Magnetic field gradient diffusion

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. 

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)... 

In addition to Ti and T2, which reflect the rotational motion of water, NMR can also be used to measure the translational motion of water. If an additional, relatively small (compared to B0), steady magnetic field gradient is incorporated into a pulsed NMR experimental setup, a translational diffusion coefficient (D, m2/s) can be measured (called pulsed field gradient NMR). 

When pulsed magnetic field gradients are applied to study diffusive processes, the MR technique is often referred to as pulsed field gradient or pulsed gradient spin echo (PGSE) MR. Application of PGSE MR techniques to quantify molecular diffusion was pioneered by Stejskal and Tanner 17,18), and the techniques typically probe molecular displacements of 10 -10 m over time scales of the order 10 M s. 

Diffusion in a Magnetic Field Gradient the Macroscopic Measurement... 

The random diffusion of molecules in a magnetic field gradient causes an irreversible loss of phase coherence in the transverse magnetization of the molecular nuclei—i.e., it causes a decrease in a measurable signal h according to the relation 12) ... 

Figure 4- Diffusion coefficients for various molecules on NaX and NaY. (see Table I.) The represent the very reliable point derived from Ti at the minimum. H20 data are from the magnetic field gradient technique. The parameters beside the molecular labels define the fraction of maximum loading 6...

Figure 5. Median jump frequencies (Sr ) 1 for water adsorbed on NaX to saturation, for water on charcoal at saturation, and that expected for bulk water (from NMR relaxation times) dashed curve marked diff diffusion coefficients by magnetic field gradient technique normalized to (Sr) 1 by choice of jump distance of 2.7 A + dielectric relaxation times of Jansen...

The PGSE experiment can detect the presence of two or more diffusivities in the species at resonance. The intensity of the spin echo is a function of the duration 8, magnitude G and the time A between the applied magnetic field gradient pulses ... 

Pulsed-field-gradient NMR (291-292), in which spin echoes are measured in the presence of a time-dependent magnetic field gradient, has been used to determine effective diffusion coefficients, Deff, in beds of zeolite powder. Barrer (35) quotes the expression for the spin-echo amplitude given by Karger (259) in the form ... 

Tanner [49] measured diffusion coefficients of water in three different types of frog muscle cells. He used a variety of magnetic field gradient techniques so as to cover a wide range of diffusion times A= 1 ms to 1 s. The time dependence of the diffusion coefficient was analyzed to obtain the intracellular diffusion coefficients and estimates of the permeability of the cell membranes. In restricted diffusion studies three 90 degree r.f. pulse sequences (stimulated echo) are often used which provides PG-NMR experiments with long diffusion times to explore the dependence of diffusion time on the echo attenuation [49]. 

The results of Zupancic, et.al. (15), are also relevent here. Zupancic investigated diffusion of butane in linear polyethylene using pulsed magnetic field gradient... 

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