Exploration of Deformation Mechanism in Isotactic Polypropylene Using a New Two-Dimensional Fast Fourier Transform Method

During stretching, lamellar stacks within semicrystalline polymers are often oriented and deformed, resulting in diverse and complex two-dimensional small-angle X-ray scattering (2D-SAXS) patterns. Accurately interpreting the information behind 2D-SAXS has been challenging. An effective method to extract the information is to list all possible deformations and determine corresponding SAXS patterns, identifying useful methods to characterize the deformed lamellar stack from their relationship. However, no such work has been carried out due to lack of suitable tools. In this study, we investigated the factors affecting the determination of 2D-SAXS using two-dimensional fast Fourier transform (2DFFT) and classical scattering equation. Results indicate that the sampling rate and the dimensions of the digital matrix are two critical factors affecting 2D-SAXS. Besides, different from the classical scattering equation, what is determined by fast Fourier transform is the average intensity over a period. Based on the above discussions, a straightforward method to simulate 2D-SAXS of oriented structures using 2DFFT was proposed and applied to a high-temperature annealed isotactic polypropylene (iPP) sample. It was found that the eyebrow-like scattering pattern could be caused by inhomogeneous lateral contraction forces during stretching of iPP. The method sheds light on the deformation mechanisms in semicrystalline polymers.