Self incoherent scattering

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

Measurements of the self-correlation function with neutrons are normally performed on protonated materials since incoherent scattering is particularly strong there. This is a consequence of the spin-dependent scattering lengths of hydrogen. Due to spin-flip scattering, which leads to a loss of polarization, this... 

The experiments on alkali iodides, PEOx-Nal or PEOx-Lil [316-318] were performed on PEO chains of 23 or 182 (-CH2-CH2-O-) monomers and Orion ratios between 15 and 50. The incoherent scattering from protonated polymers was measured using INI 1C, which yields the intermediate scattering function of the self-correlation. The experiments were performed in the homogeneous liquid phase where the added salt is completely dissolved and no crystalline aggregates coexist with the solution, i.e. at temperatures around 70 °C. 

A further factor which affects the shape of a resonance line is the transport of resonance radiation through the. parent gas. Milne s early theory of self-absorption by the imprisonment of resonance radiation has been revised by Holstein (3) and Bichermau (4), taking into account the incoherent scattering of resonance photons. Furthermore, Walsh (" ) has extended the imprisonment lifetime calculation for cases where Doppler and collision broadening of the resonance line are simultaneously present, and in addition this author has examined the complications caused by the, hfs. The line shape, linewidth, and other properties of self-absorbed lines hare been discussed recently bv Tako (6), who summarizes the various effects of self-absorption as follows ... 

For hydrocarbons in zeolites, only incoherent scattering has to be considered because of the large incoherent cross section of hydrogen. The neutron intensity scattered follows the incoherent scattering law 5i c(Q, (o), which is related to the self-motion of protons, where AQ and Aw denote the neutron momentum transfer and the neutron energy transfer, respectively. 

The basic formulation of this problem was given by Van Hove [25] in the form of his space-time correlation functions, G ir, t) and G(r, t). He showed that the scattering functions, as defined above, for a diffusing system are given by the Fourier transformation of these correlation functions in time and space. Incoherent scattering is linked to the self-correlation function, Gs(r, t) which provides a full definition of tracer diffusion while coherent scattering is the double Fourier transform of the full correlation function which is similarly related to chemical or Fick s law diffusion. Formally the equations can be written ... 

In short, incoherent scattering allows one to determine the self-diffusivity, Ds, whereas coherent scattering gives access to the transport diffusivity, Du from experiments performed at equihbrium. When the scattering is both incoherent and coherent, then both diffusivities can in principle be determined simultaneously. 

The incoherent scattering fimction, (Eq. 8a), is obtained from the time Fourier transform of the intermediate self-scattering function... 

The models, which have been developed in the literature, concern essentially incoherent scattering, i.e., self-diffusion. Much less work has been performed on jump diffusion of coherent scatterers [5,11]. If one considers only isotropic systems, the scattering fimction will always be a Lorentzian function, but the width (HWHM) of the energy spectra will differ from the simple DQ behavior. For each spectrum measured at a given Q value, one can extract a diffusion coefficient D. One has to extrapolate D(Q) to small Q values to obtain the Fickian diffusivity. 

Incoherent scattering is related to the self-correlation function and, therefore, does not contain any interference terms. Unlike in the case of coherent scattering, there is no momentum selection rale. Incoherent one-phonon scattering occurs for a continuous range of kf wave vectors, each corresponding to a phonon mode fulfilling the energy conservation. 

For this we will use a type of scattering function we have not discussed so far, which is the incoherent intermediate scattering function. Due to its large incoherent scattering amplitude it is mainly the self-correlation of the hydrogen motion that is seen in incoherent neutron scattering experiments. 

The details of the synthesis method are as follows A substrate monomer of p-cellobiosyl fluoride first synthesized and purified (10.3 mg, 2.9 x 10" mol purity 95%) was solubilized in 170 pi of acetate buffer in D2O (CH3COOH/ CH3C00Na/D20) (pD = 5.0, 0.05 M). To this solution acetonitrile (1000 pi) was added. D2O was used to enhance the scattering contrast for SANS and USANS from the self-assembled cellulose molecules and enzymes against the reaction medium as well as to reduce the incoherent scattering intensity level of the system. The polymerization was started by mixing the above solution, designated as solution A, with 30 pi of acetate buffer in D2O (pD = 5.0,... 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

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