Lyotropic liquid crystals, diffraction

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. ... 

DNAs are soluble only in aqueous solutions and their fibrous crystals can be prepared by slow evaporation from the aqueous solution. Duplex structures in the fibers have been studied by X-ray diffraction [2,3] and sohd state NMR [4-6]. Orientation of DNA strands by using hydrodynamic flow gradients in the dilute aqueous solution [7,8] and lyotropic liquid crystal... 

These structures are extensively described in the current literature (Fanum, 2008 Friberg, 1976 Birdi, 2002 Holmberg, 2004 Somasundaran, 2006). Even within the same phases, their self-assembled structures are tunable by the concentration for example, in lamellar phases, the layer distances increase with the solvent volume. Lamellar structures are found in systems such as the common hand soap, which consists of ca. 0% soap + 20% water. The layers of soap molecules are separated by a region of water (including, salts etc.) as a kind of sandwich. The x-ray diffraction analysis shows this structure very clearly. Since lyotropic liquid crystals rely on a subtle balance of intermolecular interactions, it is more difficult to analyze their structures and properties than those of thermotropic liquid crystals. Similar phases and characteristics can be observed in immiscible diblock copolymers. 

The three fundamental lyotropic liquid crystal structures are depicted in Figure 1. The lamellar structure with bimolecular lipid layers separated by water layers (Figure 1, center) is a relevant model for many biological interfaces. Despite the disorder in the polar region and in the hydrocarbon chain layers, which spectroscopy reveals are close to the liquid states, there is a perfect repetition in the direction perpendicular to the layers. Because of this one-dimensional periodicity, the thicknesses of the lipid and water layers and the cross-section area per lipid molecule can be derived directly from x-ray diffraction data. 

The calculated results in the absence of electrolyte will be now compared with the experimental results obtained regarding a lamellar lyotropic liquid crystal SDS (sodium dodecyl sulfate)/pentanol/water/dodecane swollen in a mixture of dodecane and pentanol.24 The weight fraction water/surfactant was 1.552 from the dilution line in the phase diagram, we calculated that the initial concentration of pentanol in the oil-free system was 29 wt % and the concentration of pentanol in the dodecane-based diluant was 8 wt %. The experimental values for the repeat distance were obtained from the X-ray diffraction spectrum (Figure 2 in ref 24) for various dodecane concentrations. 

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

Bonazzi, S., Capocianco, M., De Morais, M. M., Garbesi, A., Gottarelli, G., Mariani, P, Grazia M., Bossi, P, Spada, G. P, Tondelli, L. (1991). Four-stranded aggregates of oligodeoxyguanylates forming lyotropic liquid crystals A study by circular dichro-ism, optical microscopy, and x-ray diffraction, J. Am. Chem. Soc., 113 5809. 

Mindyuk OY, Stetzer MR, Heiney PA, Nelson JC, Moore S (1998) High resolution X-ray diffraction study of a tubular liquid crystal. J Adv Mater 10 1363-1366 Neto F, Antonio M, Silvio RA (2005) The physics of lyotropic liquid crystals. Oxford University Press, New York... 

Polyoxybenzoate is a stiff chain, lyotropic liquid crystalline material, as was discussed on the basis of its copolymers with ethylene terephthalate (see Sect. 5.1.4). The crystal structure of the homopolymer polyoxybenzoate was shown by Lieser 157) to have a high temperature phase III, described as liquid crystalline. X-ray and electron diffraction data on single crystals suggested that reversible conformational disorder is introduced, i.e. a condis crystal exists. Phase III, which is stable above about 560 K, has hexagonal symmetry and shows an 11 % lower density than the low temperature phases I and II. It is also possible to find sometimes the rotational disorder at low temperature in crystals grown during polymerization (CD-glass). 

In the phrase liquid-crystalline, the crystalline adjective refers to the faa that these materials are sufSdentiy ordered to diffract an X-ray beam in a way analogous to that of normal crystalline materials. On the other hand, the liquid part specifies that there is frequently sufSdent disorder for the material to flow like a liquid. liquid crystals can be divided into thermotropic, that exhibit a phase transition with change of temperature, and lyotropic, that exhibit phase transition as a function of both temperature and concentration of the LC molecules in a solvent. Both low molecular wdght materials and polymers " can show liquid crystallinity. In the case of polymers, it frequently occurs in very stiff chains such as the Kevlars and other aromatic polyamides. It can also occur with flexible chains, however, and it is these flexible chains in the elastomeric state that are the focus of the present discussion. LC networks of flexible chains have the following three properties (1) they can be extensively deformed (as described for elastomers throughout this book), (2) the deformation produces alignment of the chains, and (3) alignment of the chains is central to the formation of LC phases. Elastomers of this type have been the subject of numerous studies, as described in several detailed reviews. ... 

Here we will focus on the bulk static structures of the phases formed by low molar mass calamitic (rod-like) mesogens. The principles involved in structural studies of columnar phases, and of polymeric and lyotropic systems, are very similar. The study of liquid crystal surfaces requires reflectivity and/or glancing angle diffraction techniques [4-6]. 

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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