### Abstract

A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.

Original language | English (US) |
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Pages (from-to) | 289-297 |

Number of pages | 9 |

Journal | Molecular Physics |

Volume | 95 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1998 |

### All Science Journal Classification (ASJC) codes

- Biophysics
- Molecular Biology
- Condensed Matter Physics
- Physical and Theoretical Chemistry

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## Cite this

*Molecular Physics*,

*95*(2), 289-297. https://doi.org/10.1080/00268979809483161