Estimation of Relaxation Modulus of Polymer Melts by Molecular Dynamics Simulations: Application of Relaxation Mode Analysis

Abstract

A framework for estimating the linear relaxation modulus of polymer melts by molecular dynamics (MD) simulations is presented on the basis of relaxation mode analysis (RMA). Conventional calculations of the relaxation modulus based on the Green–Kubo formula are computationally very expensive owing to long relaxation times and poor convergence of stress autocorrelation functions: In practice, reliable calculations usually require a time average over \(\mathcal{O}(10\tau _{1}{\text{--}}100\tau _{1})\), where τ1 is the longest relaxation time of a chain in the melt. RMA is a method that systematically extracts relaxation modes and rates of a polymer chain from the time correlation functions of coordinates of polymer segments. In the present method, the relaxation modulus is evaluated by fitting the data of the stress autocorrelation functions to the generalized Maxwell model whose relaxation times are determined from the relaxation rate spectrum obtained by RMA. It is demonstrated that the stress relaxation modulus of a polymer melt is well estimated by the present method over a wide range of time scales from MD simulations of length \(\mathcal{O}(1\tau _{1}{\text{--}}10\tau _{1})\).