Computational model of a Maier-Saupe field theory for nematic liquid crystals

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 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 crystal. Computations of the spatial profile of the order parameter are presented for an isotropic-nematic interface in one dimension, a nematic defect in two dimensions, and a tactoid in two dimensions. We compare the simulation results to those given by the Landau de-Gennes free energy.