Variations in the fibre repeat between samples of cellulose I from different sources

A powder X-ray diffractometer was used to measure the fibre repeat in cellulose I with sufficient precision to detect variations between samples from different sources. The variations were correlated with the lateral dimensions of the crystallites and were attributed to different minimum-energy fibre repeats for chains in the interiors and on the surfaces of crystallites. Results were interpreted in terms of a model for internal mechanical stress in which the interior chains were under compression and the surface chains under tension to ensure identical fibre repeats for all chains. The model was used to extrapolate the fibre repeat to a value of 1.043 nm for a hypothetical, infinitely large crystal, and to 1.029 nm for a crystallite so narrow that all chains were exposed on surfaces.