The Stokes-Einstein-Sutherland equation at the nanoscale revisited

TL;DR

This study combines high-precision experiments and simulations to demonstrate that the Stokes-Einstein-Sutherland equation remains valid at the nanoscale when accounting for partial slip, resolving longstanding debates.

Contribution

It provides the first comprehensive validation of the SES equation at the molecular scale, incorporating partial slip effects through combined experimental and simulation data.

Findings

SES equation holds at the nanoscale with partial slip consideration

Experimental and simulation data agree within 4% uncertainty

Partial slip at the particle interface is essential for validity

Abstract

The Stokes-Einstein-Sutherland (SES) equation is at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature and the boundary condition for the particle-solvent interface. It is assumed that it relies on the separation of scales between the particle and the solvent, hence it is expected to break down for diffusive transport on the molecular scale. This assumption is however challenged by a number of experimental studies showing a remarkably small, if any, violation, while simulations systematically report the opposite. To understand these discrepancies, analytical ultracentrifugation experiments are combined with molecular simulations, both performed at unprecedented accuracies, to study the transport of buckminsterfullerene C60 in toluene at infinite dilution. This system is demonstrated to clearly violate the conditions of slow momentum relaxation. Yet, through a linear response to a constant force, the SES equation can be recovered in the long time limit with no more than 4% uncertainty both in experiments and in simulations. This nonetheless requires partial slip on the particle interface, extracted consistently from all the data. These results, thus, resolve a long-standing discussion on the validity and limits of the SES equation at the molecular scale.