Numerical determination of shear stress relaxation modulus of polymer glasses

TL;DR

This paper validates a simple-average method for accurately computing the shear stress relaxation modulus in simulated polymer glasses below the glass transition, especially when traditional auto-correlation methods fail.

Contribution

It demonstrates the effectiveness of the $G(t) =  - h(t)$ expression for polymer glasses, providing a reliable alternative to auto-correlation-based calculations in sluggish systems.

Findings

The simple-average expression accurately determines $G(t)$ in polymer glasses.

Auto-correlation methods become unreliable below the glass transition.

The proposed method is particularly useful for systems with quenched shear stresses.

Abstract

Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression $G(t) = \mu_A - h(t)$ for the computational determination of the shear stress relaxation modulus $G(t)$. Here, $\mu_A = G(0)$ characterizes the affine shear transformation of the system at $t=0$ and $h(t)$ the mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the glass transition. The commonly accepted relation $G(t)=c(t)$ using the shear stress auto-correlation function $c(t)$ becomes incorrect in this limit.