Form and Structure Factors, Interactions, Modeling

Jan Skov Pedersen
Aarhus University, Denmark

The lectures will deal with the more classical modeling approach for analysis of small-angle scattering data. In the first part, analytical models are considered, and in a second part, effects of inter-particle interactions are described.

An overview over the form factors of various simple geometrical objects like spheres, ellipsoids, cylinders, discs etc will be given. A few examples are treated in greater detail. In addition, the form factors of polymer models with many internal degrees of freedoms are given, also with a few examples treated in detail. It will be shown how form factors of object consisting of spherical subunits can be derived and similarly how form factors of polymer-like branched structures can be calculated for pre-defined structures. The last topic to be dealt with in the first part of the lectures is models consisting of both spherical and polymer chain subunits. It will also be described how one can use of Monte Carlo simulations for generating form factors of polymer models with complex interactions like excluded volume and electrostatic interactions. Form factors for a broad range of parameters are generated and then parameterized so that numerical expressions are available for analysis of experimental data.

In the last part of the lectures, the effects of inter-particle interactions are discussed. The main analytical results will be given for spherical particles and polymer-like particles; approximations valid for particles with some anisotropy are also described.

Throughout the lectures, examples of applications to experimental data are included.

J. Skov Pedersen (1997) Analysis of Small-angle Scattering Data from Polymeric and Colloidal Systems: Modelling and Least-squares Fitting. Advances in Colloid and Interface Science, 70, 171-201

J. Skov Pedersen (2002) Monte Carlo Simulation Techniques Applied in the Analysis of Small-Angle Scattering Data from Colloids and Polymer Systems. Editors: P. Lindner, Th. Zemb. Neutrons, X-Rays and Light 381-389, Elsevier Science

J. Skov Pedersen (2002) Modelling of Small-Angle Scattering Data from Colloids and Polymer Systems. Editors: P. Lindner, Th. Zemb. Neutrons, X-Rays and Light, 391-420, Elsevier Science

Date/time: Thursday, 23 October, 9:00