A simple model for dynamic heterogeneity in glass-forming liquids

TL;DR

This paper introduces a simple continuum model that predicts dynamical heterogeneity in glass-forming liquids, showing strong agreement with numerical simulations and providing insights into heterogeneity lifetime effects.

Contribution

The paper presents a new continuum model for dynamic heterogeneity in glass-forming liquids, enabling quantitative predictions of fluctuation correlators and analysis of heterogeneity lifetime effects.

Findings

Model predictions match numerical results for $ ext{chi}_4(t)$

Heterogeneity lifetime $ au_{ex}$ influences decay, not peak position

Method to estimate heterogeneity lifetime from decay behavior

Abstract

Liquids near the glass transition exhibit dynamical heterogeneity, i.e. local relaxation rates fluctuate strongly over space and time. Here we introduce a simple continuum model that allows for quantitative predictions for the correlators describing these fluctuations. We find remarkable agreement of the model predictions for the dynamic susceptibility $\chi_4(t)$ with numerical results for a binary hard-sphere liquid and for a Kob-Andersen Lennard-Jones mixture. Under this model, the lifetime $\tau_{\rm ex}$ of the heterogeneities has little effect on the position $t = t_4 \sim \tau_{\alpha}$ of the peak of $\chi_4(t)$, but it controls the decay of $\chi_4(t)$ after the peak, and we show how to estimate it from this decay.