Dynamic structure factor in a bidisperse polymer melt

Abstract

We present calculations of the single-chain dynamic structure factor for a polymer melt composed of linear molecules of the same chemical identity but of two different chain lengths. The fluid is treated within a dynamical mean-field approach, in which each molecule is represented as a freely jointed chain moving among stochastic obstacles. The obstacles are of two types, each representing the obstruction of local conformational changes by one of the species present. The obstacle dynamics are determined self-consistently by equating the relaxation rate of an obstacle of a given type to the smallest conformational relaxation rate of the species that it represents. Calculation of the dynamic structure factor is mapped onto the solution of a random walk with dynamical disorder, in which a walker moves on a one-dimensional lattice with hopping rates that randomly fluctuate among three states. The relevant random walk problem is solved within the effective medium approximation, and the results are employed to examine the dependence of the dynamic structure factor on time, wave vector, chain lengths, and fluid composition.