Origin of SAXS intensity in the low-q region during the early stage of polymer crystallization from both the melt and glassy state

The isothermal crystallization from the melt and glassy state of poly(trimethylene terephthalate) has been studied with wide-angle x-ray diffraction, small-angle x-ray scattering (SAXS), and ultrasmall-angle x-ray scattering (USAXS). Large scattering intensity in the low-$q$ region has been observed with SAXS and USAXS during the early stage of melt and glass crystallizations. We have quantitatively analyzed the x-ray results using the scattering equations which can simultaneously deal with the hierarchical structures consisting of the crystallites and their aggregates. The results reveal the crystallization mechanism in which the crystalline nodules cover the entire sample with the aggregation regions. The conclusion quantitatively shows that the large SAXS intensity is not due to the density fluctuations of the liquid state but due to the correlations among the heterogeneous aggregation regions of the nodules.