Transition state theory applied to self-diffusion of hard spheres

TL;DR

This paper applies transition state theory to model self-diffusion in hard sphere fluids, identifying two regimes based on packing fraction and providing parameter-free analytical expressions that match previous numerical results.

Contribution

It introduces a transition state theory framework for self-diffusion in hard spheres, distinguishing regimes and deriving analytical expressions without adjustable parameters.

Findings

Diffusion limited by free volume at low packing fractions.

Diffusion limited by velocity autocorrelation at high packing fractions.

Analytical expressions match previous numerical results.

Abstract

A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation that matches numerical results previously obtained by other authors. Two regimes are identified. For small packing fraction $\xi$, diffusion is limited by free volume; and, for large $\xi$, diffusion is limited by velocity autocorrelation. The expressions obtained in each regime do not require adjustable parameters.