# Length scale dependence of the Stokes-Einstein and Adam-Gibbs relations in model glass formers

## TL;DR

This study investigates how the validity of the Adam-Gibbs and Stokes-Einstein relations depends on length scales in glass-forming liquids, revealing that the Adam-Gibbs relation holds best for diffusion over a wide temperature range.

## Contribution

The paper demonstrates that the Adam-Gibbs relation is valid for diffusion across a broad temperature range and links the breakdown of the Stokes-Einstein relation to length scale-dependent dynamical heterogeneity.

## Key findings

- Adam-Gibbs relation holds for diffusion over wide temperature range
- Stokes-Einstein breakdown occurs below a certain temperature
- Breakdown linked to dynamical heterogeneity length scales

## Abstract

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its the thermodynamics via. the configurational entropy, and is of fundamental importance in descriptions of glassy behaviour. The breakdown of the Stokes-Einstein (SEB) relation between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.