Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations

TL;DR

This study systematically analyzes multi-point and multi-time correlations in model glass-forming liquids through molecular dynamics simulations, revealing how dynamic heterogeneities grow and persist at different scales and models as temperature decreases.

Contribution

It introduces a comprehensive analysis of the spatio-temporal structures of dynamic heterogeneities using multi-point and multi-time correlations across various glass models.

Findings

Dynamic length scale grows with decreasing temperature.

Lifetime of heterogeneities exceeds alpha relaxation time in fragile liquids.

Decoupling of time scales varies with liquid fragility.

Abstract

We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob-Andersen, Wahnstrom, soft-sphere, and network-forming liquids. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to a three-time correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies. We provide comprehensive numerical results obtained from the three-time correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the alpha relaxation time determined from a two-point correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the alpha-relaxation time in tetrahedral network-forming strong liquid, even at lower temperatures.