Small-angle neutron scattering coherent

Despite the great incoherent cross-section of the H-atom, elastic coherent neutron scattering experiments may be used at a lower resolution to detect the presence of clusters of H2O molecules. The method used is that of small-angle neutron scattering, often labeled by its acronym SANS . In such an experiment, the scattered intensity of a sample is recorded as a fnnction of the angle 6 between the wave vectors of the scattered and initial waves or, equivalently, as a function of the amplitude Q of the wave vector difference Q = k -ic2 0f the scattered beam defined by and incident beam defined by ki (the wave vector defines the direction of propagation of a wave, as seen in eq. (3.6)). As can be seen in Figure 11.1, these quantities are related by the equation ... 

C is a constant, and < > denotes an equilibrium average. For small-angle neutron scattering (SANS), the scattering factor is proportional to the coherent neutron scattering-length density 6, giving the result that... 

Figure 14 Fit of eqn [56] to the coherent small-angle neutron scattering from a biend of perdeuterated (A/l,=4600, AC/A/n=1.10) and protonated (fl/ =960, /VW =1.05) 1,4-polybutadiene at the critical composition (y>deui=0-31). Adapted from Bates, F. S. Wignall, G. D. Koehler, W. C. Phys. Rev. Lett. 1985, 55, 2425. ...

Figure 3 shows the small-angle neutron scattering (obtained at Ris0 National Laboratory, Denmark) from a dilute sample of cj) = 0.02 where the oil and water has been contrast matched resulting in coherent scattering from the surfactant film alone [5]. A fit to the data, shown as a solid line, corresponds to the form factor of a spherical shell of radius fhc = 75 A and a relative polydispersity c/rhc = 0.16. This polydispersity contains contributions from both size (volume) and shape polydispersity [5]. Their relative contributions are not accurately known, however, contrast match experiments indicate that it is the shape polydispersity which dominates. 

Information on the conformations of polymer chains in amorphous polymers has been obtained by using small-angle neutron diffraction. The technique involves measurement of the coherent scattering of neutrons by mixtures of deuterated and protonated polymer molecules. Analysis of the scattering data leads to an estimation of the radius of gyration (Section... 

A model of structure has been developped from electron microscopy and X-ray studies in Nafions (6). No basic difference exists between X-ray and neutron techniques. Nuclear interactions of neutrons with matter are characterized by the coherent scattering length and the corresponding values for H and D are very different Because of the different origins of the contrast, X-ray and neutron small angle scattering techniques are complementary. 

In die following sections we desc e the interaction of monochromatic, coherent radiation witti scattering centers, whidi results in spherical scattered waves. Interference among these waves creates the intensity pattern sensed by a detector. The connection between the observed scattered wave intensity and the structure of matter is ultimately sought. We are especially interested to find die spatial periodicities within our material that lead to interference. To this end, the mathematical techniques of Fourier transformation and convolution are presented. We end the chapter with sections on the small angle scattering from lamellar systems, and neutron scattering. 

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