Anisotropy induced director refraction inside inversion walls in nematic liquid crystals

Abstract

We compute the texture of the inversion walls which appear in nematics in a magnetic field. In the isotropic case, where the 3 curvature elastic constants are equal, the Brochard planar description is correct. In the anisotropic general case, we find an unpredicted director rotation around the field, which minimizes the elastic free energy of the wall, by transferring some curvature distortion toward the lowest elastic constant curvature mode. This rotation is calculated to first order in the elastic anisotropy. By symmetry, the planar model remains valid when there is no twist in the wall. This rotation explains the recently observed twist of neutral axes along the inversion walls in lyotropic liquid crystals. In the highly anisotropic case (polymeric nematics), the ellipticity of closed loop walls should be twice larger than that predicted Calcul de la texture des parois qui apparaissent entre deux domaines symetriques dans des cristaux liquides nematiques places dans un champ magnetique. Consideration des cas isotrope et anisotrope