Column undulation instability in a discotic liquid crystal

Gharbia, M.; Cagnon, M.; Durand, G.

doi:10.1051/jphyslet:019850046015068300

Cited by 34 publications

(17 citation statements)

References 6 publications

(11 reference statements)

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“…A tilt ^ of the columns now costs an elastic energy density T 5|iv?^-y C(m/l)^ip^, where C is the elastic constant of column compression. Taking [4] ^x~10^ cgs and [3] C-IO^^ cgs with 5^-^, we estimate ^H-10V500 -2x10^ cgs, i.e., m//-10~l With m=30 A, / is of the order of 3000 A. This value is comparable with the estimated value from previous mechanical instability threshold measurements [3,4].…”

Section: -^Mox^osupporting

confidence: 82%

“…Taking [4] ^x~10^ cgs and [3] C-IO^^ cgs with 5^-^, we estimate ^H-10V500 -2x10^ cgs, i.e., m//-10~l With m=30 A, / is of the order of 3000 A. This value is comparable with the estimated value from previous mechanical instability threshold measurements [3,4]. To observe the curvaturelike behavior of the columns, one should look at undulations of wavelength shorter than / (ql>\).…”

Section: -^Mox^osupporting

confidence: 74%

“…Mechanical instability experiments have been made to test this model, comparing curvature and compression. These experiments [3,4] gave threshold values (and then effective curvature elastic constants A^^IO"' cgs) that are anomalously large. Another way to test the elastic behavior of CLC is to use Rayleigh scattering.…”

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confidence: 99%

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Rayleigh scattering from column undulations in a discotic liquid crystal

Gharbia¹,

Othman²,

Gharbi³

et al. 1992

Phys. Rev. Lett.

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Depolarized Rayleigh scattering on a columnar discotic liquid crystal is described. Column undulations and mode quantization allow the scattering to be visible only for two directions of reciprocal space, and for well-defined light propagation angles. The observed constant angular extension of the scattering shows that column undulations are not controlled by curvature elasticity, but by an anisotropic 3D solidlike elasticity. This behavior is probably associated with column entanglement, as recently discussed by Prost. PACS numbers: 6l.30.-v, 62.20.Fe, 78.35.+C Columnar liquid crystals (CLC) are formed by a regular packing of parallel columns of disklike molecules; the columns are arranged in a two-dimensional network [ll.For CLC distortions one has predicted [2] two types of elasticity: curvature elasticity for the columns and solidlike elasticity for the 2D hexagonal crystal. Mechanical instability experiments have been made to test this model, comparing curvature and compression. These experiments [3,4] gave threshold values (and then effective curvature elastic constants A^^IO"' cgs) that are anomalously large. Another way to test the elastic behavior of CLC is to use Rayleigh scattering. Light scattering is produced by fluctuations in the dielectric tensor e. At constant density, the fluctuations of e come from the fluctuations in the liquid-crystal "director" orientation. In nematic liquid crystals there is no positional ordering of molecules. The curvature elastic energy of angular fluctuations does not depend much on their wave vector q. Rayleigh scattered light can be observed with comparable intensity in any direction [5]. In smectic liquid crystals there is, in addition, a one-dimensional ordering of layers. Arbitrary q angular deformations of the director imply layer curvature and compression energy. The minimum elastic energy is obtained for pure layer undulations, i.e., when q is inside the layers. Rayleigh scattered light now appears concentrated on a cone [6]. In columnar discotics, angular distortion of arbitrary q should imply curvature from the qn component along the columns and solidlike elasticity from qx =q -qii. Again, because curvature elasticity is much weaker than solid compression elasticity for macroscopic distortions, one expects large fluctuations to happen only when q=qii is aligned along the columns. In reciprocal space large Rayleigh scattering should be observed only in one single direction. A new problem now comes from the quantization of the distortion modes: Distortion must be zero on the solid boundaries of the liquid crystal. For smectics, where Rayleigh scattering is restricted to a cone, quantization transforms the cone into a series of discrete directions which always remain visible. For discotics, on the other hand, quantization would in general prevent any scattering along the unique allowed scattering direction. In this work we have investigated, for the fil*st time, the anisotropic elasticity of a columnar liquid crystal, using Rayleigh scattering, taking into accoun...

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Section: -^Mox^osupporting

confidence: 82%

Section: -^Mox^osupporting

confidence: 74%

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Rayleigh scattering from column undulations in a discotic liquid crystal

Gharbia¹,

Othman²,

Gharbi³

et al. 1992

Phys. Rev. Lett.

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“…To explain these results, it is tempting to, simply, transpose them in the frame of a previously published simple model [5,6], describing the column undulation's instability. To explain these results, it is tempting to, simply, transpose them in the frame of a previously published simple model [5,6], describing the column undulation's instability.…”

Section: Dilation Instabilitymentioning

confidence: 99%

Characterisation of The Columnar undulations Using Rayleigh Scattering

Sanaâ¹,

Yakoubi²,

Gharbia³

2007

AIP Conference Proceedings

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Rayleigh scattering in hexagonal columnar liquid crystal subjected to oscillatory shear AIP Conf. Proc. 935, 132 (2007); 10.1063/1.2795403Study of thermal transport in nanoparticle suspensions using forced Rayleigh scattering Abstract. Recently, we have presented the first Rayleigh scattering of the undulated columnar liquid crystal. Column striations (by dilation) or column bands (by alternating shear) and mode quantisation allow the scattering to be observable only for two symmetrical direction of reciprocal space. In this work, we use the scattered light to determine the instantaneous geometrical parameters of the structure.

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“…Then, when the system is expanded, there are two different behaviours: either the columns expand uniformly (and this costs a rather high energy, proportional to the elastic modulus B) or they keep a nearly constant thickness, but manage to fill the available space by undulation [12]. These behaviours show a strong coupling between column orientation and fluid flow [13]. In this paper, we present the first experimental observation of the transmitted depolarised light by the sheared columnar phase.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh scattering in hexagonal columnar liquid crystal subjected to oscillatory shear

Sanaâ¹,

Gharbia²

2007

AIP Conference Proceedings

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Recently, we have presented the column instability under rectilinear oscillatory shear, and we have found the following facts: (a) By varying the shear frequency at fixed amplitude we have observed the quantification of the wave length distortion modes by the sample thickness. (b) By increasing the amplitude we provoke the undulation instability. In this work, we present the undulation of the structure, when the Hexagonal columnar liquid crystal (HCLC) is submitted to alternating shear excitation. We observe for the first time the wavelength modes using Rayleigh scattering. We discuss the obtained results in comparison with the mecano-optic measurements of the band structure. These experiments give an accurate way to measure the spatial periodicity and the temporal frequency.

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Column undulation instability in a discotic liquid crystal

Cited by 34 publications

References 6 publications

Rayleigh scattering from column undulations in a discotic liquid crystal

Rayleigh scattering from column undulations in a discotic liquid crystal

Characterisation of The Columnar undulations Using Rayleigh Scattering

Rayleigh scattering in hexagonal columnar liquid crystal subjected to oscillatory shear

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