Monte Carlo simulations of solute ordering in nematic liquid crystals: Shape anisotropy and quadrupole-quadrupole interactions as orienting mechanisms

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Abstract
Monte Carlo computer simulations were used to investigate the effects of shape anisotropy and electrostatic interactions as mechanisms for orientational ordering of solutes in nematic liquid crystals. The simulation results were analyzed in terms of two theories of solute ordering which derive mean-field orientational potentials from the intermolecular pair potential. In the calculations, solute and solvent molecular shapes were approximated by hard ellipsoids. Most simulations also incorporated the interaction between point quadrupole moments placed at the centers of the ellipsoids. In the hard-core systems, orientational order parameters and distribution functions were calculated for a collection of different solutes under a variety of conditions. A theory due to Terzis and Photinos [Mol. Phys. 83, 847 (1994)] was found to underestimate the effect of shape anisotropy on orientational ordering drastically. The introduction of an effective solvent packing fraction was unable to improve the predictive power of the theory significantly. The quadrupolar systems were used to investigate a mean-field model for solute ordering which considers an interaction between the solute molecular quadrupole moment with an average electric-field gradient. The simulations indicate that the electric-field gradient sampled by the solute is highly dependent on the properties of the solute, contrary to some experimental evidence. Further, the effects of the intermolecular quadrupolar interactions on orientational ordering and the electric-field gradient were analyzed using a mean-field potential derived here and based on the theory due to Emsley, Palke, and Shilstone [Liq. Cryst. 9, 649 (1991)]. This model was found to provide a qualitatively correct but quantitatively imprecise prediction of orientational ordering.