The PFG spin-echo

The observed signal intensity at the end of the spin-echo, Iq, for the basic PFG spin-echo experiment is given by the so-called Stejskal-Tanner expression  

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Figure 933. Basic sequences for measuring molecular diffusion based on (a) the PFG spin-echo and (b) the PFG stimulated-echo. The diffusion during the period A is characterised by a series of measurements with increasing gradient strengths.

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

Metais, A. and Mariette, F. 2003. Determination of water self-diffusion coefficient in complex food products by low field h-1 PFG-NMR Comparison between the standard spin-echo sequence and the T-l-weighted spin-echo sequence. J. Magn. Reson. 165, 265-275. 

Self-difFusion coefficients were measured with the NMR spin-echo method and mutual diffusion coefficients by digital image holography. As can be seen from Figure 4.4-3, the diffusion coefficients show the whole bandwidth of diffusion coefficient values, from 10 m s on the methanol-rich side, down to 10 on the [BMIM][PFg]-rich side. The concentration dependence of the diffusion coefficients on the methanol-rich side is extreme, and shows that special care and attention should be paid in the dimensioning of chemical processes with ionic Hquids. 

Pulse field gradient (PFG) NMR spectroscopy is now generally regarded as the method of choice for measuring the translational diffusion coefficients of molecules of virtually any type under many conditions (48). H, H, F, and P variants of this method have been used successfully to study lateral diffusion of cholesterol, phospholipids, and water in model membranes (49,50). This technique introduces two identical gradient pulses of the external magnetic field into the standard spin-echo NMR... 

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-... 

Fig. 6. The pulsed field gradient (PFG) spin-echo pulse sequence.

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-... 

In general it is clear that PFG spin-echo data can provide information on the pore structure at both the gradient length scale, /q, and the diffusion length scale, y (/JA). The NMR data can be analysed to obtain simple structure factors, which may then be related to particular pore network models. ... 

Fig. 9. Modifications to the basic PFG spin-echo pulse sequence (a) stimulated echo (b) addition of alternating pulse gradients (c) addition of longitudinal eddy-current delay period.

It is also possible to perform a two-dimensional PFG spin-echo experiment employing two orthogonal magnetic field gradients. This yields a two-dimensional propagator Ps X, Y, A) that corresponds to the joint probability for molecular displacements X and Y in time A. Results have been obtained on a packed bed of glass spheres and on a sandstone, and have been compared with those predicted by numerical simulation of the flow assuming pore network models. ... 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

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