Dynamic properties, scaling and related freezing criteria of two- and three-dimensional colloidal dispersions

The static and dynamic properties of 2- and 3-dimensional dispersions of strongly interacting colloidal spheres are examined. Quasi-2-dimensional dispersions of particles interacting by long range electrostatic and dipolar magnetic forces, respectively, are investigated using Brownian dynamics computer simulations with hydrodynamic interactions included. The dynamics of 3-dimensional bulk dispersions of charge-stabilized and neutral colloidal spheres is determined from a fully self-consistent mode-coupling scheme. For systems with long range repulsive interactions the dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to more restricted scaling behaviour with an enhancement of self-diffusion and, for 2- dimensional systems, to the divergence of the short-time collective diffusion coefficient. As a consequence of dynamic scaling, a dynamic criterion for the onset of colloidal freezing related to long-time self-diffusion is shown to be equivalent to a static freezing criterion related to the 2- and 3-dimensional static structure factors. Alternative freezing criteria are given in terms of the long-time and the mean collective diffusion coefficients.