Sorption diffusivities and NMR

Figure 2. Arrhenius plot showing comparison of NMR and sorption diffusivities for benzene and o-xylene in NaX zeolite crystals. NMR data from (1) Germanus et al. (19) and (2) Karger and Ruthven (10). Uptake (corrected diffusivity) and tracer exchange data of Goddard (11-13) (50 pm and 100 pm NaX, 250 pm faujasite). ZLC data of Eic (15,16).

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. ... 

Sorption capacity is one of the major properties used for industrial applications of zeolites. H. Lee reviews the aspects of zeolites used as adsorbents. The other papers in the section deal with the theory of sorption and diffusion in porous systems, the variation of sorption behavior upon modification, and the variation of crystal parameters upon adsorption. NMR and ESR studies of sorption complexes are reported. H. Resing reviews the mobility of adsorbed species in zeolites studied by NMR. 

An intriguing aspect of these measurements is that the values of D determined from NMR and from sorption kinetics differ by several orders of magnitude. For example, for methane on (Ca,Na)-A the value of the diffusion coefficient determined by NMR is 2 x 10 5 cm2 sec-, and the value determined for sorption rates only 5 x 10"10 cm2 sec-1. The values from NMR are always larger and are similar to those measured in bulk liquids. The discrepancy, which is, of course, far greater than the uncertainty of either method, remained unexplained for several years, until careful studies (267,295,296) showed that the actual sorption rates are not determined by intracrystalline diffusion, but by diffusion outside the zeolite particles, by surface barriers, and/or by the rate of dissipation of the heat of sorption. NMR-derived results are therefore vindicated. Large diffusion coefficients (of the order of 10-6 cm2 sec-1) can be reliably measured by sorption kinetics... 

Arrhenius plot showing comparison of corrected sorption diffusivities (D0) and NMR self diffusivities (Ds) for A, butane and B, propane in 5A zeolite crystals. (x,o 55pm and 27pm Charnell crystals I. , 34pm and... 

Seff-Diffusion Confidents of Methane in ZSM-5 Measured by PFG NMR and QENS Compared with Sorption Uptake/Desorption Diffusivities"... 

It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffiisivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. 

NMR PFG measurements determine the tracer or self-diffusivity (D ) under equilibrium conditions with no concentration gradient. n any sorption rate measurement it is the transport diffusivity under the influence of a concentration gradient which is measured. In general these two quantities are not the same but the relationship between them can be established from irreversible thermodynamics. (17,18) In the low concentration limit the thermodynamic correction factor vanishes and the transport and self diffusivities should approach the same limit. Since ZLC measurements are made at low concentrations within the Henry s Law region the diffusivity values should be directly comparable with the NMR self-dif fusivities. ... 

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 9.13 Self-diffusion coefficients Ds(T) of water in Nafion. Open symbols are for temperature domains where water concentration is constant, full symbols are for temperature domains where concentrations decrease (0, ) X = 14.6, (O) X = 9.6, ( ) X = 6.65, and (A) X. = 5.4. Ds(T) is also shown for water in sulfuric acid (+). (Reprinted with permission from Guillermo, A. et al. 2009. NMR and pulsed field gradient NMR approach of water sorption properties in Nafion at low temperature. /. Phys. Chem. B 113 6710-6717. Copyright (2009). American Chemical Society Publications.)... 

NMR imaging techniques have been used for the study of sorption, diffusion and chemical reactions as well as the desorption of chemical substances in polymeric materials [23]. NMR imaging can directly provide the diffusion coefficient as a characteristic quantity of the fluidity of a component in a sample, making it possible to map molecular migration on a microscopic scale. 

C NMR spectra of CH4 in an AIPO4-II molecular sieve have revealed exchange effects between adsorbed and nonadsorbed methane gas. The diffusion of a mixture of methane and xenon in the zeoHte siUcahte has been studied by pulsed field gradient NMR spectroscopy. In situ H MAS NMR studies of the H/D exchange of deuterated propane adsorbed on H-ZSM-5 have been reported. C MAS NMR spectroscopy has been used to study the initial stages of propane activation over H-ZSM-5, and sorption properties of hnear alkanes in ferrierite. Protonated sites on sulfate-promoted zirconium oxide catalysts have been studied using H NMR spectroscopy. NMR relaxation and self-diffusion of pentane, neopentane, dodecane, benzene, cyclohexane, and... 

In order to apply this technique for quantitative characterization of counter-transport phenomena in zeolites it had to be checked first for the more simple case of single-component diffusion. As an example, benzene diffusion in H-ZSM-5 was chosen, because results for this case had been already reported by several authors. Their results, obtained from sorption kinetics as well as from NMR experiments, were in very good agreement and, thus, provided a reliable basis for comparison [13,14]. 

In Section IB we presented experimental evidence that diffusion coefficients correlate with PVC main-chain polymer motions. This relationship has also been justified theoretically (12). In the previous section we demonstrated that the presence of CO2 effects the cooperative main-chain motions of the polymer. The increase in with increasing gas concentration means that the real diffusion coefficient [D in eq. (11)] must also increase with concentration. The nmr results reflect the real diffusion coefficients, since the gas concentration is uniform throughout the polymer sample under the static gas pressures and equilibrium conditions of the nmr measurements. Unfortunately, the real diffusion coefficient, the diffusion coefficient in the absence of a concentration gradient, cannot be determined from classical sorption and transport data without the aid of a transport model. Without prejustice to any particular model, we can only use the relative change in the real diffusion coefficient to indicate the relative change in the apparent diffusion coefficient. 

Diffusion of hydrocarbons and other simple molecules in A, X and Y zeolites has been studied by a range of experimental methods including direct sorption rate measurements, chromatography and NMR. The advantages and limitations of these techniques are considered and results of recent experimental studies are reviewed with emphasis on the detailed microdynamic information obtainable by NMR. 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

At low sorbate concentrations f-+o and eqn. 6 reduces to the familiar Darken equation(33). in comparing the results of sorption and NMR diffusivity measurements it is logical to compare D0 with Ds, even though exact agreement can be expected only at low sorbate concentrations. At higher concentrations one may expect D0 Ds/(l-f). 

NMR Sorption Comparison Diffusion of the large tri-ethylamine molecule is sufficiently slow that reliable dif-fusivities can be determined from uptake rate measurements in 50]jm crystals(57) at least over a limited range of conditions. A comparative study, carried out with the same zeolite samples showed good agreement between the sorption and PFG NMR measurements, both as to the magnitude of the diffusivity ( 10 cm2.s- at 445K) and the trends with concentration and temperature(41). 

Simulations of C NMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental C NMR lineshapes, a mean residence time tj of 20 and 150 p-s for a concentration of six molecules per u.c. at 250 and 200 K, respectively, was derived. Provided that these jumps detected in C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (P) = 6Dtj is valid, where (P) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm. 

Accounting for the influences of external heat and mass transfer resistances in limiting the sorption rates, in many instances reasonable agreement between diffusion data from sorption experiments and PFG NMR may... 

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