Cooperativity and spatial correlations near the glass transition: Computer simulation results for hard spheres and disks

Abstract

We examine the dynamics of hard spheres and disks 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-->infinity.

Self-diffusion of reversibly aggregating spheres

“…Fig. 2 shows that the dependence of the normalized diffusion coefficient of hard spheres in the absence of attraction (D hs ) on φ is in good agreement with literature results [46,47,48,49,50].…”

“…The average long time self diffusion coefficient (D l ) of non-interacting hard spheres decreases with increasing volume fraction [46,47,48,49,50] and the system forms a glass above a volume fraction of about 0.585. For a recent review of theories and experiments on the glass transition in colloids see Sciortino and Tartaglia [51].…”

Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

“…6. We should emphasize that unlike in some other studies [38][39][40] we do not use this four-point function for a quantitative examination of the slow particles correlations. For the latter task we found it more convenient to analyze the wave-vector dependent analog of G 4 (r; t).…”

Real space origin of temperature crossovers in supercooled liquids

“…This statement can be quantified [5,8,56,57] by studying multi-point functions, for example, C(|i − j|, t) = P i (t)P j (t) − P i (t) P j (t) , where P i (t) is a dynamical correlator at site i (below we will consider the persistence of site i). The spatial decay of a function like C(|i − j|, t) defines unambiguously the dynamical correlation length ℓ(T ), as already discussed theoretically [5,8,56] and measured in numerical simulations [46,56,57,58,59]. Furthermore, the joint distributions of time and length scales give rise to the canonical features of glass formers, like stretched relaxation, decoupling between transport coefficients, and (kinetic and thermodynamic) strong and fragile behaviours [5,6,7].…”