Small angle neutron scattering geometry

In order to obtain comparable data from such complex systems we have developed a cell with the ability of use for measurements both in reflection and small-angle neutron scattering geometry. This cell allows studies of adsorbed surface layers and the equilibrium bulk structures for one sample in the same experiment by simple rotation of the cell. This is a particular advantage when smdying surfactants above the cmc or liquid crystals which may show one type of order at a surface and another in the bulk. 

Fig. 4 The geometry of a small-angle neutron scattering experiment. Neutrons of wavelength X are scattered by the atomic nuclei in the sample. A fraction of the neutrons, are scattered through an angle 9 and are detected by a 2-dimensional (2-D) detector at a distance L d from the sample. The wave vectors of the incident and scattered neutrons are ki and respectively. (Reproduced from Ref...

Osterberg R, Mortensen K. (1994), Fractal geometry of humic acids. Temperature-dependent restructuring studied by small-angle neutron scattering. Humic Substances in the Global Environment and Implications on Human Health, (Ed. N. Senesi, T.M. Miano), Elsevier Science, 127-132. 

Relations (6.10) and (6.11) were tested experimentally by small angle neutron scattering. Let us mention that starshaped polymers are in this same universality class the mass dependence of their radius of gyration also follows relations (6.10). However, it also depends on the number/of branches, indicating the special geometry of the object. For more details, the reader is referred to Refs. [21-25]. 

As in binary surfactant-water systems considered previously, two constraints on the geometry of the surfactant interface are active a local constraint, which is due to the surfactant molecular architecture, and a global constraint, set by the composition. These constraints alone are sufficient to determine the microstructure of the microemulsion. They imply that the expected microstructure must vary continuously as a function of the composition of tile microemulsion. Calculations show - and small-angle X-ray and neutron scattering studies confirm - that the DDAB/water/alkane microemulsions consist of a complex network of water tubes within the hydrocarbon matrix. As water is added to the mixture, the Gaussian curvature - and topology -decreases [41]. Thus the connectivity of the water networks drops (Fig. 4.20). 

Figure 7. Scattering geometry vertical scattering (reflectivity) and in-plane scattering (diffraction). The x-rays (or neutrons) with incident wave vector k strike the surface at a small angle of incidence (/), which is less than the critical angle for total external reflection, . In reflectivity measurements, the vertical incidence and exit angles are equal so the difference between k and the reflected wave vector k, is perpendicular to the scattering plane. In diffraction measurements, the difference k — k,i lies essentially in the plane.

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