A quantitative analysis of X-ray small-angle scattering of partially crystallized copolymer systems

Abstract

The quantitative description of small-angle X-ray scattering curves (SAXS) of copolymers of ethylene needs the determination of a number of structure parameters. The number of parameters, which are due to a certain model, can be kept low by adding results from other experiments. The thermodynamic description of the melting process of statistical “pseudo-eutectical” copolymer systems yields structure parameters which can be used for the calculation of SAXS. The calculation itself is done using Hosemann's formula of the linear paracrystal, modified for our problem. The superstructure of the copolymer is assumed to be built up by clusters consisting of a certain number of stacked lamellae. A quantitative description of experimental SAXS can be established fitting alone the average number of crystal lamellae within the clusters of a simplified one-dimensional model of the super-structure. It is found that the number of lamellae within a cluster contributing to constructive interference modulation of SAXS is not only determined by the paracrystalline statistics but influenced too by the degree of dense packing of crystals according to the crystallinity of the copolymer systems.