Application of the generalised SAFT-VR approach for long-ranged square-well potentials to model the phase behaviour of real fluids

In a recent generalisation of the SAFT-VR equation of state the method was extended so as to deal with short as well as long square-well ranges, namely, 1.2 ≤ λ ≤ 3.0 [B.H. Patel, H. Docherty, S. Varga, A. Galindo, G.C. Maitland., Mol. Phys. 103 (1) (2005) 129–139]. Here, we confirm the accuracy of the approach by comparison with numerical calculations of the first perturbation term and with vapour pressure and coexistence density computer simulation data. The approach is then used to model a number of real substances, from non-polar to strongly polar. We discuss in particular the values of the square-well potential model found. For this purpose we construct a relative least squares objective function and the percentage absolute average deviation (%AAD) to determine the intermolecular model parameters (m, λ , σ , ϵ / k B , ϵ h b / k B and r c ) by comparison to experimental vapour-pressure and saturated liquid density data. In order to ensure in each case that the global minimum is identified, the dimensionality of the problem is reduced by discretising the parameter-space [G.N.I. Clark, A.J. Haslam, A. Galindo, G. Jackson., Mol. Phys. 104 (22–24) (2006) 3561–3581]. Applying this method to the study of argon, n-alkanes, nitrogen, benzene, carbon dioxide, carbon monoxide, the refrigerant R1270, hydrogen chloride hydrogen bromide and water we find that the optimal models always present square-well ranges λ < 1.8 , meaning that an upper bound value of λ = 1.8 set in the original approach is sufficient to model real fluids; even polar ones. This finding is explained in terms of the averaged dipole–dipole interaction and of the long-range mean-field limit of the square-well potential.