Non-linear solutions for smectic C liquid crystals in wedge and cylinder geometries

Abstract

This paper discusses some non-linear problems for smectic C liquid crystals based on the continuum theory proposed by Leslie et al. New restrictions on the nine elastic constants are also derived. Attention is restricted to samples involving concentric cylindrical layers in which both the layer thickness and the tilt angle are assumed to be constant. Non-linear solutions are presented for a sample contained in a wedge with an electric field applied across the bounding plates, extending earlier work by Carlsson et al., and for a sample between two coaxial concentric circular cylinders to which an azimuthal magnetic field is applied. Freedericksz thresholds, which may lead to the experimental determination of some of the elastic constants, are deduced. In the absence of an applied field it is found that, under suitable restrictions on the elastic constants, there is a critical wedge angle (or critical radius ratio in the concentric cylinder case) above which a variable non-linear symmetric solution satisfying the zero boundary conditions is energetically more favourable than the zero solution.