Defects in smectic

There are many types of defects originated from the layered structure of the smectic A phase. Here, we shall only present a brief survey of the most important cases. 

Many structural defects compatible with the incompressible smectic layers can be observed under a microscope. Among them are cylinders, tores and hemispheres observed at the surfaces, radial hedgehogs observed in smectic drops, etc. Three of them are presented in Fig. 8.29a-c. Note that in aU defect structures of this type, the splay distortion plays the fundamental role but bend and twist are absent. Other, more special defects, namely, the walls composed of screw dislocations, are observed in the TGBA phase. 

These are the most striking features of smectic textures [19]. Smectic layers of constant thickness (incompressible, modulus B— oo) form surfaces called Dupin cyclides. We have seen some of them, which have the form of tori including disclinations, see Fig. 4.7b. Such cyclides can fill any volume of a liquid crystal by cones of different size. An example is afocal-conic pair, namely, two cones with a common base. The common base is an ellipse with apices at A and C and foci at O and O , see Fig. 8.30a. The hyperbola B-B passes through focus O. The focus of 

This surprising result prompted Mazenko, Ramaswamy and Toner to examine the anharmonic fluctuation effects in the hydrodynamics of smectics. We have already shown that the undulation modes are purely dissipative with a relaxation rate given by (5.3.39). To calculate the effect of these slow, thermally excited modes on the viscosities, we recall that a distortion u results in a force normal to the layers given by (5.3.32). This is the divergence of a stress, which, from (5.3.53), contains the non-linear term 0,(Vj uf. Thus, there is a non-linear contribution (Vj uf to the stress. Now the viscosity at frequency co is the Fourier transform of a stress autocorrelation function, so that At (co), the contribution of the undulations to the viscosity, can be evaluated. It was shown by Mazenko et that Atj(co) 1 /co. In other words, the damping of first and second sounds in smectics, which should go as /(oo)oo , will now vary linearly as co at low frequencies. 

A similar calculation for discxjtics yields Aq ca) co i The original work of Mazenko et argued that one of the shear viscosities should also diverge, but Milner and Martin showed that this was not the case. 

This remarkable 1 /co divergence of the viscx)sities of a smectic at low frequencies is now confirmed by several independent experiments using ultrasonic attenuation and secx)nd sound resonance. 

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Defect lines in smectics, unlike those in nematics, often do not continuously shrink with time and spontaneously disappear. Instead, there often seems to be a finite energy barrier that must be overcome if a smectic defect is to disappear. This difference between nematics and smectics is a consequence of the layer-spacing constraint that exists in smectics but not nematics. Because of this constraint, topological defects in smectics cannot be removed without ripping layers, and this requires a finite energy. 

Figure 10.34 Defects in smectic phases (a) a tilt wall, (b) an edge dislocation, and (c) a screw dislocation. (Adapted from Kleman et al. 1977, by permission of Taylor and Francis.)...

Directing 3D Topological Defects in Smectic Liquid Crystals and Their Applications as an Emerging Class of Building Blocks... 

Directing 3D Topological Defects in Smectic Liquid Crystals... 

J. Jeong, M.W. Kim, Confinement-induced transition of topological defects in smectic liquid crystals From a point to a line and pearls. Phys. Rev. Lett. 108, 207802 (2012)... 

The description of parabolic cyclide surfaces is based upon two confocal parabolas in mutually perpendicular planes, with the vertex of one parabola passing through the focus of the other. These parabolas represent line defects in smectic liquid crystals. Parts of some typical parabolic cyclide surfaces are pictured in... 

I.W. Stewart, On the parabolic cyclide focal-conic defect in smectic hquid crystals, Liq. Cryst, 15, 859-869 (1993). 

In liquid crystalline mesophases, there also exist domain boundaries in polydomain samples, in addition to domain disclinations. However, judging from the fact that neither the mobility nor the p,x-product depend on the size of the domains in a polydomain sample, these structural defects hardly affect the carrier transport properties of smectic mesophases [48-50]. Until now, the exact reason why structural defects in smectic mesophases are less harmful to carrier transport has not been explained. It is possible that the flexibility of the molecular orientation in mesophases, or the soft structure of mesophases, makes local carrier transport possible at defect sites. This is another outstanding feature of carrier transport in the mesophases, which distinguishes mesophases from crystalline materials. It provides... 

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