Diffraction patterns unoriented

In diffraction patterns made from unoriented samples, the crystalline pattern is superimposed on an amorphous halo. As shown in Fig. 5, the percentage of amorphous material may be calculated by comparing the intensities of the two portions of the diffraction pattern. When the amorphous fraction is large, as in samples which have been quenched rapidly from the melt to a low temperature, the crystal structure may be greatly disrupted. Various interpretations of the intermolecular and intramolecular order which may be deduced from the diffraction patterns of such samples are discussed by Kilian and Jenckel. 

The diffraction pattern obtained from an unoriented, partially crystalline polymer, or from a powdered crystalline material where the crystallites are unoriented, consists of a series of concentric circles. Such a pattern is illustrated in Figure 2.31.4 Its exact pattern can be used to identify an unknown polymer. The origin of these circles can be... 

Figure 2.31 Illustrative diffraction pattern obtained from an unoriented polymer.4 Reproduced by permission of John Wiley and Sons.

X-ray diffraction (in crystalline polymers) Unoriented crystalline polymers show X-ray diffraction patterns, which resemble powder diagrams of low-molecular crystals, characterised by diffraction rings rather than by spots. As a result of orientation the rings contract into arcs and spots. From the azimuthal distribution of the intensity in the arcs the degree of orientation of the crystalline regions can be calculated (Kratky, 1941). 

Figure 8. Wide-angle x-ray diffraction patterns of the (a) oriented and (b) unoriented portions of the quenched sample...

In contrast to the other keratins, which produce diffraction patterns with high orientation and detail, soft keratin produces unoriented (i.e., powder) diffraction patterns with diffuse rings that have spacings of about 4.5 and 9.5 A. Soft keratin, the type found in the skin, is believed to have little secondary structure. The pattern observed in a particular case undoubtedly depends upon species and preparation conditions. 

However, also completely unoriented specimens of membrane preparations give a diffraction pattern, in this case a diffuse, continuous one, which allows important structural conclusions. Wilkins et al. have first identified this pattern with scattering... 

Figure 4.31. Schematic X-ray diffraction patterns of liquid crystalline phases (a) unoriented nematic (b) oriented nematic (c) unoriented smectic A or C (d) oriented smectic A (e) oriented smectic C (f) unoriented smectic B phase.

Isotactic polypropylene (iPP), when quenched from the melt in cold water, gives rise to a metastable, solid mesophase, which transforms into the stable a form by annealing at elevated temperatures [25-27]. The X-ray powder diffraction pattern of this disordered form of iPP presents only broad halos at 20 = 14.8 and 21° (Fig. 33A). Oriented fibers of iPP in this mesomorphic form can be obtained by stretching the corresponding unoriented films [25]. The X-ray fiber diffraction patterns present broad peaks on well-defined layer lines as shown in Fig. 33B the chain periodicity corresponds to 6.5 A, as in the crystalline a form. 

Figure 10.8 X-ray diffraction patterns from (a) unoriented smectic A and (b) oriented smectic A.

The PP-A, PP-B, and PP-F were "balanced" biaxially stretched films whose constituent crystalline regions consisted of two distinguishable populations of crystallites. One population exhibited preferential (040) planar orientation (b axis parallel to N), and the other exhibited preferential (110) planar orientation (<110> reciprocal lattice vector parallel to N). These orientations are illustrated in the left-hand diagram in Fig. 1. The PP-D film exhibited two different orientations. The majority of the crystallites had their c axis parallel to (T), and a minor population was oriented with the a axis parallel to (T) (see the right-hand diagram in Fig. 1), The occurrence of all four different types of orientation depicted in Fig. 1 was detected in the PP-E film. Finally, no preferred crystalline orientation was observed in the case of the PP-C in addition, the diffraction patterns corresponded to neither the a-monoclinic structure nor the smectic mesomorphous state of polypropylene, the latter being characteristic of the polymer when it is very rapidly cooled from the molten state. Evidence from the diffraction patterns, which were diffuse, indicated that the crystalline order in this film was intermediate between the above-mentioned mesomorphous state and the a-monoclinic structure. The relatively low density of this film is consistent with this observation. Upon annealing at 408 K, this film exhibited unoriented a-monoclinic x-ray diffraction patterns and a pronounced increase in density (see below). 

For both oriented and unoriented specimens. X-ray diffraction patterns were recorded on X-ray film and integrated intensities were obtained for each diffraction order h by measuring the area of the diffraction peak. Structure amplitudes F h) were obtained from the measured intensities by applying standard correction factors [24, 39,40]. Electron density profiles, p(x), on a relative electron density scale were calculated from... 

It should cause no surprise that for polymer crystals with very small sizes, a definitive structural analysis is difficult using only unoriented diffraction patterns. This is not only due to the small number of observable diffractions and their general broadening, but also to the fact that high angle diffraction rings often consist of the superimposition of several refiections of different indices. In certain special cases, eg, when a structural similarity to a known substance is suspected on the basis of chemical composition, it may be possible to make identification by comparison, but even this procedure contains possible errors. 

Fig. 4.26 X-ray diffraction pattern for unoriented (a) and oriented (b). (BiU-meyer (1984), p. 294, reprinted with permission of John Wiley and Sons, Inc.)...

Figure 9.10 Schematic X-ray diffraction patterns from an unoriented and an oriented crystalline polymer. Definition of the azimuthal angle (j).

X-ray diffraction patterns of essentially unoriented 8 form and e form SPS films, annealed at different temperatures, show that both crystalline forms are transformed in the y form. However, while for the 8 form film this transformation involves an intermediate helical mesomorphic phase [45,52,161], for the e form film a direct transformation toward the y phase is observed [44],... 

TEM (Fig. 5.1a). The width can be several micrometers and the thickness only a few hundred angstroms. The electron diffraction pattern shows that only the hkO reflections are detected in the case of trigonal POM, which indicates that the chain stems stand up in the direction normal to the crystal surface. Stokes is the first to indicate the possibility of chain folding by measuring the electron diffraction patterns of unoriented trans-l,A-polyisoprene, he found that the chain axis is normal to the film plane [9]. Later, Fischer, Till, and Keller made direct observations of polymer single crystals with a chain-folded structure. The concept of chain folding originates from this experimental evidence [10]. 

A flat-plate X-ray diffraction pattern was obtained from an unoriented sample of polyethylene using CuKa radiation. It consisted of three rings of radius 22.2 mm, 36.6 mm and 19.7 mm. The specimen-to-film distance was 50 mm. Calculate the d-spacing of the planes giving rise to these reflections. It is thought that these... 

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