Neutron scattering quasielastic

For H in metals the measured QENS intensity, after the necessary ra v data corrections (background subtraction, detector efficiency, etc.) is proportional to the incoherent scattering function S , (Q, co) which can be written as the two-fold Fourier transform (in space and time) of the single-particle, space-time van Hove correlation function, Gg(r,t), 

For translational long-range jump diffusion of a lattice gas the stochastic theory (random walk, Markov process and master equation) [30] eventually yields the result that Gg(r,t) can be identified with the solution (for a point-like source) of the macroscopic diffusion equation, which is identical to Pick s second law of diffusion but with the tracer (self diffusion) coefficient D instead of the chemical or Fick s diffusion coefficient. 

Spatial Fourier transformation of the self-correlation function (Eq. (26.7)) yields the intermediate scattering function. 

Thus a plot of A vs. Q yields a straight line, and from its slope the self-diffusion coefficient is derived. This so-called Q law (valid for sufficiently small Q) is indicative of translational diffusion. 

In some intermetallic compounds clusters of isoenergetical sites occur which are well separated from other sites, see for instance the case of TaV2H in Fig. 26.4, and which form closed loops on those loops the H atom performs a spatially restricted jump motion (jump rotation) for some time until, by thermal fluctuations, eventually it is able to jump into the neighboring loop. For rotational diffusion over a loop of N sites after sufficiently long time the FI atom can be found on any of the N sites with equal finite probability. The time-independent (i.e. long-time) contribution to Is(Q,t) yields an elastic contribution m = 0) after temporal Fourier transformation  

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Direct experiment-simulation quasielastic neutron scattering comparisons have been perfonned for a variety of small molecule and polymeric systems, as described in detail in Refs. 4 and 18-21. The combination of simulation and neutron scattering in the analysis of internal motions in globular proteins was reviewed in 1991 [3] and 1997 [4]. 

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]. 

M Bee. Quasielastic Neutron Scattering Principles and Applications m Solid State Chemistry, Biology and Materials Science. Philadelphia Adam Hilger, 1988. 

Figure 10 Elastic incoherent structure factors for lipid H atoms obtained from an MD simulation of a fully hydrated DPPC bilayer, and quasielastic neutron scattering experiments on DPPC bilayers at two hydration levels for (a) motion in the plane of the bilayer and (b) motion m the direction of the bilayer normal.

When the various results obtained by combined elastic and quasielastic neutron scattering measurements on star shaped polymers in dilute solutions... 

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

Bee M (1988) Quasielastic neutron scattering. Adam Hilger, Bnstol... 

Polybutadiene in the Melt. A Quasielastic Neutron-Scattering Study. 

Phys. Condens. Matter, 15, S1127 (2003). Self-Motion and the a-Relaxation in Glass-Forming Polymers. Molecular Dynamic Simulation and Quasielastic Neutron Scattering Results in Polyisoprene. 

Macromolecules, 35, 7110 (2002). Segmental Dynamics of Atactic Polypropylene as Revealed by Molecular Simulations and Quasielastic Neutron Scattering. 

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... 

Triolo, A., Russina, O., Arrighi, V., Juranyi, R, Janssen, S., and Gordon, C. M., Quasielastic neutron scattering characterization of the relaxation processes in a room temperature ionic liquid, /. Chem. Phys., 119, 8549-8557, 2003. 

The study of molecular dynamics in polymers is of great interest because the structural changes of the crystal lattice are intimately related to the onset of molecular motions which generate a special type of dynamical disorder within the crystals [101-104]. In this final section, we prerent an experimental account of the molecular dynamics of copolymers with 60/40 and 80/20 VF2/F3E mole fraction composition using incoherent quasielastic neutron scattering. 

The chain dynamics of PDMS have also been studied by quasielastic neutron scattering.346... 

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). 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

Bee, M., Quasielastic Neutron Scattering. Adam Hilger, Bristol, 1988. 

The nature of ions in aqueous solution has been studied using a wide variety of techniques, including X ray and neutron diffraction, and quasielastic neutron scattering, NMR, IR, and UV spectroscopies. The ions are generally considered to have primary and secondary hydration spheres, although there is relatively little quantitative information available concerning the second sphere in solntion. The rate of exchange of the... 

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. 

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