A simple model for dynamic heterogeneity in glass-forming liquids

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 (HARD) liquid and for a Kob-Andersen Lennard-Jones (KALJ) mixture. We explain why the existence and position of the peak of $\chi_4(t)$ provides no information about the lifetime $\tau_{\rm ex}$ of the heterogeneities. We show that $\chi_4(t)$ depends weakly on $\tau_{\rm ex}$, but find a way to use this weak dependence to estimate $\tau_{\rm ex}$ from $\chi_4(t)$.Comment: Main text: 5 pages, 3 figures. Supplemental material: 2 pages, 1 figur