## Abstract

For a multicomponent system of particles in equilibrium, an exact integral equation is derived for the pair connectedness function (which measures the probability that two particles, with centers a distance r apart, are connected). The pair connectedness function, mean cluster size, and percolation thresholds for mixtures of randomly centered (noninteracting) spheres and permeable spheres are then obtained analytically in the Percus-Yevick (PY) approximation. (The permeable- sphere model provides a one-parameter bridge from randomly centered sphere mixtures to hard- sphere mixtures.) For this family of models, connectedness is defined by particle overlap. It is found that, within the PY approximation, a multicomponent mixture of randomly centered spheres percolates at ξ_{3} = π/6Σ_{i}ρ_{i}R _{i}^{3}, = 1/2, independent of the concentration and size distributions of the particles. For the permeable-sphere case the percolation threshold depends on the relative densities, size, and interparticle permeability among the species. The loci of the percolation thresholds of a binary mixture of permeable spheres are explicitly determined.

Original language | English (US) |
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Pages (from-to) | 761-767 |

Number of pages | 7 |

Journal | The Journal of Chemical Physics |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - 1985 |

## All Science Journal Classification (ASJC) codes

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