A Microscopic Model of the Stokes-Einstein Relation in Arbitrary Dimension

TL;DR

This paper revisits the microscopic foundations of the Stokes-Einstein relation across arbitrary dimensions, explaining deviations observed in practice and extending previous models to more general conditions.

Contribution

It generalizes the statistical mechanics model of the SER to all dimensions and structured solvents, providing a microscopic explanation for observed deviations.

Findings

Reproduces SER-like results in infinite-dimensional fluids.

Identifies potential microscopic origins of deviations in self-solvation.

Extends analysis to partially structured solvents and all spatial dimensions.

Abstract

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.