DYNAMICS OF QUASI-2-DIMENSIONAL COLLOIDAL SYSTEMS

In this paper we examine the asymptotic long time dynamics of quasi tw o-dimensional colloidal suspensions over a wide range of concentration s. At low concentrations the dynamics is determined by uncorrelated bi nary collisions among the constituent particles. These collisions amon g the particles lead to logarithmic corrections to the well-known line ar growth in time of the mean squared displacement of the particles in the suspension. The self-scattering function of the suspension can be related to the mean squared displacement via the Gaussian approximati on, which we examine in detail for systems of low concentration. At hi gher concentrations caging effects influence the dynamics of the suspe nsion, which we account for by developing a formal mode coupling theor y for colloidal systems from first principles. Equations for the dynam ics of the memory functions that account for caging effects are derive d and solved self-consistently, for the case of instanteous hydrodynam ic interactions, by utilizing the Gaussian approximation for the scatt ering functions of the colloidal system and assuming a particular form for the cumulants of the position. We find that the functional form s uggested by Cichocki and Felderhof for the time dependence of the mean squared displacement of quasi two-dimensional colloidal systems in th e limit that hydrodynamic interactions are instantaneous is compatible with the predictions of mode coupling theory. Furthermore, we explici tly evaluate the long time diffusion coefficient and other parameters as a function of concentration.