Diffusion in type A zeolites: New insights from old data

Microporous and Mesoporous Materials 162 (2012) 69–79

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Diffusion in type A zeolites: New insights from old data Douglas M. Ruthven ⇑ Department of Chemical Engineering, University of Maine, Orono, ME 04469-5737, USA

a r t i c l e

i n f o

Article history: Received 20 September 2011 Received in revised form 8 December 2011 Accepted 10 December 2011 Available online 17 December 2011 Keywords: Diffusion Zeolite A LTA Adsorption kinetics Mass transfer

a b s t r a c t The extensive kinetic data accumulated, over many years, from a series of experimental studies of the kinetics of adsorption/desorption of a wide range of different sorbates in type A zeolites are reviewed and analyzed in an attempt to develop a coherent understanding of the behavior of these systems. Kinetic data for large laboratory synthesized crystals and small commercial crystals, measured under similar conditions, have been studied in detail. In well dehydrated crystals the sorption rates are generally controlled by intracrystalline diffusion but exposure to traces of water leads to the development of surface resistance and a pronounced reduction in the sorption rate. Zeolite samples of different origin show widely different sorption rates but the diffusional activation energies (for a given sorbate) are essentially constant. The differences between the different samples appear to be due mainly to differences in the cation distribution caused by differences in the initial dehydration procedure. The ideal cation distribution (in 5A) in which all window sites are unoccupied is realized only in very carefully dehydrated samples in which the water was removed slowly at gradually increasing temperature under a high vacuum. In the small commercial 5A crystals many of the windows are blocked, even though all the cations could theoretically be accommodated in the 6-ring sites. This is probably due to cation hydration reactions which are likely to occur when the dehydration conditions are not carefully controlled. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Zeolite A was the first zeolite to be successfully synthesized in the laboratory [1] and, even after half a century it is still one of the most widely used industrial adsorbents. The remarkable relationship between the crystal structure and the macroscopic adsorptive properties was first recognized by Breck et al. and elucidated in detail in their seminal paper [2]. The structural simplicity of the type A framework coupled with the well defined channel system make this material an obvious candidate for fundamental studies of diffusion under sterically hindered conditions. As a result, over the last 50 years, there have been numerous experimental and theoretical studies of diffusion in various different ionic forms of zeolite A. However, although some simple general principles have been demonstrated the accumulated array of experimental data presents a somewhat confusing picture. This is largely because the experimental results have for the most part been reported as separate studies focusing on particular systems or particular phenomena. A broad but selective overview of the entire data set reveals some interesting general patterns of behavior that can be understood in a straightforward way in terms of the structure, the distribution of the exchangeable cations and the effect of traces of water. On this basis the generally observed behavior as well as ⇑ Tel.: +1 207 581 2283; fax: +1 207 581 2323. E-mail address: [email protected] 1387-1811/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.micromeso.2011.12.025

the discrepancies between the results from different experimental studies can be plausibly if not definitively accounted for. Diffusion of propane and n-butane in 5A were among the first systems to be studied in detail by both macroscopic (uptake rate and chromatographic measurements) and microscopic (pulsed field gradient nuclear magnetic resonance (PFGNMR)) measurements [3]. The initial measurements showed differences of several orders of magnitude but this was based on a comparison between commercial 5A and samples of 5A crystals prepared in the laboratory and dehydrated under carefully controlled conditions. Later comparative measurements carried out with the same or similar 5A crystals showed good agreement between the microscopic and macroscopic measurements [4,5]. Detailed studies by PFGNMR and NMR tracer desorption showed that in hydrothermally treated 5A crystals the intracrystalline self-diffusivity is much larger than the diffusivity derived from the desorption rate measurements, suggesting the existence of a surface barrier [6]. The large difference between the macroscopically and microscopically measured diffusivities for the small commercial 5A zeolite crystals may therefore be explained on this basis. However, a detailed study of the sorption kinetics suggests that the actual behavior is more complex. The present paper is largely a review of experimental data that have been previously published in the open literature but some important measurements that were previously reported only in the original theses and post-doctoral reports are also included [7–13], as these data can now be understood.

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

Nomenclature a Cs D Do D1 E f  =fg0

mt/m1

specific external area of sample heat capacity (per unit crystal volume) intracrystalline diffusivity thermodynamically corrected diffusivity (see Eq. (9)) pre-exponential factor (see Eq. (10)) diffusional activation energy ratio of reduced partition function for transition state to partition function per unit volume for the gas phase (see Eq. (15)) heat transfer coefficient for sample surface rate coefficient (see Eq. (1)) lattice parameter (12.3 Å)

h k l

L p q r R Rg t T

ratio of mass adsorbed or desorbed at time t to mass adsorbed or desorbed at equilibrium parameter kR/D (see Eq. (5)) partial pressure of sorbate at equilibrium with adsorbed phase concentration q adsorbed phase concentration ratio of diffusivity for fully ‘‘open’’ and fully ‘‘closed’’ forms (see Eq. (11)) mean equivalent radius of zeolite crystal universal gas constant time temperature (K)

2. Diffusion measurements

and the long time asymptote (mt/m1 > 0.75) is given by:

The experimental techniques that have been applied to measure intracrystalline diffusion in zeolites have been reviewed in detail elsewhere [14]. The data considered here were obtained mainly from gravimetric uptake rate measurements, chromatographic measurements and zero length column (ZLC and tracer ZLC) measurements, carried out at the University of New Brunswick, and pulsed field gradient (PFGNMR) measurements of self-diffusion carried out by Professor Kärger and his students at the University of Leipzig. Details of the samples studied are summarized in Table 1.

lnð1  mt =m1 Þ ¼ lnð6=p2 Þ 

ð4Þ

R2

p Plots of fractional uptake vs. t and of ln(1  mt/m1) vs. t are therefore useful for establishing the rate controlling resistance from transient sorption curves. If the effects of both surface resistance and internal diffusion are both significant the kinetic model is obviously more complicated. Retaining the assumption of an isothermal linear system (which is generally a good approximation for a differential concentration step, provided that diffusion is not too fast) the expression for the uptake curve, for a step change in bulk concentration at t = 0, is:

3. Kinetic models [14] If the uptake rate is controlled by surface resistance, the adsorption or desorption curve (for a linear system subjected to a step change in sorbate concentration at the external surface at time zero) will show a simple exponential approach to equilibrium:

