Microstructure of two-phase random media. II. The Mayer-Montroll and Kirkwood-Salsburg hierarchies

S. Torquato, G. Stell

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It is shown that the Mayer-Montroll (MM) and Kirkwood-Salsburg (KS) hierarchies of equilibrium statistical mechanics for a binary mixture under certain limits become equations for the n-point matrix probability functions Sn associated with two-phase random media. The MM representation proves to be identical to the Sn expression derived by us in a previous paper, whereas the KS representation is different and new. These results are shown to illuminate our understanding of the Sn from both a physical and quantitative point of view. In particular rigorous upper and lower bounds on the Sn are obtained for a two-phase medium formed so as to be in a state of thermal equilibrium. For such a medium consisting of impenetrable-sphere inclusions in a matrix, a new exact expression is also given for Sn in terms of a two-body probability distribution function ρ2 as well as new expressions for S3 in terms of ρ2 and ρ3, a three-body distribution function. Physical insight into the nature of these results is given by extending some geometrical arguments originally put forth by Boltzmann.

Original languageEnglish (US)
Pages (from-to)3262-3272
Number of pages11
JournalThe Journal of chemical physics
Issue number6
StatePublished - 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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