Quantitative electron diffraction techniques have been especially important for the determination of linear polymer structures. This is because chain-folded lamellae are the only approximation to single crystals that can, in most cases, be grown. As outlined in Chapter 4, the usual method for determining crystal structures with electron diffraction data from polymers has been to collect an hk0 net from untilted lamellae and to use a conformational search around linkages between the rigid subunits of a chain model to find the best molecular packing. In this search, the crystallographic residual is minimized simultaneously with an atom—atom nonbonded potential energy. More recently, this technique, which is borrowed from fiber x-ray analysis (e.g., see Atkins, 1989), has been applied to three-dimensional electron diffraction data sets. Even when electron diffraction intensities are not used quantitatively for structure analysis, single-crystal patterns are of considerable benefit for identifying plane-group or space-group symmetry, measurement of cell constants, and, in general, as an aid for indexing fiber x-ray patterns. Tables of unit cell constants and symmetry based on electron diffraction measurements can be found in standard works on polymer physics (Geil, 1963; Wunderlich, 1973). A list of crystal structures determined from electron diffraction intensity data is given in Table 11.1. Specific examples based on the use of direct phase determination will be discussed in the following sections.
KeywordsLinear Polymer Kind Permission Conformational Search Chain Axis Direct Phase
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