Computer simulation studies of anisotropic systems. XVIII. Re-entrant phase separation in nematogenic mixtures of cylindrical and spherical particles

Addition of a solute composed of quasi-spherical molecules to a nematic liquid crystal is known to depress the nematic–isotropic transition temperature. A biphasic régime, consisting of coexisting nematic and isotropic phases, is also created at the transition. A molecular field theory of such mixtures, developed by Humphries and Luckhurst, predicts, in addition, the appearance of a re-entrant biphasic region following the nematic phase for a narrow range of compositions. This unusual re-entrant phase separation has not been observed for real nematogenic mixtures, presumably because the system freezes before the re-entrant phases can be formed. Here we report the observation of this biphasic régime for a model nematogenic mixture, formed from cylindrical and spherical particles, which was studied using the Monte Carlo technique of computer simulation. The particles are confined to the sites of a simple cubic lattice but still retain their rotational freedom; in consequence the mixture is unable to freeze in the conventional sense. The temperature variation of the heat capacity and the solute–solute radial distribution function reveal the predicted transition to the re-entrant biphasic régime. The internal energy and the second-rank orientational order parameter were also determined as a function of temperature. The predictions of the Humphries–Luckhurst theory are found to be in good qualitative accord with the results of the simulation.