# Researh Note: Stokes-Einstein relation in simple fluids revisited

## TL;DR

This paper revisits Zwanzig's formulation of the Stokes-Einstein relation in simple fluids, showing the coefficient's dependence on sound velocity ratios and linking it to interaction potentials across various model systems and liquid metals.

## Contribution

It demonstrates the dependence of the Stokes-Einstein coefficient on sound velocity ratios and relates it to the interaction potential, providing predictive insights for simple fluids.

## Key findings

- The SE coefficient varies with the ratio of transverse to longitudinal sound velocities.
- Correlation between interaction softness and the SE coefficient is observed.
- Re-evaluation of the SE coefficient in liquid metals at melting temperature.

## Abstract

In this Research Note the Zwanzig's formulation of the Stokes-Einstein (SE) relation for simple atomistic fluids is re-examined. It is shown that the value of the coefficient in SE relation depends on the ratio of the transverse and longitudinal sound velocities. In some cases, this ratio can be directly related to the pair interaction potential operating in fluids and thus there can be a certain level of predictivity regarding the value of this coefficient. This Research Note provides some evidence in favour of this observation. In particular, analyzing the situation in several model systems such as one-component plasma, Yukawa, inverse-power-law, Lennard-Jones, and hard-sphere fluids, it is demonstrated that there are certain correlations between the interaction softness and the coefficient in SE relation. The SE coefficient is also re-evaluated for various liquid metals at the melting temperature, for which necessary data are available.