The Adam-Gibbs relation for glass-forming liquids in 2, 3 and 4 dimensions

TL;DR

This study tests the Adam-Gibbs relation across different dimensions in computer simulations, confirming its validity in 3 and 4 dimensions but not in 2, where no universal alternative relation fits all models.

Contribution

The paper provides the first systematic simulation-based test of the Adam-Gibbs relation in 2, 3, and 4 dimensions, revealing dimensional dependence of its validity.

Findings

Valid in 3 and 4 dimensions

Invalid in 2 dimensions

No universal alternative relation in 2D

Abstract

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in 2, 3, and 4 spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in 3 and 4 dimensions. But in 2 dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.