Viscous liquid dynamics modeled as random walks within overlapping hyperspheres

TL;DR

This paper introduces a hypersphere model for viscous liquids, simulating random walks in high-dimensional spaces to replicate the slowing dynamics near glass transition, aligning with experimental observations.

Contribution

It presents a novel high-dimensional hypersphere percolation model for viscous liquids, capturing their slow dynamics and comparing well with real glass-forming liquids.

Findings

Slowing down of dynamics with decreased hypersphere density

Mean-square displacement similar to experimental glass-formers

Model reproduces frequency-dependent fluidity behavior

Abstract

The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the number of particles. We study random walks within overlapping hyperspheres in 12 to 45 dimensions, i.e., above the percolation threshold, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; thus decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the Random Barrier Model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. $\mathbf{119}, 248001\,(2017)$].