A calculation of the self-diffusion coefficient for a dilute solution of Brownian particles

The linear concentration dependence of the self-diffusion coefficient Ds is calculated for a suspension of interacting Browian particles. The Einstein expression for the mean square displacement of a tagged particle is converted into a time correlation function and evaluated using perturbation methods. The derived concentration dependence of Ds in a system of hydrodynamically interacting hard spheres is in accord with previous literature results. Furthermore, the effects of short and long range potentials on Ds are determined.