Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach

TL;DR

This paper combines liquid state theory and mode-coupling theory to analyze the structure and dynamics of soft repulsive particles, revealing a dynamic scaling near the glass transition and comparing theoretical predictions with simulations.

Contribution

It introduces a combined theoretical framework to study soft sphere glassy dynamics and explores the influence of the zero-temperature glass transition on finite-temperature behavior.

Findings

Identifies the fluid-glass transition locus in phase diagram.

Demonstrates dynamic scaling of relaxation times and susceptibilities.

Shows qualitative agreement with driven athermal dynamics simulations.

Abstract

We combine the hyper-netted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature -- volume fraction phase diagram. The zero-temperature (hard sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that `mean-field' mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.