The role of divergent terms in the Frank energy of nematic liquid crystals

The role of the divergent part of the Frank energy in the equilibrium state of nematic liquid crystals is considered. This term is needed to be considered in the boundary conditions only. It is shown that the divergent term plays the same role as Rapini–Papoular surface energy in the case of the boundary surface or the polar angle of director disturbances and leads to the azimuthal deflection of the director. The nematic equilibrium problem is considered in the case of small periodic boundary perturbations.