Neutron scattering intensity

Figure 2 Evolution of the neutron scattering intensities with time. Only spherical micelles of P123 block copolymer are present in the synthesis mixture within the first few minutes of the reaction (300 s), during the hydrolysis of the silica precursor. Then, hybrid organic-inorganic cylindrical micelles are detected (300-1400 s). The SBA-15 hexagonal phase is formed when the precipitation occurs, after 1400 s.

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. 4.7 Small-angle neutron scattering intensity versus q for a 25wt% solution of (PEO26PPO39PEO26) in D20 (Mortensen and Pedersen 1993).

Figure 1. Guinier plot of SANS for casein sub-micelles in 0.07 M NaCl solution in D20. Protein concentration is 16.1 mg/ml. I is coherent neutron scattered intensity.

The neutron scattered intensity (macroscopic differential scattering cross section d (Q)/dfi) is given by ... 

FIGURE 9.6 Low-angle neutron scattering intensity as a function of scattering vector Q (A-1) for propylammonium vermiculite immersed in a 0.25 M propylammonium chloride solution at four different temperatures, T = 309 K (continuous line), 311 K (dashed line), 313 K (crosses) and 315 K (solid circles). The low-angle peak at 0.1 A-1 is due to a gel phase with a clay layer spacing of 60 A. The data therefore show the temperature-induced gel-crystal phase transition occurring between 311 and 313 K. Note that body temperature is 311 K and that cell fluids are typically 0.2 M. 

The normalized neutron scattering intensities, 1(Q), are related to the neutronscattering density profiles normal to the clay sheets, p(z), via the crystallographic structure factor, S(Q), as... 

Eqs. (2.19) aud (2.20) affect neutron scattering intensities via the magnetic form factor /( ) ... 

FiglirC S Rexp jRconv, cf Eqs. (2) and (3), associated with the neutron scattering intensities from H, C, and O in iso-C4.Ei and D2O, as a function of scattering angle. The average of the experimentally determined values of ReXp is "anomalously" smaller than the conventionally expected value RCOnv by ca. 20%. 

It should be noted that there are some difficulties in obtaining accurate values of the KBI from the available thermodynamic data (Kato 1984 Zaitsev et al. 1985, 1989). Matteoli and Lepori (1984) have made an extensive comparison between the values of Gy calculated by different authors (e.g., Ben-Naim 1977 Donkersloot 1979a, b Patil 1981) and found large discrepancies between the reported results. Another method of obtaining the KBI is the small-angle x-ray or neutron scattering intensities from mixtures see, for example, Nishikawa (1986), Nishikawa et al. (1989), Hayashi et al. (1990), Misawa and Yoshida (2000), Almasy et al. (2002), and Dixit et al. (2002). 

Fig. 1.1 INS spectroscopy in relation to optical (photon) spectroscopies. INS spectra are within the wavenumber range 16-4000 cm", the same as the mid-infrared range. The vertical axis is the neutron scattering intensity expressed as the scattering law (or function), see text.

Fig. 3. Neutron scattered intensity vs. scattering vector for a 17 mol% cesium sulfonated polypetenamer. Numbers above each curve indicate weight percent D20. (reprinted with permission from ref 20. Copyright 1982 American Chemical Society)...

Figure 5.19 Small-angle neutron scattering intensity obtained with a styrene-butadiene diblock copolymer having spherical butadiene microdomains. The peaks at very small q are due to a body-centered cubic lattice structure of ordered microdomains. The solid curve is the calculated intensity of independent scattering from solid spheres of mean radius 124 A. (From Bates etal.34)...

Figure 6.5 Neutron scattering intensity data obtained with a diblock copolymer of deuterated 1,4-polybutadiene and hydrogenous 1,2-polybutadiene. (From Bates and Hartney.10)...

Transport coefficients like the diffusion constant, the viscosity or the sound velocity, and dynamic light scattering or inelastic neutron scattering intensities are all dynamical properties of a system in thermal equilibrium. We concentrate here on the viscosity and on sound velocity and attenuation. 

The molecular weight of a protein is related to the normalised neutron scattering intensity at zero angle by the following formula [5] ... 

Finally, a review was done by Higgins et al. (2005) in which they combined the experiments and a theory based on the lattice Bom-Green-Yvon (BGY) approach to predict coexistence curves, neutron scattering intensities, and pressure-voiume-temperature surfaces. This work allowed to better understand some of the correlations between the microscopic structure and macroscopic behavior of several common polymer mixtures. 

Figure 7. Excess neutron scattering intensity, as a function of q, the...

Plate VI (Chapter 9) Example showing conversion of 2D normalised scattering data to 1D data. The sectors delimited by the white lines show regions selected for determining the neutron scattering intensity perpendicular and parallel to the applied magnetic field H). 

Inelastic neutron scattering from both y- and a-Ce under pressure was investigated by Rainford et al. (1977). Their results indicate that the s-f exchange interaction, J, in y-Ce increases with increasing pressure as predicted by Coqblin. Also they find no experimental evidence for a magnetic contribution to the inelastic neutron scattering intensity of a-Ce. They conclude that if there is some residual 4f electronic character in a-Ce its dynamical response is too weak or diffuse to be observed in their experiment. 

Fig. 47. Neutron scattering intensities of the ferromagnetic (open circles) and antifenomagnetic (solid circles) peaks for b-[Gd,9 Yj]jj. The zero-field state is ferromagnetic.

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.

Fig. 29 Upper panels. Neutron scattering intensities obtained from a CPCl/Hex nematic micellar solution in the (qv,qvv)-plane at different shear rates (a) j =0.94 s , (b) y=34.5 s ,and (c) 7= 250 s . The nematic phase was made in deuterated water at concentration c = 35.2wt.% and molar ratio [Hex]/[CPC1] = 0.49 [301], Lower panel. Shear rate dependence of the orientational order parameter y (Eq. 5) obtained from the SANS cross-sections shown in the upper panel. The continuous line is a guide for the eyes. The increase of the order parameter was interpreted in terms of a transition between the tumbling and the flow-alignment regimes [290,303]...

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