Uptake intracrystalline diffusion

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],... 

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]. 

Alternatively one can in principle derive both micropore and macropore diffusivities from measurements of the transient uptake rate for a particle (or assemblage of crystals) subjected to a step change in ambient sorbate pressure or concentration. The main problem with this approach is that the overall uptake rate may be controlled by several different processes, including both heat and extraparticle mass transfer as well as intraparticle or intracrystalline diffusion. The intrusion of such rate processes is not always obvious from a cursory examination of the experimental data, and the literature of the subject is replete with incorrect diffusivities (usually erroneously low values) obtained as a result of intrusion of such extraneous effects. Nevertheless, provided that intraparticle diffusion is sufficiently slow, the method offers a useful practical alternative to the Wicke-Kallen bach method. 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

This methods depends on the implicit assumption that the uptake rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation if diffusion is sufficiently slow or if the zeolite crystals are sufficiently large but the dominance of intracrystalline diffusional resistance should not be assumed without experimental verification. In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7). 

Adsorption investigations (determination of equilibrium data, uptake rates, adsorption kinetics, and intracrystalline diffusion). 

The experimental method used in TEOM for diffusion measurements in zeolites is similar to the uptake and chromatographic methods (i.e., a step change or a pulse injection in the feed is made and the response curve is recorded). It is recommended to operate with dilute systems and low zeolite loadings. For an isothermal system when the uptake rate is influenced by intracrystalline diffusion, with only a small concentration gradient in the adsorbed phase (constant diffusivity), solutions of the transient diffusion equation for various geometries have been given (ii). Adsorption and diffusion of o-xylene, / -xylene, and toluene in HZSM-5 were found to be described well by a one-dimensional model for diffusion in a slab geometry, represented by Eq. (7) (72) ... 

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. 

Aromatic Compounds in NaX. Molecular transport of aromatic compounds in zeolite NaX has been studied by both nmr and uptake measurements. On the basis of Equation 4,and if surface barriers are absent, both methods should lead to comparable results. Though uptake measurements by the variable - pressure, constant - volume method by Biilow and coworkers (16,17) apparently are in satisfactory agreement with the nmr data (18), extensive uptake measurements including chromatographic methods are continuously found to yield diffusivities of about two orders of magnitude below these values (19,20). In principle, this discrepancy might be explained by the existence of surface barriers, which remain invisible for nmr studies of intracrystalline diffusion, but which may control the uptake rate. 

The intracrystalline diffusivities of the hydrocarbons were measured under the conditions of the temperature range of 373-773 K and the pressure range of 0-1.33 kPa by the constant volume method [9]. The apparatus and the procedure are the same as employed by Hashimoto et al. [4,5]. Change in the total pressure caused by adsorption was recorded by use of a piezometric sensor with a transducer, the response of which is first enough to measure accurately the pressure change. To eliminate the influence of several factors (such as mass conductivity between the sorbate and the pressure sensor) on the pressure change, the blank tests were conducted without zeolites. Comparing these data obtained with those with zeolites, an uptake curve of the amount adsorbed was obtained. 

Measurements performed in a tapered element oscillating microbalance (TEOM) reveal that diffusivities can be derived from uptake data monitored under full reaction conditions. In this way the effect of acid leaching on the diffusional behaviour of w-hexane in Pt/H-Mordenite is investigated. It is shown that acid leaching largely enhances the -hexane uptake rate, but does not result in a net increase in the intracrystalline steady state diffusivity. It is concluded that the accelerated uptake after acid leaching merely arises from the shorter intracrystalline diffusion path resulting from the mesoporous structure. 

The apparent simplicity of this approach is, however, deceptive. For measurement of intracrystalline diffusion the method works well when diffusion is relatively slow (large crystals and/or low diffusivity), but when sorption rates are rapid the uptake rate may be controlled by extracrystalline diffusion (through the interstices of the adsorbent bed) and/or by heat transfer. The intrusion of such effects is not always obvious from the shape of the uptake curve, but it may generally be detected by changing the sample quantity and/or the sample configuration. It is in principle possible to allow for such effects in the mathematical model used to interpret the uptake curves (Fig. 2), and indeed the modeling of nonisothermal systems has been studied in considerable detail [8-12]. However, any such intrusion will obviously diminish the accuracy and confidence with which the intracrystalline diffusivities can be determined. 

