Collective diffusion, self-diffusion and freezing criteria of colloidal suspensions

In this paper, we examine collective and self-diffusion properties of dispe rsions of spherically shaped colloidal particles at intermediate and long t imes. Our analysis is based on a fully self-consistent (rescaled) mode coup ling theory (MCT) adjusted to describe the overdamped dynamics in concentra ted suspensions of neutral and charged colloidal particles. The dynamical q uantities studied in dependence on various experimentally controllable syst em parameters are the particle mean-squared displacement, long-time collect ive and self-diffusion coefficients, dynamic structure factors, nonexponent iallity factors and collective and self-memory functions. The results of ou r theoretical treatment are compared with Brownian dynamics computer simula tion data, experiment and other existing theories. It is shown that the res caled MCT can be successfully applied to a wide range of dynamical properti es. Our calculations reveal in particular an exponential long-time mode of the dynamic structure factor for a limited range of wave numbers and at suf ficiently high concentrations. A dynamic scaling behavior of the dynamic st ructure factor and self-intermediate scattering function is predicted for t he important case of salt-free charge-stabilized suspensions. As a conseque nce of the dynamic scaling, the static freezing criterion for colloids by H ansen and Verlet [Phys. Rev. 184, 151 (1969)] is shown to be equivalent wit h the dynamic criterion by Lowen [Phys. Rev. Lett. 70, 1557 (1993)] related to long-time self-diffusion. (C) 2000 American Institute of Physics. [S002 1-9606(00)50332-8].