Influence of anisotropic elasticity on pattern formation in a cholesteric liquid crystal contained between two plates

We study the transition between the twisted and untwisted states of a cholesteric liquid crystal bounded between two plates and constrained to have homeotropic anchoring at the plate surfaces. Previous theories predict that the twisted-untwisted transition should be second order, while experiments show that it is first order. In this paper we use a variational technique to show that either a first- or a second-order transition is possible, depending on the values of the Frank elastic constants $K_{11}$, $K_{22}$, and $K_{33}$. The previous experiments were conducted on materials whose elastic constants are such that a first-order transition is predicted.