Influence of flexoelectricity on the stable configuration of a nematic layer with opposite boundary conditions

We discuss the influence of flexoelectricity on the critical thickness of a hybrid aligned nematic liquid crystal cell. We show that the critical thickness is independent of the flexoelectrical properties of the nematic only under the hypothesis that the distorted-undistorted transition is of second order. Afterall, the only effect of flexoelectricity is to introduce a very large elastic anisotropy. On the other hand, if first order transitions are considered, the flexoelectricity may play an important role. We also consider the surface polarization which can be different from zero for symmetry considerations. The analysis shows that its influence on the critical thickness or on the order of the transitions is negligible when there is no applied electric field. Some considerations on the terms connected with the surface polarization are also reported. The analysis is performed by supposing the nematic material a perfect insulator. J. Physique 47 (1986) 341-350 FÉVRIER 1986, :