Elastic interactions between topological defects in chiral nematic shells

Darmon, Alexandre; Dauchot, Olivier; López-León, Teresa; Benzaquen, Michael

doi:10.1103/physreve.94.062701

Cited by 15 publications

(10 citation statements)

References 33 publications

(65 reference statements)

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“…To the left a representative slice of the shell inside is drawn (as a projection onto the plane perpendicular to the paper, see the two coordinate systems for guidance) to illustrate the Bouligand cut director field that results from the nonconstant shell thickness. While multiple configurations of topological defects in the director field are possible, we have here chosen the case of a single s = +2 defect at the top (indicated with a black dot).…”

Section: Resultsmentioning

confidence: 99%

Through the Spherical Looking‐Glass: Asymmetry Enables Multicolored Internal Reflection in Cholesteric Liquid Crystal Shells

Geng

Jang

Noh

et al. 2017

Advanced Optical Materials

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tunable lasers [5] and chiral mirrors, [6] wavelength-selective photonic couplers/distributors, [7,8] photonic ink, [9] pH-, hydrogen peroxide and biosensors, [10][11][12] spontaneous nanoparticle segregation, [13] and unclonable patterns for secure authentication generated by arrays of ChLC shells. [14] So far, the optical properties were analyzed under the assumption that all light is reflected at the exterior of the ChLC and-with the exception of one paper suggesting a slightly ellipsoidal deformation [15] -that the droplets are perfect spheres, with full rotational symmetry. Is this assumption justified and does the neglect of possible deviations have consequences on the optical properties?For shells, full rotational symmetry is not necessarily to be expected, since perfect density matching between the inner isotropic liquid and the surrounding ChLC phase is difficult to achieve, and because experiments have shown that at least a nonchiral nematic prefers asymmetric shells, as this allows minimization of the free energy cost related to topological defects. [16] While recent theoretical work [17] suggests that a short-pitch ChLC promotes symmetric shells with a close to central position of the inner droplet, this has until now not been experimentally corroborated. In this paper we show that ChLC shells can change over time from nearly symmetric to strongly asymmetric, via a close competition between symmetry-restoring elasticity of the cholesteric helix and symmetry disrupting buoyancy. We demonstrate that this variation in shell geometry has dramatic implications for the photonic behavior.Symmetric shells and asymmetric shells with thick top (promoted by an inner phase denser than the ChLC) illuminated by white light Spheres of cholesteric liquid crystal generate dynamic patterns due to selective reflection from a helical structure subject to continuously curved boundaries. So far the patterns are investigated exclusively as function of reflections at the sphere exterior. Here it is shown that the cholesteric shells in a microfluidics produced double emulsion enable also a sequence of internal reflections if the shells have sufficiently thin top and thick bottom. While such asymmetry is promoted by buoyancy when the internal droplet has lower density than the liquid crystal, the elasticity of the cholesteric helix prefers a symmetric shell geometry, acting against gravity. This subtle balance can hide the internal reflections for long time. Eventually, however, the asymmetry is established, revealing a new class of photo nic patterns characterized by colored sharp concentric rings. With the complete knowledge of the diverse light-reflecting behavior of cholesteric liquid crystal shells, and utilizing the tunability of the structure period by, e.g., temperature, electric field, or exposure to various chemical species as well as polymer stabilization for making the shells long-term stable, they may be developed into remarkable new optical elements for photonics, sensing, or security pattern generation.

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Section: Resultsmentioning

confidence: 99%

Through the Spherical Looking‐Glass: Asymmetry Enables Multicolored Internal Reflection in Cholesteric Liquid Crystal Shells

Geng

Jang

Noh

et al. 2017

Advanced Optical Materials

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“…R and q are the radius of the droplet and the inverse of the cholesteric pitch, respectively . (C) Top view of CLC shells observed under POM corresponding to a specific defect configuration: four defects with winding number +1/2, two defects with winding number +1, one defect with winding number +1, two defects with winding number +1/2, one defect with winding number +3/2, one defect with winding number +1/2, and a single defect with winding number +2 . Adapted with permission from ref .…”

Section: Cholesteric Liquid Crystals Confined In Single Double Triple...mentioning

confidence: 99%

Liquid Crystals in Curved Confined Geometries: Microfluidics Bring New Capabilities for Photonic Applications and Beyond

et al. 2021

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The quest for interesting properties and phenomena in liquid crystals toward their employment in nondisplay application is an intense and vibrant endeavor. Remarkable progress has recently been achieved with regard to liquid crystals in curved confined geometries, typically represented as enclosed spherical geometries and cylindrical geometries with an infinitely extended axial-symmetrical space. Liquid-crystal emulsion droplets and fibers are intriguing examples from these fields and have attracted considerable attention. It is especially noteworthy that the rapid development of microfluidics brings about new capabilities to generate complex soft microstructures composed of both thermotropic and lyotropic liquid crystals. This review attempts to outline the recent developments related to the liquid crystals in curved confined geometries by focusing on microfluidics-mediated approaches. We highlight a wealth of novel photonic applications and beyond and also offer perspectives on the challenges, opportunities, and new directions for future development in this emerging research area.

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“…The equilibrium position of the two pairs of boojums results from the balance between: (i) a repulsive defect interaction of elastic nature and (ii) an attractive force due to the shell thickness gradient. 5,6,36 As the inner droplet de-swells, the shell becomes thicker, and the attractive term associated with the thickness gradient becomes more important, keeping the defects close together at the top of the shell. When the inner radius reaches a critical value, h/R E 0.5, we observe an abrupt transition, in which one pair of boojums rapidly migrates towards the thick part of the shell, while the other one remains at its thinnest part.…”

Section: De-confinement Transitionmentioning

confidence: 99%

“…In particular, theory and simulations have established the energy landscape for nematic shells with planar molecular anchoring. [4][5][6][7][8][9][10][11]17,18,20,21,29,[33][34][35][36][37] For very thin concentric shells, the shell ground state has four disclination lines at the vertices of a tetrahedron, as shown in Fig. 1(b).…”

Section: Introductionmentioning

confidence: 99%