Relaxation Dynamics of Entangled Linear Polymer Melts via Molecular Dynamics Simulations

TL;DR

This paper uses molecular dynamics simulations to analyze the relaxation dynamics of entangled linear polymer melts, comparing results with theoretical models and revealing the significant role of constraint release in relaxation mechanisms.

Contribution

It provides detailed simulation data on polymer relaxation, tests theoretical predictions, and highlights the impact of constraint release on dynamic properties.

Findings

CLF shows a $t^{1/4}$ scaling regime that develops with chain length.

Proportionality between $S(q,t)$, $G(t)$, and $P(t)$ is not observed, indicating CR effects.

At late times, $G(t)$ approximately scales as $P(t)^2$, supporting double reptation models.

Abstract

We present an extensive analysis of the relaxation dynamics of entangled linear polymer melts via long-time molecular dynamics simulations of a generic bead-spring model. We study the mean-squared displacements, the autocorrelation function of the end-to-end vector, $P(t)$, the single-chain dynamic structure factor, $S(q,t)$, and the linear viscoelastic properties, especially the shear stress relaxation modulus, $G(t)$. The simulation data are compared with the theoretically expected scaling laws for different time regimes of entangled melts, and with analytical expressions that account for different relaxation mechanisms in the tube model, namely, reptation, contour length fluctuation (CLF), and constraint release (CR). CLF involves a $t^{1/4}$ scaling regime in the time-dependence of $(1-P(t))$. With increasing chain length, a gradual development of this scaling regime is observed. In the absence of CR, the tube model further predicts that at long times, the chain dynamics is governed by one central quantity, the ``surviving tube fraction'' $\mu(t)$. As a result, one expects $S(q,t) \propto G(t) \propto P(t)$ in that time regime. We test this prediction by comparing $S(q,t)$ and $G(t)$ with $P(t)$. For both quantities, proportionality with $P(t)$ is not observed, indicating that CR has an important effect on the relaxation of these two quantities. Instead, to a very good approximation, we find $G(t)\propto P(t)^{2}$ at late times, which is consistent with the dynamic tube dilation or double reptation approximations for the CR process. In addition, we calculate non-local mobility functions, which can be used in dynamic density functional theories for entangled inhomogeneous polymer blends, and discuss the effect of entanglements on the shape of these functions.