Simulation of SAXS patterns from oriented lamellar structures and their elliptical trajectories

Abstract

Small-angle X-ray Scattering (SAXS) patterns are useful for studying the organization of crystalline and amorphous regions that make up a semi-crystalline polymer and influence its properties. To understand how these patterns originate and evolve during deformation, three distinct SAXS patterns (2-point, 4-point ‘eyebrow’, and 4-point ‘butterfly’) were generated using simple microstructural models and compared in detail with experimental data from poly(ethylene-co-octene). As the patterns typically contain a single unique reflection, it is not possible to fully determine the structure from the patterns alone. Therefore, structural models with lamellar stacks were used to simulate SAXS patterns. When stack orientation (interlamellar shear) and chain slip act to rotate lamellae in the same sense, the result is an ‘eyebrow’ pattern. Opposite senses give a ‘butterfly’ pattern. Experimental patterns often have reflections where the peak position traces out an ellipse. Adding moderate amounts of rotational disorder to the models produces this effect without any elliptical correlations or deformed lattice in the material.