Dynamics in nonentangled concentrated polymers solutions. III. Exact calculations of the frequency dependent relaxation times and normal mode autocorrelation function to first order in concentrations

We investigate approximations to a full dynamical theory of the concentration dependence of the viscoelasticity of polymer solutions in order to alleviate the impediments which arise by virtue of the frequency dependence of the individual polymer mode relaxation rates within the effective medium theory. The problem is considered for the simplest situation under which these frequency dependences appear, namely, in the leading concentration correction for the dimensionless relaxation rates ? a(?). These ? a(?) are evaluated numerically for short chains by use of fast Fourier transform methods. The exact ? a(?) are compared with the previous static approximation and are used to calculate the concentration dependent normal mode autocorrelation function Z a(?). The steady state ? a(?) provide an average relaxation rate approximation to Z a(?) with a form in good agreement with low concentration viscoelastic data.