Unified percolation scenario for the $\alpha$ and $\beta$ processes in simple glass formers

TL;DR

This study proposes a unified percolation framework to understand the alpha and beta relaxation processes in simple glass formers, linking particle mobility transitions to relaxation phenomena across different materials and dimensions.

Contribution

It introduces a double-percolation scenario that correlates particle immobility and mobility percolation with alpha and beta relaxations, providing a unified theoretical perspective.

Findings

Percolation of immobile particles aligns with the alpha process during cooling.

Mobile particle percolation indicates the beta process in the glass state.

In 2D systems, mobile and immobile percolation occur simultaneously, with no distinct beta relaxation.

Abstract

Given the vast differences in interaction details, describing the dynamics of structurally disordered materials in a unified theoretical framework presents a fundamental challenge to condensed-matter physics and materials science. Here, we numerically investigate a double-percolation scenario for the two most important relaxation processes of supercooled liquids and glasses, the so-called alpha and beta relaxations. For several simple glass formers, we find that when monitoring the dynamic shear modulus as temperature is lowered from the liquid state, percolation of immobile particles takes place at the temperature locating the alpha process. Mirroring this, upon continued cooling into the glass state, the mobile-particle percolation transition pinpoints a beta process whenever the latter is well separated from the main (alpha) process. For two-dimensional systems under the same conditions, percolation of mobile and immobile particles occurs nearly simultaneously and no beta relaxation can be identified. Our findings suggest that a general description of glassy dynamics should be based on a percolation perspective.