A Kinetic Criterion for Stokes-Einstein Relation Breakdown Based on Effective Collisional Geometry

TL;DR

This paper introduces a kinetic framework using an effective collision diameter to interpret the breakdown of the Stokes-Einstein relation in supercooled liquids, linking geometric saturation to cooperative dynamics.

Contribution

It presents a novel kinetic criterion based on effective collisional geometry that explains the SE relation breakdown in supercooled liquids.

Findings

Effective collision diameter increases with cooling and saturates before SE breakdown.

Saturation of $d_{eff}$ sets a geometric upper bound for collisional cross-section.

The criterion provides a physically interpretable, mean-field perspective on glassy dynamics.

Abstract

Here we propose a kinetic framework for interpreting the Stokes-Einstein (SE) relation breakdown in supercooled liquids by introducing an effective collision diameter, $d_{\mathrm{eff}}$, derived from transport data. Numerical simulation of a model CuZr alloy reveal that $d_{\mathrm{eff}}$ increases upon cooling but saturates near the first peak of the radial distribution function just before SE breakdown. This saturation defines a geometric upper bound for the collisional cross-section beyond which further slowdown is governed by cooperative, heterogeneous motion rather than local collisional transport. Our analysis yields a compact criterion for SE breakdown in a mean-field perspective and provides physically interpretable inputs for future data-driven models of glassy dynamics.