Diffusion systems showing discrepancies

As a result of these difficulties the reported diffusivity data show many apparent anomaUes and inconsistencies, particularly for 2eohtes and other microporous adsorbents. Discrepancies of several orders of magnitude in the diffusivity values reported for a given system under apparendy similar conditions are not uncommon (18). Since most of the intmsive effects lead to erroneously low values, the higher values are probably the more rehable. 

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. 

The anomalous surface conduction was studied extensively by O Brien and by Hunter, and they could show that the Stem layer conduction is about thirty times larger than the diffuse layer conduction at low salt concentration. This explains substantial discrepancies between the electrophoresis and the conductance estimates of zeta potential. For thin double-layer systems such as this, the zeta potential is usually calculated from the electrophoretic mobility using Smoluchowski s formula, which in O Brien s case corresponds to a zeta potential of 50 mV [8]. Complex conductivity measurements result in f = —160 mV. 

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... 

Calculations show that the model of a non-equilibrium surface layer is an alternative to kinetic-controlled adsorption models. On the basis of the purely diffusion-controlled adsorption mechanism the proper consideration of a non-equilibrium diffusion layer leads to a satisfactory agreement between theory and experimental data for various studied systems, systematically demonstrated for the short-chain alcohols [132], The non-equilibrium model is applicable in the concentration range from 10 to 10 mol/cm at different values of the Langmuir constant at- For l < 10 mol/cm a consideration of non-equilibrium layer effects is not necessary. For ai > 10 mol/cm and large surfactant concentration the Ay values calculated from the proposed theory do not compensate the discrepancy to the experimental data so that other mechanisms have to be taken into account. An empirical formula also proposed in [132] for the estimation of the non-equilibrium surface layer thickness leads to a better agreement with experimental data, however this expression restricts the validity of the non-equilibrium surface layer model as alternative to non-diffusional adsorption kinetics. 

The recently reported tracer ZLC data for propane and propene in NaX show a similar discrepancy and for these systems there is evidently a clear difference in the trend of diffusivity with sorbate loading, as well as in the order of magnitude of the diffusivity values (Fig. 15a). 

The transport and sorption of water in miscible PES/Phenoxy blends has been studied at 40 °C as a function of blend composition [17]. The isotherms are essentially linear over much of the activity range. The highest values of sorption, diffusion and permeation have been observed for PES with a volume percent of 100, and the lowest values for pure phenoxy. The intermediate compositions show decreasing values with decreases in PES content. In an earlier study of this system [18], the isotherms for the pure components and blends were reported to be practically coincident, except for activities >0.7 where the sorption at a given activity was increased significantly with the phenoxy content of the blend. The differences in sample preparation or incomplete removal of solvent may be responsible for these discrepancies. 

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