Cooperativity and Spatial Correlations near the Glass Transition: Computer Simulation Results for Hard Spheres and Discs

TL;DR

This study uses computer simulations to analyze how cooperativity and spatial correlations develop in hard sphere and disc systems near the glass transition, revealing persistent dynamic correlations over time.

Contribution

It introduces a simple method to quantify dynamic correlations and demonstrates finite cooperativity at long times in systems approaching the glass transition.

Findings

Finite cooperativity observed as time approaches infinity.

Dynamic correlations depend on the choice of dynamical quantities.

Quantification of cooperativity relates to the reduction of effective degrees of freedom.

Abstract

We examine the dynamics of hard spheres and discs at high packing fractions in two and three dimensions, modeling the simplest systems exhibiting a glass transition. As it is well known, cooperativity and dynamic heterogeneity arise as central features when approaching the glass transition from the liquid phase, so an understanding of their underlying physics is of great interest. Cooperativity implies a reduction of the effective degrees of freedom, and we demonstrate a simple way of quantification in terms of the strength and the length scale of dynamic correlations among different particles. These correlations are obtained for different dynamical quantities $X_i(t)$ that are constructed from single-particle displacements during some observation time $t$. Of particular interest is the dependence on $t$. Interestingly, for appropriately chosen $X_i(t)$ we obtain finite cooperativity in the limit $t \to \infty$.