### Abstract

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 S_{n} associated with two-phase random media. The MM representation proves to be identical to the S_{n} 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 S_{n} from both a physical and quantitative point of view. In particular rigorous upper and lower bounds on the S_{n} 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 S_{n} in terms of a two-body probability distribution function ρ_{2} as well as new expressions for S_{3} in terms of ρ_{2} and ρ_{3}, 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 language | English (US) |
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Pages (from-to) | 3262-3272 |

Number of pages | 11 |

Journal | The Journal of chemical physics |

Volume | 78 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1983 |

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*,

*78*(6), 3262-3272. https://doi.org/10.1063/1.445245