Diffuse spin motion

Restricted diffusion, correlated motion of spins, or any deviation from a free behavior of the molecules will result in a propagator shape different from a Gaussian one. A wide range of studies have dealt with such problems during the last two decades and NMR has turned out to be the method of choice for quantifying restricted diffusion phenomena such as for liquids in porous materials or dynamics of entangled polymer molecules. 

The spectral density function, f(a>), reflects the electronic spin motion and depends sensitively on the dimensionality of the process. For ID diffusion,... 

Let us finally also mention here the results of proton nuclear relaxation time 7 measurements on TEA(TCNQ)2 [53,54], From the frequency dependence of 7, it is deduced that the spin motion is a nearly one-dimensional diffusion. Moreover, the temperature dependence of the on-chain spin diffusion rate shows a quite remarkable feature while it is thermally activated below 220 K, it suddenly becomes temperature independent above 220 K. 

Furthermore, quantitative characterizations of the spin motion in trans-(CH) have been performed by measurements of the proton NMR relaxation time 7 and analysis of the ESR line width [70,71]. The spin motion can be described in terms of highly one-dimensional diffusion. The diffusion rate along the chains is very fast D[ 1013 rad/s (i.e., a diffusion coefficient of ca. 5 x 10 3 cm2/s), and the anisotropy is extremely high Z>j /Z>x > 105. The very high anisotropy is also an argument for the soliton picture neutral... 

Measurements of diffusion and motion were the first application of the spin echo as detailed in Hahn s famous 1950 paper. The advent of good pulsed gradients has improved this technique dramatically, and both the physiological and the materials applications in restricted geometries have attracted much recent attention. Callaghan and Stepisnik s review lays out both the mathematical framework and the range of applications in a very clear manner. 

The large diffusion coefficient of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violation of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner method of diffusion measurements. Mair et therefore investigated the effect of a common,... 

Spectral diffusion of saturation can be detected in various ways, including electron-electron double resonance (ELDOR), effects on adiabatic rapid passage spectra, saturation recovery, and CW saturation. Of these, ELDOR is by far the most attractive in principle, because the effect is observed directly. Unfortunately, the requisite equipment is not widely available. We look forward to increased use of ELDOR, particularly time-resolved ELDOR, to study special motions of slowly diffusing spin labels. 

The methodological background to obtaining the transport properties from discrete compartments is the formalism used by Cory and Garroway (50) to obtain the displacement profile (15) of molecules in a dispersed system. Detailed information on the mole cular motion may be obtained by measuring the A dependence of the apparent diffusion coefficient caused by a possible obstruction of the spin motion. The stimulated echo sequence, Fig. 9a, is usually used to probe various diffusion times, A. As is seen from the fig-... 

Echo detection of selectively-burned holes in photosynthetic systems led to estimates of distances between 25 and 50 A. If the contributions to spectral diffusion from motion, nuclear spin flip-flops, and instantaneous diffusion are smaller than the contribution from dipolar interaction between unpaired electrons, the spectral diffusion can be used to determine the interspin distance. (97-100). 

In the absence of microscopic characterization, chain defects are more difficult to model. Many kinds of defects or imperfections may exist that disturb the spin motion. So far, three parameters have been introduced to describe the spin motion the intra- and interchain diffusion rates and and the chain length N. Accounting for the influence of possible defects leads to the introduction of additional parameters. Many theoretical papers have been produced on the random walk problem in the presence of impurities, traps, or random hopping rates. It is out of the scope of this chapter to present a detailed discussion of this topic. Let us just envisage briefly a few typical cases. 

Up and spin-down states, is normally negligible compared to molecular selfdiffusion in liquids. However, with viscous systems with little motional averaging of dipolar coupling and with the aid of very strong field gradients, NMR diffusometry is able to detect this immaterial transport mechanism competing with molecular diffusion. Spin echoes can be attenuated on this basis just as with any other incoherent displacement process [181]. 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

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... 

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

Fig. 12a and b. Calculated 2H spin alignment spectra for diffusive motion, a unrestricted rotational diffusion for different mixing times x2 b diffusion restricted to angular regions as indicated for long mixing times t2... 

Note added in proof The calculated spin alignment spectra for diffusive motion plotted in Fig. 12 are incorrect, in particular the oscillations in the central part, due to a sign-error in the computer program. 

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

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