Topological zoo of free-standing knots in confined chiral nematic fluids

Seč, David; Čopar, Simon; Žumer, S.

doi:10.1038/ncomms4057

Cited by 101 publications

(127 citation statements)

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“…From a theoretical point of view, such images provide a useful simulation tool with which to assess the structure of these phases. As with strong homeotropic anchoring, the splaybend isosurfaces in the BPs can exhibit a helical structure around the defects (42).…”

Section: Resultsmentioning

confidence: 99%

“…Other configurations, such as the so-called diametrical spherical structure (DSS), where the director field forms concentric tori of double twist cylinders, the lyre and the yeti morphologies, which are related each other and the structure of the first one resembles a lyre instrument, represent metastable states whose free energy is well above that of the RSS configuration (by approximately 10 4 kT). For droplets with strong homeotropic anchoring, the defects form different types of "knots," particularly at high pitch (p ≥ 0.75 μm) (42). A key feature of that work is that the topological complexity of the system arises from a balance between the tendency by the low-chirality medium in the bulk to adopt a smectic-like structure, and the strong homeotropic anchoring that governs orientation at the droplet's interface.…”

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confidence: 99%

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Blue-phase liquid crystal droplets

Martínez‐González

Zhou

Rahimi

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Blue phases of liquid crystals represent unique ordered states of matter in which arrays of defects are organized into striking patterns. Most studies of blue phases to date have focused on bulk properties. In this work, we present a systematic study of blue phases confined into spherical droplets. It is found that, in addition to the so-called blue phases I and II, several new morphologies arise under confinement, with a complexity that increases with the chirality of the medium and with a nature that can be altered by surface anchoring. Through a combination of simulations and experiments, it is also found that one can control the wavelength at which blue-phase droplets absorb light by manipulating either their size or the strength of the anchoring, thereby providing a liquid-state analog of nanoparticles, where dimensions are used to control absorbance or emission. The results presented in this work also suggest that there are conditions where confinement increases the range of stability of blue phases, thereby providing intriguing prospects for applications.blue phases | chiral liquid crystals | droplets | confinement B lue phases of liquid crystals (LCs) are characterized by a local director field that forms double-twisted cylinders, arranged into defect regions that are periodically repeated in space (1, 2). The symmetry properties of blue phases (BPs) have attracted considerable attention, as have their potential applications in a wide range of technologies (3-7). Theoretical and computational studies of the bulk structure and dynamics of BPs have helped elucidate their nature (1, 8, 9-15) in considerable detail. In the bulk, however, BPs are only found in a narrow range of temperature, between the cholesteric and the isotropic phases (1-6, 10-18), thereby placing limits on their practical utility. Recent efforts have therefore focused on increasing their stability over wider ranges of temperature and chirality, for example through addition of nanoparticles (19, 20, 21-23), polymers (24-26), or by manipulating their flexoelectricity (14).Confined chiral liquid crystals are of interest for applications in optical devices (27)(28)(29)(30)(31). Simulations of chiral LCs in channels have shown that their defect structure can be manipulated through confinement, thereby raising intriguing prospects for technology (32)(33)(34)(35). Chiral LC droplets have also been studied both numerically (36-38) and experimentally (39,40). More recent, intriguing simulations of planar chiral droplets with strong anchoring by Seč et al. (41) have examined their phase behavior as a function of chirality. In particular, it was reported that the twist bipolar structure (BS) is stable in the low chirality regime, whereas the radial spherical structure (RSS) is preferred at high chirality. The BS state has a cylindrical symmetry, where the director field is uniform along the symmetry axis of the droplet and rotates in the perpendicular direction forming bent cholesteric layers. In the RSS state, the director field also forms curved ...

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Blue-phase liquid crystal droplets

Martínez‐González

Zhou

Rahimi

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…In addition to the confinement of flat homeotropic cells, similar effects of handedness reversal can occur in other geometries, such as that of spherical or complex-topology high-genus cholesteric LC droplets, cylindrical capillaries, etc. [21,22,23,24,25]. In many LCs with low-value twist elastic constants, such as chromonic LCs [21,23,24], director twist often occurs to replace more energetically costly splay and bend deformations.…”

Section: Discussionmentioning

confidence: 99%

Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals

Ackerman

Smalyukh

2016

Phys. Rev. E

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Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chiral liquid crystal ground state can arise in the proximity of twisted-soliton-bound topological point defects. In chiral nematic liquid crystal confined to a film that has a thickness less than the cholesteric pitch and perpendicular surface boundary conditions, twisted solitonic structures embedded in a uniform unwound far-field background with chirality-matched handedness locally relieve confinement-imposed frustration and tend to be accompanied by point defects and smaller geometry-required energetically costly regions of opposite twist handedness. We also describe a new spatially localized structure, dubbed a "twistion", in which a twisted solitonic three-dimensional director configuration is accompanied by four point defects. We discuss how our findings may impinge on the stability of localized particle-like director field configurations in chiral and non-chiral liquid crystals.

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“…Defect structures in NLC and their colloidal composites (25) have been extensively studied for their potential in selfassembly and light control (26), but also to further the theoretical understanding of topological phenomena in director fields (23,27). Objects of interest include chiral solitons (28,29), fields around knotted particles (30)(31)(32)(33)(34)(35), and knotted defects in nematic colloids (36)(37)(38)(39)(40)(41)(42). Each of these cases is unique, as the rules of knot theory interact with the rules and restrictions of each underlying material and confinement.…”

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confidence: 99%

Knot theory realizations in nematic colloids

Čopar

Tkalec

Muševič

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals.liquid crystal colloids | knot theory | topological defects | knotted fields

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Topological zoo of free-standing knots in confined chiral nematic fluids

Cited by 101 publications

References 52 publications

Blue-phase liquid crystal droplets

Blue-phase liquid crystal droplets

Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals

Knot theory realizations in nematic colloids

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