Calculation of the dynamic structure factor in polymer melts

Abstract

In this work, we present calculations of the dynamic structure factor for monodisperse melts of linear polymers. Our calculations are based on a model in which a freely jointed chain encounters fluctuating obstacles whose relaxation is self-consistently determined from that of the chain conformation. The calculation of the structure factor is related to the solution of a one-dimensional random walk with dynamical disorder, which is treated within the dynamical effective medium approximation. This model has been applied previously to the calculation of the self-diffusion coefficient and the mean-squared displacement of a chain segment. We present calculations of the structure factor over a wide range of wave vectors, times, and entanglement molecular weights. Our predictions are compared with calculations from the theories of Ronca and of de Gennes, and with the experimental results for polyethylene-butylene-2 obtained by Richter et al. from neutron spin echo measurements. Our calculations show semiquantitative agreement with the experimentally determined structure factors for the time range accessible to these experiments.