Can the second virial coefficient be a predictor for the critical temperature?

Abstract

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is employed to calculate critical parameters of several model fluids. It is found that no matter how dis-continuous or continuous attractive perturbation part of whole interaction potential is, the 3rd-order TPT is accurate reliably for prediction of the critical parameters only on condition that the interaction potential is long-ranged or intermediate-ranged. Even when the 2nd-order macroscopic compressibility approximation TPT (2nd-order MCA-TPT) completely fails, the 3rd-order TPT still performs well. The 3rd-order TPT is then used to investiagte in detail validity and range of a recently emerging empirical rule. It is found that the empirical rule only applies for potentials consisting of a hard sphere core and a continuous and attractive perturbation tail, whether the attractive perturbation tail is differentiable with respect to particle separation or not does not matter. But for potentials with dis-continuous perturbation tail and those diaplaying two fluid–fluid critical points, the empirical rule fails completely.