Diffusion quasielastic neutron scattering

A dynamic transition in the internal motions of proteins is seen with increasing temperamre [22]. The basic elements of this transition are reproduced by MD simulation [23]. As the temperature is increased, a transition from harmonic to anharmonic motion is seen, evidenced by a rapid increase in the atomic mean-square displacements. Comparison of simulation with quasielastic neutron scattering experiment has led to an interpretation of the dynamics involved in terms of rigid-body motions of the side chain atoms, in a way analogous to that shown above for the X-ray diffuse scattering [24]. 

Specification of. S SkCG, CO) requires models for the diffusive motions. Neutron scattering experiments on lipid bilayers and other disordered, condensed phase systems are often interpreted in terms of diffusive motions that give rise to an elastic line with a Q-dependent amplitude and a series of Lorentzian quasielastic lines with Q-dependent amplitudes and widths, i.e.. 

Springer T (1972) Quasielastic neutron scattering for the investigation of diffusive motions in solids and liquids. Springer, Berlin Heidelberg New York... 

Lateral diffusion of phospholipids in model membranes at ambient pressure has been studied over the years by a variety of techniques including fluorescence recovery after photobleaching (FRAP), spin-label ESR, pulse field gradient NMR (PFG-NMR), quasielastic neutron scattering (QENS), excimer fluorescence and others.In general, the values reported for the lateral diffusion coefficient (D) range from 10 to 10 cm /s in the... 

Diffusion of atoms from the point at which they dissociate on a metal surface to the edge of the metal crystallite is one of the component steps of hydrogen spillover. Quasielastic neutron scattering experiments have produced direct evidence for the diffusion coefficients of hydrogen on the surface of catalysts. The mean time between diffusional jumps for hydrogen on a Raney Ni surface has been found to be 2.7 0.5 x 10 9s at 150°C.72 For H on the surface of Pt crystals dispersed within a Y type zeolite the mean time between surface jumps was found73 to lie between 3.0 and 8 x 10-9s at 100 °C. 

The process of molecular diffusion may be viewed conceptionally as a sequence of jumps with statistically varying jump lengths and residence times. Information about the mean jump length /(P and the mean residence time t, which might be of particular interest for a deeper understanding of the elementary steps of catalysis, may be provided by spectroscopic methods, in particular by quasielastic neutron scattering (see next Section) and nuclear magnetic resonance (NMR). 

R. Hempehnann, Quasielastic Neutron Scattering and Solid State Diffusion , "Oxford Series on Neutron Scattering in Condensed Matter, Vol. 13, Oxford University Press, Oxford, 2000. 

Incoherent quasielastic neutron scattering measured as a function of hydration for powders of deuterated phycocyanin has been used to probe water motions (Middendorf et al., 1984). The simplest model accounting for the data was jump diffusion of water molecules between localized-sorption sites and the development of clusters of surface water at higher hydration (half-coverage of the surface, 0.15 h). This model is consistent with the picture developed from sorption thermodynamics. 

Inelastic and quasielastic neutron scattering have special advantages for studying certain of the motional properties of protonated or organic species within zeolites and related microporous materials. These advantages and various experimental methods are outlined, and illustrated by measurements of torsional vibrations and rotational diffusion of tetramethylammonium (TMA) cations occluded within zeolites TMA-sodalite, omega, ZK-4 and S APO-20. 

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

T. ringer. Quasielastic Neutron Scattering /or the Investigation of Diffusive Motions in Solids and Liquids, Springer, Berlin, 1972. 

Furthermore, neutron scattering techniques, viz. quasielastic neutron scattering, are a valuable tool for studying other dynamic processes in solid hydrate research, such as rotatory and translatory diffusion of water molecules and hydrogen atoms, respectively (see, for example. Refs. 10, 32, 33). 

Further studies were carried out in the quest for the double critcal point of the mixture 2-methyl-piridine(2MP)/D20. Within such studies we came across a remarkable anomaly appearing within 2MP neat liquid at applied pressures of about 200 bars. It manifests itself as a marked change of regime of the translation and rotational-diffusion coefficients versus density (pressure). To add more intrigue, the pressure range at which such an anomaly takes place basically coincides with that where the DCP was suspected to be located. In fact, the concurrent use of quasielastic neutron scattering and molecular dynamics simulations, evidenced a pronounced change of slope in the density dependence of both the translation and rotational diffusion coefficients for densities of p=0.975 g/cm. In turn, the description of the liquid structure carried out in terms of static pair distributions derived from computer simulations revealed indications of the presence of dynamical equilibria within the liquid as attested by clear isosbestic points. 

Table 2 includes as well the results of recent diffusion studies by molecular dynamics (MD) calculations and by quasielastic neutron scattering. Both methods consider the process of self-diffusion and reflect the transport properties over diffusion paths of typically a few nanometers. In view of the satisfactory agreement with the PFG NMR data, there should be no doubt that genuine... 

Table 2 Comparison of PFG NMR Diffusivities with the Results of Quasielastic Neutron Scattering and MD Simulations and of Macroscopic Nonequilibrium ( Sorption ) Measurements ...

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

Before the introduction of measuring techniques such as pulsed field gradient (PEG) NMR ([14,16,45], pp. 168-206) and quasielastic neutron scattering (QENS) [49,50], which are able to trace the diffusion path of the individual molecules, molecular diffusion in adsorbate-adsorbent systems has mainly been studied by adsorption/desorption techniques [ 16]. In the case of singlefile systems, adsorption/desorption techniques cannot be expected to provide new features in comparison to the case of normal diffusion [51,52]. In adsorption/desorption measurements it is irrelevant whether or not two adjacent molecules have exchanged their positions. But it is this effect which makes the difference between normal and single-file diffusion. 

D. J. Cebula, R. K. Thomas, and J. W. White, Diffusion of water in Li-montmorillonite studied by quasielastic neutron scattering, Clays and Clay Minerals 29 241 (1981). 

Broadly speaking, the aim of an incoherent neutron scattering study is to characterize the individual translational and rotational diffusive motions of the scatterer (in this case, the proton held by an ion or molecule) at small energy transfers in the so-called quasielastic neutron scattering (QNS) region and the quantized vibrations at higher energy transfers in... 

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