Focal conic domains

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. 

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...

Unaligned, disrupted smectics, such as those prepared by quenching from an elevated temperature into the smectic state, are frequently filled with focal conic domains (Sethna and Kleman 1982 Lavrentovich 1986 Larson and Mather 1997). Parabolic focal conic domains can be packed to fill space as shown in Fig. 10-30a. Another packing, which... 

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 formation of focal-conic textures is characteristic of smectic phases (Gray and Goodby, 1984). These textures are the result of smectic layers arranged in Dupin cyclides (Friedel, 1922). The common defects included in these arrangements have the form of ellipses and hyperbolae in certain confocal relationship. Dependent on the direction of observation relative to the defects, the dark lines shown in Figure 4.20 may be observed in focal-conic domains. 

Fig. 2.1 a Polarized optical microscopy (POM) image of FCDs in a bulk thick (120 mm) cell of dodecylcyanobiphenyl (12CB) with different orientation (1) ellipses parallel to the plane of view, (2, 3) ellipses perpendicular to the plane of view [33]. Reproduced with permission [33]. Copyright 2009, Taylor Francis, b A schematic illustration of ideal SmA phase [34]. Each rod represents LC molecules. Reproduced with permission [34]. Copyright 1991, EDP Sciences Schematic illustrations of layer stmcture of a negative Gaussian curvature focal conic domain with (c) non-zero and (d) zero eccentricity... 

Fig. 2.2 a Schematic illustration of smectic layer red plane) construction of a tori focal conic domain on randomly planar anchoring induced surface. The green rods represent liquid crystal molecules, b SEM image of array of tori focal conic domains and (c) its corresponding cross-polarized optical microscopy image... 

Engineering Focal Conic Domain Structure Through Confinement... 

Generation of Focal Conic Domains with Non-zero Eccentricity in Thin Films... 

C. Blanc, M. Kleman, Tiling the plane with noncongruent toric focal conic domains. Phys. Rev. E 62, 6739-6748 (2000)... 

J.P. Bramble, S.D. Evans, J.R. Henderson, T.J. Atherton, N.J. Smith, Observations of focal conic domains in smectic liquid crystals aligned on patterned self-assembled monolayers. Liq. Cryst. 34, 1137-1143 (2007)... 

A. Honglawan, D.A. Beller, M. Cavallaro, R.D. Kamien, K.J. Stebe, S. Yang, Pillar-assisted epitaxial assembly of toric focal conic domains of smectic-A liquid crystals. Adv. Mater. 23, 5519-5523 (2011)... 

Y.H. Kim, D.K. Yoon, M.C. Choi, H.S. Jeong, M.W. Kim, O.D. Lavrentovich, H.-T. Jung, Confined self-assembly of toric focal conic domains (The effects of confined geometry on the feature size of toric focal conic domains). Langmuir 25, 1685-1691 (2009)... 

W. Guo, S. Herminghaus, C. Bahr, Controlling smectic focal conic domains by substrate patterning. Langmuir 24, 8174-8180 (2008)... 

G.P. Alexander, B.G.G. Chen, E.A. Matsumoto, R.D. Kamien, Power of the poincare group elucidating the hidden symmetries in focal conic domains. Phys. Rev. Lett. 104, 257802 (2010)... 

W. Guo, C. Bahr, Influence of anchoring strength on focal conic domains in smectic films. Phys. Rev. E 79, 011707 (2009)... 

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