Diffusion in zeolite crystals

The effect of temperature on diffusivities in zeolite crystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

Table 3 Measurements of diffusion in zeolite crystals historical development...

For sufficiently small particles 0 0 and 1, so the measured rate constant approaches the intrinsic rate constant (k). By making replicate measurements under similar conditions, with different particle size fractions it is possible to determine both the intrinsic rate constant and the effective interparticle diffusivity. Haag [67] suggested that this approach could be used to determine intracrystalline diffusivities in zeolite crystals. A more complete experimental study in which the diffusivity of 2,2-dimethyl butane in HZSM-5 was determined both chromatographically and from measurements of the cracking rate under diffusion-limited conditions was reported by Post et al. [68] - see Fig. 11. This approach has the advantage that it makes steady-state rather than transient measurements, but it is limited to sorbates for which a suitable catalytic reaction occurs. 

The experimental methods for measurement of transport and self-diffusion in zeolite crystals (and in other microporous materials) are reviewed. Large discrepancies between distent techniques are commonly observed and appear to be related to the scale of the measurements, suggesting that structural defects may be more important than is generally believed. 

The same method is also applicable, in principle, to the measurement of micropore diffusivities in zeolite crystals but, except when micropore diffusion... 

Ruthven, D.M., and Stapleton, P., Measurement of liquid phase counter-diffusion in zeolite crystals by the ZLC method, Chem. Eng, Sci., 48(1), 89-98 (1993). 

The preceding sections provide selected examples showing how sorption and diffusion in zeolite crystals can be exploited to yield technologically useful processes. It is therefore appropriate to conclude this review with a short discussion of the remarkable progress that has been achieved in recent experimental studies of diffusion in zeolite crystals. 

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. 

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. 

Single Crystals. Naturally-occurring zeolites are sometimes found as large single crystals. Tiselius (34, 35) used this feature to study diffusion in zeolites. Diffusion of water in heulandite crystals was followed by an... 

In view of the calculated values of < )c and ( )ni (Table 2) the limitation to internal oxygen diffusion under the experimental conditions is even lower in the zeolite erystal than in the catalyst particle. The Thiele modulus in zeolite crystals for a severe deactivation state corresponding to activity = 0.20 [7] is < )c = 3.09 10 3 (Sample 5), for an initial coke content of 1.9 wt% (approximately 40 wt% of the coke content needed for blockage of the internal zeolite channels). This low value of Thiele modulus is evidence that oxygen-coke contact is not limited by internal diffusion in the deactivated eatalyst. 

Because of the rigid crystal structure and small window size, ionic diffusion in zeolites is slow and the activation energy is high (Barrer, 1980). Except on samples of very fine particle size, the exchange rate is controlled by intracrystalline rather than liquid-phase mass transfer. 

A regular pore structure is found in crystalline zeolites or molecular sieves but when these materials are used as catalysts, tiny zeolite crystals (1-2 fj,m) are combined with a binder to make practical-size pellets (1-5 mm). Spaces between the cemented crystals are macropores of irregular shape and size, and diffusion in these macropores has to be considered as well as diffusion in the micropores of the zeolite crystals. The cylindrical capillary model is used to describe diffusion in zeolite catalyst and other catalysts and porous solids because of its simplicity and because most of the literature values for average pore size are based on this model. However, the... 

For pores only slightly larger than the size of the molecules, the diffu-sivity is much less than that predicted by Eq. (4.7). For example, measured diffusion coefficients of -alkanes in zeolite crystals (molecular sieves) range from 10 to 10 cm /sec, compared to about 10 cm /sec from Eq. 

Ammonia, which possesses a large dipole moment, has been used extensively as a probe molecule for the characterisation of both Lewis and Bronsted acidic sites. Figure 22 shows the significant difference in the FR data between ammonia in zeohte crystals and in pellets. The FR spectra of ammonia in zeolite crystals demonstrated that the rate of the ammonia adsorption on different acidic sites in the crystals controls the overall dynamics of the processes occurring in the systems, hi the case of pellets, the rate-controlhng step was found to be macropore diffusion with (Fig. 22a,2,b,2) or without (Fig. 22c,2) surface resistances [77]. 

Thus, it appears from the evidence cited that transport by diffusion in the liquid layer is not the rate-limiting step in zeolite crystal growth, but that the incorporation of solute by surface integration kinetics may well be. Data from [22] suggests that a first order surface reaction is the rate limiting step for silicalite crystal growth, under the conditions studied. 

Despite the development of microscale modeling for reaction—diffusion in zeolite, the complex of MTO reaction mechanism impedes the application of microscale modeling to MTO process. Up to now, the reliable reaction kinetics based on element reactions in MTO process is still under development (van Speybroeck et al., 2014). However, a reduced or simplified microscale model could be applied. Basically, the diffusion effect is negligible if the crystal radius is small enough. Then mass equation, i.e., Eq. (1), could be simplified by neglecting the species ffux term. In this case, MTO processes over ZSM-5 and SAPO-34 catalyst could be simulated by use of the single-event kinetics by Alwahabi and Froment (2004a) as an input. 

Molecular dynamics simulation is perhaps the most powerful computational technique available for obtaining information on time dependent properties of molecular or atomic motion in zeolite crystals. It is used to obtain thermodynamic quantities and detailed dynamical information on sorption and diffusion processes in zeolite systems. For instance, the extent to which intramolecular vibration and framework motion assist sorption and diffusion of molecules can be simulated. The major limitation is its inability to model diffusion of larger sorbed molecules and electronic polarisability due to the huge amount of computer time and memory requirements. However, with the improvement in supercomputers and improved computing facilities, the full application of M.D. simulation to zeolite studies is becoming feasible. 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

Krishna (2000), starting from the fundamental concepts of Maxwell J. C. and Stefan X, describes the conhguration diffusion, also called surface diffusion, within zeolite crystals by means of the following set of equations, namely the generalized MS approach (Kapteijn et al, 2000 Krishna, 2000). Nevertheless, this set of equations can also be used to describe diffusion in other nanostructured materials such as carbon nanotubes ... 

---