Scaled particle theory for hard sphere pairs. I. Mathematical structure

Frank H. Stillinger, Pablo G. Debenedetti, Swaroop Chatterjee

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g (r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g (r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g (r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.

Original languageEnglish (US)
Article number204504
JournalJournal of Chemical Physics
Volume125
Issue number20
DOIs
StatePublished - Dec 7 2006

All Science Journal Classification (ASJC) codes

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

Fingerprint Dive into the research topics of 'Scaled particle theory for hard sphere pairs. I. Mathematical structure'. Together they form a unique fingerprint.

  • Cite this