Smectic and columnar liquid crystals: concepts and physical by Patrick Oswald
By Patrick Oswald
Liquid crystals let us practice experiments that supply perception into primary difficulties of contemporary physics, resembling section transitions, frustration, elasticity, hydrodynamics, defects, progress phenomena, and optics. Smectic and Columnar Liquid Crystals: recommendations and actual homes Illustrated through Experiments is because of the own examine and of the graduate lectures given through the authors on the École Normale Supérieure de Lyon and the college of Paris VII, respectively. The publication examines lamellar (smectic) and columnar liquid crystals, which, as well as orientational order, own 1D, 2nd or 3D positional order. This quantity illustrates unique actual suggestions utilizing methodically various experiments, theoretical advancements, and diagrams. themes contain rheology and plasticity, ferroelectricity, analogies with superconductors, hexatic order and 2D-melting, equilibrium shapes, facetting, and the Mullins-Sekerka instability, in addition to section transitions in unfastened movies and membrane vibrations. Nematic and cholesteric liquid crystals are lined by means of the authors in a separate quantity entitled Nematic and Cholesteric Liquid Crystals: strategies and actual houses Illustrated via Experiments. Smectic and Columnar Liquid Crystals is a perfect creation and a useful resource of reference for theoretical and experimental reports of complex scholars and researchers in liquid crystals, condensed subject physics, and fabrics technological know-how.
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Additional info for Smectic and columnar liquid crystals: concepts and physical properties illustrated by experiments
Finally, let us note that the cybotactic groups are anisotropic, with ξ// ≈ 5ξ⊥ , typically. b) Divergence of the elastic constants K2 and K3 As we have seen, the lamellar structure of smectics is incompatible with twist and bend deformations of the director field n. Such behavior suggests that the Frank constants K2 and K3 of the nematic phase diverge upon approaching the transition. To prove this result, let us neglect the anisotropy of the medium and assume that the correlation lengths are equal (ξ // = ξ⊥ = ξ), as are the Frank constants (K1 = K2 = K3 = K).
C) Landau-Ginzburg-de Gennes free energy As usual, let us expand the free energy as a power series of the order parameter Ψ. It is important to note that Ψ is complex, while the energy is a real quantity. On the other hand, the energy is necessarily invariant with respect to translations, and thus independent of the phase φ of the order parameter. The energy must only depend on the product ΨΨ* = |Ψ|2 yielding, to lowest order: fL = 1 | |2 1 | |4 α Ψ + β Ψ + ... 27) In this expression, β takes into account for the coupling with the quadrupolar 21 SMECTIC AND COLUMNAR LIQUID CRYSTALS order parameter discussed in the previous section.
J. Physique (France), 35 (1974) 301. , “100 Years of Liquid Crystal Chemistry,” Mol. Cryst. Liq. , 165 (1988) 45. , Phys. Rev. , 31 (1973) 349.