Cooperative diffusion in colloidal mixtures

In this work we develop a general method to examine cooperative diffusion, i.e., the partial dynamic structure factors, in multicomponent colloidal mi xtures of spherical particles. Using a multivariable projection operator fo rmalism based on the many-body Smoluchowski diffusion equation, we derive a n exact microscopic expression for the matrix of irreducible memory functio ns associated with the partial dynamic structure factors and the long-time cooperative diffusion coefficients of the system. Starting from this micros copic expression, we present a derivation of a self-consistent mode couplin g scheme (MCS) for cooperative diffusion in colloidal mixtures. This scheme accounts not only for the direct particle interactions, but also for the f ar-field part of the solvent mediated hydrodynamic interactions. Combined w ith our recent work on the mode coupling theory of tracer-diffusion and lin ear viscoelasticity of colloidal suspensions, this MCS provides a unified m ethod for calculating dynamic and low-shear rheological properties of multi component colloidal dispersions. The MCS can be used to study polydispersit y and mixing effects in concentrated colloidal systems. Some applications r elated to cooperative diffusion, interdiffusion, and glass transition in bi nary mixtures are discussed to illustrate the method. (C) 1999 American Ins titute of Physics.