Corrections to preaveraging approximation within the Kirkwood–Riseman model for flexible polymers: Calculations to second order in ε with both hydrodynamic and excluded volume interactions

Abstract

The polymer hydrodynamic radius RH is calculated to second order in the ε=4−d (d is the dimension) perturbation theory using the Kirkwood–Riseman model in conjunction with the renormalization group. Excluded volume effects on RH are modeled by the two-parameter theory, and the hydrodynamic radius is evaluated both with and without the preaveraging approximation. These second order in ε calculations are then used to evaluate the leading corrections in ε to the preaveraging approximation for RH. Gaussian and self-avoiding chains in three dimensions yield nondraining limit preaveraging corrections of 26% and 16%, respectively, whereas simulations by Zimm and others using the same rigid body model of dynamics produce only about a 12% correction for Gaussian chains. It thus appears that the dynamical renormalization group theory only provides a qualitative prediction of the preaveraging error to this order in the ε-perturbation theory.