Breakdown of the Stokes-Einstein relation in two, three and four dimensions

TL;DR

This study investigates how the breakdown of the Stokes-Einstein relation varies across two, three, and four dimensions in glass-forming liquids, revealing that higher dimensions exhibit less breakdown and challenging previous assumptions about fragility and heterogeneity.

Contribution

It provides a comparative analysis of SE relation breakdown across multiple dimensions and links this to activation energies and heterogeneity measures, offering new insights into glassy dynamics.

Findings

Breakdown of SE relation decreases with increasing dimension.

Higher-dimensional systems show increased fragility.

Heterogeneity measures generally correlate with SE breakdown.

Abstract

The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3 and 4 dimensions, in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two dimensional systems we study show deviations from the pattern of behavior of the three and four dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics.