Modeling small-angle X-ray scattering in quiescently crystallized polymers in the absence of long-period dispersity

To explain the single and wide first-order long-period peak observed in semicrystalline polymers, classical small-angle X-ray scattering (SAXS) theory regards the dispersity in lamellar thickness/long period as the key structural feature of semicrystalline polymers. Other factors affecting the SAXS pattern such as the lateral size of a lamellar stack, the number of lamellar crystals in a stack and linear crystallinity have been overlooked as secondary factors, preventing structure extraction from SAXS. In this study, we attempted to establish a scattering equation for semicrystalline polymers formed during quiescent crystallization without considering dispersity in the long period/lamellar thickness. The results indicate that the lateral size is the key factor leading to the unique SAXS pattern in semicrystalline polymers and the absence of the linear region in the correlation function. SAXS in semicrystalline polymers results from minor lamellar stacks with small intersection angles with the incident X-rays. On the basis of the results, we suggest employing a revised interface distribution function to obtain structural information after recovering higher-order weak long-period peaks by a difference method. Half of the q⁴ correction is to eliminate the influence of the form factor, while the other half is to remove the factor of 1/q² in the structure factor. This study helps to further our understanding of SAXS in semicrystalline polymers.