SMALL-ANGLE SCATTERING OF INTERACTING PARTICLES .1. BASIC PRINCIPLES OF A GLOBAL EVALUATION TECHNIQUE

Indirect Fourier transformation is a well established method for the e valuation of small-angle scattering data. This technique, however, is restricted to dilute solutions, as for higher concentrations particle interactions can no longer be neglected. As the scattering intensity c ontains intra-and interparticle scattering contributions, the evaluati on of scattering data is no longer just the solution of a linear weigh ted least-squares problem because the scattering intensity can, under certain conditions, be written as the product of the particle form fac tor and the so-called structure factor, which leads to a highly nonlin ear problem. In this paper a global evaluation technique including the structure factor is presented so that it is possible to determine the form factor and the structure factor simultaneously. This technique c an be understood as a generalized version of the indirect Fourier tran sformation method. Like in the indirect Fourier transformation, there are no models or no analytical restrictions used for the form factor, and the structure factor is parameterized with up to four parameters f or a given interaction model. A simultaneous determination of these tw o functions is possible due to the different analytical behavior of th ese functions, which also leads in most cases to the existence of a gl obal minimum in the parameter surface. An algorithm to solve this nonl inear least-squares problem has been developed and applied to simulate d data for a variety of different uncharged systems.