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 form of the Helmholtz free e nergy contains the second virial coefficient, but the effect of higher virial coefficients may be taken into account indirectly by resummati on theories such as the y-expansion theory of Barboy and Gelbart or by renormalised two-particle theories such as that due to Parsons. A com parison of order parameters and equation of state data calculated by c omputer simulation and by Onsager, y-expansion-Onsager and Parsons the ories shows good qualitative agreement. The resummation of higher viri al coefficients is seen to offer improved quantitative agreement with simulation at the level of the second virial coefficient. The predicte d phase diagram at this level of approximation is symmetric about the equal mixture of prolate and oblate ellipsoids as a result of the prol ate-oblate symmetry of the excluded volume. The direct inclusion of hi gher virial coefficients has not been attempted but it is anticipated that this would give an asymmetric phase diagram.