Evaluation of small-angle scattering data of charged particles using the generalized indirect Fourier transformation technique

Abstract

Small-angle x-ray and neutron scattering are widely used techniques to study the structure of colloidal particles in the size range up to 100 nm. The indirect Fourier transformation technique is well established to obtain model free real space information, but the interpretation of the results is limited to cases where particle interaction can be neglected. The extended generalized indirect Fourier transform (GIFT) allows one to separate inter- and intraparticle effects, but needs models for the particle interaction. We present the application of three different models for the calculation of interaction effects of charged particles, represented by the structure factor. With this extension, useful real space information can be obtained by the GIFT method for solutions with volume fractions up to about 0.3 without any assumption for the shape of the particles. Only the interaction effects need a model assumption, and the parameters determined from this model can give some additional information. Simulations show that it is impossible to determine charge and ionic strength simultaneously. There exists another ambiguity between the parameter sets for charge, radius, and volume fraction, but we show how this problem can be overcome in most cases. The practical applicability of the method is demonstrated by means of the micellar system CTAB in different concentrations from 1% up to 20% and with varying amounts of added salt to screen the charges and change the particle shape.