MODEL FITTING: A CRITERION FOR POLYMER STRUCTURE IDENTIFICATION AFTER DIRECT METHODS. Mary P. McCourt, Department of Mathematics and Natural Sciences, D'Youville College & Electron Diffraction Department, Hauptman-Woodward Institute, Buffalo, NY

Although direct phasing methods have been found to be effective for determining polymer crystal structures from electron diffraction or x-ray diffraction data sets, there can be instances where the resultant potential or electron density maps cannot be interpreted directly in terms of atomic positions. For example, there may be algebraic ambiguities due to poor connectivity of Miller indices (e. g. an undersampled reciprocal lattice) or insufficient resolution to visualize the positions themselves. Fitting of polymer chain models to the resultant can be quite useful, therefore, for identification of a structure and derivation of atomic coordinates to permit calculation of an R-factor. Examples of electron diffraction data sets from single crystal orientations, e. g. mannan I and poly (pivalolactone) will be discussed in this context, where the model compensates for unmeasured data in the `missing cone'. In another example, poly (ethylene sulfide), where data from lamellar crystals and fibers are combined to sample all of reciprocal space, model fitting overcomes bond length distortions due to dynamical scattering. In fiber x-ray determination, direct methods have been used to solve the crystal structure of poly ([[epsilon]]-caprolactone). Despite the high resolution of the data set, the non-planar chain conformation is best visualized when a chain is fit to the electron density profile. Finally, in the analysis of poly (tetramethyl-p-silphenylene), the low resolution of the x-ray data requires the correct space group and phase set to be chosen on the basis of the chain skeleton. In all of these applications, the construction is used as a figure of merit for ab initio analysis rather than as the basis for a trial and error search.

Research supported by a grant from the NSF (CHE94-17835)