1 X mt 6L2 expðb2n Dt=R2 Þ ¼1 2 2 m1 n¼1 bn ½bn þ LðL  1Þ

ð5Þ

where L = kR/D and bn represents the roots of the equation,

mt ¼ 1  e3kt=R m1

ð1Þ

bn cot bn þ L  1 ¼ 0

1 mt 6 X 1 n2 p2 Dt=R2 ¼1 2 e m1 p 1 n2

b cot b  1 ¼ b2 =3;

ð2Þ

ð3Þ

p

b2 ¼ 3kR=D ¼ 3L

ð7Þ

Eq. (5) then reverts to the solution for surface resistance control (Eq. (1)). The curves calculated from Eqs. (5) and (6) have a characteristic shape, depending on the value of the parameter L, so, in the range where both resistances are important (10 > L > 0.1) it is possible to estimate both the parameters k and D by matching the experimental uptake curve to the dimensionless theoretical curve.

In the initial region (mt/m1 < 1/2) this reduces to:

rffiffiffiffiffiffi Dt

ð6Þ

For L?1 (large k, small Dc) bn?np and Eq. (5) reverts to Eq. (2), the solution for intraparticle diffusion control. In the other limit for L?0, b is small so we may use only the first term in the series expansion:

where k is the surface rate coefficient and R the effective radius of the crystal (approximated as a spherical particle). In contrast, for intracrystalline diffusion control under conditions of constant diffusivity (Henry’s law regime or for a small differential concentration change), the adsorption or desorption curve is given by:

mt 6 ¼ m1 R

p2 Dt

Table 1 Details of zeolite samples. Adsorbent

Crystal size (lm)

Si/Al

Cations per pseudo cell +

NaA (Yucel) CaA (Yucel 1) CaA (Yucel 2) CaA(Shdanov) Linde 5A (lot 550045) Linde 5A (lot 550043)

7.3, 34 7.3, 34 27.5, 54 24 3.6 3.9

% Na exch. +

++

Total cations (Na equiv.)

Na

Ca

1.07 1.04

11.3 11.5

11.3 0.6

– 5.46

– 95

1.07 1.01

11.1 11.8

0.43 2.5

5.35 4.66

96.3 79

Ideal structure: Si/Al = 1.0; 12Na+ equiv. cations per pseudo cell. Excess Al is probably present as amorphous Al2O3. Linde 4A crystal sizes: lot 470017 = 3.4 lm; lot 450339 = 4.1 lm; ‘4A pellet’ = 3.5 lm.

D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

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When mass transfer resistance is small (small crystals, large diffusivity and negligible surface resistance) the isothermal approximation breaks down and the sorption rate may be determined mainly by the rate of heat transfer. In the limiting case of heat transfer control the uptake curve (for a linear system) is then given by:

 0    mt b ha t ¼1 0 exp  0 Cs 1 þ b m1 1þb

ð8Þ

where:

a0 ¼

ha R2 ; Cs D

b0 ¼

 2 q DH ðC s =Rg Þ RT

Under these conditions the uptake curve contains no useful kinetic information. 4. Rate controlling resistance In the earlier studies of adsorption/desorption kinetics in zeolites it was generally assumed, without direct experimental verification, that intracrystalline diffusion is rate controlling. Detailed kinetic studies with several different sorbates in different size fractions of both 4A and 5A zeolite crystals confirm that, at least in well dehydrated crystals, intracrystalline diffusion is indeed the dominant resistance [17,18]. This conclusion is also supported by detailed analysis of the shapes of the transient adsorption/desorption curves and by partial loading ZLC experiments [19,20]. However, recent studies by interference microscopy have shown that surface resistance is quite common and is indeed rate controlling for some systems [15,16]. The existence of a substantial surface resistance to mass transfer would provide an obvious explanation of the observed discrepancy between the uptake rate and self-diffusion measurements with hydrothermally treated 5A crystals but the kinetic evidence suggests that, in freshly dehydrated samples of commercial 5A, the sorption rate is in fact controlled by intracrystalline diffusion; surface resistance develops only after the sample has been exposed to trace amounts of water vapor. Some examples showing conformity with the diffusion model for several different sorbates in freshly dehydrated Linde 5A crystals (Lot 550045) are given in Figs. 1 and 2. In Fig. 1 curves 2–4 were all obtained with the same Linde 5A (3.6 lm) adsorbent

Fig. 1. Gravimetric sorption curves for n-butane in Linde 5A crystals (lot 550045) at 323 K. Pressure step is 27–21 Torr (approximately). Theoretical lines (curves 2–4) are calculated according to Eq. (2) assuming isothermal diffusion control with the given time constants. The experimental curves (1) for a comparable sample of 3.5 lm NaX for which under similar conditions, the uptake rate is limited by heat transfer, and (5) for a sample of carefully dehydrated large (55 lm) crystals are also shown for comparison by broken lines.

Fig. 2. Desorption curves for N2 from Linde 5A zeolite crystals (lot 550045; 3.6 lm) at 250 K and 273 K. (a) Shows conformity with the diffusion model (Eq. (2)) and the effect of regeneration conditions. For runs 1 and 2 of expts. 28 and 23, respectively D  2.4  1010 and 3.2  1012 cm2 s1. (b) Shows the decline in rate and change in shape of the desorption curves in successive runs at 273 K (expt. 23). Data from Tezel [10].

sample over similar pressure steps while curve (5) is for a sample of laboratory synthesized 55 lm crystals under similar conditions. Despite the difference in the crystal sizes the rates are very similar, showing the very large difference in diffusivities between these samples. Curve 2 is for a fresh sample after the initial activation at 400 °C while curves 3 and 4 were obtained with aged samples which had been regenerated several times. In all cases the initial rate appears to be diffusion controlled but curve 2 (the fastest) shows a significant deviation from the isothermal diffusion model at high fractional uptakes. This is probably due to the intrusion of heat transfer resistance which becomes a serious issue in uptake rate measurements for fast systems [21]. An uptake curve, measured under similar conditions in the same apparatus, for n-butane in small crystals of NaX zeolite (for which the equilibrium is similar to 5A but the kinetics are much faster) is shown for comparison (curve 1). This curve shows the rapid initial uptake followed by a slow approach to equilibrium which is typical of heat transfer control (see Eq. (8)). Despite the difference in diffusivities for the fresh and aged samples the activation energies are similar. This point is discussed in more detail below. Fig. 2a shows the desorption curves for nitrogen from Linde 5A crystals for two different experiments with freshly regenerated zeolite samples. All curves conform closely to the isothermal diffusion model (Eq. (2)) but with very different time constants reflecting the different regeneration conditions. Fig. 2b shows the desorption curves for a series of steps carried out successively without regeneration of the adsorbent. The pressure was always

