Intracrystalline diffusivity

Also shown are the corresponding curves calculated for the same system assuming a diffusion model in place of the linear rate expression. For intracrystalline diffusion k = 15Dq/v, whereas for macropore diffusion k = 15e /R ) Cq/q ), in accordance with the Glueckauf approximation (21). 

Fig. 15. Theoretical breakthrough curves for a nonlinear (Langmuir) system showing the comparison between the linear driving force (—), pore diffusion (--------------------), and intracrystalline diffusion (-) models based on the Glueckauf approximation (eqs. 40—45). From Ref. 7.

There are two types of stmctures one provides an internal pore system comprising interconnected cage-like voids the second provides a system of uniform channels which, in some instances, are one-dimensional and in others intersect with similar channels to produce two- or three-dimensional channel systems. The preferred type has two- or three-dimensional channel systems to provide rapid intracrystalline diffusion in adsorption and catalytic apphcations. 

For noncoustaut diffusivity, a numerical solution of the conseiwa-tion equations is generally required. In molecular sieve zeohtes, 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 ... 

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.

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. 

For intracrystalline diffusion paths sufficiently small in comparison with the crystallite radii, the effective diffusivity as defined by Eq. (3.1.6) maybe expanded in a power series [9, 63, 64], leading to... 

Fig. 3.1.11 Relative effective intracrystalline diffusivities D(t)/D0 as function of JDot for n-hexane under single-component adsorption (circles) and for n-hexane (triangles) and tetrafluoromethane (rectangles) under two-...

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. 

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... 

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. 

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]. 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

A good example for reactant shape selectivity includes the use of catalysts with ERI framework type for selective cracking of linear alkanes, while excluding branched alkanes with relatively large kinetic diameters from the active sites within the narrow 8-MR zeolite channels [61, 62]. Here molecular sieving occurs both because of the low Henry coefficient for branched alkanes and because of the intracrystalline diffusion limitations that develop from slow diffusivities for branched alkane feed molecules. 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

Jobic, H. and Methivier, A. (2005) Intracrystalline diffusion in zeolites studied by neutron scattering techniques. Oil Gas Sci. Technol., 60 (5) 815-830. 

Webb, E.B., III and Grest, G. (1998) Influence of intracrystalline diffusion in shape selective catalytic test reactions. Catal. Lett., 56, 95-104. 

Figure 13.14 was published as Figure 11 from the article Intracrystalline Diffusion in Zeolites Studied by Neutron Scattering Techniques by H. Jobic and A. Methivier, Oil and Gas Science and Technology - Rev. IFP, Vol. 50 (2005),... 

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 ... 

For the system n-decane / NaCaA type zeolite, the synergistic effect of both sample pretreatment and presorption, on the sorption uptake is shown in Figure 6. The region of intracrystalline diffusion was estimated by sorption uptake measurements on crystals with different sizes [41]. 

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