Critical thickness of a hybrid aligned nematic liquid crystal cell

Abstract

We discuss the director deformation inside a hybrid aligned nematic (HAN) cell, assuming that the surface interaction is of the (w/2) sin2 (ϕ — Φ) kind, and we suppose that the anchoring energy for homeotropic alignment is greater than the planar one. In the absence of an external electric field, we show that a critical thickness dc, below which the nematic liquid crystal (NLC) is undistorted, exists. Furthermore we investigate theoretically dc vs. the reduced electric field (E/Ec, where Ec is a threshold field depending upon the anchoring energies and the intrinsic constants of the NLC). The last analysis shows that there are two critical thicknesses dc(H) and dc(P): for d < dc(H) the sample is homeotropic (HOM), while for d > dc(P) it is planar (PLAN). Finally we point out that if the anchoring energies are the same on the upper and lower plates of the sample, the HAN-configuration is realizable only if E/Ec < 1