Simulation of a Non-Markovian process modelling contour length fluctuation in the Doi-Edwards model

Abstract

A new method for simulating stochastic processes with memory is introduced and applied to discuss the dynamics of polymers in concentrated solutions and melts. The motion of the polymers is described by reptation in a tube (Doi-Edwards model) including contour length fluctuations as introduced and treated approximately by Doi [1]. The resulting dynamics of the chain ends is given by a Non-Markovian stochastic process. In order to correct for the effects due to the discrete-time simulation and to discuss limiting cases it is necessary to understand the short-time scaling properties of such processes. The simulation results explain the empirical 3.4 power law for the molecular weight dependence of viscosity and longest relaxation time and confirm Doi's approximate results.