Perturbation solution of the one particle generalized Smoluchowski equation

Abstract

The generalized Smoluchowski equation (GSE) can be used as the basis for a theory of the light scattering spectrum for a system of macromolecules in solution. We consider the solution of the one particle reduced GSE equation for the case of spherical macromolecules at low concentration through the use of a closure‐effecting ansatz that relates the one and two particle distribution functions and an expansion in the macromolecule concentration. The equations which result are well defined in the mathematical sense, and solutions are obtained for the first two terms in the expansion in a form suitable for application the light scattering problem. Although we restrict ourselves here to the usual model of the GSE with the hydrodynamic interactions given by the Oseen expression, more complicated forms for the hydrodynamic interaction could also be accomodated in the theory at the expense of considerably more lengthy calculations. A brief, formal application of the results obtained to the light scattering problem is also included.