Microstructure of two-phase random media. I. The n-point probability functions

S. Torquato, G. Stell

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The microstructure of a two-phase random medium can be characterized by a set of general n-point probability functions, which give the probability of finding a certain subset of n-points in the matrix phase and the remainder in the particle phase. A new expression for these n-point functions is derived in terms of the n-point matrix probability functions which give the probability of finding all n points in the matrix phase. Certain bounds and limiting values of the Sn follow: the geometrical interpretation of the Sn and their relationship with n-point correlation functions associated with fluctuating bulk properties is also noted. For a bed or suspension of spheres in a uniform matrix we derive a new hierarchy of equations, giving the S n in terms of the s-body distribution functions ρs associated with a statistically inhomogeneous distribution PN of spheres in the matrix, generalizing expressions of Weissberg and Prager for S2 and S3. It is noted that canonical ensemble of mutually impenetrable spheres and the associated set of ρs define, in the limit of an unbounded system, a statistically homogeneous and isotropic medium, as does (trivially) a canonical ensemble of mutually penetrable spheres.

Original languageEnglish (US)
Pages (from-to)2071-2077
Number of pages7
JournalThe Journal of chemical physics
Issue number4
StatePublished - 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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