Growth of Dynamic and Static Correlations in the Aging Dynamics of a Glass-Forming Liquid

TL;DR

This study uses molecular dynamics simulations to analyze how static and dynamic correlation lengths grow with waiting time during the aging process of a glass-forming liquid, revealing non-monotonic finite-size effects and growth patterns.

Contribution

It introduces a finite-size scaling approach to quantify the growth of static and dynamic correlation lengths during aging in glass-forming liquids, a novel analysis not previously reported.

Findings

Static length scale grows logarithmically with waiting time.

Dynamic length scale follows a power-law growth with waiting time.

Finite-size effects show a peak at intermediate system sizes.

Abstract

Using extensive molecular dynamics simulations, we have performed finite-size scaling (FSS) in the aging regime of a model glass-forming liquid to investigate how the length scales associated with amorphous order (static length) and dynamic heterogeneity (dynamic length) evolve with waiting time. The $\alpha$-relaxation time in the aging regime reveals non-monotonic finite-size effects with a peak at an intermediate system size, which, as far as we know, are not found in the equilibrium systems, and the peak position shifts to larger system sizes with decreasing temperature and increasing waiting time, indicating a growth of a characteristic length scale with waiting time. The extracted correlation volume associated with amorphous order increases logarithmically with the waiting time. Detailed analysis of the dependence of the length scale on waiting time allowed us to estimate the static length scale in the deep supercooled liquid regime. The dynamic length scale, obtained from FSS and block analysis of the four-point dynamic susceptibility, follows a power-law growth with waiting time. The values of the length scales obtained agree well with those obtained from different spatial correlation functions.