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

the diffusion pump was used in experiment 28, giving a much lower residual pressure. When a sample of the (7.3 lm) Yucel CaA crystals was dehydrated at 673 K but without the diffusion pump the diffusivity for n-butane was reduced by two orders of magnitude, to a level similar to that for the commercial Linde 5A. This sample was used in a series of uptake rate measurements involving controlled hydration of the sample, as described below. During this series of experiments the uptake rate declined dramatically and the form of the transient uptake curve changed from diffusion control to surface resistance control. 6. Controlled hydration experiments

Fig. 3. Adsorption of propane in Linde 5A at 323 K showing change in shape of the uptake curve in successive pressure steps. (1) 14–19 Torr, (2) 19–24 Torr, (4) 24– 32 Torr, (7) 98–127 Torr. Data from Tezel [10].

less than 140 Torr (Henry’s law region) so the diffusivity is not significantly concentration dependent. It is clear that, not only does the rate decline from step to step but the shape of the curves changes from the form characteristic of a diffusion controlled process (Eq. (2)) to that for surface resistance control (Eq. (1)). A similar pattern of behavior is shown in Fig. 3 for propane in a series of successive adsorption runs, carried out in the same way. For this system the isotherm at 323 K is well outside the Henry’s law region and the diffusivity therefore increases substantially with loading. For both nitrogen and propane the sorption curves obtained directly following high temperature (673 K) dehydration conform approximately to the diffusion model (Eqs. (2)–(4)) but after several concentration steps the curves approach the simple exponential decay characteristic of surface control (Eq. (1)). That this same trend is observed for both adsorption (propane) and desorption (nitrogen), suggests that the change is not due to prolonged exposure to the sorbate but rather correlates directly with the number of steps to which the sample was exposed. At the start of each concentration step the sample is exposed briefly to the dosing chamber. Since well dehydrated 5A zeolite is highly hydrophilic it seems plausible to suggest that the changes in adsorption behavior may be due to the scavenging of traces of water from the walls of the dosing chamber by the adsorbent. 5. Effect of pre-treatment The effect of the dehydration procedure has been studied in some detail [10,49,50]. The commercial samples are marketed in dehydrated form so, for the Linde 5A sample, the initial dehydration procedure was not under our control. Our standard procedure involved dehydration overnight at 350–400 °C under a high vacuum (using a normal rotary vacuum pump plus a diffusion pump to reduce the pressure to less than about 105 Torr). For both the laboratory synthesized crystals (Yucel CaA) and the commercial crystals, regeneration under these conditions yielded reasonably reproducible but very different diffusivities for the two different zeolite samples (Do  6  1010 cm2 s1 and 6  1012 cm2 s1 for n-butane at 273 K in the Yucel CaA and Linde 5A, respectively). More severe regeneration conditions did not lead to higher diffusivities for either the 4A or 5A samples. However, less severe conditions (lower temperature and/or lower vacuum) led to substantially reduced diffusivities. This is illustrated in Fig. 3a. In experiment 23 the sample was dehydrated at 673 K using only the rotary vacuum pump (pressure  102–103 Torr) whereas

To study the effect of water this sample (hydrothermally treated 7.3 lm Yucel CaA) was exposed sequentially to several step changes in butane pressure and the uptake rate was followed gravimetrically [10]. Following each step the sample was exposed briefly to water vapor. The amount of water added was estimated from the sample weight by comparison with the isotherm for butane on a dry sample of the same adsorbent at the same temperature and pressure. Such a procedure assumes that the equilibrium isotherm for n-butane is not significantly affected by the presence of small amounts of water. After 8 steps at 273 K the sample was evacuated without raising the temperature and further uptake rate measurements were made at 295 K and then at 313 K. The results are summarized in Table 2 and Fig. 4. The first run at 273 K shows some evidence of heat transfer limitation in the final stages of the uptake (although this is not apparent from the figure due to the long time scale) but the initial region p of the uptake curve is accurately linear in t, in conformity with the diffusion model (Eq. (3)). The diffusivity is however very much smaller than for a carefully dehydrated sample of the same crystals. Runs 2–9 show excellent conformity with the isothermal diffusion model over the entire range, with successively decreasing diffusivities (although as a result of the curvature of the isotherm the diffusivity increases with loading). Runs 11–14 show increasing surface resistance and conform closely to the dual resistance model (Eq. (5)) while run 16 approaches the limiting case of full surface resistance control (Eq. (1)). The parameters D/R2 and L derived by fitting the experimental curves to Eq. (5) are summarized in Table 3. It is evident that both the diffusivity and the surface rate constant decrease with increasing water content. From steps 1–8 (at 273 K) the diffusivity decreases by a factor of 30 for a water content of about 0.5 molecules per cage. The seventh column of Table 2 gives the ratio of the diffusivity in the wet adsorbent to the diffusivity in a properly pre-conditioned dry sample of the same zeolite crystals for the same pressure step at the same temperature. This ratio varies from about 102–104, showing the dramatic closure of the pore system at water contents which are still only a small fraction of the saturation capacity. Because water is so strongly adsorbed it is probably retained preferentially in the outer layers of the crystal and in that region the water loading will be much greater than the average value. The strong effect of small amounts of water and the transition to surface resistance control can be understood on that basis. Regeneration at 673 K under high vacuum restored the diffusivity to approximately the same level as the initial value for the pre-treated sample (D  3.1  1011 cm2 s1) but the high diffusivity characteristic of the virgin crystals was never fully recovered. 7. Concentration and temperature dependence of diffusivity Outside the Henry’s law region the intracrystalline diffusivities in these systems are strongly concentration dependent. In general

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79 Table 2 n-Butane–CaA: effect of water on diffusivity. Run

T (K)

1 6 8 9 11 13 14 16

273 273 273 295 295 313 313 313

p step (Torr)

D (cm2 s1)

Water (mol/cage)

