Brownian Motion of a Rough Sphere and the Stokes−Einstein Law

Using molecular dynamics computer simulation, we have calculated the velocity autocorrelation function and diffusion constant for a variety of solutes in a dense fluid of spherical solvent particles. We explore the effects of surface roughness of the solute on the resulting hydrodynamic boundary condition as we naturally approach the Brownian limit (when the solute becomes much larger and more massive than the solvent particles). We find that when the solute and solvent interact through a purely repulsive isotropic potential, in the Brownian limit the Stokes−Einstein law is satisfied with slip boundary conditions. However, when surface roughness is introduced through an anisotropic solute−solvent interaction potential, we find that the Stokes−Einstein law is satisfied with stick boundary conditions. In addition, when the attractive strength of a short-range isotropic solute−solvent potential is increased, the solute becomes dressed with solvent particles, making it effectively rough, and so stick boundary conditions are again recovered.