SAXS data analysis of a lamellar two-phase system. Layer statistics and compansion

Abstract

An analysis of small angle x-ray scattering (SAXS) data from three injection molded poly(ethylene terephthalate) (PET) samples is carried out. Two of the samples are annealed at different temperatures. The chosen concept of data analysis is that of Ruland's interface distribution function (IDF) of lamellar two-phase systems. The IDF can be expanded into a series of distance distributions, containing the information on the topological properties of the ensemble of lamellar stacks in the semicrystalline sample.

The paper describes the stepwise refinement of a topological model. The final model is described by only few parameters of physical meaning. It unifies the well-known concepts of an ensemble of non-uniform stacks, finite stack size and one-dimensional paracrystalline disorder in an analytical expression. In order to deduce this expression, the concept of inhomogeneity (imagine a variation of the long period from stack to stack) is generally treated in terms of “compansion”, a suggested superposition principle. Its mathematical equivalent in one dimension is the Mellin convolution.