### Abstract

We examine the n-point matrix probability functions S_{n} (which give the probability of finding n points in the matrix phase of a two-phase random medium), for a model in which the included material consists of fully penetrable spheres of equal diameter (i.e., a system of identical spheres such that their centers are randomly distributed in the matrix). Exploiting the special simplicity of the model we give an explicit closed-form expression for S_{3} as well as sharp bounds on S_{3} and S_{4}. Our best lower bound on S_{3} and our corresponding upper bound on S _{4} satisfy certain asymptotic forms (for both small and large separation of points) that are satisfied by the exact S_{3} and S _{4} for impenetrable as well as penetrable spheres, even though the bounding properties of our expressions can only be guaranteed for penetrable spheres. These expressions (and the resulting approximation for S_{4} in terms of S_{1} and S_{2} obtained from them) are thus highly appropriate approximants for both systems to be used in composite-media transport-coefficient expressions that involve integrals over the S_{n}. The S_{3} expression has in fact been suggested some time ago by Weissberg and Prager; our methods here provide further justification for this expression as well as one means of systematically generalizing it to S _{n} for higher n.

Original language | English (US) |
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Pages (from-to) | 1505-1510 |

Number of pages | 6 |

Journal | The Journal of chemical physics |

Volume | 79 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1983 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

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