POLYDISPERSITY IN FLUIDS, DISPERSIONS, AND COMPOSITES; SOME THEORETICAL RESULTS

Abstract

We summarize some results of our theoretical study of polydispersity. After considering the effects of polydispersity on the structure of a solution or suspension of hard spheres in a continuum solvent, focusing on the pair distribution function g 2(r) we give some general relations between g 2(r) and thermodynamic quantities. For the log-normal and Shulz distributions, explicit analytic expressions are obtained for g 2(r) through first order in solute concentration, as well as corresponding expressions for the scattering function I(k). We also note the way hard-sphere polydispersity can be used to model monodisperse particles interacting via soft potentials and vice versa. Next we consider dispersions and composites consisting of a polydisperse distribution of particles or inclusions in a matrix (which can be a void or a solid or fluid continuum). Such systems include not only the solutions considered above but also a wide variety of solid porous and random media. Here we focus on the n-point matrix func...