Statistical–mechanical theory of self-diffusion in dilute suspensions of macroions

Self-diffusion in dilute suspensions of macroions is studied theoretically based on the nonlinear non-Markov Langevin equations for macroions recently derived by one of the present authors (M.T.). Not only the short-time self-diffusion coefficient of macroion but also its long-time self-diffusion coefficient are then found analytically as a function of charge and volume fraction. The theoretical results, including a crossover map in charge–volume fraction plane, are then tested by the Brownian-dynamics simulations on macroions and small ions. Thus, they are shown to agree with the simulation results well within error.