Hard ellipsoid rod-plate mixtures: Onsager theory and computer simulations

The liquid crystal phase transitions for a classical fluid mixture of hard ellipsoids with aspect ratios 10 : 1 and 1 : 10, and equal volume, have been studied at two compositions using Onsager theories and by computer simulation. The original Onsager from of the Helmholtz free energy contains the second virial coefficient, but the effect of higher virial coefficients may be taken into account indirectly by resummation theories such as the y-expansion theory of Barboy and Gelbart or by renormalised two-particle theories such as that due to Parsons. A comparison of order parameters and equation of state data calculated by computer simulation and by Onsager, y-expansion-Onsager and Parsons theories shows good qualitative agreement. The resummation of higher virial coefficients is seen to offer improved quantitative agreement with simulation at the level of the second virial coefficient. The predicted phase diagram at this level of approximation is symmetric about the equal mixture of prolate and oblate ellipsoids as a result of the prolate-oblate symmetry of the excluded volume. The direct inclusion of higher virial coefficients has not been attempted but it is anticipated that this would give an asymmetric phase diagram.