Interaction between a +1 defect in a nematic thin film and the surface wall and flexoelectric response at the defect site

Within the Landau-de Gennes theory, we have investigated the interaction between a +1 defect whose nuclei is ‘circular’ nuclei (i.e. the director flux lines around the defect nuclei are circular) and the surface wall, using the one-dimensional finite-difference iterative method. +1 point defects will evolve into line defects perpendicular to the sample plane due to the existence of the surface wall. Therefore, we consider cylindrically symmetric solutions containing the line defect. The free energy of liquid crystal molecules around the defect nuclei and the surface energy produced by the surface wall are competing with each other. This competition makes polar angle of the director around the defect nuclei change considerably in a certain region, and the scale of this region will decrease with the surface anchoring strength increasing. On application of a DC electric field normal to the sample plane, the defect exhibits a flexoelectric response. We demonstrate that the field-driven structural changes at the defect site involve changes in both azimuthal and polar angles defining the local director.