Generalized equation of state for square-well potentials of variable range

An equation of state for square-well fluids of short and long potential range lambda is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour-liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to lambda less than or equal to 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation of state to ranges up to lambda = 3, and show that, in this case, the phase behaviour of the fluid is essentially that of a fluid of infinite potential range (van der Waals limit). At short ranges (lambda < 1.8) the calculated coexistence is virtually identical to that of the previous approach, hence ensuring that its application within a SAFT-VR framework is consistent with previous work. The extension of the approach to longer ranges is of interest in the context of modelling of polar fluids, and in the implementation of cross-over approaches to treat the critical region.