11–23 53–68 86–106 10–22 43–60 10–23 23–45 68–87

11

0 0.34 0.47 0.73 1.1 1.5 1.8 2.2

3.1  10 3.3  1012 7.4  1013 1.1  1012 7.7  1012 1.9  1012 2.0  1012 2  1012

D0 (cm2 s1) 9

4  10 5.2  109 5.5  109 5.8  109 1.4  108 7.4  109 1.45  108 1.73  108

D/D0

D/DNaA

0.008 6.35  104 1.35  104 1.9  104 5.5  104 2.6  104 1.4  104 1.2  104

20,000 1600 340 480 1375 650 350 300

Sample: 7.3 lm Yucel Crystals (Yucel 1). D is diffusivity of pre-treated CaA sample (Yucel 1); D0 is diffusivity for fully dehydrated sample of the same crystals at given p and T. D0 /DNaA = 2.5  106, 9  105, and 4  105 at 273 K, 295 K and 313 K.

Fig. 4. Adsorption of n-butane in CaA (7.3 lm crystals) showing effect exposure to water vapor. Details are given in Table 2. Data are from Tezel [10].

Table 3 Parameters D/R2 and L (=kR/D)derived by fitting uptake curves for n-butane–CaA (Fig. 5) to Dual Resistance Model (Eq. (5)). Run

L

11 13 14 16

10 5 1 <0.1

D/R2 (s1) 5

5.8  10 1.4  105 1.5  105 –

3 k/R (s1) 1.74  104 2.1  104 4.5  105 1.73  105

the diffusivity increases strongly with loading, reflecting the monotonic type 1 form of the isotherm. Assuming an ideal vapor phase and considering the gradient of chemical potential as the driving force leads to the well known relationship between the Fickian diffusivity (D) and the thermodynamically corrected (or Maxwell–Stefan) diffusivity (Do):

D ¼ Do

d ln p d ln q

ð9Þ

In principle both D and Do are concentration dependent but, for these systems, extensive measurements (see for example [22–24]) have shown that the concentration dependence of the Fickian diffusivity can be accounted for, within experimental error, by the thermodynamic factor and the corrected diffusivity is essentially constant. For such systems the self-diffusivity (D) should approach the corrected diffusivity (D  Do) even at loadings beyond the Henry’s law region. An example of such behavior is shown for propane – 5A in Fig. 5. This figure also shows the approximate constancy of the corrected diffusivity (Do) and the approximate

Fig. 5. Variation of diffusivity for propane (D, Do or ) with loading for various different samples of 5A zeolite at 358 K and 323 K. } PFGNMR ( ) Shdanov crystals; , d ZLC/TZLC (Do, ) Yucel crystals; 4, N (Do, D) Linde 5A crystals lot 550045 (uptake rate). Data are from Ref. [20].

agreement with the self diffusivities measured by TZLC and PFGNMR which is observed for the carefully dehydrated Shdanov and Yucel crystals. The PFGNMR self-diffusivities are in fact slightly larger than the macroscopically measured (TZLC) values and this is consistent with recent results from interference microscopy (IFM) that suggest the presence of some surface resistance in such crystals [26,27]. However, detailed analysis of the uptake curves and measurements with different crystal sizes (see Figs. 1–3) show that, in well dehydrated crystals, the rate is controlled mainly by intracrystalline diffusion. The large difference in diffusivity between the commercial Linde 5A crystals and the laboratory synthesized crystals as well as the dramatic reduction in diffusivity for an incompletely dehydrated sample are also apparent from Fig. 5. Similar but less extensive data showing large differences in diffusivity (for CO2) between different samples of 4A have also been reported [22]. Intracrystalline diffusion is an activated process so the temperature dependence is given by an Arrhenius expression:

Do ¼ D1 expðE=Rg TÞ

ð10Þ

Since the thermodynamic correction factor (in Eq. (5)) is temperature dependent it is evident that the activation energy should be calculated from the corrected diffusivity rather than from the Fickian diffusivity. It is however common practice to estimate the diffusional activation energy from the temperature dependence of the Fickian diffusivity at a fixed partial pressure. Outside the Henry’s law region such a procedure will lead to erroneously low values.

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

Fig. 6. Arrhenius plot showing temperature dependence of corrected diffusivity for N2 in 5A (Yucel crystals) and in various different samples of 4A zeolite. Data of Xu [28], Yucel and Ruthven [17], Derrah [29], Kumar [30], van de Voorde [31], and Cao et al. [32]. See also Ruthven [33].

Fig. 7. Arrhenius plot showing temperature dependence of corrected diffusivity for CO2 in 5A (Yucel crystals) and in various different samples of 4A zeolite. Data of Yucel [22], Derrah [8], Haq [34] (CO2-4A). ZLC data of Xu [28] (N) and PFGNMR data of Kaerger [35] (h) for CO2-5A (Yucel crystals) are also shown for comparison. See also [36].

Fig. 8. Arrhenius plot showing temperature dependence of corrected diffusivity for CH4 in 5A (Yucel crystals) and in various different samples of 4A zeolite. Data of Xu [28], Yucel and Ruthven [17], Kumar [30], Cao et al. [32], and Haq [34].

Fig. 9. Arrhenius plot showing temperature dependence of corrected diffusivity for C2H6 in 5A (Yucel crystals) and in various different samples of 4A zeolite. Data of Xu [28], Yucel [17], Tezel [10].

Fig. 10. Arrhenius plot showing temperature dependence of corrected diffusivity for C3H8 in two different samples of 5A (Yucel and Shdanov crystals and Linde lot 550045) and in a sample of commercial 4A zeolite. Data of Brandani [20], Kaerger and Ruthven [4], Tezel [10], Loughlin [7], and Nelson [37].

Fig. 11. Arrhenius plot showing temperature dependence of corrected diffusivity for nC4H10 in 5A crystals (Yucel, Shdanov and Linde lot 550045) and in various partially Ca exchanged samples. Of 4A zeolite crystals. Measurements for the 5A lab. crystals (Yucel and Shdanov) were made by PFGNMR (d), ZLC (h) and uptake rate (N, j). Data of Yucel [18], Kaerger and Ruthven [4], Eic and Ruthven [38], Loughlin [7], Ruthven [39] and Walker [40].

