Concentration dependent friction coefficients of polymer molecules in dilute solutions. I

A cluster expansion theory is developed for the self- and cooperative-friction coefficients of polymer chains in the steady-state limit as a virial series in concentration. The derived equations are general and are valid for both good and theta solutions. The self- and cooperative-friction coefficients are shown to be the same in a theta solvent. As a test of the theory, the leading concentration dependence of the translational and rotational friction coefficients are calculated for θ solutions. Our results for the coefficient of concentration dependence of the translational friction coefficient is (ks)θ=0.75 [η] (where [η] is the intrinsic viscosity) in excellent agreement with the experimental data of Mulderije. The details of the explicit calculations are given in the following paper.