  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.