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

Fig. 12. Arrhenius plot showing temperature dependence of corrected diffusivity for nC7H16 in 5A (Yucel crystals) and in Linde 5A. Data of Doetsch [25], Eic [38]. Note consistency between data for different size fractions and between gravimetric (filled symbols) and ZLC (open symbols) data for Linde lot 550043.

ple of zeolite by both ZLC and uptake rate measurements as well as by PFGNMR, with consistent results (see Figs. 5, 7 and 10–13). Although there is some experimental scatter the general pattern is quite clear. As expected the diffusivities for 4A are much smaller than for 5A and the activation energies are substantially larger, reflecting the smaller effective aperture of the partially obstructed 4A windows. More surprisingly, for both 4A and 5A, we see large differences in diffusivity for various zeolite samples but with very little difference in the activation energy. A large reduction in diffusivity with little change in activation energy suggests that the rate controlling energy barrier (the pore aperture) remains constant while the length and tortuosity of the diffusion path increases. The behavior of a three dimensional cubic pore system consisting of discrete cages interconnected through ‘‘windows’’ which may be either ‘‘open’’ or ‘‘closed’’ (obstructed by a cation) has been examined both by Monte Carlo simulation [39] and using the effective medium approximation [43–46]. According to the effective medium approximation the diffusivity in a partially closed system is given by:

D Dopen

¼

 2 1 ð3e  1Þ 2  3e þ 4 r " #1=2 2 1 ð3e  1Þ 8 2  3e þ þ þ 4 r r

ð11Þ

where r = Dopen/Dclosed and e = fraction of ‘‘closed’’ windows. In the limit when r is large this reduces to:

D ¼ 1  1:5e ðValid for Dopen

Fig. 13. Arrhenius plot showing temperature dependence of corrected diffusivity for C10H22 in 5A (Yucel crystals) and in Linde 5A (lot 550045). Data of Eic [38], Vavlitis [41], Bulow [42].

8. General pattern of behavior: differences between zeolite samples Figs. 6–13 summarize, in the form of Arrhenius plots, the extensive experimental data that have been accumulated for diffusion of several light gases in different samples of 4A and 5A zeolites. The activation energies and pre-exponential factors are given in Table 4. In several cases measurements have been made for the same sam-

e < 2=3Þ

ð12Þ

It is evident that, for a system in which the ratio of the diffusivities for the ‘‘open’’ and ‘‘closed’’ sieves is large, the diffusivity will drop dramatically when the fraction of ‘‘open’’ windows falls to about 1/3. At this point the effective medium approximation is no longer valid but kinetic information can still be obtained from the Monte Carlo simulation. Such simulations show that for a ‘‘closed’’ sieve the diffusivity starts to increase when the fraction of ‘‘open’’ windows exceeds about 12% and increases very rapidly when the 1/3 threshold is approached. This is consistent with the results of percolation measurements which show that the equilibrium capacity starts to increase well below the percolation threshold [47,48]. In this region the pore system consists of a network of pores controlled only by ‘‘open’’ windows separating regions of the structure that are accessible only through ‘‘closed’’ windows. The uptake curve will then show a rapid initial uptake followed by a slow exponential approach to equilibrium, qualitatively similar to the curves for heat transfer control but on a much longer time scale.

Table 4 Summary of activation energies and pre-exponential factors for diffusion in NaA and CaA zeolites. NaA crystals (Yucel)

CaA crystals (Yucel and Shdanov)

Linde 5A

Sorbate

E (kJ/mol)

D1 (cm2 s1)

E (kJ/mol)

D1 (cm2 s1)

D1 (cm2 s1)

N2 CO2 CH4 C2H6 C3H8 nC4H10 nC7H16 nC10H22

24.2 25.0 25.0 24.7 36.4 39.7 – –

2.2  105 2.3  105 1.4  106 1.34  106 1.2  108 7.3  109 – –

10.5 9.4 6.3 6.3 16.7 16.7 31.7 48

6.2  105 1  104 1.8  105 6.3  106 3.7  106 1.1  106 2.4  106 5  105

– – – – 1.1  108 7.3  109 3.4  108 1.7  106

Activation energies for Linde 5A are essentially the same as for Yucel and Shdanov crystals. Reported data for smaller molecules in Linde 5A are probably unreliable as diffusion is too fast to measure accurately in such small crystals.

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D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79 Table 5 Comparison of diffusivities for several different sorbates in laboratory synthesized CaA and Linde 5A crystals. (Yucel Lot 2 and Linde 5A Lot 550045.) Sorbate

DYucel/DLinde

C3H8 nC4H10 nC7H16 nC10H22 CF4[18]

230 190 200 150 250

DYucel2/DYucel 1  3. The fastest sample (Yucel 2) is taken as the base case. The ratios are essentially independent of T as activation energies for both zeolites are the same.

Such behavior has been observed for CO2 in 4A Linde (lot 470017) [22]. When the diffusivity ratio for the ‘‘open’’ and ‘‘closed’’ forms is large the activation energy changes very sharply from the value characteristic of a ‘‘closed’’ sieve to that for an ‘‘open’’ sieve at the 1/3 threshold [39]. The data shown in Figs. 6–13 are consistent with this model. The large difference in diffusivity between the laboratory synthesized CaA crystals and the commercial 5A samples (Linde lots 550043 and 550045), with very little difference in activation energy, suggests that almost two thirds of the windows in the Linde 5A sample are ‘‘closed’’. Similarly the difference between the various 4A samples (which show essentially constant activation energy) suggests that in the different samples different fractions (less than two thirds) of the windows are blocked. Further support for this hypothesis comes from comparing the diffusivities for different sorbates (on freshly regenerated zeolite samples). If the difference in diffusivity between the different samples is indeed due to differences in the fractions of ‘‘open’’ and ‘‘closed’’ windows the ratios of the diffusivities for the different samples should be the same for different sorbates. Diffusivity ratios relative to the fastest samples of laboratory synthesized crystals (Yucel sample 2) are summarized in Tables 5 and 6, together with the values of e estimated from Eq. (8). It may be seen that despite some variations the data are broadly consistent with this pattern. Exact conformity cannot be expected since the diffusivities are also sensitive to small differences in the pre-conditioning procedure and/or aging of the samples.

