Introduction to modelling of small-angle scattering data
Jan Skov Pedersen
Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Denmark
In this lecture, an introduction to direct modelling of small-angle scattering will be presented. This approach is often used when the sample consists of a dispersion or solution of particles or molecules. A geometrical model of the scattering particles/objects is assumed and the calculated small-angle scattering of the model, the form factor, is fitted to the measured data employing least-squares methods. Some of the most used form factors will be presented including inhomogeneous models of the core-shell type. Also, some form factors of polymer-like objects will be given, including models of branched chains and models for block copolymer micelles. When the particle positions are correlated, structure factors that have to be included in the analysis. Some of the structure factors will be presented including how to take them into account for systems with anisotropy and flexibility. Finally, absolute scale modelling will be discussed. In this approach molecular properties and concentrations of the components are considered as restraints to reduce the number of fit parameters.