Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting

Analysis and modeling of small-angle scattering data from systems consisting of colloidal particles or polymers in solution are discussed. The analysis requires application of least-squares methods, and the basic principles of linear and non-linear least-squares methods are summarized with emphasis on applications in the analysis of small-angle scattering data. These include indirect Fourier transformation, square-root deconvolution, size distribution determinations, and modeling. The inclusion of corrections for instrumental smearing effects is also discussed. The most common analytical expressions for model form factors and structure factors are summarized. An example of analysis of small-angle neutron and X-ray scattering data from block copolymer micelles is given.