A simple nonlinear equation for structural relaxation in glasses

TL;DR

This paper introduces a simple nonlinear rate equation to model the complex, non-exponential structural relaxation in glasses, capturing temperature and history dependence and suggesting cooperative rearrangements.

Contribution

It proposes a new nonlinear rate equation for glass relaxation that accounts for history dependence and cooperative dynamics, improving understanding of aging in disordered materials.

Findings

The equation accurately fits extensive experimental relaxation data.

Relaxation parameters depend on temperature and history.

Evidence suggests cooperative rearrangements on a super-molecular scale.

Abstract

A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation d\delta/dt = a [1-exp (b\delta)], where '\delta' is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where 'a' and 'b' are both temperature-, and more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single non-equilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a super-molecular scale.