A new Fourier transformation method for SAXS of polymer lamellar crystals

Abstract

For a long time, the scattering of semi-crystalline polymers was assumed to be from the electron density correlation in a lamellar stack. The Fourier transform for scattering can help obtain the correlation function and interface distribution function (IDF), from which the structural information can be obtained. Recently, we found that the scattering of the interface electrons involved in an evanescent wave (Iⁱ_ev) is the actual origin (Li et al., IUCrJ, 2019, 6, 968–983). It is necessary to develop a new Fourier transform method to obtain structural information. In this study, a method similar to the classical method was proposed; nevertheless, the aim of multiplying q² or q⁴ is to reduce the influence of the form factor, while the scattering in Fourier transform should be Iⁱ_ev, which is roughly equal to the increased scattering during crystallization. The functions obtained by the Fourier transforms K_ev and are similar to the correlation function and IDF in shape, respectively. Nevertheless, both of them are determined mainly by three items, i.e., the self-interference term of the first interface F₁₁, the interference term between the first and second interfaces F₁₂, and the interference term between the first and third interfaces F₁₃, with no relation with the density correlation. They can give information on the lamellar thickness and long period but not on amorphous thickness since both the “self-correlation region” in the so-called “correlation function” and the first peak in IDF are dominated by F₁₁, which does not include the parameter of amorphous thickness. With the revised procedure, the lamellar thickness and long period can be obtained readily from real scattering, whether for a lamellar two-phase system or a lamellar system with a broad thickness distribution. Based on the above-mentioned results, we suggest the removal of the concept of correlation function but the retention of IDF. can be regarded as a new IDF, which represents the probability of finding an interface apart from the first interface of a lamellar stack at a distance of Z.