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The Frank elastic constants for a nematic liquid crystal have been calculated by computer simulations for a fluid of hard ellipsoids and by the Poniewierski-Stecki method for ellipsoids with and without an attractive square well. Required for the Poniewierski-Stecki method is the direct correlation function c(1,2) and its dependence on the mutual molecular orientations. This was addressed using several models: the Parsons model, a two-term virial expansion, and the PY and HNC theories of Patey et al. In the Parsons model for c(1,2), the derived Frank elastic constants for hard ellipsoids were in agreement with the Poniewierski-Holyst values for hard spherocylinders. However, the agreement with simulation values was less satisfactory, as the simulation values exceeded the Parsons model values and the discrepancy grew with increasing particle asymmetry. The Frank constants, derived using a hard-core potential with an exterior SW (convex peg in a round hole), were in fair agreement with experimental data on prolate and oblate molecules, at the expense of employing overly large-order parameters (characteristic of uniaxial hard particle models). Omitted long-range correlations in the c( 1,2), present even in the hard-body models, is suspected to be the cause of the discrepancy of the simulation and experimental Frank constants with those calculated on the basis of short-range models for c(1,2).

We present the first calculations, by computer simulation, of the Frank elastic constants of a liquid crystal composed of freely rotating and translating molecules. Extensive calculations are performed for hard prolate ellipsoids at a single density, and for hard spherocylinders at three densities. For ellipsoids, the resulting Frank constants are of the same order of magnitude as those found experimentally, and in the expected ratios. For spherocylinders, elastic constants increase rapidly with density. Existing density functional theories are only moderately successful in predicting elastic constants. Includes an erratum, published in vol. 42; 6; 1990 -p. 3641

We present the results of the first molecular-dynamics simulations of a molecular liquid, namely a system of prolate hard ellipsoids of revolution, near the isotropic-nematic liquid-crystal phase transition. Collective rotational motion in the isotropic phase slows down on approach to the transition. It is found that the most important contribution to the rotational slowing down is due to static correlations as measured by the Kirkwood factor g2. The results suggest that the dynamics factor j2, which occurs in the hydrodynamical theory of collective reorientation, is small and negative.

We report here a Monte Carlo study of the thermodynamic and structural properties of a two-dimensional system of 2500 particles interacting by a repulsive inverse sixth power potential. Particular effort was made in the melting region, both to identify the defect structures and to ascertain the thermodynamic changes associated with the transition. Significant precursor fluctuations occurred on both the solid and fluid sides, and the unbinding of dislocation pairs was observed on melting. More complex defect patterns, including grain boundary loops, were also generated near melting. The Kosterlitz–Thouless, Halperin–Nelson, and Young dimensionless elastic constant approached the universal value 16 in the solid, and the orientational correlation range tended to diverge in the fluid near freezing. However, we were unable to distinguish between a very weak (V/V0.7%) first order and a continuous transition, since both spatial structures and temporal relaxations became exceedingly long.