Mechanisms and shape predictions of nematic disclination branching under conical confinement

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

Recent studies have shown that lyotropic nematic liquid crystals (LLCs) are exceptional in their viscoelastic behavior. In particular, LLCs display a remarkable softness to twist deformations, which may lead to chiral director configurations under achiral confinement despite the absence of intrinsic chirality. The twisted escaped radial (TER) and the twisted polar (TP) are the two representative reflection symmetry breaking director configurations in the case of cylindrical confinement with homeotropic anchoring. We demonstrate how such reflection symmetry breaking of micellar LLCs under cylindrical confinement is affected by intrinsic chirality, introduced by the addition of a chiral dopant. Similarities and differences between the effects of intrinsic chirality on the defect-free TER configuration, and on the TP configuration incorporating two half-unit twist disclination lines, are discussed. In the TP case, topological constraints facilitate stable heterochiral systems even in the presence of a small amount of chiral dopant, with unusual regions of rapidly reversing handedness between homochiral domains. At moderate dopant concentrations, the TP structure becomes homochiral. At high dopant concentrations, for which the induced cholesteric pitch is much smaller than the diameter of the capillary, the cholesteric fingerprint structure develops.

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.

The effect of anchoring on the nematic flow in channels

Understanding the flow of liquid crystals in microfluidic environments plays an important role in many fields, including device design and microbiology. We perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal flowing under an applied pressure gradient in two-dimensional channels with various anchoring boundary conditions at the substrate walls. We investigate the relationship between the flow rate and the pressure gradient and the corresponding profile of the nematic director, and find significant departures from the linear Poiseuille relationship. We also identify a morphological transition in the director profile and explain this in terms of an instability in the dynamical equations. We examine the qualitative and quantitative effects of changing the type and strength of the anchoring. Understanding such effects may provide a useful means of quantifying the anchoring of a substrate by measuring its flow properties.

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

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.