Time-dependent self-diffusion in model suspensions of highly charged Brownian particles

A quantitative comparison is reported between the predictions of two theories of the time-dependent self-diffusion properties of suspensions of highly charged Brownian particles. The first theory, based on the overdamped N-body Fokker-Planck dynamics, involves a mode-mode coupling approximation for the time-dependent self-friction function, whereas the second one makes use of short-time conditions derived from the N-body Smoluchowski equation. In both cases, the relevant dynamic properties can be expressed in terms solely of the radial distribution function g(r). This quantity is first calculated using the rescaled mean spherical approximation (RMSA). By comparing with computer simulation results for g(r), it is found that the RMSA becomes increasingly inaccurate as the freezing transition is approached. We observe, however, that the RMSA itself provides a device to fit the simulation results for g(r). Using this procedure, the time-dependent self-diffusion coefficient, calculated from both theories, is in good agreement with Brownian dynamics simulations. © 1988.

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