for k_s are in agreement with experiments on poly(α‐methylstyrene) and polystyrene in cyclohexane at their Θ temperatures. An explanation for the general increase in f (as well as the polymer viscosity), as c is raised, is provided in terms of the increased destruction of correlated intrachain scattering of fluid because of the intervention of uncorrelated fluid scatterings by other chains between the successive fluid scatterings by a given polymer.