Theoretical predictions of disclination loop growth for nematic liquid crystals under capillary confinement

Abstract

The combination of low elasticity modulus, anisotropy, and responsiveness to external fields drives the rich variety of experimentally observed pattern formation in nematic liquid crystals under capillary confinement. External fields of interest in technology and fundamental physics are flow fields, electromagnetic fields, and surface fields due to confinement. In this paper we present theoretical and simulation studies of the pattern formation of nematic liquid crystal disclination loops under capillary confinement including branching processes from a m=+1 disclination line to two m=+1/2 disclination curves that describe the postnucleation and growth regime of the textural transformation from radial to planar polar textures. The early postnucleation and growth of emerging disclination loops in cylindrical capillaries are characterized using analytical and computational methods based on the nematic elastica that takes into account line tension and line bending stiffness. Using subdiffusive growth and constant loop anisotropy, we found that the solution to the nematic elastica is a cusped elliptical geometry characterized by exponential curvature variations. The scaling laws that govern the loop growth reflect the tension to bending elasticity balance and reveal that the loop dilation rate depends on the curvature and normal velocity of the disclination. The line energy growth is accommodated by the decrease in branch-point curvature. These findings contribute to the evolving understanding of textural transformations in nematic liquid crystals under confinement using the nematic elastic methodology.

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

“…In this section, largely based on references [7][8][9][10] we derive the disclination shape equation by formulating the force balance equation due to internal and external stresses on the line. Internal stresses include line tension and line bending forces are derived using Frank elasticity.…”

Nematic Liquid Crystals under Conical Capillary Confinement: Theoretical Study of Geometry Effects on Disclination Lines

“…For the loop growth and pre-saturated stages the line viscosity term is negligible comparing to other terms [11] but it becomes important in the relaxation mode. point, κ 0 = dφ/ds| s=0 , and the stiffness ratio "a" (1/ length 2 ) of tension to bending moduli:…”

“…studies [7,8]. In our previous work [8,9,11], we focused on one possible transformation under capillary confinement, between the planar radial (PR) texture with a +1 axial singular disclination into a planar polar (PP) texture with a pair of off-axis +1/2 disclinations. Here, we consider the effect of conical confinement as opposed to cylindrical, on the texture transformation process.…”

“…The early stage and loop growth have been investigated for confined nematics in cylindrical geometries [11,12]; here we focus on the early and late stages, characterization of the branching process and the effect of the conical confinement. The intermediate stage will be investigated in future work.…”

“…Here, we consider the effect of conical confinement as opposed to cylindrical, on the texture transformation process. The nature of the PR→PP transition in principle can be explained by nucleation and growth (NG) [11] in which a number 'n' of +1/2 loops nucleate and grow along the initial +1 line. The distance L between nucleating loops is a function of capillary size; for a cylindrical confinement it can be estimated by R c = L/n, where R c is the capillary radius.…”