Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals

Meiboom, S.; Sammon, M.; Brinkman, W. F.

doi:10.1103/physreva.27.438

Cited by 146 publications

(97 citation statements)

References 19 publications

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“…Blue phases provide a particularly fascinating example of liquid crystal ordering as they correspond to complicated director fields which, even in equilibrium, are threaded by a regular network of disclinations [8][9][10][11][12][13]. Identifying their structure presented a considerable theoretical challenge the resolution of which is clearly summarised in the review by Wright and Mermin [4].…”

Section: Introductionmentioning

confidence: 99%

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Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

Dupuis¹,

Marenduzzo²,

Yeomans³

2005

Phys. Rev. E

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We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semi-analytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (towards experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O 5 structure -which has not been observed experimentally -shrinks, while that of BP I (O − 8 ) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration.In these situations disclinations are formed via the merging of isolated aligned defects.61.30. Mp,83.80.Xz,61.30.Dk Typeset using REVT E X 1

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Section: Introductionmentioning

confidence: 99%

“…The nomenclature used here refers to the symmetry group which characterises the lattice of disclinations formed in the blue phases following [4,11,12] been proposed as a model for BP II. The defect structure in each phase in shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

Dupuis¹,

Marenduzzo²,

Yeomans³

2005

Phys. Rev. E

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“…It is also worth mentioning that, in the expansion (1 ), the term proportional to (K 22 + K 24 ) is often omitted because it can be converted to a surface integral by applying Gauss's theorem. However, for some types of boundary value problems [7] and in the presence of defects [8] the surface term does contribute to the total free energy. The list of formal properties of the OZF expansion must be completed with inequalities among the elastic constants that follow from the stability analysis of (I).…”

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confidence: 99%

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Longa

Monselesan²,

Trebin³

1987

Liquid Crystals

151

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Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau--de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermodynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data.

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“…The ordered arrangement of the undulating disclination lines and the defect lines that weave in and out of holes in the twisted planar case (Fig. 6 B and F) is reminiscent of those seen in blue phases (12,13).…”

Section: Numerical Free-energy Minimizationmentioning

confidence: 86%

“…For instance, the disclination line networks characteristic of blue phases (11,12) have been proposed to organize colloidal inclusions (4,13). But, can similar 3D disclination line networks be designed in the simpler nematic LC?…”

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confidence: 99%

Lassoing saddle splay and the geometrical control of topological defects

Tran

Lavrentovich

Beller

et al. 2016

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

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Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives . Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.liquid crystals | topological defects | saddle splay | disclinations T he investigation of mechanisms, both chemical and geometrical, to control and manipulate defects in liquid crystals (LCs) is essential for the use of these defects in the hierarchical self-assembly (1-3) of photonic and metamaterials (4, 5), as well as for studies in low-dimensional topology (3, 6-10). For instance, the disclination line networks characteristic of blue phases (11, 12) have been proposed to organize colloidal inclusions (4, 13). But, can similar 3D disclination line networks be designed in the simpler nematic LC? The ubiquitous use of nematic LCs (NLCs) in the display industry is a testament to their efficacy in applications. Wide-ranging studies on the role of nematic elasticity in designing tailored defect structures have focused primarily on the familiar splay, twist, and bend deformations. Recently, however, there has been a renewed interest in exploiting saddle-splay deformations (8,14,15). By confining nematics in cells with properly designed boundary conditions, we demonstrate an array of controlled, defect-riddled minimum energy states that form as a result of saddle-splay distortions, excitable by the system's surfaces. Energy ConsiderationsWe begin with the Frank free energy for a nematic (16, 17):where n ≡ nðxÞ is the (unit) nematic director and K 1 , K 2 , and K 3 are elastic constants that measure the energy cost for splay, twist, and bend deformations, respectively. The final term with the elastic constant K 24 is the saddle splay and, as a total derivative, is absent from the corresponding Euler-Lagrange equation. However, it contributes to the energy when there are defects, potentially stabilizing them by balancing the energy cost of creating a...

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Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals

Cited by 146 publications

References 19 publications

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Lassoing saddle splay and the geometrical control of topological defects

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