2π Disclinations in Nematics for Cylindrical Systems

Abstract

Line disclinations of uniaxial nematics are classified into two types: 2nπ ones which are topologically removable and (2n+1)π ones which are not. The equilibrium configurations of the director of 2π disclinations in cylindrical geometry are examined by nonlinear equations derived by Frank elastic theory. The equilibrium equations for splay-bend and bend-twist deformations are solved exactly. For the bend-twist cases, the effect of a magnetic field induced by the central current is examined. When the disclinations are non-singular, the solutions are described by hyperbolic and trigonometric function. In other cases they are in general expressed in terms of elliptic functions.