Abstract
Abstract Liquid crystal layers subjected to an electric or a magnetic field can have several types of instabilities. This paper reviews recent theoretical studies concerning equilibrium structures of planar layers. Using the Oseen-Frank elasticity theory, the Freedericksz transition and the transition to static periodic domains of planar nematic and cholesteric films are reconsidered. A perturbation treatment of nonlinear torque balance equations for the director is suitable to derive amplitude equations for the film distortions under the action of a field and to predict the topological features of phase diagrams for equilibrium states. The competition between the Freedericksz effect and the formation of periodic distortions is studied varying material and geometrical parameters. Some results are useful to optimize cholesteric mixtures for application in display devices in such a manner, that the occurrence of periodic domains is avoided.
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