Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor and correlation length

TL;DR

This study examines the growth of dynamic heterogeneity in a glass-forming fluid, introducing a new method to evaluate correlation length and analyzing its relation to relaxation times, revealing logarithmic growth consistent with Adam-Gibbs theory.

Contribution

A novel procedure to evaluate dynamic correlation length from four-point structure factor in glassy fluids, tested on large particle systems near the mode-coupling transition.

Findings

Dynamic correlation length xi(t) grows logarithmically with relaxation time tau_alpha.

Mode-coupling power laws fit data over limited volume fractions but with different exponents.

Correlation length behavior aligns with Adam-Gibbs relation.

Abstract

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80 000 particle system to test a new procedure to evaluate a dynamic correlation length xi(t): we determine the ensemble independent dynamic susceptibility chi_4(t) and use it to facilitate evaluation of xi(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the alpha relaxation time tau_alpha, chi_4(tau_alpha), and xi(tau_alpha). We find that mode-coupling like power laws provide a reasonable description of the data over a restricted range of volume fractions, but the power laws' exponents differ from those predicted by the inhomogeneous mode-coupling theory. We find xi(tau_alpha) ~ ln(tau_alpha) over the full range of volume fractions studied, which is consistent with Adams-Gibbs-type relation.