Properties of the square-well fluid of variable width. II. The mean field term

Abstract

The perturbation expansion of the Helmholtz free energy of a square-well fluid is analyzed. A closed-form expression is found for the first-order term in that expansion as a function of the density and of the attractive range of the well. The procedure is based on the interpolation of the extreme cases of long and short ranges, for which exact asymptotic results are known. The proposed interpolation formula is tested against Monte Carlo calculations of the same first-order term for different values of the range and the density, obtaining a root-mean-square deviation of 2.2%. Previous analytic approximations as that of van der Waals are discussed.