Coarsening dynamics in uniaxial nematic liquid crystals

Chuang, Issac; Yurke, Bernard; Pargellis, A. N.; Turok, Neil

doi:10.1103/physreve.47.3343

Cited by 86 publications

(82 citation statements)

References 36 publications

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“…As an extension of the theory of − 1 2 defects, the introduced formalism describes a wider range of disclination networks. Notable examples of systems that exhibit transitions between different director profiles are confined cholesteric phases [17], optically induced defects [28] and transient defects that are created by quenching from the isotropic phase [29]. Studies of random blue phases [30] and entangled structures in random or structured pores [15] could also benefit from improved classification of disclination profile variations.…”

Section: Resultsmentioning

confidence: 99%

Quaternions and hybrid nematic disclinations

Čopar

Žumer

2013

Proc. R. Soc. A.

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Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterized by their director profile. In certain confined colloidal suspensions and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile in closed disclination loops and use it to apply topological classification to linked loops with arbitrary variation of the profile, generalizing the self-linking number description of disclination loops with the winding number − 1 2 . The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations, allowing application of said theory to structures that occur in practice.

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Section: Resultsmentioning

confidence: 99%

Quaternions and hybrid nematic disclinations

Čopar

Žumer

2013

Proc. R. Soc. A.

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“…Such a description, valid for distances much larger than the defect core, typically involves time dependent Ginzburg-Landau equations or their generalizations. A few cases have been studied extensively, including domain coarsening in O(N) models [3,4], in nematics [5][6][7][8], and in smectic phases as effectively encountered in models of Rayleigh-Bénard convection or lamellar phases of block copolymers [9][10][11][12][13][14][15]. In the case of modulated phases, the motion of a single defect has been widely studied within the well known amplitude equation formalism.…”

Section: Introductionmentioning

confidence: 99%

Grain boundary pinning and glassy dynamics in stripe phases

2002

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We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value Rg ∼ λ0 ǫ −1/2 exp(|a|/ √ ǫ), where ǫ ≪ 1 is the dimensionless distance away from threshold, λ0 the stripe wavelength, and a a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.

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“…Most of it has involved statistical studies, either of the evolution of disclination lines as annihilation of pairs took place [6] or of the coarsening dynamics of defect strings and loops [7]. Recent experiments [8] have addressed directly the dynamics of the annihilation of parallel 1=2 disclination lines in a planar nematic sample.…”

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Backflow-Induced Asymmetric Collapse of Disclination Lines in Liquid Crystals

Oswald

Ignés‐Mullol

2005

Phys. Rev. Lett.

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We present experiments where opposed pairs of planar parallel disclination lines of topological strength s 1 move due to their mutual attraction. Our measurements show that their motion is clearly asymmetric, with 1 defects moving up to twice as fast as ÿ1 ones. This is a clear indication of backflow, given the intrinsic isotropic elasticity of our system. A phenomenological model is able to account for the experimental observations by renormalizing the orientational diffusivity estimated from the velocity of each defect. DOI: 10.1103/PhysRevLett.95.027801 PACS numbers: 61.30.Jf, 61.30.Hn, 61.72.Lk, 83.80.Xz Topological defects were first postulated in order to explain the plasticity of metals. Then, they were proved to be essential for understanding phase transitions, disordered systems, frustrated media, convective instabilities, as well as some biological shapes, etc. In real systems, defects interact, leading to complex dynamics that often result in the annihilation of pairs of defects of opposite signs. Such phenomena arise, for instance, during solid recrystallization, but they can similarly be observed in liquid crystals where they are much easier to study experimentally.In nematic (or cholesteric) liquid crystals, defects are disclination lines that break locally the orientational order. Their motion induces a distortion of the director field, starting at the defect core and propagating diffusively in the bulk. Early analysis assumed that the dynamical director field was the same as under static conditions at all times [1]. This quasistatic approximation leads to a logarithmic divergence of the calculated total dissipated energy, which requires one to introduce a cutoff length at large distances from the core of the defect. Ryskin and Kremenetsky [2] later showed that this characteristic length comes out naturally from the dynamic equations and is of the order of the orientational diffusivity divided by the velocity of the defect. This length defines an active zone around the defect in which the quasistatic approximation is valid. On the other hand, liquid crystals flow as liquids. One thus may expect that defect motion, which is mainly due to an inplace rotation of the director, is affected by hydrodynamics (the so-called backflow effects). Recent numerical simulation in two dimensions [3] of the annihilation of two planar disclination lines of strengths s 1=2 in nematics have confirmed this point. It was found numerically that backflow breaks the symmetry of the collapse dynamics between defects, even in isotropic elasticity, the 1=2 defect moving faster than the ÿ1=2 one. A similar conclusion was reached in simulations for the collapse of 1 disclinations in smectic-C films [4]. These results are consistent with the analysis by Kats et al. [5] who found that positive disclinations always exert a stronger influence on the flow velocity than negative ones.There has been some experimental work dealing with the interaction between parallel disclination lines. Most of it has involved statistical studies...

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Coarsening dynamics in uniaxial nematic liquid crystals

Cited by 86 publications

References 36 publications

Quaternions and hybrid nematic disclinations

Quaternions and hybrid nematic disclinations

Grain boundary pinning and glassy dynamics in stripe phases

Backflow-Induced Asymmetric Collapse of Disclination Lines in Liquid Crystals

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