A comprehensive approach to an equation of state for hard spheres and Lennard Jones fluids

Abstract

We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms (n = 1, 2, 3, 4, 5) for surface tension Smn(r), r ≥ d/2 with intermolecular separation r as a variable, where m is an arbitrary real number (pole). Among the equations of state obtained in this way are Percus—Yevick, scaled particle theory and Carnahan—Starling equations of state. In addition, we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately. It is found that for both hard sphere fluids as well as Lennard—Jones fluids, with m = 3/4 the derived equation of state (EOS) gives results which are in good agreement with computer simulation results. Furthermore, this equation of state gives the Percus—Yevick (pressure) EOS for the m = 0, the Carnahan—Starling EOS for m = 4/5, while for the value of m = 1 it corresponds to a scaled particle theory EOS.