Square-well and square-shoulder fluids : simulation and equations of state

We explore the properties of a simple analytic equation of state, proposed by Heyes and Woodcock [D. M. Heyes and L. V. Woodcock, Mol. Phys. 59, 1369 (1986)] which is a development of the van der Waals equation of state, improved with an analytically simple yet accurate hard‐core component for the compressibility factor. We call this the hard‐sphere van der Waals (HSvdW) equation of state. We show, for the first time, that the HSvdW equation of state gives analytic values for the critical parameters and that it gives significantly more realistic values for the critical density than the van der Waals and other cubic equations of state. For single‐component square wells of arbitrary well width, the HSvdW equation of state also produces a critical temperature and pressure in agreement with those from a recent Gibbs Monte Carlo simulation study. The chief advantage over a similar equation of state with an alternative form for the hard‐core compressibility factor, such as Carnahan–Starling, is that it leads to...