Electrically driven hybrid instabilities in smectic C liquid crystal films

Novel static hybrid instabilities in smectic C liquid (SmC) crystal films are described. The Frederiks transition, well known for nematic liquid crystals, also takes place in smectic C layers, but; here, is spatially periodic and coupled to undulations of the smectic layer. The Helfrich-Hurault undulational instability, typical for smectic A liquid crystals, occurs in SmC liquid crystals too, but the wave vector of the undulation of the layers is oblique to the applied external field. In addition, this modified Helfrich-Hurault instability not only involves layer undulations, but also contains deformations of the director field, which are typical for the Frederiks transition. The coupled transformations depend on all three coordinate axes, thus characterizing 3-dimensional patterns. There are parameter ranges, where both types of static instabilities, which differ by the spatial wave number, compete with each other near codimension-2 bifurcations.