9. Cation locations and structure modification The cation sites in type A zeolite and the site preferences for various different cations are reasonably well established, at least for dry conditions [51]. Site 1 (SI), (eight per pseudo cell) lies close to the centers of the 6-rings in the corners of the cell. Site 2 (SII) lies within the 8-rings (slightly off center) so that the cations in these sites obstruct the diffusion path. Site 3 is energetically less favorable and is generally occupied only when the other sites have been filled. In the dry sieve small cations such as Na+ and Ca++ generally prefer the 6-ring sites (SI) but this site preference decreases in the presence of water. Larger cations such as K+ generally prefer the 8ring sites (SII) [52]. In the ideal structure the pseudo cell contains 12 monovalent cations. Therefore, if more than two thirds of the Na+ ions are exchanged for Ca++ there will be less than eight cations per pseudo cell and, at least in principle, these can all be accommodated in the type 1 sites, leading to a completely open pore system (the ideal 5A structure). For many years this simple picture was generally accepted but there is now substantial evidence that the actual situation is more complicated. Long range electrostatic interactions

Table 6 Comparison of diffusivities in three different 4A samples (D/DNaA). Sorbate

Linde 4A crystals lot 450339

Linde 4A pellet Cao et al. [32]

Linde 4A crystals lot 470017

Ar N2 CH4 C2H6 Kr Avge e (from Eq.12)

– 0.26 0.12 0.48 – 0.29 0.47

– 0.13 0.12 – 0.12 0.123 0.58

0.035[29] 0.04 0.06 0.02 – 0.04 0.64

DNaA corresponds to the Yucel 4A crystals (7.3, 34 lm). Ratios are independent of T since activation energies are essentially the same for the different 4A samples.

are quite important and often control the actual cation distribution. For example energy calculations suggest that in mixed cation systems the displacement of Ca++ from SI to SII may substantially reduce the lattice energy [53]. This is confirmed by single crystal X-ray diffraction studies showing that in dry CaA there are 5 Ca++ cations per pseudo cell in the 6-ring sites and one in an 8-ring site [54]. This leads to the interesting conclusion, supported by some experimental evidence, that the 83% exchanged CaNaA sieve (with 5Ca++ and 2Na+ cations per pseudo cell) should be more open than the fully Ca++ exchanged form. Based on percolation studies Ohgushi et al. [55] have suggested that there may be only four Ca++ cations per pseudo cell in the SI sites, allowing for an energetically efficient tetrahedral distribution of the divalent cations. In partially hydrated samples the situation is further complicated by cation hydration, and consequent sensitivity of the cation distribution to the regeneration temperature. It has been shown that a high regeneration temperature favors occupation of the SII sites [56]. In a detailed study of CaX zeolite Coe et al. [57,58] have shown that even very small traces of water at elevated temperature can lead to hydroxylation of the Ca++ cations:

Caþþ þ 2H2 O ¼ CaðOHÞþ þ H3 Oþ

ð13Þ

This reaction, which would also be expected to occur under similar conditions in 5A, leads to the replacement of one divalent cation by two monovalent cations with the result that the 8-ring sites may be occupied more fully than is expected on the basis of the ideal cation distribution. Furthermore the hydronium ion so created can react irreversibly with the zeolite framework, removing Al, forming a hydroxyl nest and eventually forming amorphous alumina:

ð14Þ

The combined result of these reactions is to eliminate one of the SI sites as a hydroxyl nest and to transfer one of the Ca++ cations in hydroxylated form as Ca(OH)+ to a SII site (which is occupied preferentially by the larger cation). If two of the 6 Ca++ cations per pseudo cell (in the ideal Ca structure) are reacted in this way the resulting structure will contain only four Ca++ cations per cell, to be accommodated on the six remaining SI sites, with two Ca per cell held as Ca(OH)+ in the SII (window) sites. This would allow the remaining Ca++ cations to be distributed tetrahedrally on the SI sites, thus minimizing the electrostatic repulsion energy which, for divalent cations, is quite significant. It therefore seems

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reasonable to assume that such a structure would be quite stable. Reaction (13) would be irreversible and would therefore lead to a permanent reduction in the guest diffusivities. 10. Effect of water at ambient and high temperatures The effect of traces of water at moderate temperatures can be reasonably explained by reversible hydration of the cations. In the 5A sieve the Ca++ cations will be preferentially hydrated. This will cause additional window blocking since the hydrated Ca++ cations will tend to migrate from the SI to SII sites. If the hydrated cations are concentrated near the crystal surface this will lead to the development of surface resistance whereas if the distribution of hydrated cations is uniform throughout the crystal there will be a reduction in the intracrystalline diffusivity with no increase in activation energy. The data shown in Figs. 2 and 3 (and Figs. 6– 13) show both these effects. Such a process would be reversed by dehydration under vacuum at elevated temperature, thus restoring the diffusivity. The desorption curves for N2 in Linde 5A at 250 K, shown in Fig. 2a, provides an extreme example, since the observed diffusivity (D  2.4  1010 cm2 s1) corresponds to the value for N2 in ideal 4A crystals suggesting that all windows are obstructed by cations (see Fig. 6). In the ideal 4A structure all SII sites contain Na+ cations. These cations will be relatively unshielded and will therefore be easily hydrated by traces of water vapor leading, as with 5A, to further obstruction of an increasing fraction of the windows with a resultant reversible decrease in diffusivity but a constant diffusional activation energy. This would explain the much lower diffusivity observed for N2 in experiment 23 in comparison with experiment 28 (Fig. 2). However, it has also been shown that exposure to water vapor at high temperature can lead to a more permanent reduction in the diffusivity for 4A (pore closure) which is not reversed by dehydration under vacuum. The detailed studies of Kondis and Dranoff [49,50] show clearly that this can occur in the manufacture of commercial 4A during the initial dehydration, which is normally carried out by exposing the hydrated zeolite to very high temperature (>800 K) for a very short time. The constancy of the activation energy between the different 4A samples suggests that the observed reduction in diffusivity must involve window blocking although the precise mechanism is still uncertain. The mechanism outlined above will not apply to the Na form as it requires a divalent cation. However, it is well known that at sufficiently high temperatures water can attack the zeolite framework, leading to dealumination by a mechanism similar to that shown in Eq. (14). If this reaction were to occur preferentially at the 8-rings it would lead to irreversible window blockage by the amorphous alumina so produced but there seems to be no obvious reason for preferential attack at the 8-rings. 11. Transition state theory

