PFG self-diffusivity

Pulsed Field Gradient (PFG) Self Diffusion Measurement(24)... 

Combining the PFG self diffusion measurement with a measurement of the correlation time provides a means of determining directly the mean jump distance. 

For the n-butane-5A system both sorption and ZLC results are in substantial agreement with NMR PFG self diffusivity data. However, for all NaX systems studied the NMR self diffusivities are approximately two orders of magnitude larger than the ZLC values. This discrepancy is difficult to understand. Most of the more obvious explanations can be ruled out on the basis of the experimental evidence. For example, the possible intrusion of extraneous heat and/or mass transfer resistances is excluded by the agreement between the sorption, exchange and ZLC results. For NaX crystals both NMR and ZLC results show that differences in the origin of the sample and the initial dehydration procedure have only a relatively small effect on the diffusivity. (27) The absence of significant surface barriers (for aromatics-NaX) is... 

Figure 4.4-3 Self-diffusion and mutual diffusion coefficients in the methanol/[BMIM][PFg] sys-...

Fig. 3.1.4 Anisotropic self-diffusion of water in and filled symbols, respectively). The horizon-MCM-41 as studied by PFG NMR. (a) Depen- tal lines indicate the limiting values for the axial dence of the parallel (filled rectangles) and (full lines) and radial (dotted lines) compo-perpendicular (circles) components of the axi- nents of the mean square displacements for symmetrical self-diffusion tensor on the inverse restricted diffusion in cylindrical rods of length temperature at an observation time of 10 ms. / and diameter d. The oblique lines, which are The dotted lines can be used as a visual guide, plotted for short observation times only, repre-The full line represents the self-diffusion sent the calculated time dependences of the...

Fig. 3.1.5 Temperature dependence of the coefficient of long-range self-diffusion of ethane measured by PFG NMR in a bed of crystallites of zeolite NaX (points) and comparison with the theoretical estimate (line). The theoretical estimate is based on the sketched models of the prevailing Knudsen diffusion...

Pulsed field gradient NMR (PFG-NMR) spectroscopy has been successfully used for probing interactions in several research fields.44-53 The method was developed by Stejskal and Tanner more than 40 years ago54 and allows the measurement of self-diffusion coefficient, D, which is defined as the diffusion coefficient in absence of chemical potential gradient. 

An important technical development of the PFG and STD experiments was introduced at the beginning of the 1990s the Diffusion Ordered Spectroscopy, that is DOSY.69 70 It provides a convenient way of displaying the molecular self-diffusion information in a bi-dimensional array, with the NMR spectrum in one dimension and the self-diffusion coefficient in the other. While the chemical-shift information is obtained by Fast Fourier Transformation (FFT) of the time domain data, the diffusion information is obtained by an Inverse Laplace Transformation (ILT) of the signal decay data. The goal of DOSY experiment is to separate species spectroscopically (not physically) present in a mixture of compounds for this reason, DOSY is also known as "NMR chromatography."... 

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. 

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. ... 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

The self-diffusion coefficient of water in Nafion, as measured by PFG is shown in... 

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. 

The self-diffusion of benzene in PIB [36], cyclohexane in BR [37] and toluene in PIB [38-40] has been investigated by PFG NMR. In addition more recently Schlick and co-workers [41] have measured the self-diffusion of benzene and cyclohexane mixtures in polyisoprene. In the first reported study of this kind, Boss and co-workers [36] measured the self-diffusion coefficients of benzene in polyisoprene at 70.4 °C. The increase in Dself with increasing solvent volume fraction could be described by the Fujita-Doolittle theory which states that the rate of self-diffusion scales with the free volume which in turn increases linearly with temperature. At higher solvent volume fractions the rate of selfdiffusion deviates from the Fujita-Doolittle theory, as the entanglement density decreased below the critical value. 

In principle, any of the techniques described for studying self-diffusion may be applied to both single- and multicomponent systems. So far, however, most selfdiffusion measurements of multicomponent systems have been carried out by PFG NMR. Such measurements are possible by applying a set of samples with deuterated compounds with only one species (namely that to be measured) in the protonated form [98], by simultaneously considering different nuclei (e.g. H and 19F [79]), and by Fourier transform PFG NMR [91,92]. 

Pulsed field gradient NMR (PFG-NMR) is a powerful, nondestructive technique of measuring self-diffusion coefficients in a colloidal dispersion [69-71]. Molecules associated with an aggregate or a particle will diffuse more slowly than their free dissolving state. More specifically, when a water-soluble species is partially adsorbed onto an abrasive particle, the measured overall diffusion coefficient (D ) of the species is decreased. If the diffusion coefficient of the free dissolving species can be measured in the absence... 

First we will review the relevant NMR techniques and their most recent developments (1) pulsed-field gradient (PFG) NMR (315-18) for the measurement of translational molecular self-diffusion and (2) (6,7,10,19,20)... 

According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal F versus (Sg) The observation time of self-diffusion is the separation between the two field gradient pulses, t. Owing to their relatively large gyromagnetic ratio and to their natural abundance of 1, protons provide very suitable conditions for NMR self-diffusion studies, but C 44), F 45), and Xe 46-48) resonances have also been used successfully in recent PFG NMR studies of zeolites. 

Fig. 1. Parameter calculations for the PFG NMR spin-echo attenuation due to anisotropic self-diffusion in a diffusion system of axial symmetry with D > Di 49).

Gas-phase self-diffusion coefficient gas PFG NMR applied to the gas phase 3.4 X 10 m s ... 

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-... 

This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x, y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those 42,43). For the self-diffusion of methane in ZSM-5/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). 

In Fig. 18 the self-diffusivities obtained by different experimental techniques are compared. It appears that in both the absolute values and the trends in the concentration dependence, the QENS data, the PFG NMR results, and the data derived from sophisticated uptake experiments using the piezometric or single-step frequency-response techniques agree. Nevertheless, disagreement with some sorption results has to be stated. Additional information on the molecular reorientation of benzene in zeolite X has been obtained by QENS and NMR lineshape analysis. 

Fig. 18. Self-diffusion coefficients of benzene in NaX at 458 K PFG NMR, O (97) and (92) (JENS, A (13) deduced from NMR lineshape analysis, (10). Comparison with nonequilibrium measurements T, sorption uptake with piezometric control (93) , zero-length column method (96) o, frequency-response and single-step frequency-response technique (98). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.

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