Small-angle neutron scattering vector

Fig. 3.2 Small-angle neutron scattering intensity as a function of wave vector magnitude for a rfPS-PB diblock forming micelles in PB, c = 5x l(T2gcm 3. Symbols, experimental results line, theoretical scattering profile for a uniform sphere (Selb et al. 1983).

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...

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 ... 

Matsuoka H, Schwahn D, Ise N. Observation of cluster formation in polyelectrolyte solutions by small-angle neutron scattering. 1. A steep upturn of the scattering curves from solutions of sodium poly(styrenesulfonate) at scattering vectors below 0.01 A. Macromolecules 1991 24 4227-4228. 

Fig. 8. Small-angle neutron scattered intensity plotted versus scattering vector q for salt-free deuterium oxide solutions of poly(2-vinyl pyridine), which possessed a molecular weight M = 281,000 g/mol prior to 45% methyl quaternization. Four different pol3mtier concentrations were examined 22 g/L (circles), 8.8 (squares), 4.5 g/L (upward triangles), and 2.2 g/L (downward triangles). Adapted from Ref 114.

Figure 63 (a) X-ray diffraction patterns of organically modified Closite-30B nanoclay and nanocomposites, (b) small-angle neutron scattering patterns I(q) versus q (wave vector) plot of indicated PU and nanocomposites, (c, c ) AFM image of PU and its nanocomposites with height profile, and (d) POM image PU-nanoclay composite [9]. 

To discuss the data obtained from small-angle neutron scattering in more detail, the basic results of the chain statistics of isolated macromolecules will be briefly reviewed. The radius of g3rration is related to the end-to-end vector r of a macromolecule (see Figure 4(a)) by Rg = flexible chain (see Figure 4),... 

Figure 49 The small angle neutron scattering (SANS) scattering intensity vs. the scattering wave vector q for the silica/silicone oil at particle volume fraction (j)=0.055, under an electric field strength of IkV/mm. Two model curves are presented sticky hard-sphere (SI IS) and fractal model (a = 165 nm, X df = 1.6). Reproduced with permission from C. Gehin, J.

Figure 8.1 (a) Schematic diagram of a small-angle neutron-scattering experiment, (b) Vector diagram of scattering process for an incident wave vector ko and scattered wave vector k. 

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