Modified Stokes-Einstein Relation for Small Brownian Particles

TL;DR

This paper reveals limitations of the classical Stokes-Einstein relation for small Brownian particles and proposes a modified relation that extends its applicability to smaller particle sizes.

Contribution

The authors identify the failure of the SE relation for small particles and introduce a revised formula excluding kinetic effects to improve accuracy.

Findings

SE relation fails for particles comparable to fluid molecules

Modified relation reduces error for small particles

Extended applicability range of diffusion predictions

Abstract

The Stokes-Einstein (SE) relation has been widely applied to quantitatively describe the Brownian motion. Notwithstanding, here we show that even for a simple fluid, the SE relation may not be completely applicable. Namely, although the SE relation could be a good approximation for a large enough Brownian particle, we find that it induces significant error for a smaller Brownian particle, and the error increases with the decrease of the Brownian particle's size, till the SE relation fails completely when the size of Brownian particle is comparable with that of a fluid molecule. The cause is rooted in the fact that the kinetic and the hydrodynamic effects depend on the size of the Brownian particle differently. By excluding the kinetic contribution to the diffusion coefficient, we propose a revised Stokes-Einstein relation and show that it expands significantly the applicable range.