### Abstract

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 S_{n} follow: the geometrical interpretation of the S_{n} 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 ρ_{s} associated with a statistically inhomogeneous distribution P_{N} of spheres in the matrix, generalizing expressions of Weissberg and Prager for S_{2} and S_{3}. It is noted that canonical ensemble of mutually impenetrable spheres and the associated set of ρ_{s} 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 language | English (US) |
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Pages (from-to) | 2071-2077 |

Number of pages | 7 |

Journal | The Journal of chemical physics |

Volume | 77 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1982 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*The Journal of chemical physics*,

*77*(4), 2071-2077. https://doi.org/10.1063/1.444011