Bulk properties of two-phase disordered media. II. Effective conductivity of a dilute dispersion of penetrable spheres

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Abstract

The calculation of the effective electrical conductivity σ* of a dilute dispersion of equisized spheres of radius R distributed with arbitrary degree of penetrability is considered. It is demonstrated that σ*, through second order in the inclusion volume fraction φ2, can be written in terms of the zero-density limits of the pair-connectedness and pair-locking functions, and certain polarizability tensors which involve one and two inclusions. Rigorous upper and lower bounds on σ*, through order φ22, are shown to depend upon, among other quantities, the aforementioned pair distribution functions and are evaluated for two models: an interpenetrable-sphere model and a certain sphere distribution in which the minimum distance between sphere centers is greater than or equal to 2R. An approximate expression obtained for the low-density expansion of σ* for dispersions of penetrable spheres always lies between the derived bounds on σ*. The study demonstrates that the effect of connectivity of the inclusion phase on σ*, through second order in φ2, can be substantial relative to the conductivity of dispersions of spheres characterized by a pair-connectedness function that is zero for all sphere separations.

Original languageEnglish (US)
Pages (from-to)4776-4785
Number of pages10
JournalThe Journal of chemical physics
Volume83
Issue number9
DOIs
StatePublished - Jan 1 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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