On the Field-Induced Cholesteric-Nematic Transition in Cholesteric Liquid Crystals with Homeotropic Boundary Conditions

The influence of homeotropic boundary conditions on the cholesteric-nematic transition is discussed, starting from the assumption that the director field consists of only components perpendicular to the helix axis, which is directed parallel to the boundary planes. Attention is paid to the solution of Cladis and KJeman for the simpler case without magnetic field. Their solution, consisting of regularly spaced line signularities, is derived in another more transparent way. Besides it is shown that even director fields without singularities are possible. The presence of a magnetic field complicates the solution considerably. Now the relevant Euler-Lagrange equation is solved in an approximate way by partly resorting to the difference method. The usefulness of the method is demonstrated by applying this technique to the nematic-cholesteric transition and the Freedericksz transition in nematics.