Desmeared, slit-smeared and projected SAXS: a comparison of various methods of evaluation for segmented polyurethanes

Abstract

Evaluation methods for X-ray small angle scattering of segmented polyurethane elastomers are discussed using the assumption of isolated, randomly distributed hard segment domains in order to test the reliability of evaluation.

Projection of the intensity distribution onto the meridian of the scattering diagram reduces the analysis to a one-dimensional problem, since the projections is related to a chord through the three-dimensional structure. Furthermore, the chord may be identified with the one-dimensional structure of an ideal lamellar stack, so that the projection of the intensity is comparable with the well-known result of J. J. Hermans for lamellar stacks.

The projection has to be calculated in the three dimensional Fourier space either by desmearing the slit-smeared scattering intensity or by projecting it directly onto the meridian. Practically identical results are obtained by both procedures, so that the desmearing operation may be omitted in the present case. We show that the damping function, which is due to domain boundary diffuseness, can be suitably and directly eliminated from the slit-smeared intensity by applying a method proposed by Koberstein.

A reproducibility of the final structural parameters within 10–15% can be achieved using the methods described.