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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 functions S n, which give the probability that n points all lie in the matrix phase (as well as certain closely related functions), and consider transport and material properties (e.g., conductivity, modulii of elasticity) that can be expressed in terms of the S n. We discuss in quantitative detail the (small) effects of polydispersity on such properties (via a study of S n for n≤3rpar; for randomly centered spherical inclusions and parallel cylindrical inclusions with randomly placed axes. Finally, we discuss an application to gel size-exclusion chromatography, and consider some consequences of a polydisperse pore-size distribution.
