Heterogeneous Diffusion in Highly Supercooled Liquids

TL;DR

This study uses molecular dynamics simulations to reveal that particle diffusion in highly supercooled liquids is highly heterogeneous on short time scales, with active regions dominating displacement, but becomes homogeneous over longer periods.

Contribution

It demonstrates the transient heterogeneity of diffusion in supercooled liquids and links it to the van Hove function's long tail, providing new insights into microscopic dynamics.

Findings

Heterogeneous diffusion occurs on time scales comparable to the alpha relaxation time.

Active regions significantly influence the mean square displacement.

Diffusion becomes homogeneous after about three alpha relaxation times.

Abstract

The diffusivity of tagged particles is demonstrated to be very heterogeneous on time scales comparable to or shorter than the $\alpha$ relaxation time $\tau_{\alpha}$ ($\cong$ the stress relaxation time) in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Einstein-Stokes value. The van Hove self-correlation function $G_s(r,t)$ is shown to have a long distance tail which can be scaled in terms of $r/t^{1/2}$ for $t \ls 3\tau_{\alpha}$. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure ($\sim 3 \tau_{\alpha}$).