Clustering and some other physical effects of van der Waals potentials

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Abstract
Molecular Dynamics and Monte Carlo computations for the original van der Waals model potentials, consisting of a hard core and inverse power attractive tails, are reported. The results show that the cusp at the minima of these potentials gives rise to anomalous phenomena in the low and intermediate density regions which derive from clustering effects. A new improved analytic equation-of-state for the van der Waals model is presented. This is based on a simple but accurate semi-empirical expression for the hard sphere reference fluid and Andrews' development for the attractive perturbation. A comparison of this first order perturbation equation with the ‘exact’ machine data highlights the limitations arising from clustering effects. The pair radial distribution function in the low density regime is not well-represented by using an expansion about the hard sphere distribution function and the attractive potential's second and third virial coefficients, used in Modified Enskog Theory (MET).