Fickian crossover and lengthscales from two point functions in supercooled liquids

TL;DR

This study uses molecular dynamics simulations to identify multiple length scales and regimes in particle motion of supercooled liquids, revealing how heterogeneities influence diffusion near the glass transition.

Contribution

It demonstrates that two-point functions can be used to extract characteristic heterogeneity length scales and identifies three distinct dynamical regimes in supercooled liquids.

Findings

Three regimes in relaxation times with distinct scaling behaviors.

The Fickian crossover length matches the maximum heterogeneity size.

Exponential displacement distributions indicate heterogeneity before Gaussian diffusion.

Abstract

Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The lengthscale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characterisitic timescale is several times larger than the alpha relaxation time. A second crossover lengthscale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back in the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.