Nematic liquid crystal in the wedge and edge geometry in the case of homeotropic alignment.

Nematic liquid crystal confined to a wedge or edge is studied on the assumption that the confining surfaces provide strong and weak homeotropic anchorings, respectively. Both infinite and finite systems are considered. The model based on the Frank-Oseen and Rapini-Papoular formalisms predicts two textures of opposite rotations of the director as in the case of strong anchoring on both surfaces. However, the presence of weak anchoring results in a length scale lambda which characterizes the crossover between the regions close to the apex and far from it. The ratio lambda/b , where b is the extrapolation length, is a function of the opening angle alpha. Both stable and metastable textures are considered and the mechanism by which a texture loses its stability is found. It is related to the formation of a defect-like structure at the surface of weak anchoring whose distance from the apex is lambda(alpha) and the loss of stability is signalled by the divergence of lambda. Only in the limit alpha --> 2tau, the defect-like structure transforms into a defect of strength -1/2 located at a finite distance from the apex.

Effective free-energy method for nematic liquid crystals in contact with structured substrates.

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free-energy function characterizing the patterned substrate, we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimizations of the free-energy functional were performed in order to test the predictions of the effective free-energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition, the effective free-energy method allows one to determine the energy barriers between two states in a bistable nematic device.

Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate.

A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank-Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal between the patterned grating surface and a flat substrate with strong homeotropic anchoring.

Orientational phase transition and the solvation force in a nematic liquid crystal confined between inhomogeneous substrates.

A nematic liquid crystal confined between two identical flat solid substrates, with an alternating stripe pattern of planar and homeotropic anchoring, is studied in the framework of the Frank-Oseen theory. By means of numerical minimization of the free energy functional we study the effect of the sample thickness D on the location of the phase transition between a uniform alignment, either planar or homeotropic, and a distorted nematic texture. The solvation force f due to distortions of the nematic director is also studied. It is found that f is always attractive, and for D small compared to the periodicity of the surface structure it exhibits two distinct asymptotic behaviors: f approximately -D(-1/2) or f approximately -D(-1), depending on the relation between D and the extrapolation lengths.

Uniform and nonuniform textures of a nematic liquid crystal in contact with an inhomogeneous substrate.

A semi-infinite sample of a nematic liquid crystal in contact with a flat solid substrate, possessing an alternating stripe pattern of planar and homeotropic anchoring, is studied in the framework of the Frank-Oseen model. The case of strong anchoring on one of the stripes is treated by means of bifurcation analysis, whereas the case of weak anchoring is studied by means of numerical minimization of the free energy functional. We find a second order phase transition between the uniform homeotropic or planar alignment and a distorted director configuration. The effect of the stripe width and the anchoring strength on the location of this transition and on the bulk orientation of the nematic director is also studied.