Binary mixture of hard disks as a model glass former: Caging and uncaging

TL;DR

This study introduces a measure for the cage effect in glass-forming systems using a binary mixture of hard disks, revealing a timescale gap that explains two-step relaxation phenomena.

Contribution

It proposes a novel measure based on the rigidity matrix to identify uncaging events and analyzes the uncaging timescale gap in a binary disk mixture.

Findings

Identified a gap in uncaging timescales between different cage types.

Longer cage durations for single-disk cages compared to multi-disk cages.

Observed two-step relaxation behavior linked to uncaging timescale gap.

Abstract

I have proposed a measure for the cage effect in glass forming systems. A binary mixture of hard disks is numerically studied as a model glass former. A network is constructed on the basis of the colliding pairs of disks. A rigidity matrix is formed from the isostatic (rigid) sub--network, corresponding to a cage. The determinant of the matrix changes its sign when an uncaging event occurs. Time evolution of the number of the uncaging events is determined numerically. I have found that there is a gap in the uncaging timescales between the cages involving different numbers of disks. Caging of one disk by two neighboring disks sustains for a longer time as compared with other cages involving more than one disk. This gap causes two--step relaxation of this system.