Lyotropic liquid crystals, diffraction pattern

Whether quasicrystalline structures are limited to alloys remains an open question. It is possible that their occurrence is much more widespread than had been previously thought. Indeed there is evidence for quasicrystallinity in both thermotropic and lyotropic liquid crystals. Diffraction patterns of decagonal symmetry have been recorded in lyotropic liquid crystals [K. Fontell, private communication], (Fig. 2.19), and there is theoretical evidence for the existence of a quasicrystalline structure within the blue phase of cholesterol (Chapters 4, 5). (The decagonal structure has quasisymmetry perpendicular to the tenfold axes, and translation symmetry along them.) Viruses crystallise in icosahedral clusters and the list continues to grow. In addition to five-fold symmetry, it has been shown that eight and ten- fold quasisymmetry is possible. ... 

Figure 2.19 Pseudo-five fold diffraction pattern of a decagonal phase (65 C from the ten-fold axes Cu - K

The structures of the various lyotropic mesophases mentioned so far have been elucidated over the years primarily using low-angle X-ray diffraction. An X-ray diffraction pattern of a liquid crystal provides information not only on the state of organization of the hydrocarbon chains but also on the crystallographic lattice of the micellar structure. It must be emphasized, however, that often the X-ray method alone cannot define the absolute structure of a liquid crystal phase because too few diffraction lines are observed. In these cases, a knowledge of the position and extent of the mesophase region in the phase diagram, measurements by other techniques (NMR, optical microscopy), and information such as the size, shape and chemical nature of the surfactant are necessary before a reliable identification can be made. 

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