Intracrystalline zeolitic diffusion

The third step, migration inside the micropore, is also denoted as intracrystalline zeolite diffusion or configurational diffusion. 

It should be mentioned that—if zeolites are technically applied as formed pellets—transport limitation may be due to both intracrystalline zeolitic diffusion and long-range diffusion as just considered. Denoting the mean radii of the crystallites and of the pellets by rc and rp, respectively, the respec-... 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

In general, for zeolitic self-diffusion at sufficiently high temperatures, the mean molecular displacements outside the crystal are much larger than those inside the zeolites that is to say, long-range self-diffusion, Di.r., is much faster than intracrystalline self-diffusion, Dintra- For observation times comparable with the mean lifetimes of the adsorbed molecules in the individual crystallites, the spin-echo attenuation can be approximated by the superposition of two exponentials of the type of Eq. (6)... 

As Fig. 25 shows, the intracrystalline self-diffusion coefficient of methane in ZSM-5 is between coefficients in zeolites NaCaA and NaX (5,71,114,115,). This order can be interpreted in terms of the minimum apertures of the zeolite channels, which are approximately 0.45, 0.55, and 0.75 nm for 5A, ZSM-5, and X-type zeolites. Due to the hydrophobic nature of ZSM-5, the mobility of water in ZSM-5 considerably exceeds the mobility in zeolites NaA and NaX. A change in the Si02/Al203 ratio of ZSM-5 does not alter the self-diffusion coefficient of methane. On the contrary, for water in ZSM-5 an increase in the self-diffusion coefficients with decreasing A1 concentrations in the framework is indicated. 

A reduction of the intracrystalline self-diffusion coefficient, Dintra, of a probe molecule (e.g., methane) as measured by PFG NMR has to be regarded as proof of the existence of coke, modifiers, etc. in the volume phase of the zeolite crystal. 

There are several models to describe intracrystalline diffusion (step 3) in microporous media. Diffusion in zeolites is extensively described in Ref. 30. For the modeling of permeation through zeolitic membranes, such a model should take the concentration dependence of zeolitic diffusion into account. Moreover, it should be easy applicable to multicomponent systems. In Section III.C, several models will be discussed. 

KaX than in smaii-port zeolites such as NaCaA. For hydrocarbons in HaX it has been found that the coefficients of intracrystalline self-diffusion decrease with increasing concentration (concentration dependences of type I and II (6).i. By contrast, for not toe high gas phase concentrations (i.e., as long as molecular transfer in the intercrystalline space proceeds by Knudsen diffusion)... 

Table I. Comparison of the Intracrystalline Mean Life Times t and the Quantities linu.0 1, calculated on the Basis of the Coefficients of Intracrystalline Self-Diffusion for Aromatic Compounds in Zeolite NaX...

A plot of the relative intensity of the broad constituent versus the observation time (i.e. the separation between the two field gradient pulses) contains information which is analogous to that of a tracer exchange experiment between a particular crystallite containing e.g. labelled molecules and the unlabelled surroundings. Therefore, this way of analysis of PFG NMR data of zeolitic diffusion has been termed the NMR tracer desorption technique [60]. The first statistical moment ( time constant ) of the NMR tracer desorption curve represents the intracrystalline mean lifetime Tintra of the molecules under study. 

Deviations from normal diffusion, i.e. from molecular propagation within a quasi-homogeneous, essentially infinitely extended medium, may be taken into account by introducing an effective diffusivity Dgff. It is defined in the same way as the self-diffusivity, i.e. via Eqs. 6 and 7, however, without the requirement of the validity of Pick s laws 1 and 2. Therefore, Dgff may become a function of the (observation) time. In the considered case of zeolitic diffusion and for intracrystalline diffusion paths being sufficiently small in comparison with the crystallite radii, the effective diffusivity may be shown to be represented by a power series [106-108], leading to... 

Fig. 16 Coefficient of intracrystalline self-diffusion of methane in zeolite (o) Na75,Ca-X, >) Na30,Ca-X, and ( ) Na-X determined by PFG NMR. The numbers inserted in the symbols indicate the concentration in molecules per supercage. From [152] with permission...