‘2 f   hK 1 fg0

Sorbate

D1 (NaA)

D1 (CaA)

D1 (Eq. (15))

N2 CO2 CH4 C2H6

2.2  105 2.2  105 1.2  106 1.35  106

6.2  105 1  104 1.8  105 6.3  106

4  105 7.8  105 1.7  105 1.3  105

per unit volume for the molecule in the gas phase. If the molecule rotates in the transition state to the same extent as in the gas phase the ratio f  =fg0 should approximate the reciprocal of the reduced 0 translational partition function (1=ftrans ) which is easily calculated. For diffusion of several light molecules in the Yucel 4A and 5A crystals a comparison of the experimental values of D1 with the theoretical values, estimated from Eq. (15) on the basis of this approximation is shown in Table 7 [28]. For N2, CO2, CH4, and C2H6 the agreement is quite close (within a factor of about 2 for 5A) but for the monatomic gases and O2 the experimental values of D1 are much smaller than the predicted values. Such differences might be due to a substantial contribution to the partition function in the transition state from the degree of freedom in the plane of the window which is neglected in the simple model. A further prediction that follows from Eq. (15) is that for small non-polar species, for which the Henry constants for 4A and 5A may be expected to be similar, the values of D1 for the same molecule diffusing in ideal 4A and 5A structures should also be similar; since the difference in diffusivity then arises almost entirely from the difference in the activation energy. This prediction is approximately fulfilled as may be seen from Table 7, providing further evidence in support of the proposed model. In an earlier publication [33] the similarity in diffusional activation energies for the same molecule in different samples of 4A zeolite was noted and explained on the basis of the window blocking theory, as outlined above, but with one critical difference. It was assumed that the slowest sample corresponded to the ideal 4A structure in which all windows contain a Na+ cation and that the faster 4A samples contain a certain fraction of ‘‘open’’ windows with no SII cation. Such a hypothesis can explain the 4A kinetic data. However, it leads to values of D1 for the more open 4A samples which are much larger than the corresponding values for 5A, which is inconsistent with Eq. (15). The assumption that the fastest of the 4A samples must represent the ideal 4A structure, which yields reasonably consistent values of D1 for 4A and 5A appears to be more reasonable. We have therefore to assume that in the slower samples (which have lower diffusivities but the same activation energies) a certain fraction of the windows is blocked by framework damage (probably involving dealumination with deposition of amorphous alumina) as noted above. 12. Variation of E with molecular diameter

In the type A zeolite the molecule in passage through the 8-ring window is clearly identifiable as the transition state, making these systems particularly suitable for the application of transition state theory [59–61]. According to transition state theory the pre-exponential factor in Eq. (6) should be given by:

D1 ¼

Table 7 Comparison of pre-exponential factors (D1/cm2 s1) for NaA and CaA with theoretical values from Eq. (10).

ð15Þ

where ‘ is the jump distance (12.3 Å for the type A structure), h is Planck’s constant, K1 is the pre-exponential factor in the van’t Hoff expression for the temperature dependence of the dimensionless Henry constant (K ¼ K 1 eDU=RT ) and f  =fg0 is the ratio of the reduced partition function for the transition state and the partition function

It has long been recognized that intracrystalline diffusivities in small pore zeolites are strongly dependent on the size of the diffusing molecule relative to the pore diameter or, in the case of the A zeolites, the window diameter. More specifically it has been shown that the diffusional activation energies in 4A and 5A correlate directly with the van der Waals radii of the guest molecules [62– 64]. The validity of such a correlation despite very large difference in the actual diffusivities between different samples has always seemed somewhat surprising. The present study strongly suggests that the differences between different type A zeolite samples arise from the blocking of different fractions of the 8-ring windows, depending inter alia on the initial dehydration conditions, the degree of hydration and the structural integrity of the framework

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thus providing a rational explanation for the constancy of the activation energies between samples with very different diffusivities. Fig. 14 shows this correlation. For the larger molecules the correlation is unambiguous but it is much less clear for the smaller molecules for which the repulsive interactions are negligible and activation energies are therefore small. In this region the energy required to leave the local site may be greater than the repulsive energy associated with passage through the 8-ring and the correlation with molecular diameter then breaks down. This appears to be the situation for N2 and CO2 in 5A. However, activation energies as low as this are difficult to measure with any accuracy. For 4A zeolite the activation energies are substantially larger, reflecting the smaller window aperture. However, the activation energies for N2, CO2, CH4 and C2H6 are all essentially the same (25 kJ/mole) despite the variation in molecular diameter. This may reflect the energy involved in displacement of the SII cation rather than the repulsive energy associated with passage of the guest molecule through the window. 13. Evidence from sorption kinetic data Despite the simplicity of the channel structure the kinetic behavior of the type A zeolites is quite complex. In carefully dehydrated samples the sorption kinetics appear to be controlled mainly by intracrystalline diffusion and conformity with the diffusion model has been confirmed both by detailed analysis of the transient sorption curves and by measurements with different crystal size fractions. However, in the faster diffusing samples heat transfer is often rate limiting in the later stages of the uptake. In samples subjected to several successive adsorption (or desorption) steps we observed a notable decrease in the sorption rate. This effect is largely but not totally reversed by regeneration at 400 °C under vacuum. Detailed analysis of the sorption curves suggests that the decline in rate is due to both a reduction in intracrystalline diffusivity and the development of surface resistance. Similar behavior was observed in a sample of hydrothermally treated CaA crystals subjected to controlled addition of traces of water vapor, suggesting that, in the earlier uptake rate experiments, the adventitious scavenging of traces of water from the glass surface of the apparatus may have been responsible for the observed changes in kinetics. Preferential adsorption of water in the outer layers of the crystals would explain both the sensitivity of the kinetics to small amounts of water and the transition from diffusion to surface resistance control. Different (structurally intact) samples of both the Na+ and Ca++ forms (4A and 5A) show large difference in sorption rates (for the same guest molecule), often spanning several orders of magnitude,

Fig. 14. Variation of activation energy for diffusion on 4A and 5A with molecular diameter.

