PHASE-TRANSITION AND DIRECTOR FLUCTUATIONS IN THE 3-DIMENSIONAL LEBWOHL-LASHER MODEL OF LIQUID-CRYSTALS

Monte Carlo computer simulation techniques are used to study the orien tational phase transition in the three-dimensional Lebwohl-Lasher mode l which couples molecular rotors placed on a cubic lattice by the pote ntial P-2(cos theta(ij)). The orientational transition is a model of t he nematic-isotropic phase transition in liquid crystals. The simulati ons involve the determination of energy and order parameter distributi on functions which permit free energy functions to be derived. The dat a have been analysed by finite size scaling methods to reveal the natu re of the phase transition which is found to be weakly first order wit h stability limits of the nematic and isotropic phases being extremely close to the equilibrium transition temperature, in good agreement wi th experimental studies of room temperature nematogens. Results are re ported for the specific heat, the axial and biaxial susceptibilities, as well as the enthalpy and nematic order parameter discontinuity at t he transition. It is shown that the inclusion of a term P-4(cos theta( ij)) in the potential enhances the first-order character of the transi tion and displaces the stability limits further from the equilibrium t ransition temperature. The director fluctuations have been analysed, a nd it is found that, whereas the fluctuations in the isotropic phase f ollow ordinary Brownian motion, the fluctuations in the nematic phase correspond to fractional Brownian motion. By introducing a symmetry-br eaking field, -h(2)cos theta(i)(2):, a field-induced crossover between fractional and normal Brownian motion is observed in agreement with r ecent neutron scattering studies on deuterated p-azoxyanisole.