PFG NMR experiments

Pulsed field gradient (PFG)-NMR experiments have been employed in the groups of Zawodzinski and Kreuer to measure the self-diffusivity of water in the membrane as a function of the water content. From QENS, the typical time and length scales of the molecular motions can be evaluated. It was observed that water mobility increases with water content up to almost bulk-like values above T 10, where the water content A = nn o/ nsojH is defined as the ratio of the number of moles of water molecules per moles of acid head groups (-SO3H). In Perrin et al., QENS data for hydrated Nation were analyzed with a Gaussian model for localized translational diffusion. Typical sizes of confining domains and diffusion coefficients, as well as characteristic times for the elementary jump processes, were obtained as functions of A the results were discussed with respect to membrane structure and sorption characteristics. ... 

Callaghan points out the analogy between PFGE NMR experiments in the short-gradient-pulse limit and diffraction experiments. Under the short gradient pulse condition the echo intensity obtained from a PFG NMR experiment can be written as ... 

These calculated intracrystalline diffusion coefficients are particularly appropriate for comparison with those determined from pulsed field gradient (PFG) NMR experiments. Time-independent equilibrium properties such as adsorbate conformations are also readily accessible. The classical nature of the simulations allows a particle s trajectory to be followed, and from this it is possible to determine all kinds of information, such as how often a particle diffuses through a certain region. 

Figure 2. Pulse sequence diagram of a Hahn spin-echo experiment with field gradient pulses. Rf- and field gradient pulses are denoted by 90°, 180° and FGP, respectively. The FGP pulses have a length 5 and are separated by an interval A as in the spin-echo sequence given in Fig. 1. VD is a time delay which may be variable in which case also A is variable. A PFG NMR experiment may also be performed with variable 5 or gradient strength (G) and fixed A. Normally, 6 is chosen between 0 and 10 ms and A between 0 and 400 ms. The time delay t depends on the T1 relaxation time of the pure oil of the emulsion but is normally between 130 and 180 ms.

Recently, Li et al. [16] performed PFG-NMR experiments on oil-in D20 emulsions. D20, with similar chemical properties as H20, was chosen because the NMR resonance frequency of deuterium is quite different from that of hydrogen. Therefore they could select the experimental parameters so that only NMR signals from oil molecules are observed. In their calculations they assumed a log-normal distribution. Because of the very different diffusion coefficients of the two oils used, they were only able to obtain stable converged distribution parameters for the n-octane sample during the non-linear fitting procedure. 

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-... 

Figures 42 and 43 show scanning electron micrographs of two ZSM-5 samples of different configurations coffin-shaped crystals and polycrystalline grains. To emphasize the relationship between sample dimensions and diffusion paths followed during the PFG NMR experiment, magnifications are referenced against typical root mean square displacements for methane and propane molecules during typical PFG NMR observation times.

SJ Gibbs, CS Johnson Jr. A PFG NMR experiment for accurate diffusion and flow studies in the presence of eddy currents. J Magn Reson 93 395-402, 1991. 

This is directly evidenced by the echo attenuation of the proton resonance in PFG-NMR experiments of phosphonic acid functionalized oligomer [104], Only the echo of the phosphonic protons is attenuated ivhile the echo of the oligomer protons is only slightly affected by the magnetic field gradient (Fig. 23.9). The reader may recall that complexation of phosphoric acid and a basic polymer does not show any sign of this effect (see Fig. 23.7), which opens the way to the development of true single ion conductors. 

Figure 23.9 Echo attenuation of the proton resonance in PFG-NMR experiments of a phosphonic acid funtionalized oligomer [104]. Only the echo of the phosphonic protons is attenuated while the echo of the oligomer protons is only slightly affected by the magnetic field gradient.

Under the influence of a constant field gradient go in addition to the pulsed ones, the spin echo attenuation in the PFG NMR experiments is given by the relation... 

Figure 13 Theoretical dependence of the signal decay in PFG NMR experiments for different values of the ratio DJD, calculated from Eq. (38) by means of Eq. (39). Also, comparison with experimental data at 193 (O), 223 ([ ]), 273 ( 0), and 298 K (A) for methane in ZSM-5 and a concentration of 12 molecules per unit cell. (From Ref. 156.)...

In many cases the rate of molecular mass transfer through the bed of zeolite crystallites (see Sec. III.D.) is found to be so fast that the propagator determined in the PFG NMR experiment may be easily separated into its two constituents. 

Fig. 3 The ratio Dapp/Antra between the apparent and the intracrystalline diffusivity in PFG NMR experiments with zeolite crystallites of radius R as a function of the normalized observation time f = Dappf/R. From [69] with permission...

Flow NMR spectroscopy allows investigations of reaction processes nearly in real time and under process conditions in a wide temperature and pressure range. Modem multipulse and PFG NMR experiments can be used, which increase the quahty of the data and reduce the experiment time. Typical commercial NMR probe flow cells have an active volume of 60-120[i.l and a total volume of about 120-240 ]tl, which is significantly smaller than that of about 600 ]tl of conventional 5 mm tubes, and a small fraction of the total reactant volume. 

Fig. 7.10 Ion diffusion in (a) pentaglyme (EO5DME) and (b) oligoethers from MD simulations [49] and pulsed field gradient (pfg)-NMR experiments [69]...

A straight-line fit of PFG-NMR data for measured diffusivity (or reciprocal tortuosity) against A should thus yield an intercept equal to the unrestricted intraparticle diffusion coefficient Dq (or I/Xq), and DppQ=DJXj, (where is the free diffusion coefficient for bulk water at the temperature at which the PFG-NMR experiment is conducted, and Xp is the tortuosity of the pore space occupied by the fluid). 

Diffusion is the most important transport mechanism in an operating PEMFC, and the diffusion coefficients are the basic input parameters for the performance analysis as well as the modeling of a PEMFC. Though there are several experimental methods for the measurement of diffusion coefficients, the PFG NMR experiment is the most accepted method for the direct measurement of diffusion coefficients. In a PFG NMR measurement, the target molecules are probed by nuclear spins and their motions are tracked by a time-dependent field gradient as originally proposed by Stejskal and Tanner [6]. 

Jenkins et al. used high-resolution H MAS NMR in combination with 2D exchange NOESY and PFG NMR diffusion experiments to characterize the methanol swollen polymer anion-exchange membranes. High-resolution MAS NMR observed resonances from water and methanol in both free environment and membrane-associated environment within the anion-exchange membranes. H high-resolution MAS PFG NMR experiments identified different molecular diffusion environments in the solvent, while H 2D NOESY NMR experiments confirmed spatial contacts between membrane-associated species and the membrane [186]. 

Simorellis, A. K. and Flynn, P. F., A PFG NMR experiment for translational diffusion measurements in low-viscosity solvents containing multiple resonances, J. Magn. Reson. 170, 322-328 (2004). 

For the non-ionic surfactant C 2(EO)5 the resulting residence time on the particle, tb = 13.4 ms, was consistent with purely diffusion controlled adsorption, while the kinetics of incorporation into the adsorption layer is fast compared to this time scale. At higher concentrations additional contributions of micelles to the exchange rate were found to increase the exchange rate [23]. PFG-NMR experiments can probe surfactant exchange dynamics at a time scale as fast as the ms range, which had not been achieved by any other method at solid/liquid interfaces. 

Hakansson, B., Jonsson, B., Linse, P. and Soderman, O., The influence of a nonconstant magnetic-field gradient on PFG NMR experiments. A Brownian-dynamics computer simulation study, J. Magn. Reson., 124, 343-351 (1997). 

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. 

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