Nematic liquid-crystal director configuration for general elastic coefficients

We provide a general analytical solution for the director field of a nematic liquid crystal confined between two horizontal plates. The derivation goes beyond the common one-constant approximation where the elastic coefficients are assumed equal. The solution remains valid in the presence of an applied magnetic or electric field. The effect on the bulk director of various director anchoring angles at the confining plates is derived and analyzed. Further, a generalization of the Freedericksz transition to other anchoring angles is investigated.