Timescale bridging in atomistic simulations of epoxy polymer mechanics using non-affine deformation theory

TL;DR

This paper employs non-affine lattice dynamics to connect atomistic simulations and experimental data, successfully bridging a vast timescale gap in understanding the viscoelastic behavior of epoxy polymers below the glass transition.

Contribution

It introduces a timescale bridging approach using NALD to predict polymer mechanics across many orders of magnitude in frequency, validated against simulations and experiments.

Findings

Non-affine displacements significantly reduce low-frequency elastic modulus.

Theoretical predictions match experimental data at ~1 Hz.

Internal stresses enhance the mechanical response of the polymer.

Abstract

Developing a deep understanding of macroscopic mechanical properties of amorphous systems which lack structural periodicity, has posed a key challenge, not only at the level of theory but also in molecular simulations. Despite significant advancements in computational resources, there is a vast timescale disparity, more than 6 orders of magnitude, between mechanical properties probed in simulations compared to experiments. Using the theoretical framework of non-affine lattice dynamics (NALD), based on the instantaneous normal modes analysis determined through the dynamical matrix of the system, we study the viscoelastic response of a cross-linked epoxy system of diglycidyl ether of bisphenol A (DGEBA) and poly(oxypropylene) diamine, over many orders of magnitude in deformation frequency, below the glass transition temperature. Predictions of the elastic modulus are satisfactorily validated against the non-equilibrium molecular dynamics simulations in the high-frequency regime, and against experimental data from dynamic mechanical analysis at frequencies $ \sim 1 {\rm Hz}$, hence successfully bridging the timescale gap. The comparison shows that non-affine displacements at the atomic level account for nearly two orders of magnitude reduction in the low-frequency elastic modulus of the polymer glass, compared to affine elasticity estimates. The analysis also reveals the role of internal stresses (as reflected in the instantaneous normal modes), which act as to strengthen the mechanical response.