Abstract
The structure of a dispersion of interpenetrating spheres (particles or pores), of uniform or of varying sizes, is characterized by its n-particle correlation functions. Such correlations are used to derive the general expression for the interfacial area. Two simple limiting cases, randomly placed and totally impenetrable spheres, are considered in detail, as well as the Blum-Stell model for spheres of limited interpenetrability. In the random case the interfacial area depends only on the number concentration of spheres and on the second and third moments of the distribution of sphere radii. The surface area is maximized, either at constant number concentration or at constant volume fraction of the particle phase, when the spheres are of uniform size. The general expression for the distribution of the interfacial area over the various components in a multisized dispersion is also reported. The results are generalized to the case of inclusions of any shape.
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