Surface disclinations in nematic liquid crystals

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Abstract
It is shown that in nematic liquid crystals the disclinations which are attached to the external boundaries of the specimens can be described by a Peierls-Nabarro type model known from the theory of crystal dislocations. Mathematically, dislocations with planar cores and surface disclinations are then completely analogous if the isotropic one-constant approximation and a planar distribution of the director are assumed. Solutions are first given for disclinations in a half-cylinder of large radius and the possibility of an asymmetry in the distribution of the director on the surfaces, which may be caused by an asymmetry in the anchoring forces, is discussed. Disclinations confined to one of the surfaces of a thin nematic layer are also studied. It is shown that the boundary conditions on the other surface may introduce an asymmetry into the distribution of the director in the bulk of the specimen. This long-range asymmetry should be distinguished from the intrinsic, short range asymmetry

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