Fiber diffraction as a useful supplement to single-crystal electron diffraction data in the direct three-dimensional structure analysis of polymers

Abstract

When zonal electron diffraction data from chain-folded lamellae are combined with the three-dimensional (3-D) information from a microfiber, it is possible to determine a polymer crystal structure by direct methods to visualize the atomic arrangement in the unit cell. An analysis of the polyethylene sulfide) structure (space group Pbcn, a = 8.51, b = 4.94, c = 6.69 Å) is presented as an example of such a determination. The crystallographic phases—including 17 of 20 unique zonal hkO data collected earlier from chain-folded lamellae, as well as two other phases permitted for origin definition in three dimensions—served as a basis set for extension into three dimensions by the Sayre equation. The phase extension into the 3-D indices of the fiber diffraction set (39 unique amplitudes including 32 estimated from 14 overlapped maxima) was quite accurate, especially for the most intense reflections. Combination of these phases with amplitude values to generate the three-dimensional potential map allowed direct visualization of the atomic distribution in the unit cell. The structure could then be refined by a match of a chain model to the observed potential distribution, after optimizing the bonding geometry. These results demonstrate that, with the use of fiber data as a supplement, alternative experimental approaches to true three-dimensional structure determinations exist in polymer electron crystallography, even if epitaxial crystallization methods cannot provide the necessary orthogonal orientation of the chain packing. By this approach, the “missing cone” problem for goniometry in the electron microscope can be largely overcome.