First-order phase transitions in the hard-ellipsoid fluid from variationally optimized direct pair correlations

The statistical mechanics of a fluid of hard prolate ellipsoids of revolution is addressed using density-functional methods. A variational approach is introduced for the calculation of the direct pair correlation function of the isotropic liquid, which is then used in a density-functional theory for the first-order transitions in the fluid. These calculations use, for the first time, a density functional that can properly describe the narrow real-space peaks at the crystallization transitions, and that can accommodate simultaneous or separate translational and orientational ordering. As a result, transitions to the solid, as well as to the plastic and nematic phases, are obtained. The resulting phase diagram is in good agreement with Monte Carlo results.