Ripple instability threshold in twisted cholesteric films: Multicritical boundaries and the effect of pretilt angles

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Abstract
The stability of twist configurations in cholesteric liquid-crystal films in the presence of an external field applied parallel to the twist axis is considered. First, a general method for finding, in the absence of pretilt at the cell boundaries, the point on the instability line at which the character of the instability mode changes from uniform in the film plane to one with in-plane ripple is developed. The locus of these points (in parameter space) forms a phase boundary with multicritical behavior of the Lifshitz type. Some typical results are presented. Next, pretilt angles are allowed. In this case a uniform instability mode threshold no longer exists; however, a transition to a ripple state is still possible. Methods of analyzing such transitions are presented, along with typical results. The connection between the methods and results presented here and the development of modern liquid-crystal displays is noted.