Optimized cluster theory correction to the van der Waals model of mixtures

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Abstract
The correction to the van der Waals mean field model for mixtures is shown to be significant compared to the excess thermodynamic properties of mixing hard spheres and square‐well molecules under typical experimental conditions. Calculation of this correction to higher powers in the perturbation series of the attractive potential relative to the kinetic energy but in the mean field approximation, which leads to the one fluid model, results in an order of magnitude error. On the other hand, the optimized cluster theory, which reorders the perturbation series by graph theoretical techniques, provides quantitative predictions of the correction except near the critical line. The cluster theory is sufficiently accurate that it predicts heat capacities of mixtures larger than those of the pure components at the same volume and temperature as the mixture, in nearly quantitative agreement with the results obtained from molecular dynamics.