COMPLETE SAXS DATA-ANALYSIS AND SYNTHESIS OF LAMELLAR 2-PHASE SYSTEMS- DEDUCTION OF A SIMPLE-MODEL FOR THE LAYER STATISTICS

A structural model for the analysis of SAXS data from lamellar two-pha se systems is proposed and applied on data sets from three injection m oulded poly(ethylene terephthalate) (PET) samples. The concept of data analysis is based on Ruland's interface distribution function (IDF). The suggested model is defined by few parameters of physical meaning. It unifies the well known concepts of an ensemble of non-uniform stack s, finite stack height and one-dimensional paracrystalline disorder in an analytical expression. In order to deduce this expression, the not ion of an inhomogeneous structure within the sample is mathematically treated in terms of ''compansion'', a general superposition principle. Its mathematical equivalent in one dimension is the Mellin convolutio n. The theory of the Mellin convolution may be used to find analytical functions even for the convoluted. An example is given, which in futu re work may be used to describe the thickness distributions of amorpho us and crystalline layers. In the application part of this study gauss ians are used to describe the thickness distributions in each local st ack. The introduction of compansion adds one extra parameter, which de scribes the heterogeneity of die sample. Compansion makes the global t hickness distributions become more asymmetrical.