Statistical–mechanical theory of short-time self-diffusion in dilute suspensions of highly charged colloids

The short-time self-diffusion of highly charged colloids is studied theoretically. Generalized Langevin equations for the momenta of colloids are derived from a statistical–mechanical point of view. The mean-square displacement of colloids is then calculated for short times. The finite size effect of small ions on short-time self-diffusion of colloids is thus investigated. The short-time self-diffusion coefficient is shown to decrease as the ratio of a single diffusion coefficient of a colloid to that of a small ion increases. The dependence of the short-time dynamics on charges and volume fractions is also discussed. The present theory is valid even for such small ions which do not satisfy the so-called Stokes–Einstein relation. For medium size of small ions which satisfy that relation, the validity of the theory is confirmed by Brownian-dynamics simulations.