An evaluation method for SAXS-patterns of fibrillar two-phase systems containing oriented particles of moderate anisotropy and short range correlation

Abstract

Starting from the theoretical background of Rulands interface distributions, an evaluation method for small angle x-ray patterns arising from oriented fibrillar two-phase structures is proposed. If the fibril contains highly oriented particles with only moderate anisotropy and if the correlations between those particles within the fibril are of short range only, every axial section of the scattering pattern shows a one dimensional Porod law. A procedure of successive model confinement using the well known tools of nonlinear regression analysis is described. The result of such an analysis for the scattering pattern of an oil diluted SBS block copolymer recorded with synchrotron radiation under first-cycle stretching is reported. Atλ=4 nm four contributions to the scattering pattern could be identified: a) fibrils containing well-defined cylinders standing upright; b) fibrils containing lying cylinders under destruction; c) stretched-out polybutadiene chains, connecting two polystyrene cylinders and causing the observable layer line pattern; and d) stretched-out polybutadiene chains looping through the neighboring PS domain and returning to their starting domain. In addition, a simple method for determining the height-to-diameter ratio of cylinders from the form factor envelope is proposed.