The Stokes-Einstein-Sutherland equation at the nanoscale revisited

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. However, a number of experimental studies showed a remarkable small, if any, violation of this equation down to the size of a nm, where there is no scale separation. To resolve this puzzle we combine analytical ultracentrifugation experiments and molecular dynamics simulations to study the transport of buckminsterfullerene C$_{60}$ suspended in toluene at infinite dilution. We show that this system clearly violates the conditions of slow momentum relaxation. Yet, through a linear response to a constant force, we show both in experiments and in simulations that the SES equation can be recovered in the long time limit with no more than 4% uncertainty. This nonetheless requires partial slip on the particle interface, extracted consistently from all the data. Our results, thus, resolve a long-standing discussion on the validity and limits of the SES equation at the molecular scale