Microfibril dimensions from small-angle X-ray scattering

Model calculation based on parallel cylindrical fibrils with a distribution of radii are used to derive fibrillar radii obtained from the transverse intensity profile of the small-angle X-ray scattering (SAXS) peaks. The results are expressed in terms of moments of the distribution function of the radii. The traverse integral breadth of the peak leads to ({ R^4}/{ R^3}), the initial slope gives ({ R^6}/{ R^4})1/2, the asymptotic slope in the transverse wings yields { R^2} or ({ R^4}/{ R^2})1/2 and the analysis of the characteristic function gives ({ R^2}/{ R^1}). The first two methods are applied to the SAXS patterns of well oriented samples of nylon 6, for which it is found that a positively skewed distribution of fibrillar radii. The relation between these analyses of uniaxially oriented systems and other SAXS and wide-angle diffraction methods is considered.