Electrical Friedericksz transition in a nematic cell with periodic polar anchoring energy

The threshold value for the electrical Friedericksz transition in a nematic liquid crystal cell with the periodic energy of director anchoring with the cell surface has been derived, and the above-threshold spatial distribution of the director in the applied electric field has been determined. The threshold value was shown to depend non monotonously on the number s of anchoring energy periods across the cell length. The above-threshold distribution of the director at integer s traces a periodic variation of the anchoring energy. The amplitude of the director's periodic deviation grows with the reduction of the ratio between the cell thickness and the anchoring energy period.