Computer simulations of the ordering in a hybrid cylindrical film of nematic liquid crystals

Nematic liquid crystal in a cylindrical sample: Theoretical analysis of the electrical response

The electrical responses of a nematic liquid crystal sample confined between two cylindrical surfaces are investigated in the framework of elastic continuum theory. The responses are the result of the molecular reorientation induced by both the applied electric field and the cylindrical geometry of the sample. The nematic medium is considered as a parallel RC circuit since the capacitance and the resistance are under the same difference of potential. The electrical properties, including the total electric current, are determined from the molecular reorientation of the director. The elastic anisotropy has been shown to influence substantially the profile of the electrical current, capacitance, and resistance characterizing the equivalent circuit for the medium.

Nematic liquid crystals in planar and cylindrical hybrid cells: Role of elastic anisotropy on the director deformations

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 K(11)>K(33), a case not common for ordinary (lyotropic and thermotropic) liquid crystals, it is possible to find a completely uniform cell even for K(11)<K(33) in both the geometries considered here.

Molecular organization of nematic liquid crystals between concentric cylinders: role of the elastic anisotropy

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 K(11)/K(33) if K(22)=K(33) are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K(11)/K(33), spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K(22)/K(33) 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.