Periodic stripe domains and hybrid-alignment regime in nematic liquid crystals: Threshold analysis

Recently we investigated the occurrence of static periodic stripes in a hybrid aligned nematic cell. Assuming that the tilt anchoring was stronger at the planar wall than at the homeotropic wall, we have found the critical thickness of the cell for the transition from planar to periodic alignment as a function of the surface energy in the presence of a magnetic field. Here we study, for the same kind of cell, the critical thickness between the periodic and the aperiodic deformed structure by means of an appropriate numerical technique. As expected, such a threshold was found to be greater than the asymptotic threshold between planar and aperiodic structures. We performed an experiment, which allowed us to give an estimate of the surfacelike elastic constant ${\mathit{K}}_{24}$.