Self-consistent theory of collective Brownian dynamics: theory versus simulation.

A recently developed theory of collective diffusion in colloidal suspensions is tested regarding the quantitative accuracy of its description of the dynamics of monodisperse model colloidal systems without hydrodynamic interactions. The idea is to exhibit the isolated effects of the direct interactions, which constitute the main microscopic relaxation mechanism, in the absence of other effects, such as hydrodynamic interactions. Here we compare the numerical solution of the fully self-consistent theory with the results of Brownian dynamics simulation of the van Hove function G(r,t) and/or the intermediate scattering function F(k,t) of four simple model systems. Two of them are representative of short-ranged soft-core repulsive interactions [(sigma/r)(mu), with mu>>1], in two and in three dimensions. The other two involve long-ranged repulsive forces in two (dipolar, r(-3) potential) and in three (screened Coulomb, or repulsive Yukawa interactions) dimensions. We find that the theory, without any sort of adjustable parameters or rescaling prescriptions, provides an excellent approximate description of the collective dynamics of these model systems, particularly in the short- and intermediate-time regimes. We also compare our results with those of the single exponential approximation and with the competing mode-mode coupling theory.