Iso-g(2) processes in equilibrium statistical mechanics

Frank H. Stillinger, Salvatore Torquato, Juan M. Eroles, Thomas M. Truskett

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22 Scopus citations


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 languageEnglish (US)
Pages (from-to)6592-6597
Number of pages6
JournalJournal of Physical Chemistry B
Issue number28
StatePublished - Jul 19 2001

All Science Journal Classification (ASJC) codes

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


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