Intercrystalline diffusivities

When the oxide is formed by anodizing in acid solutions and the sample is then left to rest at the OCP, some dissolution can occur. This process has been studied by a numbers of authors,70-75 especially in relation to porous oxides [cf. Section 111(4)]. It was found that pore walls are attacked, so that they are widened and tapered to a trumpet-like shape.70 71 Finally, the pore skeleton collapses and dissolves, at the outer oxide region. The outer regions of the oxide body dissolve at higher rates than the inner ones.9,19 The same is true for dissolution of other anodic oxides of valve metals.76 This thickness dependence is interpreted in terms of a depth-dependent vacancy concentration in the oxide75 or by acid permeation through cell walls by intercrystalline diffusion, disaggregating the microcrystallites of y-alumina.4... 

The intercrystalline diffusion resistance makes a major contribution to the total resistance at low temperatures. Isosteric heat of adsorption increases with the number of carbons from 4-4 kcal/molefor CHA to 10.9 kcal/molcfor n-CJho. 

A method is presented for obtaining the diffusion coefficients of Ci to C4 hydrocarbons on H and Na mordenite by analysis of their chromatographic curves. It is shown that in such a transient device the role of the intercrystalline diffusion may be important for the estimation of the total mass-transfer resistance. The diffusion coefficients decrease with increase in the number of carbon atoms. They are about one order of magnitude smaller on mordenite in the Na form than in the H form. The energies of activation are higher for intracrystalline diffusion than for intercrystalline diffusion. The resistance from intercrystalline diffusion makes an important contribution to the total mass-transfer resistance at low temperature. 

Adsorption and diffusion of linear and branched Ce alkanes in silicalite-1 were investigated by Zhu et al. (34,35). They also developed a mathematical model taking into account the thermodynamical factor for intercrystalline diffusivities, enabling the determination of intracrystalline diffusivity from the uptake curve operated outside the linear adsorption range, van Donk et al. (36) also made transient uptake measurements to investigate the diffusivity of -hexane in Pt/H-mordenite. 

Almost identical uptake and steady-state diffusivities were found on the 2.5 and 25 pm crystals, indicating that the resistance to intracrystalline diffusion is dominating in the SAPO-34 s crystals with sizes larger than 2.5 pm. Therefore, the proper uptake and steady-state diffusivity of intercrystalline diffusion can be measured with such large crystals. The steady-state diffusivity of methanol is about 1.65 X 10 m /s, as shown in Fig. 14. 

Recently Ryoo et al. [13] have suggested a new method to hinder the xenon intercrystalline diffusion at RT by putting liquid OMCTS in the external void volume between the NaY zeolite crystallite particles. In this work, we extended this method to other zeolites in order to extract new informations on the internal microporosity. 

Galwey and Laverty [13] concluded, from complementary kinetic investigations, that dehydration of Ca(OH)2 was satisfactorily represented by the first-order equation. The overall rate of H2O release was sensitive to the locally prevailing water vapour pressure and its distribution within the reactant mass. Kinetic characteristics were strongly influenced by the rates of intracrystalline and intercrystalline diffusive escape of product water which strongly depended on reactant compaction/dispersal within the heated zone. Measured values of and for Ca(OH)2 dehydration could not be identified with a single reaction step because... 

When the zeolite is mixed with silica-alumina (60% weight of zeolite), the benzene concentration profiles present an adsorption front which lasts more than 30 min. On one hand the intercrystalline diffusion rate is decreased by the presence of the silica-alumina which has a mesoporosity centered around 50 A (pore diameter) on the other hand benzene also adsorbs on the silica-alumina. This result shows the important influence on the mass transport of the binder in industrial catalysts. 

The mass transport in macropores of sorbent pellets is assumed to proceed via intercrystalline diffusion that obeys the Fick law, with q denoting micropore sorption phase concentration ... 

The set of equations (4.17) to (4.21) inclusive was solved analytically by Ruckenstein etal. (1971) who compared the mass of adsorbate adsorbed at a given time, mt, with the amount adsorbed after an infinite lapse of time, moo, (when the crystals were saturated with adsorbate). They expressed the ratio mt/mn, as a function of time t. It should be noted that, for small quantities of adsorbate introduced to the system the ad orption isotherm is linear and q = Kp. The intercrystalline diffusivity can then be regarded as independent of adsorbate concentration. The theoretical fractional approach to equilibrium was shown to be... 

Figure 4.2 Uptake curves for intercrystalline diffusion (source Garg and Ruthven 1972).

Generally, however, the aim is to avoid conditions leading to film diffusion control. This means that the focus is shifted towards transport processes that occur at the intermediate level (that is, in the mesopores and macropores within the macroparticle or pellet itself) and those which occur at the smallest dimensional level (viz., in the very micropores of the molecular sieve) [45, 89]. Within the mesopores and macropores between the primary zeolite crystallites transport will be dominated by molecular and ionic intercrystalline diffusion possibly coupled to surface diffusion processes, while, in the zeolite micropores themselves, intracrystalline diffusion occurs, also possibly coupled... 

The important property of ZSM-5 and similar zeolites is the intercrystalline catalyst sites, which allow one type of reactant molecule to diffuse, while denying diffusion to others. This property, which is based on the shape and size of the reactant molecules as well as the pore sizes of the catalyst, is called shape selectivity. Chen and Garwood document investigations regarding the various aspects of ZSM-5 shape selectivity in relation to its intercrystalline and pore structure. 

A quantitative analysis [34], based on the adsorption isotherms and the intercrystalline porosity, yielded the remarkable result that a satisfactory fit between the experimental data and the estimates of Aong-range = Pinter Anter following Eqs. (3.1.11) and (3.1.12) only lead to coinciding results for tortuosity factors a differing under the conditions of Knudsen diffusion (low temperatures) and bulk-diffusion (high temperatures) by a factor of at least 3. Similar results have recently been obtained by dynamic Monte Carlo simulations [39—41]. 

Eiler JM, Baumgartner LP, Valley JW (1992) Intercrystalline stable isotope diffusion a fast grain boundary model. Contrib Mineral Petrol 112 543-557... 

If a NS monocrystal takes up a single component from a fluid phase and Intercrystalline transport does not influence the uptake rate, one should be aware of the possibility that, besides intracrystalline diffusion, the following processes may either contribute or even govern the uptake rate ... 

---