Applications of direct methods for structure determination to problems in electron and x-ray fibre diffraction of polymers

In this review, the prospect of determining polymer crystal structures directly from single crystal electron or x-ray powder/fibre diffraction intensity data is explored. When care is taken to collect the best data set from a polymer, i.e. sampling the most intense regions of the three-dimensional reciprocal lattice, structure analyses can be carried out effectively by the conventional direct phasing methods employed in small molecule crystallography, even though the data sets are relatively small. This means that constraints imposed by multiple beam interactions in electron diffraction and reflection overlap in x-ray diffraction often do not limit the structure analysis. Several three-dimensional single crystal electron diffraction structure analyses are presented to illustrate the problems encountered. These include: polyethylene, poly(epsilon-caprolactone), isotactic poly(butene-1) form III, isotactic polypropylene beta-form,poly(p-oxybenzoate) and poly(ethylene sulfide). Techniques for sampling the complete reciprocal lattice are discussed. If an adequate number of data is collected, it is also possible to refine the structure by constrained least squares. In any case Fourier refinement is always useful. From powder x-ray diffraction the crystal structure of polyethylene has been determined by direct methods; from fibre x-ray intensities, this review reports the direct analyses of poly(epsilon-caprolactone), poly(ethylene terephthalate) and poly(tetramethyl-p-silphenylene siloxane). Rietveld methods might also be useful for the structure refinement. Direct structure analyses are advantageous in that they circumvent a priori assumptions about the molecular model and also the linkage bonds to base conformational refinement. Instead, individual atomic positions or molecular envelopes are observed directly in potential or electron density maps, to which the model can then be fit, a situation analogous to current practice in protein crystallography.