NONLINEAR SOLUTIONS FOR SMECTIC-C LIQUID-CRYSTALS IN WEDGE AND CYLINDER GEOMETRIES

This paper discusses some non-linear problems for smectic C liquid cry stals based on the continuum theory proposed by Leslie et al. New rest rictions 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 constan t. Non-linear solutions are presented for a sample contained in a wedg e with an electric field applied across the bounding plates, extending earlier work by Carlsson ct 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 ab sence of an applied field it is found that, under suitable restriction s on the elastic constants, there is a critical wedge angle (or critic al radius ratio in the concentric cylinder case) above which a variabl e non-linear symmetric solution satisfying the zero boundary condition s is energetically more favourable than the zero solution.