Intra-crystalline diffusion

Within micropores, surface forces are dominant and an adsorbed molecule never escapes completely from the force field of the surface. Diffusion within this regime has been called configurational diffusion, intra-crystalline diffusion, micropore diffusion, or simply surface diffusion. The Maxwell-Stefan formulation, which is generally accepted for diffusion in the bulk fluid phase, can be extended to describe surface diffusion by considering the vacant sites to be a (n + l)-th pseudospecies on the surface [38,47,49-52]. Using the Maxwell-Stefan diffusion formulation, the following relationship was obtained for surface diffusion. 

Intra-crystalline diffusion is an activated process and its temperature dependence can generally be correlated by an equations such as Dc = Dcoexp[- /(RT)]... 

When type X is utQized, in any of its ion exchange forms, for dehydration or possibly for sweetening (sulfur removal), there is little likelihood that the intracrystalline diffusion will be the dominant resistance to mass transfer. Large aromatic sulfurs would of course be an exception. When type X is used for adsorption of hydrocarbons or aromatics then it is possible that the micro-pore diffusion might dominate. When type A is used there is always a distinct possibility that intra-crystalline diffusion will be slow and may dominate the mass transfer, even for relatively small molecules. This is especially true when the chosen structure is a K A or type 3A. Selection of other small pore structures, for separations or purification applications can also create situations where the dominant resistance is found in the crystaUites. 

Copper ions exchanged microporous molecular sieves, in particular Cu-ZSM-5, are active catalysts for the selective catalytic reduction of NO and N2O with hydrocarbons in the presence of O2 (HC-SCR). It has been reported that the catalytic activity may be controlled by intra-crystalline diffiisivity and by geometry-limited diffusion depending on the hydrocarbon molecular size and the zeolite pore size [1]. Therefore, it is of interest to prepare Cu-Al-MCM-41 mesoporous molecular sieves and to compare their activity with that of Cu-ZSM-5. 

Equation (9.48c) shows that at high values of 0 (low temperature) the apparent activation energy of the permeation equals that of the diffusivity provided that intra-crystalline diffusion is still the controlling mechanism. 

The activation energy for intra-crystalline diffusion for n-butane is 30 kj mol" [72,74,89], For the isosteric heat of adsorption values of =38 kJ mol" are reported by Kapteyn and by Vroon, which value is considerably lower than other values (=50 kJ mol ) reported in literature. For CH4 a good agreement between Ccdculated and measured fluxes is obtained, for n-butane the agreement is reasonable to bad at low pressure and good at higher pressure. A difficult problem is the value of the saturation concentration. In many cases no reliable experimental data are known and theoretical estimates have to be made usually imder the questionable assumption that is independent of temperature. For n-butane the theoretical sorption capacity of MFI/silicalite equals about 2.1x10 mol g" (equivalent to 12 molecules per unit cell). 

For a direct check of the existence or non-existence of surface barriers we have applied the nmr tracer desorption technique. For a few selected systems, Table I gives a comparison between the mtracrvstaiiine mean life times a,and the quantities T ,n., l J 1 calculated from the coefficients oi intra-crystalline diffusion on the basis of Equation 11. The order of - magnitude agreement between these quantities indicates that under the given conditions in fact a substantial influence of surface barriers on molecular transport may be excluded,... 

Comparison with other molecular sieves (Fig. 11) shows that the yields obtained with FER are very high indeed. As elaborated upon elsewhere [6-8], we have proposed that the isomerisation involves a bi-molecular mechanism in which e.g. di-methylhexene isomers crack selectively to isobutene and n-butene (Fig. 12). The mono-molecular mechanism requires the energetically unfavourable primary carbenium ions. Molecular modelling [7] has provided support for this mechanism in that the branched octenes can be formed in the intra-crystalline voids of FER but their diffusion out of the pores is hindered. 

To render the equation amenable to analytical analysis, we have assumed constant intra-crystalline diffusivity in the above equation. 

Steps 1 and 5 depend on the following factors permeation conditions (temperature and partial pressures), the nature of the chemical species and the type of crystalline material. Steps 1 and 5 are, generally, assumed to be fast processes. Steps 2, 3 and 4 are usually activated processes (Barrer, 1990). Intra-crystalline zeolite diffusion is described as configurational diffusion. 

Although the electrical conductivity is enhanced by the relatively high mobility associated with intra-chain transport, one must have the possibility of inter-chain charge transfer to avoid the localization inherent to systems with a one-dimensional electronic structure [237,238]. The electrical conductivity becomes three-dimensional (and thereby truly metallic) only if there is high probability that an electron will have diffused to a neighboring chain prior to traveling between defects on a single chain. For well-ordered crystalline material in which the chains have precise phase order, the interchain diffusion is a... 

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