Polygonal textures

Note 2 One branch of the hyperbola (either above or below the plane of the ellipse) is usually missing in the polygonal texture. 

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. 26. Elements of a smectic A complex polygonal texture. Upper surface one polygon with four ellipses. Lower surface two polygons. The whole space may be divided into three pyramids (ABCDK, AEHKJ, BFGKJ) and three tetrahedra (ABJK, ADHK, BCGK).

Fig. 1.1.7. Focal conic textures in smectic A. (a) The polygonal texture. Crossed polarizers. (Friedel. ) (6) Simple fan-shaped texture. Crossed polarizers. (Sack-...

Fig. 5.15 Schematical illustration of photoisomerization of molecular motor, a Molecular structure of chiral motor 21. b Polygonal texture of a LC film doped with 1 wt% chiral motor 21. c Glass rod rotating on the LC during irradiation with ultraviolet light. Frames 1-4 (from l ) were taken at 15 s intervals and show clockwise rotations of 28° (Irame 2), 141° (frame 3) and 226° (Same 4) of the rod relative to the position in fiame 1. Scale bars, 50 pm. d Surface structure of the liquid-crystal film (atomic force microscopy image 15 pm ). Reproduced with permission from [103]. Copyright 2006 Nature Publishing Group...

THF and chloroform. It was found from measurements using a polarizing optical microscope that PCBT and PPCHT exhibit fan-shaped and polygonal textures, respectively, in the cooling process, indicating monotropic mesophases. The typical fan-shaped texture of PCBT is shown in Figure 12.1. Furthermore, analysis of the X-ray diffraction patterns and molecular mechanics calculations demonstrated that the LC phase observed in the polymers is assignable to a smectic A2 phase. 

The SMLC cholesterics most frequently present polygonal textures with domains of a negative Gaussian curvature. In these domains the focal conditions are not exaetly satisfied [91], and unlike the situation in smectics, the cholesteric layers might deviate from the exact geometry of Dupin cyclides... 

Figure 6. Polygonal texture in a cholesteric liquid (MBBA and Canada balsam) observed under natural light (a) coverslip level, (b) lower glass level, t. Translation defects (there are other unmarked translation defects in the micrographs). Scale bar 20 pm.

Figure . Stereoviews of smectic A textures of 8CB (see Fig. 1). (a, b) A stereo-pair in natural light, showing focal conics, each ellipse being penetrated by a branch of a hyperbola passing through one of the two foci of the corresponding ellipse, (c, d) A stereopair of a polygonal texture, with ellipses in the two separated planes of the slide and the cover-slip. Scale bar 100 im.

Polygonal textures such as those shown in Fig. 6 associate not only horizontal segments (curvi- or rectilinear), but also vertical ones, joining centres to the vertices of polygons at the upper and lower faces of the mesomorphic slab, between the slide and the coverslip. The positions of these segments are shown schematically in Fig. 31 a for the cholesteric phase occupying the vertical prism AA CC BBT)D. The cholesteric axes, normal to layers, join points belong-... 

Like cholesteric lyotropic solutions of polypeptides, cellulose ethers form a confocal, or more frequently, a polygonal texture, as well as textures of the fingerprint type, in solutions. 

More recently it has been proved that it is possible to prepare cholesteric homopolymers.Krigbaum et al. observed fan-like texture for polyester synthesized from 4,4 -dihydroxy-a-methylstilbene and (+)-3-methyladipic acid. These authors suggested the formation of a strongly twisted cholesteric. Indeed, in low molecular weight cholesterics with high twist, the defects and textures resemble those of smectics, especially smectic A. Such cholesteric substances may yield non-planar textures. They may appear in fan-shaped, focal conic or polygonal textures. In the case of... 

Fig. 15 - Typical polygonal texture of smectic A phase containig ellipses of FCD-I located at the cell boundary. In between the large FCD-I one observes clear gaps that are filled with spherically curved layers. The macroscopic size of the smallest domains is defined by the balance of the elastic constant K and the anisotropy of the surface energy when one proceeds with temperature from the deep smectic A phase (a) towards the smectic B ph (b) the critical size increases and the smallest domains disappear. 

The appearance of focal conic structures depends on the direction of viewing. When the epitaxial interactions between the mesophase and the substrate surface, cause the axes of the focal conic units to lie vertical, the polygonal texture appears (Figs. 1.23 and 1.24). On the other hand, samples with focal conic units lying obliquely to the viewing direction, give the characteristic fan texture (Fig. 1.25). [A note of caution for decades, when faced with an undecipherable optical texture with a jumbled mass of domains, workers in the liquid crystal field have often taken the easy option and simply called it a focal conic fan texture to disguise the fact that they had no idea what it was. They have usually been correct, but not always, and mesophases of very different structures have been seriously misidentified on more than one occasion.]... 

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