Spin echo attenuation

Zibrowius et al. (77) used an NMR spin-echo attenuation technique to estimate the ratio of the diffusion tensor element related to motion along the y-axis (the straight channel) and the average of the other two elements. For a methane loading of 8 molecules per unit cell, the ratio was estimated to be less than 5 at room temperature ... 

Figure 1 Diffusional spin echo attenuation of Boc-Phe in MPS1 gels with DMF-d7 as solvent on A at 30 °C by varying field-gradient pulse duration (diffusing time) A, where the Boc-Phe concentration is 10 wt%. (A) A = 10 ms and (B) A=100 ms.

Note that the spin-echo attenuation depends in a characteristic way on the NMR parameters A and S, as well as on the self-diffusion constant D and the frictional damping f. Equation (75) is quite general and applies to all time intervals. 

The absolute value of the line gradient is constant and the resulting spin-echo attenuation is uniform in the sample. In the article by Stepisnik... 

The square of the line gradient is not constant. In consequence, the spin-echo attenuation depends upon the spin location in the sample... 

Fig. 17. The planar distribution of the spin-echo attenuation log[E] (in arbitrary units) for isotropic diffusion in the near field of a coil at the fixed value of y G f(h)D. ...

For a diffusion tensor of axial symmetry with Dj > D., Fig. 1 shows the influence of a diffusion anisotropy on the PFG NMR spin-echo attenuation as simulated in numerical calculations 49). The quantitative analysis shows, however, that for principal tensor elements not too different from each other (i.e., for tensor elements within one order of magnitude), the ini-... 

Fig. 1. Parameter calculations for the PFG NMR spin-echo attenuation due to anisotropic self-diffusion in a diffusion system of axial symmetry with D > Di 49).

In general, for zeolitic self-diffusion at sufficiently high temperatures, the mean molecular displacements outside the crystal are much larger than those inside the zeolites that is to say, long-range self-diffusion, Di.r., is much faster than intracrystalline self-diffusion, Dintra- For observation times comparable with the mean lifetimes of the adsorbed molecules in the individual crystallites, the spin-echo attenuation can be approximated by the superposition of two exponentials of the type of Eq. (6)... 

Figure 6 represents typical plots of the spin-echo intensity in PFG NMR experiments. Comparing the slopes of these representations with those of standard liquids, one obtains the mean self-diffusivities, which are found to decrease with increasing sorbate concentration (5,12,16,59,60). It appears from Fig. 6 that within the accuracy of the measurement no deviation from a single exponential decrease may be observed. A comparison of the experimental spin-echo attenuation (Fig. 6) with the results of numerical calcula-... 

Under the influence of a constant field gradient go in addition to the pulsed ones, the spin echo attenuation in the PFG NMR experiments is given by the relation... 

Calculations of the spin-echo intensity are complicated by the fact that surface relaxation may play a significant role. A general formalism for calculating PFG spin-echo attenuation for restricted diffusion in isolated pores has recently been proposed that allows for wall relaxation effects. Expressions have been obtained for the cases of diffusion within a sphere, and for planar and cylindrical geometries.These show that diffraction effects are still apparent even when surface relaxation is rapid. Also, the locations of the minima in the spin-echo intensities are not particularly affected by varying the surface relaxation parameter, Analysis of PFG spin-... 

The quantitative information provided by PPG NMR about the existence of additional transport resistances on the external surface of the zeolite crystallites (surface barriers) results from a comparison of the values for the intracrystalline mean life time determined directly (viz. Tintra) by an analysis of the time dependence of the spin-echo attenuation (and, hence, of the propagator), and determined indirectly (viz. tP ) from the intracrystalline diffusivity on the assumption that molecular exchange between different crystallites is controlled by intracrystalhne diffusion. On the additional assumption that the shape of the crystallites may be approximated by spheres with a mean square radius (R ) one has in the latter case [87,103]... 

Although there is a difference between the exponent in Eq. 11 used to fit the spin-echo attenuation data and the exponent obtained from plots of vs. for consistency we used the same symbol a regardless of the... 

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