Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

Abstract

The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus--Yevick (PY) theory, and using standard thermodynamic relations, a hitherto unknown PY equation of state, $p/ρk_BT=-(9/η)\ln(1-η)-(16-31η)/2(1-η)^2$, is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan--Starling equation of state. The extension to polydisperse hard-sphere systems is also presented.

5 pages, 1 figure; v2: extension to mixtures; new version of figure