but with almost constant activation energies. This is probably due to differences in the distribution of the exchangeable cations between the 6-ring (SI) and 8-ring (SII) sites leading to different fractions of ‘‘open’’ and ‘‘closed’’ windows. The cation distribution appears to be determined largely by the initial dehydration conditions for the virgin material but it can certainly be modified by subsequent treatment, especially by the addition of relatively small amounts of water, for which these materials have a very high affinity. The high temperature/high humidity conditions used in the initial dehydration of industrial 5A adsorbents apparently lead to partial occupation of the 8-ring sites whereas if the initial dehydration is carried out slowly under high vacuum at temperatures below 400 °C the ideal cation distribution is approached in which most of the 8-ring windows are unobstructed. In three of the industrial Linde 5A samples which were studied only slightly more than one third of the 8-ring windows appear to be ‘‘open’’. At this point, according to the effective medium approximation, the intracrystalline diffusivity is greatly reduced relative to the ‘‘open’’ structure and becomes very sensitive to small changes in the window site occupancy level. The distribution of the SI and SII sites throughout the lattice can be thought of as forming two interlocking cubic arrays. There is both theoretical and experimental evidence that in CaA no more than five of the six Ca++ cations per cage can be accommodated at the SI sites and that a tetrahedral distribution of four cations per cage on the SI sites is energetically favorable. If the remaining two Ca++ cations per cage are located on the SII sites they could also be distributed tetrahedrally to yield what would probably be the minimum energy array. In that arrangement one third of the windows would be obstructed, as observed for the Linde 5A samples. Although speculative this hypothesis would provide a rational explanation for the prevalence of such a structure. The behavior of 4A is qualitatively similar in that there are large differences in diffusivity between samples with almost constant activation energies. This again suggests blocking of the 8-ring windows, probably as a result of hydration of different fractions of the SII cations (thus further obstructing the 8-ring windows). This effect would be reversed by more efficient dehydration of the sample. However, more permanent blocking was evident in some samples and this appears to be due to structural degradation rather than to differences in cation distribution.

14. Evidence from NMR fast tracer desorption studies Although the picture outlined here provides a simple and coherent explanation for the complexities of the observed kinetic behavior there is strong evidence from comparisons between PFGNMR self-diffusion and NMR tracer desorption measurements suggesting that the much slower sorption rates shown by the small commercial 5A crystals (even when fully dehydrated) in comparison with carefully dehydrated larger crystals, is due to the presence of a surface barrier [6]. At least for ethane and methane the intracrystalline self-diffusivities in both the small and large crystals appear to be very similar. Recent evidence from interference microscopy has shown that even in apparently well formed crystals, the sorption kinetics can be influenced and indeed controlled by structural defects. However, it is not at all obvious that structural defects can explain the present discrepancy in the observed kinetics for the small commercial crystals, especially since kinetic measurements with the carefully dehydrated crystals show good agreement between the macroscopic and microscopic measurements. One possibility is that the hydrothermal reactions and consequent window blocking may occur predominantly at the outer surface of the crystals. This could still explain the constancy of the

D.M. Ruthven / Microporous and Mesoporous Materials 162 (2012) 69–79

activation energies since the surface rate coefficient would be directly proportional to the diffusivity for the ‘‘open’’ windows multiplied by the fraction of open windows in the outer layer or layers of the crystal [64,65]. It would also explain the large difference between the tracer desorption and intracrystalline diffusivities as observed in the NMR studies but it would not explain the observed form of the desorption curves which is more consistent with intracrystalline diffusion control than surface resistance. However, surface resistance control with a sufficiently wide distribution of crystal size can mimic diffusion kinetics so such an explanation is certainly worth considering. The difficulty is that the breadth of the crystal size distribution needed to adequately explain the form of the uptake curves is much broader than the actual size distribution. It seems more likely that severe hydrothermal treatment leads to occupation of SII sites through the creation of additional cations by hydration reactions. Depending on the precise conditions and the duration of the treatment such reactions will occur either predominantly near the surface (leading to surface resistance) or uniformly through the crystal, leading to a greatly reduced intracrystalline diffusivity. Acknowledgements The financial support received from the Natural Sciences and Engineering Research Council of Canada (NSERC) over many years as well as more recent support from the National Science Foundation (GOALI Program Award 0553861), and the contributions made by many former students, notably Drs K.F. Loughlin, H.Yucel and O.H.Tezel, whose work is discussed in this article, are gratefully acknowledged. References [1] R.M. Milton, US Patent 1 (882) (1959) 243. [2] D.W. Breck, W.G. Eversole, R.M. Milton, T.B. Read, J. Am. Chem. Soc. 78 (1956) 5963. [3] D.M. Ruthven, in: J.R. Katzer (Ed.), Proceedings of the Fourth International Zeolite Conference, Chicago, 1976, ACS Symposium Series, vol. 40, 1977, p. 320. [4] J. Kärger, D.M. Ruthven, J. Chem. Soc. Faraday Trans. I 77 (1981) 1485. [5] J. Kärger, D.M. Ruthven, Zeolites 9 (1989) 267. [6] J. Kärger, AIChE Jl 28 (1989) 417–422. [7] K.F. Loughlin, Ph.D. Thesis, University of New Brunswick, Canada, 1970. [8] R.I. Derrah, Ph.D. Thesis, University of New Brunswick, Canada, 1973. [9] H. Yucel, Ph.D. Thesis, University of New Brunswick, Canada, 1978. [10] O.H. Tezel, Ph.D. Thesis, University of New Brunswick, Canada, 1984. [11] R. Kumar, Ph.D. Thesis, University of New Brunswick, Canada, 1979. [12] M. Eic, Ph.D. Thesis, University of New Brunswick, Canada, 1987. [13] I.H. Doetsch, Post-Doctoral Report, University of New Brunswick, 1974. [14] J. Kärger, D.M. Ruthven, Diffusion in Zeolites and Other Microporous Solids Chs. 7,9,10, John Wiley, New York, 1992. [15] H.G. Karge, J. Kärger, Molecular sieves – science and technology 7, in: H.G. Karge, J. Weitkamp (Eds.), Springer-Verlag, Berlin, 2008. pp. 135–205. [16] L. Heinke, P. Kortunov, D. Tzoulaki, J. Kärger, Adsorption 13 (2007) 215–223. [17] H. Yucel, D.M. Ruthven, J. Chem. Soc. Faraday Trans. 1 76 (1980) 60–70. [18] H. Yucel, D.M. Ruthven, J. Chem. Soc. Faraday Trans. 1 76 (1980) 71–83.

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