Atomistic Framework for Glassy Polymer Viscoelasticity Across Twenty Frequency Decades

TL;DR

This paper develops an atomistic framework that accurately predicts the viscoelastic behavior of glassy polymers over twenty decades of frequency, bridging multiple experimental and computational methods.

Contribution

It introduces a time-dependent memory kernel into non-affine deformation theory, enabling multiscale frequency response predictions for polymer glasses.

Findings

Successfully predicts shear modulus and relaxation spectrum across 20+ frequency decades.

Shows quantitative agreement with various experimental and simulation techniques.

Provides a unified theoretical approach for multiscale polymer glass characterization.

Abstract

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a time-dependent memory kernel within the Generalized Langevin Equation for atomistic non-affine motions, yielding frequency-dependent mechanical response. Applied to poly(methyl methacrylate) (PMMA), the method captures the shear modulus and relaxation spectrum across more than twenty decades in frequency, from hundreds of terahertz to the millihertz regime, thus bridging polymer mechanics from ordinary to extreme scales. Our predictions show quantitative consistency with independent estimates from oscillatory-shear molecular dynamics, Brillouin scattering, ultrasonic spectroscopy, Split-Hopkinson testing, and dynamic mechanical analysis (DMA), demonstrating a unified theoretical-computational route for multiscale characterization of polymer glasses.