PFG NMR studies

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. ... 

PFG NMR studies in porous media have also been carried out using 13C [77], 15N [78], 19F [79] and 129Xe NMR [78]. The lower limit of diffusivities accessible by H PFG NMR is of the order of 10"13 mV. However, such low diffusivities may only be measured under suitable conditions, in particular for large nuclear magnetic relaxation times T and Ti [32]. 

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. 

Molecular exchange between the crystallites and the intercrystalline space may, however, be controlled by processes other than ordinary diffusion. A substantial retardation of molecular exchange may be caused by transport resistances on the external surface of the crystallites. It has been shown in PFG NMR studies that such surface barriers may be brought about during the process of zeolite manufacturing (e.g. by hydrothermal treatment) [1,6] and by coke depositions [1,7]. In this case, irrespective of possibly large rates of molecular redistribution within the crystallites, the rate of molecular escape out of the crystallites may be slowed down dramatically. In effect, in this case, the product molecules should be distributed essentially homogeneously over the whole space of the individual crystallites. 

Another deviation from the pattern of ordinary diffusion must be expected if the reactant and product molecules are subjected to single-file conditions, i.e. if (i) the zeolite pore system consists of an array of parallel channels and if (ii) the molecules are too big to pass each other. In this case, the molecular mean-square displacement z t)) is found to be proportional to the square root of the observation time, rather than to the observation time itself. First PFG NMR studies of such systems are in agreement with this prediction [8]. By introducing a mobility factor F, in analogy to the Einstein relation for ordinary diffusion. 

Table 5 shows the results of diffusion measurements with carbon monoxide, methane, and xenon in a comparative C, H, and Xe PFG NMR study [178,179]. For all adsorbates the values of timra and are found to be on... 

Fig. 18 Apparent coefficients of intracrystalline self-diffusion of n-hexane as observed by time- and space-resolved PFG NMR in a bed of zeolite Na-X with restricted ( ) and unrestricted ( ) sorbate supply in dependence on the sorbate concentration. The real diffusivities open symbols) were calculated from these values by using the correspondence presented by Fig. 3. The full line with the indicated error bars represents the range of intracrystalline diffusivities as observed in previous PFG NMR studies with closed sample tubes. From [163] with permission...

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...

It is worth noting that within a range of 20 %, five different methods of analyzing the crystallite size, viz., (a) microscopic inspection, (b) application of Eq. (3.1.7) for restricted diffusion in the limit of large observation times, (c) application of Eq. (3.1.15) to the results of the PFG NMR tracer desorption technique, and, finally, consideration of the limit of short observation times for (d) reflecting boundaries [Eq. (3.1.16)] and (e) absorbing boundaries [Eq. (3.1.17)], have led to results for the size of the crystallites under study that coincide. 

Owing to its ability to monitor the probability distribution of molecular displacements over microscopic scales from hundreds of nanometers up to several millimeters, PFG NMR is a most versatile technique for probing the internal structure of complex materials. As this probing is based on an analysis of the effect of the structural properties on molecular propagation, the properties of the material studied are those which are mainly of relevance for the transport processes inherent to their technical application. 

Studies of flow-induced coalescence are possible with the methods described here. Effects of flow conditions and emulsion properties, such as shear rate, initial droplet size, viscosity and type of surfactant can be investigated in detail. Recently developed, fast (3-10 s) [82, 83] PFG NMR methods of measuring droplet size distributions have provided nearly real-time droplet distribution curves during evolving flows such as emulsification [83], Studies of other destabilization mechanisms in emulsions such as creaming and flocculation can also be performed. 

Pulsed field gradient NMR has become a standard method for measurement of diffusion rates. Stilbs [272] and others have exploited in particular the FT version for the study of mixtures. An added advantage of PFG-NMR is that it can be employed to simplify complex NMR spectra. This simplification is achieved by attenuation of resonances based on the differential diffusion properties of components present in the mixture. 

DOSY was developed to provide useful displays of PFG-NMR data sets that incorporate all reliable information about the system under study obtained from PFG-NMR data and prior knowledge. Various pulse sequences for DOSY have been developed [273,274]. 

The isotherm characterizing the binding phenomenon of small molecules with surfactant micelles or polymers has been largely studied by means of PFG-NMR. 

Lateral diffusion of phospholipids in model membranes at ambient pressure has been studied over the years by a variety of techniques including fluorescence recovery after photobleaching (FRAP), spin-label ESR, pulse field gradient NMR (PFG-NMR), quasielastic neutron scattering (QENS), excimer fluorescence and others.In general, the values reported for the lateral diffusion coefficient (D) range from 10 to 10 cm /s in the... 

Nowak et al. (63) presented a comparative study of the diffusivities of rigid models of methane, ethane, and propane in silicalite. (The details of the calculation are reported in the preceding section.) The calculated diffusion coefficients decreased as the length of the carbon chain increased, and the effect was found to be far more pronounced for ethane than propane. The calculated diffusivities, in units of 108 m2/s, were 0.62, 0.47, and 0.41 for methane, ethane, and propane, respectively. The ethane value is in satisfactory agreement with PFG-NMR measurements [0.38 (77), 0.3 (80), 0.4 (42) for silicalite. The value for propane, however, was calculated to be almost an order of magnitude larger than the NMR results of Briscoe et al. (80). [The agreement with the value of Caro et al. (71) is better, but still an overestimation.]... 

Hills and Snaar [15] used the PFG-NMR technique to study cellular tissue and related multicompartment systems. By fitting their data they showed how to obtain dynamic information about membrane permeability, and they intended to use the given strategy to study plant tissue and food preparations. 

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