Self consistent field theory of isotropic-nematic interfaces and disclinations in a semiflexible molecule nematic

A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects in the nematic phase (disclinations). Nematogens are modeled by worm-like chains, with microscopic interaction potential of the Maier-Saupe (MS) type, with an added isotropic excluded volume contribution. The thermodynamic fields obtained by numerical minimization of the free energy are the molecular density and the nematic tensor order parameter. Interfaces with both homeotropic and planar alignment are studied, as well as biaxiality and anisotropy around ±1/2 disclinations. The effects induced by fluid compressibility, interaction strength, and elastic anisotropy that follows from chain flexibility on both types of nonuniform configurations are discussed. Defect core sizes decrease as the system becomes less compressible, eventually reaching a constant value in the incompressible limit. The core size is influenced by the nematic interaction strength u₂ and chain persistence length l_p, decreasing as the order increases in the nematic region through manipulation of l_p and u₂. In incompressible limit and for fixed far field nematic order, the core size is seen to be on order of chain contour length for rigid chains, and it decreases as the chains become more flexible.