Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids

TL;DR

This study introduces a multi-time correlation approach to uncover hidden time scales in the heterogeneous dynamics of glass-forming liquids, revealing couplings over broad time scales and a scaling relation between heterogeneity size and dynamics.

Contribution

It presents a novel multi-time correlation method to analyze heterogeneous dynamics and establishes a dynamical scaling relation in glass-forming liquids.

Findings

Heterogeneous dynamics exhibit couplings over a wide range of time scales.

The heterogeneity time scale exceeds the alpha-relaxation time at low temperatures.

A scaling relation $ au_{hetero} \,\sim\, \xi^{3}$ is identified between time and length scales.

Abstract

A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics $\tau_{\rm hetero}$ is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics $\tau_{\rm hetero}$ becomes larger than the $\alpha$-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale $\tau_{\rm hetero}$ and the length scale $\xi$ of dynamical heterogeneity as $\tau_{\rm hetero} \sim \xi^{z}$ with $z=3$.