A new numerical method is presented for simultaneous smoothing, desmearing and Fourier transformation of X-ray and neutron small-angle scattering data. The method can only be applied to scattering curves from dilute particle systems, i.e. for scattering media whose distance distributions are zero beyond a certain value. The distance distribution of the scattering medium is approximated by a linear combination of about 20 to 30 cubic B-splines. These spline functions have a restricted extension in real space. Their coefficients are adjusted by a weighted least-squares operation so that the series, after being Fourier transformed and smeared according to the geometry and wavelength distribution, represents an optimum smoothed approximation of the experimental data. Tendencies towards oscillations in the least-squares operation are suppressed by a new stabilization routine. The method offers a new possibility for the estimation of the radius of gyration, which is generally superior to the Guinier approximation.

For small-angle scattering, of X-rays (SAXS) and neutrons (SANS), the importance of absolute calibration has been recognized since the inception of the technique. The work reported here focuses on SAXS measurements using Kratky slit systems. In former days, only molecular weights or scattering per particle were determined, but today absolute calibration implies the use of the unit of cm À1 for the scattering curve. It is necessary to measure the so-called absolute intensity, which is the ratio of the scattering intensity to the primary intensity P 0 . Basically there are two possible ways to determine the absolute intensity. The ®rst one is the direct method, which involves the mechanical attenuation of the primary beam by a rotating disc or a moving slit. The second is the indirect method, using secondary standards. Water is well suited as a calibration standard because of the angle-independent scattering. The essential advantage is that the scattering of water only depends on the physical property of isothermal compressibility. Before presenting an example of the practical performance of this method, the most important theoretical equations for an SAS experiment on the absolute scale are summarized. With the slit collimation system, the scattering curve of water can be measured with high enough statistical accuracy. As a ®rst example, the scattering curve of the protein lysozyme on the absolute scale is presented. The second example is the determination of the aggregation number of a triblock copolymer P94 (EO 17 ± PO 42 ±EO 17 ). Taking into account that at least 10% of the polymer sample consists of diblocks, the accuracy of around 10% for the determined aggregation number is rather good. The data of P94 are also considered on the particle scale in order to obtain the radial scattering-length density distribution.

Aqueous submicron-sized dispersions of the binary monolinolein/water system, which are stabilized by means of a polymer, internally possess a distinct nanostructure. Taking this as our starting point, we were able to demonstrate for the first time that the internal structure of the dispersed particles can be tuned by temperature in a reversible way. Upon increasing the temperature, the internal structure undergoes a transition from cubic via hexagonal to fluid isotropic, the so-called L2 phase, and vice versa. Intriguingly, in addition to the structural changes in topology, the particles expel (take up) water to (from) the aqueous continuous phase when increasing (decreasing) the temperature in a reversible way. At each temperature, the internal structure of the dispersed particles corresponds very well to the structure observed in nondispersed binary monolinolein with excess water. This agreement is independent of any thermal history (including phase transitions), which proves that the structures in the dispersed particles actually are in thermodynamic equilibrium with the surrounding water phase.

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.