Anisotropic disclination cores in nematic liquid crystals modelled by a computational Maier-Saupe field theory

We develop a computational model based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic coexistence region, and that goes to infinity if the eigenvalues of the order parameter become non-physical. An elastic free energy is added which is an expansion in spatial gradients of the order parameter up to third order, allowing for parametric control over the anisotropy and elasticity of the liquid crystals. Computations of the spatial profile of the order parameter are presented for nematic disclinations in two dimensions. We compare the simulation results to recent experiments and show good agreement.