Neutron scattering coherent

Armand, and W. S. Howells, Solid State Ionics, 147, 225 (2002). Coherent Neutron Scattering from PEO and a PEO-Based Polymer Electrolyte. 

Abbreviations C, coexistence curve S, static light scattering D, dynamic light scattering T, turbidity N, coherent neutron scattering V, shear viscosity E, electrical conductance I, interfacial phenomena (ellipsometry). d Deuterated 1-octanol. 

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.

Although the formalism for X-ray and neutron diffraction is essentially the same, it is appropriate to treat them separately because of the nature of the basic interaction. For the case of neutron diffraction, neutrons are scattered isotropically by all the nuclei of the system. The degree to which this takes place is determined by the coherent neutron scattering length b, which varies from isotope to isotope (Table I). Because the scattering is isotropic, the results of a given experiment can readily be presented in terms of a total radial distribution function. 

Besides these effects on the properties of H-bonds, H/D substitutions may be used to observe exchangeable X-H groups using experimental methods such as NMR spectroscopy or neutron diffraction that are sensitive to the change of the nuclear spin when passing from H- to D-atoms. Coherent neutron scattering experiments can thus provide a precise determination of the positions of D-atoms. As these methods are not especially sensitive to H-bonds they are not, however, general methods for the study of H-bonds. 

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 ... 

The distinct intramolecular and intermolecular contributions of the differential cross-section (5) are related to the sum of all partial structure factors, which is essentially proportional to the differential scattering cross-section, weighted by the respective coherent neutron scattering lengths (6). 

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... 

The physical structure of Nafions salts has been explored by neutrons (SANS) and X rays (SAXS). The former method is sensitive to fluctuations in the coherent neutron scattering cross section while the latter detects fluctuations in the electron density. Such fluctuations arise in the Nafions from partial crystallization of the samples and from clustering of the ionic groups or water molecules in hydrated s lmples. 

For coherent neutron scattering, the double-differential scattering cross section is... 

In separation or catalytic applications, it is the transport diffusivity, Dt, which matters (this quantity is also named Fickian or chemical diffusivity). Transport diffusivities are traditionally obtained under non-equilibrium conditions [2], but they can be measured at equilibrium by coherent QENS [5]. Coherent neutron scattering is in principle more comphcated than incoherent scattering, but under certain conditions transport diffusivities can be extracted from the neutron data. 

One expects that Dg and Dt will have a different concentration dependence. Comparisons between PFG NMR, QENS, and MD simulations could only be made in the past at the level of Dg. At equihbriiun, one can now obtain experimentally Dt using coherent neutron scattering. From equihbrium MD simulations, one cannot derive Dt, but one can determine the corrected diffusivity Do. These two diffusivities are linked by considering that the driving force for diffusion is the chemical potential gradient, and not the concentration gradient... 

At the moment, very little is known about the coupling of collective density fluctuations in proteins and their hydration water (and lipids, in the case of membrane proteins). New instruments recently developed for coherent neutron scattering, combined with selective sample deuteration, may fill this gap soon, and MD simulations are expected to be helpful in the interpretation of the data [60,92]. 

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