The piezometric method involves following the pressure response in a dosing cell connected to an uptake cell containing a sample of the adsorbent. According to the results reported in the hterature, the piezometric method can be used to accurately measure intracrystalline diffusivities for fast diffusing and strongly adsorbed species such as benzene on NaX [15,16]. Furthermore, it is also claimed to provide the required accuracy needed to study combined intracrystalline processes such as diffusion and first-order reaction [17]. 

With the meaningful title Sorption kinetics and intracrystalline diffusion of methanol in ferrierite an example of disguised kinetics , [71] exemplifies the pitfalls which, in cases like the given one, will necessarily lead the researcher to completely wrong conclusions if he is only able to base his reasoning on the overall uptake and release rather than on the processes of intracrystalline mass transfer. 

Fig. 56 Correlation between the actual boundary concentration (Csurf) and the relative uptake (m) at the corresponding instant of time. Three different cases are shown the mass transport is essentially limited by intracrystalline diffusion (la/D = 100), by surface barriers la/D = 0.01), and both by intracrystalline diffusion and surface resistance la/D = 1)...

Results of a series of uptake rate measurements performed with different crystal size fractions are summarized in Figures 5.7-5.9. For butane in both 27.5 and 55 jam 5A crystals and for COj in 21.5 and 34 pm 4A crystals the uptake rate is relatively slow and is evidently controlled by intracrystalline diffusion since the time constants show the expected dependence on the... 

Despite the large difference in the apparent diffusivities derived from uptake rate measurements, measurements of the intracrystalline self-diffusivity (for C2H6-5A) by the NMR (PFG) method show little difference between the large laboratory synthesized crystals and the small Linde crystals, thus favoring the surface barrier hypothesis. The increase in activation energy, which is observed for this system on severe hydrothermal pretreatment of the smaller crystals, is also consistent with a change from intracrystalline diffusion to surface barrier control. Detailed sorption rate studies with the system n-butane-5A, however, support the opposite conclusion that the differences in... 

In the preceding analysis we considered the diffusivity as constant but if the uptake curve is measured over a large concentration step this may be a poor approximation. In many zeolitic systems the concentration dependence of the intracrystalline diffusivity is given approximately by Eq. (5.6), with Dq independent of concentration. If the adsorption equilibrium isotherm obeys the Langmuir equation this gives as the expression for the concentration dependence of the diffusivity... 

A modified Carbeny mixer was used by Ma and Lee to measure uptake rates for C4 hydrocarbons in 13X molecular sieve pellets using a helium carrier. Adsorption rates were slow and they concluded that the ratecontrolling mass transfer process was intracrystalline diffusion with a diffusiv-ity of order 10 cm s at 35°C. An independent study by Doelle and Riekert using large crystals of 13X zeolite ( 100 ftm) showed that the diffusivity of butane is, under comparable conditions, very much higher ( 10" -10 cm s ). The discrepancy appears to have arisen from the intrusion of external mass transfer resistance in the Carberry mixer. 

The prerequisites of the evaluation of data characteristic of intracrystalline processes in the case of zeolite sorbents are discussed, along with the conditions under which diffusion can be compared to self-diffusion. Selected results of investigations carried out in the author s laboratory are given in order to demonstrate the consistency of sorption kinetic data with intracrystalline mobility data of single components on molecular sieves (HS). Various types of surface barrier which may influence the uptake rate are also described. 

The validity of eqn. (3) for determining the intracrystalline self-diffusion coefficients from uptake data has been shown for the sorption of benzene by... 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

If the values of the effective self-diffusion coefficients, D rf [calculated from the complete xit) curves in TD NMR experiments, assuming diffusion-limited uptake (52)] are below the corresponding intracrystalline data, Dintra (measured directly by PFG NMR), the existence of additional mass transfer resistances in a layer near or on the outer surface of the zeolite crystals is indicated. 

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