Instability of a Biaxial Nematic Liquid Crystal Formed by Homeotropic Anchoring on Surface Grooves

A method used to treat the elastic distortion of a uniaxial nematic liquid crystal induced by homogeneous anchoring on the surface grooves is generalized to biaxial nematic liquid crystals under the homeotropic anchoring condition. Employing some approximations for the elastic constants, we obtain an additional term in the elastic energy per unit area which depends on the angle between the minor director at infinity and the direction of the grooves, with a period of π/2. This leads to instability on the surface grooves so that two states with crossed minor directors are energetically indistinguishable. Our theoretical study explains why the homeotropic alignment method developed for uniaxial liquid crystals loses efficacy for biaxial nematics.