The majority of molecules which form liquid crystals are elongated in shape. However, disk shaped molecules have also been shown to exhibit liquid crystalline phases. In this paper we report a series of constant pressure Monte Carlo simulations of model discotic molecules. We have used the Gay–Berne potential, which is in essence an anisotropic version of a shifted Lennard-Jones potential, to model the interactions between the disks. Initially we studied a system of 512 molecules over a range of pressures to determine the mesophases formed and to construct the phase diagram. The system was found to exhibit isotropic, nematic, and columnar phases. We have also studied a larger system of 2000 molecules at a single pressure to calculate more accurately the distribution functions used to describe the translational and orientational order within the various phases.
The Maier-Saupe theory of the nematic mesophase is extended to rod-like molecules interacting with a perfectly general anisotropic potential. The resulting series expansion for the pseudopotential accounts quantitatively for the observed temperature dependence of the orientational order, even when the expansion is restricted to just the first two terms. However, the agreement can only be obtained if the expansion coefficients are assumed to depend on the inverse fourth power of the molar volume. The orientational molar enthalpy of transition calculated with the parameters determined by fitting the orientational order is qualitatively correct, although rather too large. The theory is also modified to allow for deviations from a spherically symmetric distribution of the intermolecular vector in the mesophase. A comparison of this new expression for the pseudo-potential with that derived by Chandrasekhar and Madhusudana reveals that certain of their assumptions are invalid. Finally, calculations made with the new pseudo-potential indicate that a modification of the Maier-Saupe theory based solely on deviations from a spherically symmetric distribution cannot yield quantitative agreement with theory.
The Maier-Saupe theory of the nematic mesophase is extended to multicomponent systems containing axially symmetric molecules interacting with a general anisotropic intermolecular potential. Expressions are derived for the anisotropic pseudo-potential of each component as well as the orientational molar Helmholtz function for the mixture. Simplified forms of these formulae are then employed, with some success, to predict the phase diagram for two binary mixtam of nematogens. The possible application of the theory to interpret the solute activity coefficients determined by gas-liquid chromatography using a nematogen as the stationary phase is indicated.
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