NMR pulsed field gradient experiments

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. 

Three analytical expressions for the spin-echo intensity as a function of the gradient in a pulsed field gradient NMR experiment for spins diffusing in a sphere with reflecting walls are reinvestigated. It is found that none of the published formulas are completely correct. By numerical comparisons the correct formula is found. 

The self-diffusion coefficients of toluene in polystyrene gels are approximately the same as in solutions of the same volume fraction lymer, according to pulsed field gradient NMR experiments (2fl). Toluene in a 10% cross-linked polystyrene swollen to 0.55 volume fraction polymer has a self-diffusion coefficient about 0.08 times that of bulk liquid toluene. Rates of rotational diffusion (molecular Brownian motion) determined from NMR spin-lattice relaxation times of toluene in 2% cross-linked ((polystytyl)methyl)tri-/t-butylphosphonium ion phase transfer catalysts arc reduced by factors of 3 to 20 compai with bulk liquid toluene (21). Rates of rotational diffusion of a soluble nitroxide in polystyrene gels, determined from ESR linewidths, decrease as the degree of swelling of the polymer decreases (321. 

Figure 10. The basic pulse field gradient NMR spin echo experiment.

Fleisher et al. [12] studied the self-diffusion of oil and water in rape seeds. The selfdiffusion of oil was found to be completely restricted. The experiments could be explained in toms of the model of diffusion within spherical droplets and a Gaussian mass distribution of the droplet radii. At the same time Van den Enden et al. [9] introduced the technique described above. It is a rapid method for the determination of water droplet size distributions in spreads by using low resolution pulsed field gradient NMR. Their method was based on the recognition that a set of echo attenuation values (R) as a function of the field gradient pulsed width, obtained under conditions where R is independent of the time allowed for diffusion, contains all the necessary information on the water droplet size distribution (see above). A log-normal distribution of water droplet sizes was assumed. 

Independent Determination of Diffusion Coefficients. Independent methods for the determination of diffusion coefficients serve as a reference for the determination of transport parameters. Different methods can be applied to determine diffusion coefficients independently from transport experiments, e.g. determination of the lag-time (27), pulsed-field gradient NMR (25), and permeability measurements (P). 

Measurement of diffusion using pulsed field gradient NMR (PFG-NMR) is a powerful analytical tool because it combines the high specificity and information content of NMR spectroscopy with the size selectivity of diffusion coefficients. PFG-NMR employs timescales of tens of ms and has a displacement sensitivity of the order of 100 nm. PFG-NMR can determine molecular self-diffusion coefficients in liquid phases down to a lower limit of 10 " m s Due to the combination of experimental convenience and straightforward interpretation, PFG-NMR has become the method of choice for studying translational diffusion. PFG-NMR experiments have been reported using H, H, Li, C, F and other nuclei. The time A over which PFG-NMR measurements are possible is limited. 

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... 

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