Electrohydrodynamic Solutions for Nematic Liquid Crystals with Positive Dielectric Anisotropy

-The steady state electrohydrodynamic equations of motion have been solved for nematic liquid crystals which are characterized by a positive dielectric anisotropy and possess a parallel homogeneous texture when contained between transparent electrodes. It is found that a periodic distortion of the director is possible above a critical voltage which is a function of the material constants. The optical texture should be similar to that observed in the Williams domain mode. The wavelength of the distortion is a function of voltage, and the relationship is very similar to the dispersion relation calculated for a negative dielectric anisotropy material in the homeotropic texture. These calculations demonstrate that the numerous experimental observations of domain structures have a common explanation in terms of the continuum theory. A physical explanation is given for the double valued solutions observed in the parallel homogeneous negative dielectric anisotropy problem.