Pulsed field gradient experiments

Here there are two limiting regimes where one can calculate such attenuation The restricted diffusion regime occurs when the free diffusion length Rp =. J 2DA) of the imbibed solvent exceeds the average size R of the pores, R Rp. Here one has 

This regime is favoured for large values of A. The variation of the echo attenuation with the field gradient intensity gives information on the size of the pore R. The free diffusion regime occurs when R Rp, and 

If we consider the fractal distribution fV of categories of pores given in Eqn (28.5), the attenuation of the echo may be written as the following weighted sum over the restricted and free diffusion contributions 

The distinction between the free and bounded diffusion occurs when R = Rp. The diffusion coefficient D is determined from the slope at low values of ySGA. This form of attenuation is no longer exponential and presents a marked curvature for high values of ybGA due to the contribution of pores of radii R lower than R. In Fig. 28.3 are shown some typical attenuation curves for resins . The deviation from an exponential is present even at small values of A and is especially pronounced for high A The surface fractal dimension D, = 2.6 is found from a fit using Eqn (28.8) and the simplex minimization procedure .  

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A simple way to view a pulsed field gradient experiment is to add up the twist acquired by the sample magnetization in each gradient pulse and make sure they add up to zero for the desired pathway. If the twist is not zero at the beginning of acquisition of the FID, there will be no observable signal. For example, in the INEPT experiment (Fig. 8.26)... 

Mitra, P. P., and Sen, P. N. (1992). Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments Simple pore geometries. Phys. Rev. B 45, 143-156. 

In contrast to the sorption method, nmr pulsed field gradient experiments may be performed "in situ" in the closed sample, without the necessity of any sample manipulation. This is of especial relevance for the investigation of compacted and granulated material. 

In addition to the conventional application of nmr pulsed field gradient experiments to self-diffusion studies, it is also possible to determine the intracrystalline molecular life times. Referring to the corresponding classical experiment, this method has been termed nmr tracer desorption technique (7). Together with the self-diffusion measurements it provides an excellent tool for characterizing the transport properties in the intra- and intercrystalline spaces, as well as at the interface between them. So far, the nmr techniques provide the only possibility for a direct determination of the existence and of the intensity of transport resistances at this... 

FIGURE 8.15 The basic Stejskal-Tanner pulsed field gradient experiment. Reprinted from Stilbs (1987). Copyright 1987 with permission from Elsevier. 

Sdderman, O. and Olsson, U., Dynamics of amphiphilic systems studied using NMR relaxation and pulsed field gradient experiments, Curr. Opinion Colloid Interface Set, 2, 131-136 (1997). 

Many other pulsed NMR experiments are possible, and some are listed in the final sections. Most can be canied out using the standard equipment described above, but some require additions such as highly controllable, pulsed field gradients, shaped RF pulses for (for example) single-frequency irradiations, and the combined use of pulses at several different frequencies. 

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... 

Figure 2.7.2 illustrates two implementations of the diffusion-relaxation experiment using the pulsed field gradient. In the first implementation, a spin-echo... 

The stimulated echo diffusion-relaxation experiment exhibits a kernel that is similar to that of the one with the pulsed field gradients ... 

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],... 

Modem NMR diffusion measurements are all based on the Stejskal-Tanner (S-T) pulsed field gradient spin-echo experiment [174] in which a gradient pulse is... 

In this chapter we will focus on molecular ordering and confinement effects in pores. Diffusion experiments with the pulse-field gradient method ([162-165] and references therein) and characterization of the surface properties using NMR of noble gases such as 129Xe ([166-171] and references therein), or 83Kr [172], will be omitted due to excellent reviews that have appeared quite recently in these areas. 

Dixon, A. M. and Larive, C. K. (1997). Modified pulsed-field gradient NMR experiments for improved selectivity in the measurement of diffusion coefficients in complex mixtures application to the analysis of the Suwannee River fulvic acid, Anal. Chem., 69, 2122-2128. 

Artifacts may be roughly categorized into those due to inherent limitations (e.g. pulses cannot excite unlimited bandwidths even if all hardware components work perfectly) and those that result from improper set-up of the experiment or nonideal functioning of the NMR spectrometer system. In this chapter we will mainly focus on the latter two. These artifacts are more likely to appear in multiple-pulse experiments. Quite often, they are avoided by clever programming of the experiments (e.g. interleaved acquisition of data for NOE spectra, use of pulsed-field gradients instead of phase-cycling). 

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