Smectic mesophase, diffusion

Cholesteric mesophases in general resemble the nematic mesophase when observed by both small-angle X-ray diffraction, SAXD, and WAXD. The smectic mesophase, in contrast, produces both diffuse rings at 4--5 A and sharp rings at a distance generally, but not necessarily, equal to the repeat length of the monomer unit, between 15 and 50 A. 

Through the study of the different topics considered in this article, it was shown how X-ray scattering is a useful tool to characterize the most salient features of the mesophases of LCPs. For instance, a simple procedure can be used to measure the nematic order parameter and it is so far valid for all kinds of LCPs based on rod-like moieties. In the case of main-chain polymers, useful information about the conformation of the repeat unit can also be deduced from the diffuse scattering. In the case of side-chain polymers, not only the smectic period but also the amplitude and shape of the smectic modulation can be derived from the measurement of the smectic reflection intensities. Moreover, fluctuations and localized defects may be detected through their contribution to the diffuse scattering. The average distance between lyotropic LCPs can be measured as a function of concentration which tells us the kind of local packing of the particles. 

Liquid-crystalline stationary phases are particularly useful to separate isomers. Isomers that are more elongated in shape (e.g.,p-xylene) are retained in a column filled with LCSPs longer than isomers that are less elongated in shape (e.g., m-xylene). The retention of isomers of chromatographed substances considerably depends on the type of the mesophase of the liquid-crystalline stationary phase. This results from the fact that the type of mesophase affects the dissolution and diffusion of isomers of the chromatographed substance to a different degree. On the whole, nematic liquid crystals show the best separation properties in relation to isomers but, in some cases, very good separation can be obtained on smectic and cholesteric stationary phases. 

The wide angle X-ray diffraction pattern tom melt-drawn fiber of homopolyester, obtained from the reaction of l,3-bis(p-hydroxyphenyl)-l,3-propanedione and 4,4 -hexamethylenedioxy-dibenzoyl chloride, exhibits a typical smectic A mesophase, i. e., an inner reflection as spot at the meridional position and a diffuse outer reflection at the equatorial position (Figure 8.27). 

Within the layers of a smectic A mesophase the molecules are aligned parallel to the layer normal and are uncorrelated with respect to center of mass position, except over very short distances. Thus, the layers are individually fluid, with a substantial probability for inter-layer diffusion as well. The layer thickness, determined from x-ray scattering data, is essentially identical to the full molecular length. At thermal equilibrium the smectic A phase is optically uniaxial due to the infinite-fold rotational symmetry about an axis parallel to the layer normal. A schematic representation of smectic A order is shown in Fig. 4(a). 

Fig. 1.33 These figures trace the development of the diffraction pattern of a sample of a discotic mesogen as the crystalline solid is heated tmd passes through a succession of mesophases, ending as the isotropic liquid. Note the stepwise way in which reflections broaden and become diffuse, as various types of order in the stmctures tire lost. As in the similar scheme for smectic phases given in Fig. 1.30, the edge-on view of the molecular discs drawn on the left corresponds to the alignment of the diffraction pattern shown in the centre and again, for all mesophases, the sample as a whole is taken to have a random orientation of domtiins, giving rotational symmetry around the director...

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