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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 Iα, Iβ, 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 1.5° 2θ, 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.

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  1. Consider the conversion of a structure with twofold molecular symmetry to one with fourfold symmetry. In the case of the two-fold axis and monoclinic space group, there would be no logical problem with using b, but for the fourfold case and a tetragonal space group, two of the axes are the same. There, the undisputed convention is to have a and b equal, with c unique (Klug and Alexander 1974). If the monoclinic structure also uses the c-axis as parallel to the molecular axis, then one can compare the c-axis dimensions of the two different molecules.

  2. Their reported dimensions were for an 8-chain unit cell although their reported structure has a two-chain cell. Their values have been divided by two in this work to represent their two-chain cell.


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Paul Langan kindly provided the .cif file for cellulose II. The research was partly inspired by collaborative efforts with Cotton, Incorporated. Drs. Santiago Cintrón, Seong Kim and Xueming Zhang kindly commented on preliminary versions of the manuscript. Dr. Edwin Stevens consulted on the effects of preferred orientation on the cellulose Iα pattern.

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Correspondence to Alfred D. French.

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Manuscript prepared for Cellulose, Special Issue from the symposium, “100 Years of Cellulose Diffraction,” 245th National Meeting, American Chemical Society (presented in part at the symposium, “From Cellulose Raw Materials to Novel Products: Anselme Payen Award Symposium in Honor of Hans-Peter Fink”).

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French, A.D. Idealized powder diffraction patterns for cellulose polymorphs. Cellulose 21, 885–896 (2014).

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  • Cellulose crystal structure
  • Miller indices
  • Powder diffraction patterns
  • Convention