New Fourier Transformation Method for SAXS of Polymer Lamellar Crystals

For a long time, the scattering of semi-crystalline polymer was assumed to be from electron density correlation in a lamellar stack. Fourier transform for the scattering can obtain correlation function and interface distribution function (IDF), from which structural information can be obtained. Recently, we found that the scattering of the interface electrons involved in an evanescent wave (I_ev^i) is the genuine 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 as 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 the Fourier transform should be I_ev^i, which is roughly equal to increased scattering during crystallization. The functions obtained by Fourier transform K_ev and K_ev^' are similar to 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, having nothing with density correlation. They can give the information on lamellar thickness and long period but not the amorphous thickness, since both “self-correlation region” in the so-called “correlation function” and the first peak in IDF were dominated by F11, which does not include the parameter of amorphous thickness. With revised procedure, 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 above results, we suggest to remove the concept of correlation function but remain IDF. K_ev^' can be regarded as new IDF, which represents the probability of finding an interface apart from the first interface of a lamellar stack at a distance of Z.