1204.4551 (Andrés Santos)

The chemical potential route: A hidden Percus-Yevick equation of state
for hard spheres    [PDF]

Andrés Santos

The chemical potential for a fluid of hard spheres 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, $p/\rho k_BT=-(9/\eta)\ln(1-\eta)-(16-31\eta)/2(1-\eta)^2$, is unveiled. This equation of state from the chemical potential route turns out to be slightly better than the one obtained from the conventional virial route. In fact, an interpolation (with respective weights 2/5 and 3/5) between the chemical potential and compressibility routes is shown to be more accurate than the widely used Carnahan-Starling equation of state.

View original: http://arxiv.org/abs/1204.4551