### Abstract

We introduce a two-point cluster function C_{2}(r _{1},r_{2}) which reflects information about clustering in general continuum-percolation models. Specifically, for any two-phase disordered medium, C_{2}(r_{1},r_{2}) gives the probability of finding both points r_{1} and r_{2} in the same cluster of one of the phases. For distributions of identical inclusions whose coordiantes are fully specified by center-of-mass positions (e.g., disks, spheres, oriented squares, cubes, ellipses, or ellipsoids, etc.), we obtain a series representation of C_{2} which enables one to compute the two-point cluster function. Some general asymptotic properties of C_{2} for such models are discussed. The two-point cluster function is then computed for the adhesive-sphere model of Baxter. The two-point cluster function for arbitrary media provides a better signature of the microstructure than does a commonly employed two-point correlation function defined in the text.

Original language | English (US) |
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Pages (from-to) | 6540-6547 |

Number of pages | 8 |

Journal | The Journal of chemical physics |

Volume | 88 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 1988 |

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*,

*88*(10), 6540-6547. https://doi.org/10.1063/1.454440