Collect. Czech. Chem. Commun. 2008, 73, 344-357

Statistical Geometry and Cavity Correlations in the Hard Sphere Fluid

Robin J. Speedya,* and Richard K. Bowlesb

a Apartment 504, 120 Courtenay Place, Wellington 6011, New Zealand
b Department of Chemistry, University of Saskatchewan, Saskatoon, S7N 5C9 Canada


The statistical geometry of a system of hard spheres is discussed in terms of the volumes Vj that lie with a sphere diameter, σ, of exactly j sphere centres. A site that has no sphere centre within σ is called a cavity site. We focus on the probability n00(r) that two sites separated by r are both cavity sites. n00(0), n00(σ), and the limiting slope (d ln n00(r)/dr)r=0, are all known in terms of the thermodynamic properties. The Vj and n00(r) are measured by computer simulation and an empirical expression, which satisfies the known exact relations, is shown to represent n00(r) precisely in the range 0 ≤ r ≤ σ.

Keywords: Statistical geometry; Cavity correlations; Hard spheres; Thermodynamics; Fluids; Computer simulation.

References: 27 live references.