Glassy dynamics of sticky hard spheres beyond the mode-coupling regime

TL;DR

This paper applies an advanced theoretical framework, GMCT, to sticky hard spheres, achieving predictions of glassy dynamics and phase behavior that align more closely with empirical data than traditional MCT, especially regarding reentrant and glass-glass transitions.

Contribution

The study extends mode-coupling theory by employing GMCT to better predict glass transition phenomena in sticky hard spheres, capturing complex dynamics and microstructural sensitivities.

Findings

GMCT predictions closely match empirical phase diagrams.

Reentrant glassy dynamics and glass-glass transitions are preserved in GMCT.

Higher hierarchical orders in GMCT enhance sensitivity to attractive interactions.

Abstract

Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions -- an approach that may become exact if sufficiently many correlations are taken into account. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes ($A_3$ and $A_4$) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.