SAXS DATA-ANALYSIS OF A LAMELLAR 2-PHASE SYSTEM - LAYER STATISTICS AND COMPANSION

An analysis of small angle x-ray scattering (SAXS) data from three inj ection molded poly(ethylene terephthalate) (PET) samples is carried ou t. Two of the samples are annealed at different temperatures. The chos en 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 o n the topological properties of the ensemble of lamellar stacks in the semicrystalline sample. The paper describes the stepwise refinement o f a topological model. The final model is described by only few parame ters of physical meaning. It unifies the well-known concepts of an ens emble of non-uniform stacks, finite stack size and one-dimensional par acrystalline 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.