Frequency Dispersion of Sound Propagation in Rouse Polymer Melts via Generalized Dynamic Random Phase Approximation

TL;DR

This paper extends the dynamic random phase approximation to analyze sound propagation in Rouse polymer melts, revealing frequency-dependent dispersion and strong interchain interaction effects on relaxation times.

Contribution

It introduces a generalized DRPA for complex polymer systems, enabling detailed analysis of sound and dynamic form-factor propagation in Rouse melts.

Findings

Sound velocity and absorption show significant frequency dispersion.

Relaxation time is N times shorter than Rouse time, indicating strong dynamic screening.

New expression for the dynamic structural function of Rouse chains is proposed.

Abstract

An extended generalization of the dynamic random phase approximation (DRPA) for L-component polymer systems is presented. Unlike the original version of the DRPA, which relates the (LxL) matrices of the collective density-density time correlation fumctions and the corresponding susceptibilities of polymer concentrated systems to those of the tracer macromolecules and so-called broken links system (BLS), our generalized DRPA solves this problem for (5xL)x(5xL) matrices of the coupled susceptibilities and time correlation functions of the component number, kinetic energy and flux densities. The presented technique is used to study propagation of sound and dynamic form-factor in disentangled (Rouse) monodisperse homopolymer melt. The calculated sound velocity and absorption coefficient reveal substantial frequency dispersion. The relaxation time is found to be N times less than the Rouse time (N is the degree of polymerization), which evidences strong dynamic screening because of interchain interaction. We discuss also some peculiarities of the Brillouin scattering in polymer melts. Besides, a new convenient expression for the dynamic structural function of the Rouse chain in (q,p)-representation is found.