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 classi cal fluid of hard ellipsoids has been studied using a version of a the ory originally due to Onsager and by computer simulation. In the propo sed form of the Onsager theory for the Helmholtz free energy, both the second and the third virial coefficients are treated exactly, but the fourth and higher virials are resummed in a manner consistent with th e Carnahan-Starling equation of state for hard spheres. This same appr oach 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 fou rth and higher virial coefficients (rather than simply neglecting them ) degrades the agreement by overestimating the importance of the highe r virials. (ii) For 5:1 prolate and 1:5 oblate hard ellipsoids, the re summation yields a considerable improvement over an Onsager theory bas ed on the second and third virials alone. (iii) Although it seems stra ightforward to predict the liquid crystal transition densities with so me accuracy by means of these theories, accurate calculations of the d irect and pair correlation functions for hard spheres using our resumm ation ideas still poses a challenge. Only at packing fractions less th an 0.25 does the present theory portray accurately the radial distribu tion function for hard spheres.