The isotropic to nematic liquid crystal transition for hard ellipsoids: an Onsager-like theory and computer simulations

The phase transition from an isotropic to a nematic phase for a classical uid of hard ellipsoids has been studied using a version of a theory originally due to Onsager and by computer simulation. In the proposed form of the Onsager theory for the Helmholtz free energy, both the second and the third virial coeecients are treated exactly, but the fourth and higher virials are resummed in a manner consistent with the Carnahan-Starling equation of state for hard spheres. This same approach is applied to the calculation of the direct correlation function. A comparison of order parameters, transition densities and pressures calculated by simulation and by the resummed Onsager theory, suggests the following. (i) For 10:1 prolate hard ellipsoids, resumming the fourth and higher virial coeecients (rather than simply neglecting them) degrades the agreement by overestimating the importance of the higher virials. (ii) For 5:1 prolate and 1:5 oblate hard ellipsoids, the re-summation yields a considerable improvement over an Onsager theory based on the second and third virials alone. (iii) Although it seems straightforward to predict the liquid crystal transition densities with some accuracy by means of these theories, accurate calculations of the direct and pair correlation functions for hard spheres using our resummation ideas still poses a challenge. Only at packing fractions less than 0.25 does the present theory accurately portray the radial distribution function for hard spheres.