Disclination elastica model of loop collision and growth in confined nematic liquid crystals

Theory and modeling are used to characterize disclination loop-loop interactions in nematic liquid crystals under capillary confinement with strong homeotropic anchoring. This defect process arises when a mesogen in the isotropic phase is quenched into the stable nematic state. The texture evolution starts with +1/2 disclination loops that merge into a single loop through a process that involves collision, pinching and relaxation. The process is characterized with a combined Rouse-Frank model that incorporates the tension and bending elasticity of disclinations and the rotational viscosity of nematics. The Frank model of disclinations follows the Euler elastica model, whose non-periodic solution, known as Poleni's curve, is shown to locally describe the loop-loop collision and to shed light on why loop-loop merging results in a disclination intersection angle of approximately 60°. Additional Poleni invariants demonstrate how tension and bending pinch the two loops into a single +1/2 disclination ring. The Rouse model of disclination relaxation yields a Cahn-Hilliard equation whose time constant combines the confinement, tension/bending stiffness ratio and disclination diffusivity. Based on predictions made using this three stage process, a practical procedure is proposed to find viscoelastic parameters from defect geometry and defect dynamics. These findings contribute to the evolving understanding of textural transformations in nematic liquid crystals under confinement using the disclination elastica methodology.