### Abstract

The pair correlation function g^{(2)}(r) in a classical many-body system depends in a nontrivial way both on the number density ρ and on the pair interactions v(r), and a long-standing goal of statistical mechanics has been to predict these effects quantitatively. The present investigation focuses on a restricted circumstance whereby simultaneous isothermal changes in ρ and v(r) have exactly canceling effects on g^{(2)}. By appealing to the isothermal compressibility relation, we establish that an upper limit for density increase exists for this "iso-g^{(2)}" process, and at this limit in three dimensions the correspondingly modified pair interaction develops a long-ranged Coulombic character. Using both the standard hypernetted chain and Percus-Yevick approximations, we have examined the iso-g^{(2)} process for rigid rods in one dimension that starts at zero density, and maintains the simple step-function pair correlation during density increase, a process that necessarily terminates at a covering fraction of one-half. These results have been checked with detailed Monte Carlo simulations. We have also estimated the effective pair potentials that are required for the corresponding rigid-sphere model in three dimensions, for which the simple step-function pair correlation can be maintained up to a covering fraction of one-eighth.

Original language | English (US) |
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Pages (from-to) | 6592-6597 |

Number of pages | 6 |

Journal | Journal of Physical Chemistry B |

Volume | 105 |

Issue number | 28 |

DOIs | |

State | Published - Jul 19 2001 |

### All Science Journal Classification (ASJC) codes

- Physical and Theoretical Chemistry
- Surfaces, Coatings and Films
- Materials Chemistry

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## Cite this

^{(2)}processes in equilibrium statistical mechanics.

*Journal of Physical Chemistry B*,

*105*(28), 6592-6597. https://doi.org/10.1021/jp010006q