Properties of the square-well fluid of variable width

Abstract

The Helmholtz free-energy of a square-well fluid is studied as a function of the range of the well. A high-temperature perturbation expansion is carried out to second order, which is necessary to obtain accurate thermodynamic properties. The second-order term is expanded in powers of the range λ of the well, plus a short-range term that tends to zero when λ → ∞. In the long-range approximation (LRA) the short-range term is neglected and the remaining coefficients are obtained explicitly as functions of density. This LRA is asymptotically exact for large λ, has an estimated error of a few percent for λ = 3 (in units of the hard-sphere diameter), and provides a correction to the van der Waals limit. Also, for λ ≥ 3, its low density expansion is exact to the order of the fourth virial coefficient. It is compared with available Monte Carlo results for λ ˇ- 2 and with alternative approximations.