The presence of concentration and inter-particle interaction effects in small-angle scattering is both a blessing and a curse: It provides important information on inter-particle potentials and particle ordering, but it also makes the analysis much more difficult, since a structure factor derived from statistical mechanics has to be used in the analysis. In this talk I will outline on a tutorial level the basic approaches for anisotropic particles dating back to Zimm (1947) and for spherical particles in terms of integral equation theory. Empirical extensions of the Zimm approach based on Monte Carlo (MC) simulations into the integral equation theory of polymers and cylindrical particles (Polymer Reference Interaction Site Model = PRISM) will be given. This also allows charged (polyelectrolyte) systems to be described. The difficult case of slightly anisotropic particles will also be discussed and by comparison with MC simulation it will be shown that the classical `decoupling approximation’ is a very good approach. The final issues that will be covered are influence of particles structure and contrast on derived measured structure factors and approximate approaches including polydispersity effects. Whenever possible, experimental examples of application will be given.
Department of Chemistry and iNANO Interdisciplinary Nanoscience Centre Aarhus University, Denmark