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 derived analytically, in detail, for a field-controlled twisted chiral nematic slab with weak boundary coupling. The surface anchoring energy of the Rapini-Papoular type for a twisted nematic slab should be generally expressed as the interfacial energy per unit area for a two-dimensional deformation which is a nonlinear combination of the azimuthal and polar angles. Applying a variational calculation method for the two-dimensional problem to the total free energy, that is, the sum of the bulk energy and the surface energy, we derive general torque balance equations which describe the equilibrium deformation of the director.
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