Focal Conics

Figure C2.2.9. Polygonal domains of focal conics in a smectic A phase confined between parallel plates.

In addition, and most importantly, samples of typical B2 materials always seem to exhibit minority domains which behave quite differently from the stripe domains. Specifically, at zero field these minority domains have the lower An green birefringence color and show a smooth SmA-like focal conic... 

While such behavior can be seen in achiral LC phases, driven by surface constraints as illustrated in Figure 8.11, further characterization of the phase responsible for the minority domains in the B2 banana phases shows this to be the first unequivocal example of a bulk fluid conglomerate. It is worth noting here that the EO behavior of the majority domains is achiral Stripes parallel to the layers switch to a SmA-like focal conic texture, which is identical for both signs of the field, as can be seen in Figure 8.22. This EO behavior very clearly appears achiral when observing the switching in motion. 

Application of a field to the ShiCaPa phase causes switching by precession of the director around the tilt cone in alternate layers, to give a ferroelectric ShiCsPf state with uniform tilt. In this case, there can be no domains of opposite tilt since such domains would necessarily have their polarization opposing the applied field. This leads to a uniform SmC-like texture with a green birefringence color. The extinction brushes in the cylindrical focal conic rotate counterclockwise when the net tilt rotates clockwise, as indicated in Figure 8.25. As anticipated, the chiral rotation of the brushes is a direct manifestation of the chirality of the phase. Elsewhere in the sample there must be ShiCaPa domains of opposite handedness, which would possess the opposite sense of tilt for the same sign of the applied field. 

Figure 8.34 Left Gold focal conics of MHOBOW coexisting with accordion domains in 4-p.m SSFLC cell. Cell has not seen electric field. Right Same area after brief application of field above threshold for causing textural change of focal conics from gold SmA-like to bistable blue SmC -like. Transition from gold to bistable blue is still incomplete in this photomicrograph clear domain walls between two textures are easily seen.

Figure 8.35 Illustration of bistable ferroelectric EO switching observed for blue focal conic domains of MHOBOW. SmCsPF structure can be assigned for these domains. In this phase director structure in all layers is oriented identically. This structure and corresponding extinction bmsh orientation for cylindrical focal conic are illustrated at bottom of figure for two bistable ferroelectric states. Note that for material with 30° tilt angle, such as MHOBOW, two ferroelectric states look very similar in still photos. In fact, two states result from large rotation of extinction brushes through 60°, as can be easily seen when observing switching in motion.

Note 2 The smectic layers within a focal-conic domain adopt the arrangement of Dupin cyclides, since as in these figures there appear concentric circles resulting from the intersection of ellipses and hyperbolae. They also have the distinctive property of preserving an equal distance between them. 

Note 3 A focal-conic domain built around an ellipse and an hyperbola is the most common type of defect in thermotropic smectic A phases. The hyperbola passes through a focus of the ellipse and the ellipse passes through the focus of the hyperbola (see Fig. 24). Note 4 In a particular limiting case of an ellipse-hyperbola focal-conic domain, the ellipse becomes a straight line passing through the center of a circle. 

Note 5 A focal-conic domain built around two confocal parabolae is called a parabolic focal-conic domain. 

Note 6 At any point inside a focal-conic domain, the director is oriented along the straight line drawn through the point and the two defect lines (ellipse and hyperbola or two parabolae or circle and straight line). See for example BD, BC and BO in Fig. 24. 

Fig. 24. Dupin cyclide and perfect focal-conic domain construction, (a) Vertical section showing layers of the structure thick lines indicate the ellipse, hyperbola, Dupin cyclide, and central domain, (b) Focal-conic domain showing structural layers with a representation of the arrangement of the molecules within one of them.

Texture composed of focal-conic domains of the ellipse-hyperbola type with visible ellipses, or parts of ellipses, located at the boundary surfaces. 

Note 3 Neighbouring domains form a family with a common apex where the hyperbolae of these domains join each other. This common point is located at the surface that is opposite to the surface containing the ellipses (see Fig. 26). Each family is bounded by a polygon formed by hyperbolic and elliptical axes these are parts of focal-conic domains that provide a smooth variation of smectic layers between the domains of different families. These domains are the tetrahedra in Fig. 26. 

Note 4 The smectic layers pass continuously from one focal-conic to the next. 

Texture formed partly by focal-conic domains with their hyperbolae lying in the plane of observation. 

Fig. 25. Arrangement of a smectic A polygonal texture (a) general view of the focal-conic domains filling space efficiently (b) cross-section of the domains showing arrangement of...

Fig. 3 Lamellar focal conics under the polarization microscope using color contrast by means of a 2, mask...

Lamellar focal conics show a fascinating highly-ordered structure when observed under the polarization microscope. This texture consists of surfactant bilayers that are shaped like ice cream cones and stuck inside of one another. These stacks of cones are quite densely packed in the solution and, under the polarization microscope, create extended regions of amazing regularity. Figure 3 shows a photograph of such a system, taken with a polarization microscope with a A mask to achieve color contrast. 

What is most amazing of all in this picture is the degree of microscopic order present in a solution that appears quite unexceptional to the imaided eye. Usually, we associate T>eauty and aesthetic appeal with symmetry and regular shapes, just as in the examples of the ordered lamellar phase and lamellar focal conics. However, sometimes also asymmetric shapes have that special quaUty about them that conveys what we call beauty. Figure 4 shows a water-rich foam composed of dish soap with coconut oil. It consists of tightly-packed bubbles of very different sizes that create an asymmetric pattern of astounding beauty [3]. 

Recently, Sato and Hatano 67 69) found a new type of chiral lyotropic mesophase composed of Tween 80, sorbitan mono-9-octadecenoate poly(oxy-l,2-ethanediyl), and water, and discussed the ICD of achiral solute molecules intercalated into the lyotropic mesophase. As the concentration of Tween 80 is increased, three distinct phases are obtained micelle, neat phase, and reversed micelle, in that order. In the region of the volume ratio of Tween 80/(Tween 80 + water) of 0.40 to 0.63 under crossed Nicol-prisms, a focal conic texture was observed. This result indicates that the... 

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