## Abstract

Nearest-neighbor distribution functions characterize the probability of finding a nearest neighbor at some given distance from a reference point in systems of interacting particles and are of fundamental importance in a variety of problems in the physical and biological sciences. We extend the formalism of Torquato, Lu, and Rubinstein [Phys. Rev. A 41, 2059 (1990)] for identical spheres to obtain exact series representation of nearest-neighbor functions (void and particle probability densities) and closely related quantities for systems of interacting D-dimensional spheres with a polydispersivity in size. Polydispersivity constitutes a basic feature of the structure of random systems of particles and leads to a wider choice of possible definitions for nearest-neighbor functions. The most relevant definition for a polydispersed system of particles involves the nearest particle surface rather than the nearest particle center and thus we refer to them as nearest-surface distribution functions. For the special cases of D-dimensional hard and overlapping spheres, we obtain analytical expressions for the nearest-surface functions that are accurate for a wide range of sphere concentrations. Employing these results, we are able to compute the corresponding mean nearest-surface distances for polydispersed hard spheres. Finally, we determine the nearest-surface functions for bidispersed systems from Monte Carlo computer simulations and find that our theoretical results are in very good agreement with the data.

Original language | English (US) |
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Pages (from-to) | 5530-5544 |

Number of pages | 15 |

Journal | Physical Review A |

Volume | 45 |

Issue number | 8 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics