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

Abstract

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.

Formation and field-driven dynamics of nematic spheroids

“…Figure 5 shows the uniaxial S and biaxial P nematic order parameters in the vicinity of the central region of the prolate droplet during the disclination splitting process. This process is similar to disclination line-loop dynamics observed by Shams and Rey, 44,45 for which they developed a nematic elastica model for defect dynamics which captures line tension and bending of disclinations. In the presently observed defect splitting process, line torsion, in addition to tension and bending, would need to be accounted for which could be accomplished through incorporating higher order terms in the nematic elastica model.…”

Interplay between Confinement, Twist Elasticity, and Intrinsic Chirality in Micellar Lyotropic Nematic Liquid Crystals

“…As a result, the magnetic field-induced TP state persists for very long times. Shams et al − have made an extensive theoretical study of the branching from a +1 defect to two 1/2 disclinations as a function of the cylinder diameter using the one elastic constant approximation. However, the case of soft twist elasticity and therefore the formation of chiral twist disclinations has not been considered yet.…”

“…This is called the planar radial (PR) configuration; Figure a. In theory, the s = +1 defect is likely to split up into two s = 1/2 disclinations, − as the elastic energy around disclinations is proportional to s 2 . This would be the planar polar (PP) configuration, depicted in Figure b.…”

Pattern formation, structure and functionalities of wrinkled liquid crystal surfaces: A soft matter biomimicry platform

“…The Helfrich elastic model was applied to study the shape of red blood cell (Martínez-Balbuena et al, 2021) and lipid bilayer structure (Campelo et al, 2014). The elastic contribution to the anisotropic surface tension (Rofouie et al, 2017a) yields a membrane-liquid crystal tension (Rey, 1999b;2003;Shams et al, 2015)…”