Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.