Bend-stripes in hybrid aligned nematic layers

Abstract

The occurrence of bend-stripes also involving twist distortion is investigated in hybrid aligned nematic layers, with stronger tilt-anchoring at the homeotropic substrate than at the planar one. The modulated structure is found to exist above the thickness threshold d _a for the aperiodic bend-splay deformation. The periodicities of the director azimuth and polar angle are incommensurate along the normal to the cell plates. In principle, two independent periodic modes are possible, the first one stable, with threshold d _p = d _a, the second one metastable, with threshold d _p > d _a, according to the values of the torsional extrapolation lengths. Both transitions are continuous with respect to the in-plane wavenumber. The second mode can appear only if the difference between the torsional and the tilt extrapolation lengths is positive at the planar substrate. Moreover, both thresholds are independent of the saddle-splay elastic constant.