Most molecular theories of nematic liquid crystals assume that the constituent molecules are cylindrically symmetric. However, although this may be a useful approximation the molecules of real nematogens are of lower symmetry; here we develop a theory for an ensemble of such particles based on a general expansion of the pairwise intermolecular potential together with the molecular field approximation. The dependence of the orientational properties of the uniaxial mesophase on the deviation from molecular cylindrical symmetry is calculated from the series expansion of the pseudopotential. In these calculations the number of arbitrary parameters in the orientational pseudo-potential is reduced by assuming that the anisotropic intermolecular potential originates solely from dispersion forces. The theoretical predictions for the values of the ordering matrix and the entropy change at the nematic-isotropic transition are found to be in good agreement with those observed for 4,4′-dimethoxyazoxybenzene. In addition, the theory provides a reasonable account of the temperature dependence of the order parameter at constant volume for this nematogen. The allowance for deviations from molecular cylindrical symmetry appears to remove many of the discrepancies between the Maier-Saupe theory and experiment.

The Lebwohl-Lasher model of nematogens consists of a system of particles placed at the sites of a cubic lattice and interacting with a pair potential U _i,j = -ϵ _ij P ₂(cos β _ij ), where ϵ _ij is a positive constant, ϵ, for nearest neighbours particles i and j and β _ij is the angle between the axis of these two molecules. We have investigated this model using Monte Carlo simulations with periodic boundary conditions on a 30 × 30 × 30 lattice while the largest system previously studied was 20 × 20 × 20. The number of simulation runs near the transition is also significantly higher than in previous simulations to allow a more precise determination of the orientational transition temperature T ^* _NI. The transition temperature has been placed at kT/ϵ = 1·1232 ± 0·0006, refining previous estimates. Orientational order parameters <P ₂>, <P ₄> have been calculated and a new algorithm is proposed for the computation of <P ₄>. Particular attention has been devoted to pretransitional properties. Pair correlations G ₂(r), G ₄(r) as well as the second rank g ₂-factor are reported. g ₂ is found to diverge at a temperature T ^* _NI* = kT/ϵ = 1·1201 ± 0·0006 and to fit the Landau-de Gennes behaviour except near the transition. Our results indicate therefore that the Lebwohl-Lasher model can yield the small difference between the nematic-isotropic transition temperature and the isotropic phase limiting instability temperature without the need of introducing additional terms in the potential.