Neutron spin-echo methods

It thus appears that in real zeolite crystals diffusion over long distances reflects the influence of surface and internal barriers rather than the pore structure of the idealized framework. As a result the apparent intracrystalline diffusivities often show a strong dependence on the length scale of the measurement. Measurements by QENS and neutron spin-echo methods over distances corresponding to a few unit cells often approach the theoretical values derived by MD calculations for an ideal lattice. Similar values are often obtained by PEG NMR when the measurement is made over short distances. Measurements by most macroscopic methods are on the length scale of the crystals, and these tend to yield lower apparent diffusivities as a consequence of the intrusion of surface barriers and internal resistances due to structural defects. 

This chapter has considered measurements of the dynamic structure factor S q, t) of polymer solutions. Here behaviors of the first cumulant, the polymer slow mode, and the high-frequency Rayleigh-Brillouin spectrum have been considered. Neutron spin-echo methods as supplements to light scattering spectroscopy were noted. Results on Ki and the Rayleigh-Brillouin spectrum are readily summarized. The discussion of the slow mode is considerably more extended, but leads to a comparison with modem models for glass formation. 

Hans launched the constmction of the first time-of-flight reflectometer at the ILL He performed the first magnetic reflectometry studies on a prototype reQ lometer. His research interest includes the development of reQ lometry usmg the zero-field neutron spin-echo method. His studies resulted in about 190 publications as author or coauthor. 

The application of neutron spin-echo spectroscopy to the analysis of the slow dynamics of biomolecules is still in its infancy, but developing fast. The few published investigations either pertain to the diffusion of globular proteins in solution [332-334] or focus on the internal subnanosecond dynamics on the length scale, <10 A as measured on wet powders [335,336]. The latter regime overlaps with other quasi-elastic neutron scattering methods as backscattering and TOE spectrometry [337-339]. 

In the neutron spin echo technique, the normalized intermediate dynamic structure factor I(q,t)/I(qfi) is measured directly. This method has been used to probe... 

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 . 

The combination of quasi-elastic neutron scattering (QENS) and neutron spin-echo (NSE) methods allows one to probe characteristic times ranging... 

Similar to the PPG NMR method, neutron scattering techniques are successfully employed for the determination of diffusivities under equihbrium conditions. These techniques and their apphcation are discussed in Chapter 5 by H. Jobic. Particularly efficient is a novel combination of quasi-elastic neutron scattering (QENS) and a neutron spin-echo technique (NSE), which considerably expands the range of accessible diffusivities, viz. down to 10... 

Now spin echo methods are used for a small angle neutron scattering instrument and a triple axis spectrometer to increase the momentum- and energy transfer sensitivities. However, these instruments are not typical because they require novel techniques. 

It is possible to examine experimentally both the diffusion in a liquid crystal of its own molecules (self-diffusion) and the diffusion of impurities. The coefficients of self-diffusion are determined by various methods, e.g., quasi-elastic neutron scattering [100], the diffusion of tracer (radioactive) molecules [101], or the spin-echo methods in nuclear magnetic resonance spectroscopy [102]. The last method is probably the most reliable. Essentially, it is as follows initially the spins of the molecular protons are polarized by a marked pulse of a radio-frequency field then the molecules... 

A recent development in neutron spectrometry has extended the range of dynamic studies on macromolecules. The neutron spin echo (NSE) principle is utilized to determine the time Fourier transform S q.t) of the scattering function S(q.(o) at a given momentum transfer. The NSE method compares the incident and scattered velocities of each individual neutron so that the resolution and... 

Information about the elasticity can be obtained using a variety of scattering methods. Small-angle scattering is mainly used for systems with small interlamellar spacing [75,77-82], whereas light scattering can be applied for the study of swollen systems [76,83,84]. Neutron spin-echo spectroscopy has also been used to directly measure the bilayer dynamics in lamellar liquid crystalline phases [85-87]. 

Fig.9. Relaxation time map of polybutadiene observed with various kinds of methods. Quasielastic neutron scattering (O, ) [32,79], neutron spin echo ( ) [80,82], viscosity ( ) [100],2h NMR(1) [99]...

The highest energy resolution is obtained by using the neutron spin echo technique. In this type of instrument, the velocities of neutrons incident on, and scattered from, a sample are coded as the number of Larmor precessions that the neutron spins undergo in a well-defined applied magnetic field. The method requires a beam of polarized neutrons with a distribution of velocities. As indicated in Figure 7, these neutrons enter the precession-field region with their spins perpendicular to the field. As a neutron... 

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

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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