Focal conic defects

Figure 10.29 Response of an aligned smectic to layer dilation, (a) Initial equilibrium sample, (b) For a very small dilation Sh < Ink, the layer spacing simply increases, (c) A uniform rotation of the layers decreases the spacing toward that of equilibrium, but doesn t satisfy the boundary conditions, (d) Hence, the sample undergoes an mdulational instability, which also narrows the layer spacing while satisfying homeotropic boundary conditions, (e) For a large enough dilation, the undulation instability leads to formation of parabolic focal conic defects. (From Rosenblatt et al. 1977, with permission from EDP Sciences.)...

Parabolic focal conics are a special case of generic focal conic defects, which are composed of layers curved to form toroidal surfaces called Dupin cyclides (see Fig. 10-31). Each such structure contains a pair of disclination lines—one an ellipse and the other... 

Figure 10,33 (a) Isolated toric focal conic defect, (b) A pair of such defects. (Adapted with permission from Winey et al.. Macromolecules 26 2542. Copyright 1993, American Chemical Society.)... 

Problem 10.9 Why are focal conic defects so common in smectics ... 

B. Zappone, C. Meyer, L. Bruno, E. Lacaze, Periodic lattices of frustrated focal conic defect domains in smectic liquid crystal films. Soft Matter 8, 4318 326 (2012)... 

Fig. 4.3 a, b Homeotropic and schlieren textures of the nematic phase of 8CB containing 5 wt% 1 coated GNPs. c Sheared nematic texture near to the edge of the cover slip, d Focal-conic defect texture of the smectic A phase. Magnification xlOO [46], Copyright from Wiley-VCH 2011... 

Fig. 8.30 Focal-conic defect structure in SmA A pair of cones with a common elliptical base and a hyperbola connecting cone apices (a) cross-section of the upper cone by plane ABC with gaps between lines (Dupin cyclides) indicating the smectic layers (b) filling the space of the sample by cones of different size (c)...

FIGURE 15 A smectic A thin film between substrates with planar anchoring. The easy axis is vertical, and the layer planes are shown. A focal conic defect is shown in cross. section. The +1 /2 disclination loop is indicated. (Adapted from Ref. 35.)... 

Three-dimensional Fluorescent Confocal Polarizing Microscopic (FCPM) pictures of focal conic defects of SmA phase with homeotropic alignment (upper row), and their graphical illustration (bottom row), (a) Horizontal cross section (along the substrates) (b) vertical cross section. 

Textures of SmA samples with focal conic defects are shown in Figure 6.10. 

Focal Conic Defects Dupin and Parabolic Cyclides... 

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

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