DIRECTOR DEFORMATION OF A TWISTED CHIRAL NEMATIC LIQUID-CRYSTAL CELL WITH WEAK ANCHORING BOUNDARIES

On the basis of a generalization of the Rapini-Papoular expression [J. Phys. (Paris) Colloq. 30, C4-54 (1969)] for the anchoring energy, the rigorous expressions for the threshold and saturation fields are deri ved analytically, in detail, for a field-controlled twisted chiral nem atic slab with weak boundary coupling. The surface anchoring energy of the Rapini-Papoular type for a twisted nematic slab should be general ly expressed as the interfacial energy per unit area for a two-dimensi onal deformation which is a nonlinear combination of the azimuthal and polar angles. Applying a variational calculation method for the two-d imensional problem to the total free energy, that is the sum of the bu lk energy and the surface energy, we derive general torque balance equ ations which describe the equilibrium deformation of the director.