Diffraction by Smectic Phases

However, in experiment [8], instead of the delta-functi(Mi form of the intensity peaks along the z-direction (q n qa), quasi-Bragg singularities have been observed with the tails described by a power-law as shown in Fig. 5.23a, 

instead of the true Imig-range order we have a quasi-long-range order with the density correlation function (5.41b) qualitatively shown in Fig. 5.23b. 

But what is a physical sense of parameter Tj The answer is given by a theorem related to a more general question, whether true one- or two- dimensional crystals 

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In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

The number of commercially available liquid crystals that exhibit smectic and/or nematic phases at or close to room temperature, are optically transparent above 250 nm, that make relatively poor triplet quenchers, and whose structures have been reasonably well-characterized is relatively small. Two liquid crystals that do satisfy these requirements - n-butyl stearate (BS) and tranj,frflni-4 -butylbicyclohexyl-4-carbonitrile (CCH-4) - have been investigated fairly extensively using ketone photochemistry (23,27-34) and it is appropriate to provide some description of their structures before proceeding further. The smectic phases of both of these compounds have been characterized by x-ray diffraction (35-36) and other methods (37-39). 

The X-ray diffraction of polymeric liquid crystal systems and their low mass counterparts are the same in principle, but the diffraction results for the polymers are often less ideal and more difficult to interpret. In practice the oriented specimens are often preferred over the unoriented samples for an unambiguous determination. X-ray diffraction is nearly always used together with texture observations using a polarizing optical microscope. Miscibility tests are also used in some cases for confirmation. For smectic phases with higher translational and orientational orders, X-ray diffraction is the most useful (if not the only) technique for unmistakable characterization. A few examples are cited below. The details of each characterization of the various polymeric smectic phases were described by individual authors. 

We saw in Sect. 3.1.1 that for a symmetric dimer containing terminal alkyl chains to exhibit smectic behaviour then the terminal chain length must be greater than half the spacer length. This empirical rule effectively eliminates the possibility that the dimers form an intercalated structure simply because the terminal chains can only be accommodated within such a structure if the total length of the two terminal chains is equal to or less than the length of the spacer (see Fig. 16a). This view is supported by X-ray diffraction studies which reveal that for the overwhelming majority of symmetric dimers the smectic phases have a monolayer structure (see Fig. 16b). 

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