Electrohydrodynamic Solutions for the Homeotropic Nematic-Liquid-Crystal Geometry

We have solved the boundary-value problem associated with the electro-optic mode which appears in a nematic liquid crystal subjected to a dc electric field parallel to the nematic director. Above a critical voltage, the liquid breaks up into a series of cylindrical lenses similar to those observed in the Williams domain mode. The dispersion relations for $p$-azoxyanisole and $p$-methoxybenzylidene-$p-n$-butylaniline were calculated using the known material constants for these two nematogens. We show that the critical voltage is caused by the dielectric torque opposed by the bend distortion torque; the critical voltage is not sensitive to the various viscosity parameters nor the conductivities. The dispersion relation at higher voltages does involve these constants.