Quaternions and hybrid nematic disclinations

Čopar, Simon; Žumer, S.

doi:10.1098/rspa.2013.0204

Cited by 22 publications

(24 citation statements)

References 29 publications

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“…In nematics in general there is no restriction for the director in the cross-section of a disclination with half-integer winding to be in-plane and the winding profile of a disclinations can change. Because of this, all line defects with a half-integer winding number director profile, which does not change along the length of the disclination, are topologically equivalent [32][33][34].…”

Section: Topological Defects In Two Dimensionsmentioning

confidence: 99%

“…Because the total topological charge is determined by the topology of the confinement, and the anchoring conditions, the choice of the branch cut surface also changes the topological charge of the ring defect. Without selecting a branch cut surface, one can still tell if the topological charge of a defect line is odd or even: if the director profile of the defect line with half-integer winding is fixed, the topological charge is odd, and if the profile changes, it can be odd or even, depending on the number of changes [33,47]. Without a selected branch cut surface to define the signs of the topological charges, the conserved topological quantity is the sum of the topological charges modulo 2 [7,32,33,48].…”

Section: Three-dimensional Topological Defectsmentioning

confidence: 99%

“…This choice also changes the topological charge of the defect loop. In such situations we can only determine the total topological charge modulo 2 or in other words, if the total charge is odd or even [7,32,33]. Because of the homeotropic anchoring the total topological charge of the droplet must be odd (or exactly +1 for any choice of a branch cut surface).…”

Section: Droplets With Disclination Linesmentioning

confidence: 99%

“…Because of the homeotropic anchoring the total topological charge of the droplet must be odd (or exactly +1 for any choice of a branch cut surface). The topological charge of the line defect must also be odd, because it has a half-integer winding number of its cross-section and the proximity of the surface forces it to have a constant cross-section [33]. The total topological charge of the droplet therefore really is odd, because the topological charge of the two point defects with |q| = 1 is even.…”

Section: Droplets With Disclination Linesmentioning

confidence: 99%

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Topological Formations in Chiral Nematic Droplets

Posnjak¹

2018

Springer Theses

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Section: Topological Defects In Two Dimensionsmentioning

confidence: 99%

Section: Three-dimensional Topological Defectsmentioning

confidence: 99%

Section: Droplets With Disclination Linesmentioning

confidence: 99%

Section: Droplets With Disclination Linesmentioning

confidence: 99%

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Topological Formations in Chiral Nematic Droplets

Posnjak¹

2018

Springer Theses

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“…1I show the details of the director configurations around the +1/2 (red box) and −1/2 (blue box) disclination profiles. The transition between the two proceeds by rotating the director by π around an axis perpendicular to the disclination line (see figure 2 in [56]). Such a peculiar topology indeed yields zero topological point charge, as explained in [56].…”

Section: Numerical Computationsmentioning

confidence: 99%

Dispersions of ellipsoidal particles in a nematic liquid crystal

et al. 2014

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Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particle aggregates.

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Nematic Liquid Crystal Disclination Lines Driven by A Photoaligned Defect Grid

Nys

Berteloot

Beeckman

et al. 2021

Advanced Optical Materials

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behavior in the neighborhood of defects and their dynamics. [4] Disclination lines provide a topological stability that can be instrumental for new switching modes, to realize bistable switching, etc. Studying the formation, interaction, and responsiveness of LC disclinations is therefore not only interesting from a theoretical point of view but also opens up new possibilities for technological applications.Disclination lines can connect defects defined at the surface or can form closed loops in the bulk of a NLC, for example when encircling colloidal inclusions, [5] or when rapid but continuous variations in the alignment direction occur independently at opposing substrates of a device. [1d,e,h,i,3c] To realize patterned surface anchoring, scribing, microrubbing, surface topography, pillars, and photoalignment have been used. [1,2] In the case of strong anchoring, a defect in the alignment pattern with charge s generates 2|s| disclination lines in the bulk of the LC. In the case of weak anchoring and gliding, defects can become mobile and disclinations lines may connect two defects of the same charge on opposing substrates. [6] Thanks to photoalignment, stable defects can now easily be realized experimentally, as has been demonstrated in a few papers. [1d,e,3] The flexibility of photoalignment patterning in combination with the stimuli-responsiveness (e.g., electrical tunability) of LCs allows to design disclination networks with preprogrammed functionality. [2b,3c] Enhanced understanding of the LC behavior in cells with 2D patterns of topological defects is however still necessary to successfully engineer functional LC devices such as multistable photonic components, programmable origami or devices with directed self-assembly of colloidal particles. To study the interaction of NLC disclination lines and their behavior under applied voltages, we defined a square grid pattern of ½ defects on the bottom substrate in combination with a uniformly planar aligned top substrate. Different types of interconnections occur between the +1/2 and −1/2 surface defects, and the three most common types of bulk disclinations are analyzed in detail by comparing experiments with numerical simulations (with and without applied voltage). In the discussion section also a theoretical analysis is provided, explaining the curvature of the different disclination lines and including the effect of unequal elastic constants for splay, twist, and bend. To reduce the splay energy, a tilt of the director is induced close to the +1/2 surface defect. We managed to make this visible in the microscope by increasing the tilt under influence of an electric field.Photoalignment for nematic liquid crystals makes it possible to design complex alignment patterns with point defects, that can act as anchoring points for disclination lines. This feature may be used to realize novel electro-optical devices with bistability or enhanced scattering and is promising for material applications such as stimuli-responsive actuators, active matter, and assemb...

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Quaternions and hybrid nematic disclinations

Cited by 22 publications

References 29 publications

Topological Formations in Chiral Nematic Droplets

Topological Formations in Chiral Nematic Droplets

Dispersions of ellipsoidal particles in a nematic liquid crystal

Nematic Liquid Crystal Disclination Lines Driven by A Photoaligned Defect Grid

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