Remarks on the mutual diffusion coefficient of Brownian particles

Abstract

The mutual (or collective) diffusion coefficient of Brownian particles treated in most of previous microscopic theories is regarded as defined on the basis of the dynamic structure factor. It is pointed out for cases where both direct and hydrodynamic pair interactions are present between Brownian particles that this diffusion coefficient does not satisfy the generalized Einstein relation which results from conventional irreversible thermodynamics and which should be obeyed by the diffusion coefficient as would be determined by conventional gradient diffusion experiments. This is ascribed to the fact that the diffusion coefficient based on the dynamic structure factor is generally not identical with the conventional diffusion coefficient, i.e., whereas the latter diffusion coefficient describes the collective diffusion of Brownian particles under conditions of uniform temperature and pressure, the former describes that under conditions of uniform temperature and uniform chemical potential of solvent. A correct expression for the conventional diffusion coefficient is derived by taking this difference into account. Both diffusion coefficients are evaluated for the case of hard spheres.