Static splay-stripes in a hybrid aligned nematic layer

A usual aperiodic hybrid alignment can appear in a nematic layer with weak anchoring only if the cell thickness is greater than a critical value dh, below which a static periodic pattern instead of the hybrid aperiodic structure could be preferred, if the energy cost for a three dimensional deformation, involving twist, is less than the cost for the two-dimensional deformation of splay-bend type. We have studied the occurrence of the mechanical instability leading to the static periodic splay-stripes, i. e. in the case of the tilt anchoring stronger at the one of the walls, in which the anchoring is planar, for several values of the twist anchoring strengths. Here the behavior of the threshold d for the periodic stripes is presented and discussed as a function of the anchoring energies and of the ratio of nematic bulk elastic constants, in the frame of the usual continuum theory

Saddle-splay and periodic instability in a hybrid aligned nematic layer subjected to a normal magnetic field

A nematic layer with opposite boundary conditions (unidirectional planar and homeotropic) is considered, having strong anchoring at the planar wall. It is known that a periodic deformation of splay-type can intervene between the aperiodic hybrid alignment and undistorted planar state as one decreases the film thickness. This periodic state occurs due to the fact that the energetic cost for a mixed twist-splay can be lower than the surface energetic cost at the homeotropic wall in the case of undistorted planar alignment. Such a situation may also be achieved for nematics which have a bulk elastic isotropy. In this paper, the saddle-splay elastic constant K24 is shown to influence strongly the occurrence of the periodic pattern of splay-type, also in the presence of an external magnetic field normal to the cell plates, and the role of the geometrical anchoring in wedge-shaped cells is discussed