We report on a series of SANS experiments on the structure of binary water−nonionic surfactant systems accompanied by complementary ultralow shear experiments and depolarized light scattering. The analysis gives a clear picture of the temperature dependence of aqueous solutions of nonionic surfactants of the n-alkyl polyglycol ether type (C i E j ) when approaching the cloud point curve. The series is based on temperature variations from 3 °C up to a temperature of about 1.5 K below the critical point T c and concentration variations around the critical concentration c c by a factor of 3−9. Six different surfactants were studied, changing the alkyl chain length i as well as the number of ethylene oxide groups j. Excluded volume effects were taken into account in the evaluation procedure by a generalized indirect Fourier transformation procedure recently developed for the evaluation of scattering data from semidilute and dense systems. The bottom line is that all systems examined show a sphere-to-rod transition, the degree of growth and the transition temperature depending on the concentration and hydrophobicity of the surfactant. Superimposed on this transition is the onset of attractive interactions as the cloud point curve is approached, the range depending on the overall surfactant size.

Indirect Fourier transformation is a well established method for the evaluation 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 contains intra‐ and interparticle scattering contributions, the evaluation of scattering data is no longer just the solution of a linear weighted least‐squares problem because the scattering intensity can, under certain conditions, be written as the product of the particle form factor and the so‐called structure factor, which leads to a highly non‐linear 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 can be understood as a generalized version of the indirect Fourier transformation 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 for a given interaction model. A simultaneous determination of these two functions is possible due to the different analytical behavior of these functions, which also leads in most cases to the existence of a global minimum in the parameter surface. An algorithm to solve this nonlinear least‐squares problem has been developed and applied to simulated data for a variety of different uncharged systems.

The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared, e.g. the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rodlike particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any in¯uence of the form amplitude is advisable, at least during the ®rst evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum of a priori information.