Lifshitz multicritical behavior at ripple instability thresholds in cholesteric films

Transverse spiral (i.e., pure twist) director configurations occur when cholesteric liquid crystals are confined between two parallel plates such that the director is strongly anchored in fixed directions in the film plane at the boundaries. Such states, however, are no longer stable when the magnitude of an electric field applied along the twist axis reaches a critical value. The instability modes appearing at such generalized Fréedericksz instabilities are here studied using Landau theory and linear stability analysis. In particular, the surface (in a four-dimensional parameter space) on which the instability mode character changes from uniform to non-uniform (i.e., with one-dimensional stripes or ripple in the film plane) is determined analytically. The points on such a surface can have special properties, in which case they are known as Lifshitz multicritical points. For parameter values of interest, the Lifshitz character of such points is verified explicitly by considering higher order terms in the Landau free energy. Estimates for experimentally available materials values are also given.