Dynamics of confined nematic liquid crystals: Computer simulation of field-induced band formation in the presence of defects anchored on solid boundary surfaces

We present numerical simulations of the flow and director response of a nematic liquid crystal (5CB), confined between parallel plates, when an electric field is applied to the sample beforehand aligned by a magnetic field. We assume that the initial state (i.e. just before applying the electric field) of the nematic is not perfectly homogeneous due to local misalignment of the director at the contact with the boundary solid surfaces. More precisely, we consider the case of one pair of topological defects with charge ± 1/2 rigidly anchored on one plate bounding the sample; on the other hand we consider the geometry where electric and magnetic fields are orthogonal and the electric field is normal to the plates. The numerical manipulation of topological defects within the framework of Leslie–Ericksen theory is facilitated by employing a tensorial form of this theory that will be briefly described. The equations are solved for a two dimensional domain in which disclination lines reduce to points (i.e. the intersection of the disclination line with the domain of integration). The volume occupied by the misaligned regions is too small to produce a significant NMR signal, but when the electric field is applied they will play a crucial role in the development of a band pattern. The results are used to simulate NMR spectra, which compare favourably with recent experimental data exhibiting unusual characteristics.