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A Monte Carlo method for studying anisotropic systems with a new type of boundary conditions is proposed. The missing interactions at the sample box surface are replaced by interactions with ghost molecules. The orientations of these ghost particles are sampled from a ‘‘least biased’’ singlet distribution obtained self-consistently from the order parameter inside the sample. The method is tested on the Lebwohl–Lasher model with 125 and 1000 particles. Results for the transition temperature and order parameters are in good agreement with those obtained from simulation of much larger systems. The method is fairly general and should be applicable in a variety of simulations. Here we show that it can also be used to study director fluctuations in nematogen models. [ABSTRACT FROM AUTHOR]

We revisit the classical problem of the molecular orientation inside a hybrid cell filled with liquid-crystals with various elastic constant anisotropies by means of Monte Carlo simulations using the Gruhn-Hess effective pair potential. We find some unstable defect lines and we discuss their arising in the system. We study the effects of the elastic anisotropy on the profiles of the director close to the surface with weak anchoring. Our findings indicate that the elastic theory and computer simulations are in good qualitative agreement while quantitatively some discrepancies are found mainly when the ratio K11/K33is larger than one. [ABSTRACT FROM AUTHOR]

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 ensembles 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 pseudo-potential. In these calculation 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 [ABSTRACT FROM AUTHOR]

Nematic samples filling a flat cell or the annular region between two concentric cylinders with hybrid anchoring conditions at the boundaries are investigated by setting up and minimizing their Frank elastic free energy. The coupling with the surfaces is taken to be strong on one side and weak on the other. The equations are numerically solved and the conditions for which the molecular organization inside the cell becomes uniform are analyzed. The classical calculation performed by G. Barbero and R. Barberi [J. Phys. 44, 609 (1983)] is reproduced and investigated from a different point of view, in order to compare the results of planar and cylindrical geometries. The results suggest that the cylindrical cell presents some unusual features deserving a more complete investigation. Although most part of the transitional phenomena are found for K11>K33, a case not common for ordinary (lyotropic and thermotropic) liquid crystals, it is possible to find a completely uniform cell even for K11

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998); Phys. Lett. A 302, 203 (2002); G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K11/K33 if K22=K33 are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K11/K33, spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K22/K33 and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed. [ABSTRACT FROM AUTHOR]