Simple approach to the equilibrium statistical mechanics of the hard sphere fluid

Abstract

The simple physical interpretation of the statistical mechanical expression for the reciprocal of the activity of a classical fluid is explored by using it to derive the well−known equation of state for one−dimensional fluids of hard rods. Direct extension of this derivation to three−dimensional hard spheres yields analytical equations for the activity and the pressure of the fluid branch which fit the molecular dynamics data about as well as the Padé approximant or the empirical equation of Carnahan and Starling. They represent a significant improvement over existing statistical theories, e.g., that of Percus and Yevick. The approach also yields equations which qualitatively describe the hard sphere crystalline branch.