Fig. 18 Apparent coefficients of intracrystalline self-diffusion of n-hexane as observed by time- and space-resolved PFG NMR in a bed of zeolite Na-X with restricted ( ) and unrestricted ( ) sorbate supply in dependence on the sorbate concentration. The real diffusivities open symbols) were calculated from these values by using the correspondence presented by Fig. 3. The full line with the indicated error bars represents the range of intracrystalline diffusivities as observed in previous PFG NMR studies with closed sample tubes. From [163] with permission...

Studying molecular diffusion in zeolite crystallites is complicated by the small size of the objects of investigation. Inevitable deviations of the real structure of a sample from the ideal one lead to an additional complication of the situation. It is not unexpected, therefore, that in spite of considerable progress in the experimental techniques, there is still some controversy in the imder-standing of intracrystalline zeohtic diffusion (cf. the preceding chapters of this volume). 

FIGURE 5.17. Results of tracer desorp-lion study of diffusion of CjH in 5A zeolite crystals showing effect of crystal size and dehydration temperature. Filled symbols represent NMR (PFG) intracrystalline self-diffusivities. Open symbols represent tracer desorption diffusivities. Earlier self-diffusivity data for larger crystals (—) and uptake rate data > [/)(,... 

Pfeifer. H., et al.. Concentration dependence of intracrystalline self-diffusion in zeolites, Adsorpt. Sci. Technol.. 2(4), 229-240(1985). 

Intracrystalline self-diffusion of methane adsorbed in NaA zeolite was deduced from proton spin-spin relaxation measurements. It was found that, for filling factors of up to 3 molecules per cage, the data were described by ... 

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],... 

Fig. 3.1.6 Temperature dependence of the intraparticle diffusivity of n-octane in an FCC catalyst and the intracrystalline diffusivity of n-octane in large crystals of USY zeolite measured by PFG NMR. The concentration of n-octane in the samples was in all cases 0.62 mmol g 1. Lines show the results of the extrapolation of the intracrystalline diffusivity and of the intraparticle diffusivity of n-octane to higher temperatures, including in particular a temperature of 800 K, typical of FCC catalysis.

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

The development of composite micro/mesoporous materials opens new perspectives for the improvement of zeolytic catalysts. These materials combine the advantages of both zeolites and mesoporous molecular sieves, in particular, strong acidity, high thermal and hydrothermal stability and improved diffusivity of bulky molecules due to reduction of the intracrystalline diffusion path length, resulting from creation of secondary mesoporous structure. It can be expected that the creation of secondary mesoporous structure in zeolitic crystals, on the one hand, will result in the improvement of the effectiveness factor in hydroisomerization process and, on the other hand, will lead to the decrease of the residence time of products and minimization of secondary reactions, such as cracking. This will result in an increase of both the conversion and the selectivity to isomerization products. 

F or nonconstant diffusivity, a numerical solution of the conservation equations is generally required. In molecular sieve zeolites, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

The best correlation of the observed isomerization selectivities was found in terms of the diameter of the intracrystalline cavity, determined from the known crystal structure (9) of these zeolites, as shown in Figure 2. While faujasite, mordenite and ZSM-4 all have 12-membered ring ports and hence should be similar in their diffusion properties, they differ considerably in the size of their largest intracrystalline cavity both mordenite and ZSM-4 have essentially straight channels, whereas faujasite has a large cavity at the intersection of the three-dimensional channel system. 

Understanding the adsorption, diffusivities and transport limitations of hydrocarbons inside zeolites is important for tailoring zeolites for desired applications. Knowledge about diffusion coefficients of hydrocarbons inside the micropores of zeolites is important in discriminating whether the transport process is micropore or macropore controlled. For example, if the diffusion rate is slow inside zeolite micropores, one can modify the post-synthesis treatment of zeolites such as calcination, steaming or acid leaching to create mesopores to enhance intracrystalline diffusion rates [223]. The connectivity of micro- and mesopores then becomes an... 

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