By E.I. Kats, V.V. Lebedev
Liquid crystals, common in screens for digital gear and different purposes, have hugely strange homes bobbing up from the anisotropy in their molecules. it seems that a few facets of the fluid dynamics of liquid crystals, reminiscent of their viscosity, will be understood in simple terms by means of contemplating the position performed through thermal fluctuations. on the way to supply a theoretical framework for realizing the experimental effects, the authors dedicate a wide a part of the ebook to a derivation of the nonlinear dynamic equations and to a dialogue of linearized equations for many of the kinds of liquid crystals. The diagrammatic and different strategies they use are of common use in condensed subject physics, and this exposition should still therefore be of curiosity to all condensed-matter theorists.
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Additional resources for Fluctuational Effects in the Dynamics of Liquid Crystals
In real smectics we observe a specific situation, associated with the fact that although they are strongly anisotropic substances, density modulation in them is weak. The latter circumstance is accounted for by the fact that known smectics exist, as a rule, in the temperature range of the order of a few degrees and, consequently, are close to the nematic-smectic phase transition point; this transition being a second-order phase transition, or a weak firstorder transition. 2) B/pc 2 « 1. For most smectics a typical value is B '" 108 G/cm S2.
U)2 should also be taken into account in the energy density expansion for these substances. By virtue of the layered structure of these substances, the modulus C44 is small and therefore there is a region of wave vectors where our approach is also applicable for such crystals. tC 20 2. 14) is missing, therefore we can assume for them (Xl = (X2' All moduli have the same order of magnitude. 15) is small. Here K is a characteristic value of the Frank moduli. , the anisotropic shape of their molecules.
16) at an infinitesimal rotation, and, consequently, is zero due to the rotational invariance of the latter. 29) can be reduced to the form The expression in parentheses here is symmetric with respect to the subscripts i, k. 4) for smectics-B also reduces to the divergence of the symmetric tensor. 32) There appears only one dissipative term in the dynamic equation for the angle qJ. 34). 33), by analogy with nematics, can be called torsion viscosity. 17). 23), valid for smectics-A. In smectics-C the situation is more complicated.
Fluctuational Effects in the Dynamics of Liquid Crystals by E.I. Kats, V.V. Lebedev