Pulsed field gradient self diffusion measurement

FIGURE 5.4. The sequence of pulses used in the pulsed field gradient self-diffusion measure, ment. (a) rf pulse (i) Gradient pulse sequence (90°, 180°) (c) Response signal. (From ref. 22, with permission.)... 

A more sophisticated method which has found wide application in the study of intracrystalline diffusion in zeolites is the nuclear magnetic resonance (NMR) pulsed field gradient self-diffusion method. The method, which is limited to hydrocarbons and other sorbates with a sufficient density of unpaired nuclear spins, depends on measuring directly the mean square distance traveled by molecules,... 

In some adsorption systems, as an additional method, pulsed field gradient (PFG) diffusion measurements were applied to dilute colloidal dispersions, these methods are described in detail elsewhere [18, 19]. Briefly, by this method the self-diffusion coefficients for all spectrally resolvable liquid resonances can be obtained. Usually the method is applied to protons, and can in coated colloid dispersions monitor mobile species such as the solvent or free surfactants. 

It should be noted that the radiotracer and pulsed field gradient NMR techniques measure the self-diffusion coefficient of water, Ds, rather than the Fickian or interdiffusion coefficient of water through the polymer membrane, D, and some correction is required, because it is the Fickian water diffusion coefficient that is the proper transport property to use in macroscopic studies of water diffusion [17]. The relationship is ... 

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... 

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. 

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. 

Nafion absorbs MeOH more selectively than water, and the MeOH diffusion flow is higher than the osmotic water flow in Nafion membranes. Diffusion coefficients of Nafion 117 determined by different techniques have been reported. Ren et al. measured MeOH diffusion coefficients in Nafion 117 membranes exposed to 1.0 M MeOH solutions using pulsed field gradient (PPG) NMR techniques. The MeOH self-diffusion coefficient was 6 x 10 cm S and roughly independent of concentration over the range of 0.5-8.0 M at 30°C. A similar diffusion coefficient was obtained for Nafion 117 at 22°C by Hietala, Maunu, and Sundholm with the same technique. Kauranen and Skou determined the MeOH diffusion coefficient of 4.9 x 10 cm for Nafion... 

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. ... 

Packer and Rees [3] extended the work of Tanner and Stejskal by the development of a theoretical model using a log-normal size distribution function. Measurements made on two water-in-oil emulsions are used to obtain the self-diffusion coefficient, D, of the water in the droplets as well as the parameters a and D0 0. Since then, NMR has been widely used for studying the conformation and dynamics of molecules in a variety of systems, but NMR studies on emulsions are sparse. In first instance pulsed field gradient NMR was used to measure sdf-diffusion coefficients of water in plant cells (e.g. ref. [10]). In 1983 Callaghan... 

The diffusion of small molecules in rubbers is of both theoretical and practical importance. The theories of diffusion based on consideration of free volume can be tested by measurement of self-diffusion using methods such as pulsed field gradient NMR. Selfdiffusion of small molecules must be understood for applications of rubbers as seals in contact with solvents, and for example for diffusion of plasticisers and other small molecules. 

The NMR technique for measuring self-diffusion in liquids was first reported in 1965390, and its variant for multicomponent mixtures became available with the introduction of the Fourier transform. Wider use had to wait until pulsed field gradients became generally... 

Using pulsed field gradient spin echo NMR, Guering and Lindman [14] and, independently, Clarkson et al. [15] measured the self-diffusion coefficients of the components of microemulsions of sodium dodecyl sulfate (SDS), toluene, butanol, and NaCl brine. The results (Fig. 8) establish unequivocally the existence of bicontinous microemulsion. 

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

Zielinski and Hanley [AlChE J. 45,1 (1999)] developed a model to predict multicomponent diffusivities from self-diffusion coefficients and thermodynamic information. Their model was tested by estimated experimental diffusivity values for ternary systems, predicting drying behavior of ternary systems, and reconciling ternary selfdiffusion data measured by pulsed-field gradient NMR. 

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... 

For comparison, we have also reported in Fig. 3 the data obtained by Appel and Fleischer [51] with PDMS at 60°C, using the pulsed field gradient NMR technique to measure the self-diffusion coefficient. Except for the slightly higher values due to the increased temperature, it is remarkable that exactly the same trends are observed for the two sets of data corresponding to N = P. 

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)... 

A. Self-Diffusion Measurement by Pulsed-Field Gradient NMR... 

D. On the Limits of Application of Pulsed-Field Gradient NMR for Self-Diffusion Measurements in Zeolites... 

Analyzing the self-diffusion behavior of guest molecules in a microporous catalyst by the combined application of pulsed-field gradient NMR selfdiffusion techniques reveals the spatial distribution of transport resistances over the catalyst particles. In the case of coke deposits on ZSM-5, the distribution of carbonaceous residues over the crystal was found to be a function of the crystal morphology, the time onstream, and the chemical nature of the coke-producing reactant. In the case of ZSM-5 modified by H3PO4, the spatial distribution of the P compounds over the ZSM-5 crystals can be determined by self-diffusion measurements. Location of transport hindrances in a zeolite framework is based on self-diffusion measurements, in... 

Self-diffusion in liquids (and similar systems) can be measured by the pulsed-field gradient technique. For a hypothetical sample without molccu-... 

Zawodzinski et al. [64] have reported self-diffusion coefficients of water in Nafion 117 (EW 1100), Membrane C (EW 900), and Dow membranes (EW 800) equilibrated with water vapor at 303 K, and obtained results summarized in Fig. 36. The self-diffusion coefficients were deterinined by pulsed field gradient NMR methods. These studies probe water motion over a distance scale on the order of microns. The general conclusion was the PFSA membranes with similar water contents. A, had similar water self-diffusion coefficients. The measured self-diffusion coefficients in Nafion 117 equilibrated with water vapor decreased by more than an order of magnitude, from roughly 8 x 10 cm /s down to 5 x 10 cm /s as water content in the membrane decreased from A = 14 to A = 2. For a Nafion membrane equilibrated with water vapor at unit activity, the water self-diffusion coefficient drops to a level roughly four times lower than that in bulk liquid water whereas a difference of only a factor of two in local mobility is deduced from NMR relaxation measurements. This is reasonably ascribed to the additional effect of tortuosity of the diffusion path on the value of the macrodiffusion coefficient. For immersed Nafion membranes, NMR diffusion imaging studies showed that water diffusion coefficients similar to those measured in liquid water (2.2 x 10 cm /s) could be attained in a highly hydrated membrane (1.7 x 10 cm /s) [69]. 

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