Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory

An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially, a detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system that shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with the Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently and accurately in the high density regime gives, contrary to previous works, a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard ellipsoids of revolution. Our results compare well with Monte Carlo simulations and density-functional theory.