Density-functional, Landau, and Onsager theories of the isotropic-nematic transition of hard ellipsoids

We propose a density-functional theory for the isotropic-nematic transition of hard ellipsoids which is in fair quantitative agreement with the recent computer simulations of this system and which improves considerably upon the earlier theoretical attempts. The theory has an explicit oblate-prolate symmetry and leads to simple analytic expressions, e.g., for the equation of state of the isotropic phase. When the free energy of the nematic phase is expanded with respect to the Maier-Saupe quadrupole order parameter, an explicit Landau theory is produced, which is shown to underscore considerably the strength and the width of the transition. A virial expansion of the free energy produces in turn an Onsager theory for finite elongations whose results are shown to tend only very slowly to their Onsager limiting value. We also propose a Lindemann rule for orientational freezing.