Mean-field theoretical analysis of the corresponding-states behavior of model fluids with variable interaction range

In a recent communication [Fluid Phase Equilib. 272 (2008) 93–95], Duda and Orea suggested the existence of remarkably simple relationships among the critical parameters of several model fluids with variable interaction range. In addition, they introduced a new way of scaling supercritical pressure–volume–temperature (PVT  ) data for a pure substance in a corresponding-states representation. Using different mean-field theories for the square-well fluid and the Yukawa fluid, we investigate whether these approximate equations of state adhere to the new criteria formulated by Duda and Orea. It is found that most theories indeed predict the suggested simple linear relationships between the critical pressure and the critical temperature as well as between the critical density and the reciprocal of the critical temperature for long interaction ranges, but deviations from these simple rules occur for short interaction ranges. Some of the theories, however, indicate that the dependence of the critical density on the interaction range might be more complicated for the square-well fluid. The revised scaling concept of representing the reduced pressure P/PcP/Pc at a given reduced temperature T/TcT/Tc as a function of the newly defined reduced density ρσ/ρc2/3, where σσ denotes the diameter of a particle, does indeed lead to a better agreement of the data for different interaction ranges than the conventional scaling in terms of ρ/ρcρ/ρc for both model fluids studied here.