By E.I. Kats, V.V. Lebedev

ISBN-10: 1461243327

ISBN-13: 9781461243328

ISBN-10: 1461287383

ISBN-13: 9781461287384

Liquid crystals, commonly used in monitors for digital apparatus and different functions, have hugely strange homes coming up from the anisotropy in their molecules. it seems that a few elements of the fluid dynamics of liquid crystals, reminiscent of their viscosity, should be understood in basic terms via contemplating the position performed via thermal fluctuations. that allows you to supply a theoretical framework for realizing the experimental effects, the authors dedicate a wide a part of the e-book to a derivation of the nonlinear dynamic equations and to a dialogue of linearized equations for a number of the varieties of liquid crystals. The diagrammatic and different concepts they use are of normal use in condensed subject physics, and this exposition should still hence be of curiosity to all condensed-matter theorists.

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**Extra info for Fluctuational Effects in the Dynamics of Liquid Crystals**

**Example text**

1) has no specific small value attributable to the weak density modulation, and has the same order of magnitude as the Frank moduli in nematics. 2) is of the order of unity. This could be expected in the smectic phase of substances whose transition from the nematic phase into the smectic phase is a first-order transition. To study nonlinear effects in smectics it is necessary to know higher-order terms of the energy expansion in u; these terms having a fairly nontrivial and not at all arbitrary structure.

As is known (de Gennes, 1974), the scattered light spectrum is determined by the director fluctuations, linearly related to the dielectric permeability fluctuations. Therefore, the differential cross section of inelastic light scattering is proportional to the correlation function of the director fluctuations. The latter can be easily calculated from the above given expressions for the spectrum with the help of the fluctuationdissipation theorem (Landau and Lifshitz, 1960). The thus obtained correlation function has contributions of all diffusion modes of a nematic W 4 , W 5 , W 6 , W 7 .

With this circumstance borne in mind, the scattering line is a sum of two Lorentzians, proportional to the expression, determining the correlation function (bobo). Changing polarization of the incident and scattered light, it is possible to single out these contributions in the scattering cross section (de Gennes, 1974; Pokrovskii and Kats, 1977). 1 Static Properties of Smectics As we have already mentioned, the smectic phase of liquid crystals is a phase where the translational invariance is spontaneously broken along one of the directions along which the density is periodically modulated (De Gennes, 1974; Prost, 1984).

### Fluctuational Effects in the Dynamics of Liquid Crystals by E.I. Kats, V.V. Lebedev

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