Neutron scattering diffusion constant

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... 

Thermal or low-energy neutron scattering experiments have been most valuable in throwing light on molecular motion in plastic crystals. These experiments measure changes in the centre of mass of a molecule. Diffusion constants obtained from neutron experiments differ widely from those obtained from tracer experiments since neutron scattering is mainly determined by rotational diffusion. The scattering function has the form... 

Physically this description corresponds to putting an atom (mass M) in an external time-dependent harmonic potential (frequency co0). The potential relaxes exponentially in time (time constant l/x0) so that eventually the atom experiences only a frictional force. Compared with other models2 which have been proposed for neutron scattering calculation, the present model treats oscillatory and diffusive motions of an atom in terms of a single equation. Both types of motion are governed by the shape of the potential and the manner in which it decays. The model yields the same velocity auto-correlation function v /(r) as that obtained by Berne, Boon, and Rice2 using the memory function approach. 

We now wish to examine how the structure of the dressed macroion, as determined by our diffuse neutron scattering experiments, varies with applied uniaxial stress. The best data was obtained at c = 0.03 M, with r < 0.01, when the uniaxial pressure p was varied between 0 and 0.2 atm a single experiment conducted over two days on D16 gave clear ripples at different applied stresses, as described below. As in the experiments at c = 0.1 and 0.01 M described above, T and P were held constant at 10°C and 1 atm, respectively. The details of the experiment and the small-angle patterns observed are given in reference [4], Here we concentrate on how applied uniaxial pressure affects the higher g-rangc of the structure factors. 

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. 

Abstract Neutron scattering was first used to derive the self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows one to probe diffusion over space scales ranging from a few A to hundreds of A. The mechanism of diffusion can, thus, be followed from the elementary jumps between adsorption sites to Lickian diffusion. The neutron spin-echo technique pushes down the lower limit of diffusion coefficients, traditionally accessible by neutron methods, by two orders of magnitude. The neutron scattering results indicate that the corrected diffusivity is rarely constant and that it follows neither the Darken approximation nor the lattice gas model. The clear minimum and maximum in diffusivity observed by neutron spin-echo for n-alkanes in 5A zeolite is reminiscent of the controversial window effect . 

Incoherent neutron scattering (INS) can be used to study the translational, rotational, and vibrational motion of water protons on a time scale between 10" and 10 s. Thus INS provides data pertinent to the V structure and to the transition from the V structure to the D structure in liquid water. The principal use of INS has been to characterize the translational and rotational motion of water molecules through the interpretation of scattering data with model expressions. The three most important model parameters used are the self-diffusion coefficient, Ds, which can also be measured in an experiment involving isotope-labeled water molecules the residence time of a water molecule, tr, during which it vibrates about a fixed position before jumping to its next position and the correlation time, Ti, which is a time constant for the decay of correlation between the orientation of a water molecule at some initial time and at some later time. ... 

Small-angle neutron scattering has also been applied to the analysis of networks that were relaxing after a suddenly applied constant uniaxial deformation (Boue et al., 1991). Results of dynamic neutron scattering measurements of Allen et al. (1972, 1973, 1971) indicate that segments of network chains diffuse around in a network, and the activation energies of these motions are smaller than those obtained for the center of mass motion of the whole chains. Measurements by Ewen and Richter (1987) and Oeser et al. (1988) on PDMS networks with labeled junctions show that the fluctuations of junctions are substantial and equate approximately to those of a phantom network model. Their results also indicated that the motions of the junctions are diffusive and... 

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. 

That is, information on the diffusion constant is available directly. Up-to-date information on the current use of quasi-elastic neutron scattering can be obtained from the work of McGreevy (1999). 

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