Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids

The perturbation theory previously shown to give good results for the equation of state of a square-well fluid at liquid densities and temperatures is applied to more realistic potentials with soft repulsion, in particular the 6:12 potential. For an arbitrary potential function a modified potential is defined involving three parameters, namely a hard-sphere diameter, an inverse-steepness parameter for the repulsive region, and a depth parameter for the attractive region. When the latter parameters are zero, the modified potential becomes the hard-sphere potential; when they are one, it becomes the original potential. The configuration integral is expanded in a double-power series in the inverse-steepness and depth parameters, the hard-sphere diameter being chosen so that the first-order term in the inverse-steepness parameter is zero. The first-order term in the depth parameter is evaluated essentially exactly and the second-order term approximately: other second-order terms and all higher-order terms are neglected. The resulting equation of state is in good agreement with molecular dynamics, Monte Carlo results, and experimental data for argon at all temperatures and densities relevant for fluids.