Deformations smectics

Domain formed by deformed smectic layers that fold around two confocal line defects preserving equidistance of structural layers everywhere except in the vicinity of the defect lines. 

H. Pleiner and H.R. Brand, Nonlinear hydrod5mamics of strongly deformed smectic C and C liquid crystals, Physica A, 265, 62-77 (1999). 

Note 1 In the equation for g, the term go is usually equal to zero because the undistorted state of nematics is the state of uniform alignment. However, for chiral nematics, a nonzero value of go allows for the intrinsic twist in the structure. In order to describe g for smectic phases, an additional term must be added, due to the partially solid-like character of the smectic state and arising from positional molecular deformations. 

Due to the rigidity of Rp-chains, in fluorinated LCs the transition from smectic to columnar organization often takes place via modulated smectic phases (ribbon phases, c2mm, p2gg, and Colob see Fig. 20, left) which completely or partly replace the bicontinuous cubic phases at the Sm-to-Col cross-over. Similarly, in columnar phases the circular columns can be deformed to an elliptic, rectangular, or square... 

So far we have discussed 2D density modulated phases that are formed by deformation or breaking of the layers. However, there are also 2D phases with more subtle electron density modulations. In some cases additional peaks observed in the XRD pattern (Fig. 10) are related to a double layer periodicity in the structure. As double layer periodicity was observed in the bent-core liquid crystals formed by the asymmetric as well as symmetric molecules [22-25] it should be assumed that the mechanism leading to bilayers must be different from that of the pairing of longitudinal dipole moments of molecules from the neighboring layers, which is valid for smectic antiphases made by asymmetric rod-like molecules. 

Since the Blrev phase is made of smectic layer fragments the following question arises can the layer fragments have the SmC(1 structure The answer is yes. In some compounds the Blrev phase consists of bilayers which become deformed and... 

Examples of these formulations are systems based on a difunctional LC epoxy monomer (diglycidyl ether of 4-4 -dihydroxy-Q -methylstilbene), cured with methylene dianiline (Ortiz et al., 1997). The generation of liquid-crystalline microdomains (smectic or nematic) in the final material required their phase-separation before polymerization or at low conversions. This could be controlled through the initial cure temperature. Values of GIc, (kJm-2) were 0.68 (isotropic), 0.75 (nematic), and 1.62 (smectic). The large improvement produced by the smectic microdomains was attributed to an extensive plastic deformation. 

Qij = jS (rnrij - j5y)] and the layer displacement u and the modulus in the smectic A case [cp = S(s> exp ir/o(z - n) ]. Here, as in the rest of the chapter, we refer to the system of coordinates defined in Sect. 2.1. We note that u is only a good variable if we consider small deformations of the layers. For large layer deformations the phase

further discussion, we will concentrate on the parts due to symmetry variables and the order parameters, while for terms already present in the isotropic fluid see, e.g., [30, 31]. 

Before leaving the subject of the smectic state, we may remark that to explain deformations in which the area of individual molecular layers does not remain constant, it is necessary to invoke dislocations of these layers. It is likely that these dislocations are usually combined with the focal conic singularity lines, being then essentially screw dislocations. 

Alternatively, if one dilates a smectic stack by increasing its thickness by an amount Sh > 27t X, then the sample will prefer to bend the layers in an undulational instability (Rosenblatt et al. 1977 Ostwald and Allain 1985) in order to restore the lamellar spacing to its preferred value (see Fig. 10-29d). Note that the increase in thickness 8h required to produce this instability is independent of the initial thickness h of the stack. Hence for a macroscopic sample of thickness, say, h = 60 p,m, the strain Sh/h required to induce the undulational instability is extremely small, 8h/h IzrXfh 10-4. Thus smectic monodomains are extremely delicate and can easily be disrupted by mechanical deformation. 

Besides parabolic and polygonal focal domains, in samples that are reasonably aligned, isolated conic domains called torical focal conic domains can appear (Lavrentovich et al. 1994). A sketch is shown in Fig. 10-33a, and a series of such domains is shown in Fig. 10-33b. If a three-dimensional lattice of such domains forms, the smectic is broken up into discrete multilamellar polyhedra, or deformed onions. This occurs in lyotropic smectics under flow (see Section 12.4.2.3). 

The elasticity of multilamellar vesicles can be discussed in reference to that of emulsion droplets. The crystalline lamellar phase constituting the vesicles is characterized by two elastic moduli, one accounting for the compression of the smectic layers, B, and the second for the bending of the layers, K [80]. The combination has the dimension of a surface tension and plays the role of an effective surface tension when the lamellae undergo small deformations [80]. This result is valid for multilamellar vesicles of arbitrary shapes [81, 82]. Like for emulsion droplets, the quantity a/S is the energy scale that determines the cost of small deformations. 

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