Idealized powder diffraction patterns for cellulose polymorphs

Cellulose samples are routinely analyzed by X-ray diffraction to determine their crystal type (polymorph) and crystallinity. However, the connection is seldom made between those efforts and the crystal structures of cellulose that have been proposed with synchrotron X-radiation and neutron diffraction over the past decade or so. In part, this desirable connection is thwarted by the use of different conventions for description of the unit cells of the crystal structures. In the present work, powder diffraction patterns from cellulose I alpha, I beta, II, IIII, and IIIII were calculated based on the published atomic coordinates and unit cell dimensions contained in modified "crystal information files" (.cif) that are supplied in the Supplementary Information. The calculations used peak widths at half maximum height of both 0.1 and 1.5A degrees 2 theta, providing both highly resolved indications of the contributions of each contributing reflection to the observable diffraction peaks as well as intensity profiles that more closely resemble those from practical cellulose samples. Miller indices are shown for each contributing peak that conform to the convention with c as the fiber axis, a right-handed relationship among the axes and the length of a < b. Adoption of this convention, already used for crystal structure determinations, is also urged for routine studies of polymorph and crystallinity. The calculated patterns are shown with and without preferred orientation along the fiber axis. Diffraction intensities, output by the Mercury program from the Cambridge Crystallographic Data Centre, have several uses including comparisons with experimental data. Calculated intensities from different polymorphs can be added in varying proportions using a spreadsheet program to simulate patterns such as those from partially mercerized cellulose or various composites.