Analysis of small-angle x-ray diffraction from polymers

The Fourier transform method of Vonk and Kortleve for the analysis of small-angle x-ray diffraction (SAXRD) from semicrystalline polymers has been compared with a modified direct method, originally due to Tsvankin. SAXRD data for three melt-crystallized polyethylene samples have been analyzed in terms of the mean true periodicity, mean crystal length, and mean length of amorphous segments. The two methods of analysis yield substantially equivalent results for all three samples. Calibration curves for the Tsvankin analysis are tabulated, and the relative merits of the two methods of analysis are discussed. With either method, information about the diffracting structure may be deduced that is not available from a simple measurement of the position of the SAXRD maximum. In fact, direct application of the Bragg law to any but the sharpest maximum yields a spacing (the long period) that lacks direct physical significance.