Diffusion discrepancies barriers

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... 

Comparisons of estimated diffusivity values on zeolites from sorption uptake measurements and those obtained from direct measurements by nuclear magnetic resonance field gradient techniques have indicated large discrepancies between the two for many systems [10]. In addition, the former method has often resulted in an adsorbate diffusivity directly proportional to the adsorbent crystal size [11]. This led some researchers to believe that the resistance to mass transfer may be confined in a skin at the surface of the adsorbent crystal or pellet (surface barrier) [10,11]. The isothermal surface barrier model, however, failed to describe experimental uptake data quantitatively [10,12]. 

There is good experimental basis therefore to believe that, in chloroplasts and possibly in the b/c complex of bacteria, protons are not directly released or taken up from the water bulk phase but must overcome a diffusion barrier of unknown nature. The presence of these barriers could help in interpreting the severe kinetic discrepancies in the rate of ATP synthesis and its relation with the rate of electron transfer and the extent of the bulk-to-bulk proton gradient, for which a model including H diffusion barriers has been recently proposed [286] (for reviews see Refs. 278, 287). 

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... 

Aromatic Compounds in NaX. Molecular transport of aromatic compounds in zeolite NaX has been studied by both nmr and uptake measurements. On the basis of Equation 4,and if surface barriers are absent, both methods should lead to comparable results. Though uptake measurements by the variable - pressure, constant - volume method by Biilow and coworkers (16,17) apparently are in satisfactory agreement with the nmr data (18), extensive uptake measurements including chromatographic methods are continuously found to yield diffusivities of about two orders of magnitude below these values (19,20). In principle, this discrepancy might be explained by the existence of surface barriers, which remain invisible for nmr studies of intracrystalline diffusion, but which may control the uptake rate. 

The discrepancy in results between NEB and BV calculations is attributed to correlations between Li and adjacent ions during migration that are neglected in the BV calculation [33]. The electrostatic repulsions between Li and adjacent Fe and B cations and relaxations of the sublattice aroimd the Li ion can be considered in NEB calculations. Therefore, first-principles based on the NEB method are more accurate to calculate the activation barrier for ion hopping in the crystal structure than the BVS method, while the BVS method is an easy and fast computation method to predict possible diffusion pathways. 

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