Attenuation of the spin-echo

Theoretical value of rintra in the case of diffusion control Phase of the precessional motion Attenuation of the spin echo in PPG NMR experiments Larmor frequency... 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

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. ...

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-... 

Catalytic systems are inherently multicomponent. An attractive method for determining the difFusivities in multicomponent systems is Fourier transform (FT) PFG NMR spectroscopy, which allows the simultaneous determination of the self-difFusivities of the individual components in a. mixture. If the chemical shifts of the individual species are sufficiently different, the Fourier transform of the spin echo yields separate peaks for the various adsorbates, and then similar to normal PFG NMR the attenuation of the separate peaks with increasing applied field gradient intensity yields the self-diffusivities. Because the technique can also be applied at elevated temperatures, it provides the opportunity for in-situ diffusion measurements under reaction conditions. The experiment also yields the time dependence of the relative concentrations of the reactant and product molecules and thus the intrinsic reaction rate. 

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]... 

Self-Diffusion of Desmopressin and Monoolein by NMR. The self-diffusion coefficient was measured with the NMR diffusion technique using a Bruker MSL 100 spectrometer. Two magnetic field gradient pulses were applied at either side of the 180-degree pulse in a [90x-T-180y-T-echo] spin echo sequence (7,8) (Figure 2). Due to diffusion, the amplitude of a component in the spin-echo spectrum is attenuated according to (7)... 

One particular model of a biological system is a set of barriers in an otherwise homogeneous medium. If diffusion is observed over a short enough time, very little of the substance experiences the effect of the barriers, and the observed motion is characteristic of the medium alone. As the time of observation is extended, more of the substance is reflected at barriers and thus, its total displacement is less than would have been the case without the barrier bringing about less attenuation of the PG spin-echo [48, 49]. From an analysis of such data one can, in principle, obtain information on the geometry of the domains in which restricted diffusion occurs information on cell size, droplet size distribution [50] etc. 

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