Anomalous diffusion in heterogeneous glass-forming liquids: Temperature-dependent behavior

TL;DR

This paper investigates how heterogeneity affects anomalous diffusion in glass-forming liquids across temperatures, combining multiple theories to interpret experimental data and elucidate dynamic crossover phenomena.

Contribution

It extends previous models by integrating continuous-time random-walk, excitation-chain, and shear-transformation-zone theories to analyze temperature-dependent diffusion and viscosity in glass-formers.

Findings

Identification of the crossover from super-Arrhenius to Arrhenius dynamics.

Insights into the length scales of spatial heterogeneities.

Explanation of the violation of the Stokes-Einstein relation.

Abstract

In a preceding paper, Mukhopadhyay and I studied the diffusive motion of a tagged molecule in a heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation between heterogeneity and stretched-exponential decay of correlations, and we also confirmed that systems of this kind generally exhibit non-Gaussian diffusion on intermediate length and time scales. Here I extend this analysis to higher temperatures approaching the point where the heterogeneities disappear and thermal activation barriers become small. I start by modifying the continuous-time random-walk theory proposed earlier, and supplement this analysis with an extension of the excitation-chain theory of glass dynamics. I also use a key result from the shear-transformation-zone theory of viscous deformation of amorphous materials. Elements of each of these theories are then used to interpret experimental data for ortho-terphenyl, specifially, the diffusion and viscosity coefficients and neutron scattering measurements of the self intermediate scattering function. Reconciling the theory with these data sets provides insights about the crossover between super-Arrhenius and Arrhenius dynamics, length scales of spatial heterogeneities, violation of the Stokes-Einstein relation in glass-forming liquids, and the origin of stretched exponential decay of correlations.