Perturbation Theory and Equation of State for Fluids: The Square-Well Potential

Abstract

The equation of state for a fluid of molecules interacting according to the square-well potential is evaluated by treating the attractive potential as a perturbation on the hard-sphere potential. This leads to an expansion in inverse powers of the temperature. The first-order term is evaluated exactly (except for the approximation of using the Percus—Yevick expression for the hard-sphere radial distribution function). Two slightly different approximations for the second-order term are given and shown to lead to similar results. With first-and second-order terms included, the calculated equation of state is in excellent agreement with quasiexperimental Monte Carlo and molecular-dynamics results at all temperatures including the lowest temperatures for which such calculations have been made, far below the critical temperature and at liquid densities. The reasons for this good agreement, particularly at high densities, are discussed in terms of a novel formulation of the perturbation theory, and the implications of the results for fluids with more realistic potential functions are considered.