The solution of the hypernetted chain and Percus–Yevick approximations for fluids of hard nonspherical particles. Results for hard ellipsoids of revolution

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Abstract
In this paper we describe a general approach which allows the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories to be solved numerically for fluids of hard nonspherical particles. Explicit results are given for fluids of hard ellipsoids of revolution and comparisons are made with recent Monte Carlo calculations. It is found that for dense systems of highly anisotropic ellipsoids the HNC and PY closures give significantly different results. The HNC theory is superior predicting the existance of a nematic phase in qualitative agreement with computer simulations. The PY approximation strongly and erroneously suggests that the isotropic phase is stable throughout the liquid regime.