Crystal structure fibre patterns

Since polymer single crystals prepared these days are too small for x-ray diffraction experiments, the Crystal Structure of a polymer is generally determined from x-ray patterns of a fibre drawn from the polymer. Due to the alignment of the crystalline regions with the long axes of the molecules parallel to the fibre axis, the pattern is essentially identical to a rotation pattern from... 

The elucidation of the crystal structures of polymers from their x-ray diffraction patterns is frequently a difficult and laborious task. The work usually proceeds by trial and error methods in which calculated intensities for likely structures are compared with the observed intensities of diffraction spots. Furthermore, x-ray fibre photographs often contain relatively few reflections and it is always possible that more than one structure may give a reasonable fit with the observed intensity data. Additional information which can be obtained from infrared spectra can often provide considerable help with both these difficulties and in particular many trial structures can be eliminated without recourse to time-consuming calculations of x-ray intensities. 

XRD-results have shown that aluminium oxide was formed at 600-700 °C. It consists of nano-dimensional grains and have the y-structure providing the high reactivity of fibrous material. When fibres of aluminium oxide were heated to 900 °C, its crystal structure varied from y- to 0-phase, and above 1200 °C it changed to a-corundum. It is illustrated by the patterns in Fig. 1. 

If a stretched fibre of a crystalline polymer is placed in the X-ray machine, a so-called fibre pattern is observed (fig. 3.10). As discussed in chapter 4, this pattern contains information about the crystal structure of the polymer. It also contains information about the size of the crystallites and about their degree of alignment, topics discussed further in chapters 5 and 10, respectively. 

In order to obtain the maximum amount of information about the crystal structure it is necessary to align the crystallites, which can be done by methods described in detail in chapter 10. It is sufficient to note here that suitable orientation is often produced by stretching a fibre of the polymer. In the simplest cases the chain axis of each crystallite, which is designated the c-axis, becomes aligned towards the fibre axis, but there is no preferred orientation of the other two axes around the c-axis. From such a sample a fibre pattern can be obtained, of the type shown in fig. 3.10. 

In order to determine the crystal structure it is necessary to determine the positions and intensities of all the spots in the fibre pattern. The positions of the spots provide information from which the shape and dimensions of the unit cell can be calculated and the intensities provide information about the contents of the unit cell. The following section considers the relationship between the fibre pattern and the unit cell. 

The dimensions of the xylan unit cell are slightly different a = b = 1.340 nm, (fibre axis) = 0.598 nm.) Atkins and Parker T6) were able to interpret such a diffraction pattern in terms of a triple-stranded structure. Three chains, of the same polarity, intertwine about a common axis to form a triple-strand molecular rope. The individual polysaccharide chains trace out a helix with six saccharide units per turn and are related to their neighbours by azimuthal rotations of 2ir/3 and 4ir/3 respectively, with zero relative translation. A similar model for curdlan is illustrated in Figure 6. Examinations of this model shows that each chain repeats at a distance 3 x 0.582 = 1.746 nm. Thus if for any reason the precise symmetrical arrangement between chains (or with their associated water of crystallization) is disrupted, we would expect reflections to occur on layer lines which are orders of 1.746 nm. Indeed such additional reflections have been observed via patterns obtained from specimens at different relative humidity (4) offering confirmation for the triple-stranded model. 

The second type includes various lamellar models which describe the fibre structure in terms of alternating layers of crystalline and noncrystalline material. Considerations of shape and intensity of SAXS patterns and crystallinity rule out any regular lamellar structure. According to Fischer and Fakirov, the crystalline lamellae consist of mosaic blocks whose size and mutual packing depend on crystallization conditions. 

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