Conformation space renormalization of polymers. II. Single chain dynamics based on chain diffusion equation model

Abstract

A polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions. The method builds upon our chain configuration space equilibrium formulation which is based on a coarse graining procedure which utilized small chain contour length loop excluded volume interactions to define the renormalization procedure. This approach is generalized to include small loop hydrodynamic interactions within the renormalization scheme. Our coarse graining treatment is combined with the methods of Kawasaki and Gunton, designed to consider dynamical critical phenomena, to provide the chain configuration space renormalization group theory. Calculations are explicitly presented to order ε = 4−d, where d is the dimensionality of space. However, we show that the dynamical exponent can be obtained exactly from a consideration of the general renormalization scheme without the use of any ε expansion. Thus, it is demonstrated within the diffusion equation model that z = d with hydrodynamic interactions present. In the free draining limit z = 2+1/ν where ν is the exponent for the molecular weight dependence of the chain radius. In the non-free draining limit, this value of z justifies the equality of the so-called static and hydrodynamic radii exponents within the diffusion equation model.