Landau theory of cholesteric blue phases

Grebel, Haim; Hornreich, R. M.; Shtrikman, S.

doi:10.1103/physreva.28.1114

Cited by 158 publications

(108 citation statements)

References 36 publications

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“…Therefore the solutions for Q 2 and Q h as a function of the reduced temperature, τ , and field strength, E, obtained by minimising Eq. (8), are the same as those obtained for the cholesteric phase [10], provided one substitutes 2q 0 with ε f E/L 1 . Extending the analogy with cholesterics, we now consider flexoelectric phases with a higher dimensional structure; flexoelectric analogues of the cholesteric blue phases.…”

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confidence: 64%

“…As in the case of the splay-bend phase, this is identical to the free energy of the cholesteric analogue, the planar hexagonal blue phase [7,8]. Consequently, we may draw on this previous work for cholesterics to conclude that the hexagonal flexoelectric phase has lower free energy than the one dimensional splay-bend phase at sufficiently large field strength.…”

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confidence: 66%

“…For simplicity, we adopt the one elastic constant approximation where the magnitude of twist, splay and bend are taken to be equal. Since chirality and flexoelectricity induce structure in the fluid it is useful to analyse potential stable states by introducing a Fourier decomposition of the Q-tensor [7,8] …”

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Flexoelectric Blue Phases

Alexander

Yeomans

2007

Phys. Rev. Lett.

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We describe the occurence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilised by flexoelectric interactions. These phases are characterised by regions of locally double splayed order separated by topological defects and are thus highly analogous to the blue phases of cholesteric liquid crystals. We present a mean field analysis based upon the Landau-de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholesteric and flexoelectric cases. PACS numbers: 61.30.Gd, 64.70.Md, 61.30.Mp Elastic distortions in the nematic phase of liquid crystals can be categorised into three types: splay, twist and bend. Stable phases with two dimensional twist distortions have been well characterised and observed experimentally. Here we predict the occurence of structures with two dimensional splaybend distortions.When nematics are doped with chiral molecules they can show stable phases with a natural twist known as cholesterics, shown in Fig. 1(a). In general cholesteric phases comprise a one-dimensional helix. This is because topological constraints mean that it is not possible to construct a state with helical ordering in two dimensions without introducing defects, or disclination lines, into the structure. However local regions of double twist are possible. Fig. 2(a) shows a simple, two dimensional example of a director field where regions of double twist are separated by topological defects. If the free energy advantage of the double twist regions offsets the disadvantage of the disclinations phases of this type will be stable.Such states, the so-called blue phases of cholesteric liquid crystals, have indeed been observed [1]. The disclination structure is, however, more complicated than that of the simple example in Fig. 2(a). The disclinations form textures with cubic symmetry and the stable phases have space groups O 8− and O 2 . The blue phases are stable at the isotropic-cholesteric phase boundary as here the magnitude of the order is small and hence the free energy penalty associated with disclinations is low. They are stable only over a narrow temperature range ∼ 1 K, although recently this has been extended to ∼ 60 K by adding polymers or bimesogenic molecules [2,3].One might therefore ask whether analogous behaviour could be observed in a liquid crystal which shows splay and bend, rather than twist, distortions. In 1969 Meyer showed that the one dimensional splay-bend distortion of the director field, shown in Fig. 1(b), could result from flexoelectric coupling to an external field [4]. Here we extend these results to show that near the isotropic-nematic transition two dimensional splay-bend structures (e.g., Fig. 2(b)) can be stable.We shall term such phases flexoelectric blue phases. Similar director field configurations, but stabilised by a saddle splay term in the free energy, have been reported in [5]. The coupling of a liquid c...

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Flexoelectric Blue Phases

Alexander

Yeomans

2007

Phys. Rev. Lett.

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“…In fact, due to the symmetries of the confined system (the lowest-symmetry phase of which is the biaxial phase, with a distribution function f i (ω) which is an even function of the angle ϕ), the coefficients f (3) i and f (5) i are zero, and consequently only three order parameters, f (1) i , f (2) i and f (4) i , are relevant. Using Eqn.…”

Section: Theorymentioning

confidence: 99%

“…[5]). Another fruitful approach is the chiral Lebwohl-Lasher model [6,7], which has been studied from various perspectives.…”

Section: Introductionmentioning

confidence: 99%

Capillary and winding transitions in a confined cholesteric liquid crystal

2015

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We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in Atomic-Force Microscopy experiments). In contrast with previous studies, we obtain the phase diagram in the temperature vs pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar.

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Blue Phases of Chiral Liquid Crystals

2014

Fundamentals of Liquid Crystal Devices

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Landau theory of cholesteric blue phases

Cited by 158 publications

References 36 publications

Flexoelectric Blue Phases

Flexoelectric Blue Phases

Capillary and winding transitions in a confined cholesteric liquid crystal

Blue Phases of Chiral Liquid Crystals

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