Influences on the accuracy of crystallinities determined by the method of Ruland and Vonk

Abstract

X-ray diffractometry is the method of choice for the determination of crystallinities in non-thermoplastic polymers, prominently in cellulose. Obtaining quantitative measures on a sound theoretical basis includes the integration of intensities scattered by the crystalline phase over volume elements in reciprocal space. This is hampered by the occurrence of diffuse scattering, whose profile is not readily distinguishable from scattering by amorphous phases. The manner of evaluating diffractograms pioneered by Ruland and refined by Vonk allows to determine crystallinities by integrating only the coherently scattered portion of crystalline-phase intensities and extrapolating their proportion to a scattering vector of 0. However, preferred crystallite orientations within measured samples, as well as the range of scattering vectors from which the data are extrapolated, have been pointed out as sources of systematic error. We investigated the influence of these factors at the examples of two crystalline structures of cellulose and two types of technically relevant thermoplastics. We found that the method of Ruland and Vonk is rather robust when applied to cellulose, but decidedly less so when applied to polymers with highly symmetric crystalline phases. We also found that there is a range of scattering vectors that leads systematically to the most accurate measures of crystallinity. We further investigated the influence of the crystallite sizes, the crystallinities themselves and the thermal displacement factors, and found that the latter had a profound effect on the accuracies of determined crystallinities.