Diffusion surface barriers

Here, D is the diffusion constant for heat or material and the kinematic viscosity of the liquid. A consequence of the existence of such a diffusive surface barrier is that the diffusion length = D/F is to be replaced by in all formulas, as soon as growth rate V the more important become the hydrodynamic convection effects. 

Introduction of PFG NMR to zeolite science and technology has revolutionized our understanding of intracrystalline diffusion [19]. In many cases, molecular uptake by beds of zeolites turned out to be limited by external processes such as resistances, surface barriers or the finite rate of sorbate supply, rather than by intracrystalline diffusion, as previously assumed [10, 20-24]. Thus, the magnitude of intracrystalline diffusivities had to be corrected by up to five orders of magnitude to higher values [25, 26],... 

Comparison between xf a as determined on the basis of Eq. (3.1.15) from the microscopically determined crystallite radius and the intracrystalline diffusivity measured by PFG NMR for sufficiently short observation times t (top left of Figure 3.1.1), with the actual exchange time xintra resulting from the NMR tracer desorption technique, provides a simple means for quantifying possible surface barriers. In the case of coinciding values, any substantial influence of the surface barriers can be excluded. Any enhancement of xintra in comparison with x a, on the other side, may be considered as a quantitative measure of the surface barriers. 

Each serie of measurements consisted of two parallel samples with counting during and after sampling, one with the screen diffusion battery and the second as the reference sample, so that the fractional free radon daughters could be calculated. The radon daughters are collected on a membrane filter (filter diameter 25 mm, pore diameter 1.2 ym) and the decays of Po-218 and Po-214 are counted by means of alpha spectrometry with a surface barrier detector (area 300 mn ). 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

The prerequisites of the evaluation of data characteristic of intracrystalline processes in the case of zeolite sorbents are discussed, along with the conditions under which diffusion can be compared to self-diffusion. Selected results of investigations carried out in the author s laboratory are given in order to demonstrate the consistency of sorption kinetic data with intracrystalline mobility data of single components on molecular sieves (HS). Various types of surface barrier which may influence the uptake rate are also described. 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

Pharmaceutical scientists assess and express drug permeation across membrane barriers in terms of flux. Flux measures the molar unit of a drug that permeates a resistant barrier (e.g., skin or gastrointestinal epithelial cells) per unit time and surface area (Box 13.1). Permeation enhancers, such as alcohols and surfactants, increase flux by modulating resistance factors that counteract drug diffusion across barriers at the site of administration. 

The results in sections 2 and 3 describe the adsorption isotherms and diffusivities of Xe in A1P04-31 based on atomistic descriptions of the adsorbates and pores. The final step in our modeling effort is to combine these results with the macroscopic formulation of the steady state flux through an A1P04-31 crystal, Eq. (1). We make the standard assumption that the pore concentrations at the crystal s boundaries are in equilibrium with the bulk gas phase [2-4]. This assumption cannot be exactly correct when there is a net flux through the membrane [18], but no accurate models exist for the barriers to mass transfer at the crystal boundaries. We are currently developing techniques to account for these so-called surface barriers using atomistic simulations. 

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... 

From Table 2.11 and the discussion in Sect. 2.6, it is apparent that only moisture impenetrable materials are suitable for barrier dressings. In other words, nothing, except, water vapor, may be transmitted through the barrier dressing. Nutrients, it will be shown below (see Fig. 2.59), are included in this theory because they diffuse the barrier to nourish the bacteria (aerobic in this study) on the surface and colonize. As observed from these experiments, advanced bacterial growth is eventually continuous through the thicknesses of barrier and agar. 

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]. 

Extension of the equilibrium model to column or field conditions requires coupling the ion-exchange equations with the transport equations for the 5 aqueous species (Eq. 1). To accomplish this coupling, we have adopted the split-operator approach (e.g., Miller and Rabideau, 1993), which provides considerable flexibility in adjusting the sorption submodel. In addition to the above conceptual model, we are pursuing more complex formulations that couple cation exchange with pore diffusion, surface diffusion, or combined pore/surface diffusion (e.g., Robinson et al., 1994 DePaoli and Perona, 1996 Ma et al., 1996). However, the currently available data are inadequate to parameterize such models, and the need for a kinetic formulation for the low-flow conditions expected for sorbing barriers has not been established. These issues will be addressed in a future publication. 

With the development of the fast tracer desorption NMR method a more detailed investigation of these systems became possible. A study of diffusion of C2H6 in 5A by this method showed no significant surface barrier, even when the sieve was dehydrated at 600°C under conditions similar to those used commercially(28,29). 

This case study clearly illustrates the usefulness of the ZLD-TEOM technique in determining intracrystalline diffusivities in zeolites, provided that effects of other transport resistances such as the surface barrier are eliminated by varying the crystal size of the zeolites. The measured steady-state diffusivity can be directly used for predicting effects of diffusion in reactions catalyzed by zeolites. More important, the TEOM makes it possible to distinguish the deactivation caused by blockage of the active sites and by increased diffusion resistance caused by blockage of cavities or channels by coke. 

If the calculated value of is equal to the measured intracrystalline lifetime, Tinira, the rate of molecular exchange between different crystals is controlled by the intracrystalline self-diffusion as the rate-limiting process. Any increase of Timn, in comparison with Tf,j L indicates the existence of transport resistances different from intracrystalline mass transport. Under the conditions of TD NMR one has A r. > Antra, thus these resistances can only be brought about by sur ce barriers. The ratio Timra/Tfn L represents, therefore, a direct measure of the influence of surface barriers on molecular transport. 

Comparison of (effective) self-diffusion coefficients. To give a clear idea of the adsorption/desorption retardation due to surface barriers, another means to achieve data evaluation from TD NMR experiments is the calculation of an effective self-diffusion coefficient, Detr- From the fractions xit) of those molecules that have left the crystals during different observa-... 

Molecular mean lifetime in a crystal calculated under the assumption that adsorption/desorption is diffusion limited (absence of surface barriers) T-diff imra Through Di , and the crystal radius R, by Eq. (10) 0.2 ms... 

From the NMR tracer desorption and self-diffusion data (second and third lines of Table I), one obtains the relation Timm > TmlL. In the example given, intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and high-resolution electron microscopy studies 54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. 

Zelsmann and co-workers [88] have reported tracer diffusion coefficients for water in Nafion membranes exposed to water vapor of controlled activity. These were determined by various techniques, including isotopic exchange across the membrane. They reported apparent self-diffiision coefficients of water much lower than those determined by Zawodzinski et al. [64], with a weaker dependence on water content, varying from 0.5 x 10 cm to 3 x 10 cm /s as the relative humidity is varied from 20 to 100%. It is likely that a different measurement method generates these large differences. In the experiments of Zelsmaim et al., water must permeate into and through the membrane from vapor phase on one side to vapor phase on the other. Since the membrane surface in contact with water vapor is extremely hydrophobic (see Table 7), there is apparently a surface barrier to water uptake from the vapor which dominates the overall rate of water transport in this type of experiment. 

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. 

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