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Diffusion of C2H6 and C2H4 in DDR Zeolite Adam Vidoni and Douglas M. Ruthven* Department of Chemical and Biological Engineering, University of Maine, Orono, Maine 04469-5737, United States ABSTRACT: Diffusion of ethane and ethylene in large crystals of DDR clathrisil (the pure silica analogue of ZSM-58) has been studied in detail by the zero length column (ZLC) technique. The behavior of ethane and ethylene is very similar with respect to both kinetics and equilibria. Measurements were made with two different DDR samples with both He and CO2 as the carrier gas. In contrast to methane neither the equilibrium nor the diffusivity of ethane (or ethylene) is significantly affected by the presence of CO2, suggesting noncompetitive adsorption. Although the diffusivity of the C2 hydrocarbons is about an order of magnitude smaller than that of methane the activation energies are similar or even smaller. Also, in contrast to the behavior of methane, the data show clear evidence of a small but significant surface resistance (in addition to the intracrystalline diffusional resistance).
’ INTRODUCTION In recent years DD3R, the pure silica analogue of ZSM-58, has attracted a good deal of attention as a possible alternative to cationic zeolites for the removal of CO2 from natural gas and other similar processes. An experimental study of the performance of a DD3R membrane was recently presented by van den Bergh,1,2 and this has been supplemented by detailed equilibrium measurements3,4 as well as molecular simulations.57 In an earlier paper8 we showed that the intracrystalline diffusivity of methane in DDR is substantially enhanced by the presence of CO2. This result, which is consistent with the predictions of transition state theory for a competitively adsorbed species, has somewhat negative practical implications since it suggests that the kinetic selectivity for CO2 over CH4 in a mixed feed may be lower than the value predicted from single component measurements. As a logical sequel to that work it was decided to study the kinetic behavior of C2 hydrocarbons (C2H6 and C2H4) in DDR, both as single components and in the presence of CO2. The results of this investigation show that the general patterns of behavior of C2H6 and C2H4 in DDR are similar but strikingly different from the behavior of methane. In addition to the specific information gained on the diffusional behavior of C2H6 and C2H4 in DDR this study also provides useful insight concerning the zero length column (ZLC) technique and the advantages of that approach for the study of complex kinetic systems in which the sorption rate is controlled by a combination of intracrystalline diffusion and surface resistance.9 ’ EXPERIMENTAL DETAILS Two different samples of crystals of DD3R (the pure silica analogue of the clathrisil ZSM-58), synthesized by essentially similar procedures, were studied. The Si/Al ratio for both samples was greater than 1000, and there was no obvious difference in the X-ray diffraction (XRD) patterns which were consistent with the standard pattern for DDR given in the Zeolite Atlas. SEM photomicrographs are shown in Figure 1. The crystals are clearly well formed, and the size distribution for both samples is narrow with a mean crystal radius of 10 μm for DDR I and 20 μm for DDR II. Sample DDR I was used as synthesized, but the DDR-II sample was subjected to a proprietary treatment. r 2011 American Chemical Society
Measurements were carried out by the ZLC technique.1013 A small sample of adsorbent is pre-equilibrated with a known partial pressure of the sorbate at a controlled temperature and then purged at a controlled flow rate with a stream of pure carrier gas. The sorbate concentration in the effluent stream is monitored continuously using a chromatographic detector. In the present study a flame ionization detector (FID) was used, thus allowing comparative measurements to be made with both He and CO2 as carrier. In this way the effect of a competitively adsorbed species (such as CO2) could be investigated. Analysis of ZLC Response Curves. For a perfectly mixed ZLC system in which the desorption rate is controlled entirely by intracrystalline diffusion the ZLC response curve is given by: ∞ expð β2 Dt=R 2 Þ c n ¼ 2L 2 c0 n ¼ 1 ½βn þ LðL 1Þ
∑
ð1Þ
with ßn given by the roots of the transcendental equation: βn cot βn þ L 1 ¼ 0 L¼
F R2 1 Purge Flow Rate R 2 : ¼ : 3KVs D 3 Adsorbent Capacity D
ð2Þ
In the long time region only the first term of the summation is significant so eq 1 simplifies to: " # c 2L Dt ð3Þ β21 2 ≈ ln 2 ln c0 R β1 þ LðL 1Þ which defines the long time asymptote. For large values of L there is a further simplification since β1 f π. Under these conditions it is clear that a plot of log(c/co) versus t should yield a linear long time asymptote with slope π2D/R2 and intercept given by the first term on the right-hand side of eq 3 with β1 replaced by π. A plot of log(c/co) versus time thus provides a simple way to Received: October 25, 2011 Accepted: December 20, 2011 Revised: December 15, 2011 Published: December 20, 2011 1383
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difference is that, if the same radius is used in both models, the cylinder model will yield somewhat larger diffusivity values (by a factor of about 1.7).8 For consistency with previous experimental studies we have elected to retain the spherical particle model. The above approach is based on the traditional model for a ZLC system in which the desorption rate is assumed to be controlled entirely by intracrystalline diffusion (eq 1). However, recent experimental studies have shown that many zeolite crystals have significant surface resistance, so the assumption of total intracrystalline diffusion control is questionable.1618 In a recent study9 it was shown that, when surface resistance is significant, the form of the ZLC response curve remains unchanged except that the parameter L is replaced by L0 where 1 1 D 3KVs D D ¼ ¼ þ þ L0 L kR kR F R2
Figure 1. SEM photomicrographs of the two samples of DD3R crystals. ((a) DDR I; (b) DDR II).
extract the parameter values (L and D/R2) from an experimental ZLC response curve. An alternative approach is based on the use of another simple approximation to eq 1. When L is large, except at short times, the ZLC response curve is well approximated, over a wide range, by the simple expression:14,15 ! rffiffiffiffiffiffiffiffi c 1 R2 1 ð4Þ ¼ c0 L πDt This is demonstrated in Figure √ 2. Evidently, in this approximation, a plot of c/co versus 1/ t should√ be linear with a constant x axis intercept corresponding to (πD/R2) and an intercept of 1L on the y axis, from which the values of D/R2 and L are readily found. This model assumes that the adsorbent can be considered as an assemblage of uniform isotropic spherical particles. This is not strictly valid for DDR since the channel structure is twodimensional. It may therefore be argued that a model in which the adsorbent is considered as a set of uniform infinite cylinders (with transport only in the radial direction) would be more appropriate. The equations for such a model are very similar to those for the spherical particle model (summarized above). The main
ð5Þ
and L retains its original meaning (see eq 2). This means that when L0 is large (L0 > 10) the slope of the long time asymptote (π2D/R2) is not affected by surface resistance; only the intercept is modified √ in accordance with eq 5. Similarly, √ the plot of c/co versus 1/ t, suggested by eq 4 should yield (πD/R2) and 1L0 for the x and y intercepts. We thus reach the important conclusion that, provided that measurements are made at L >10, the ZLC response curves with and without surface resistance may be analyzed in exactly the same way. Measurements at different flow rates allow the magnitude of any surface resistance to be determined from the variation of the parameter L0 with flow rate, as given by eq 5. Representative experimental ZLC response curves showing conformity with both eqs 3 and 4 are shown in Figure 3. The parameters derived from both √ the long time asymptote (eq 3) and from the c/co versus 1/ t plot (eq 4) are consistent; the average values of L0 and D/R2 are summarized in Table 1. If these curves are analyzed according to the traditional ZLC model consistent diffusivity values are obtained, but the apparent value of the Henry constant (K0 ) increases monotonically with flow rate, as illustrated in Table 1. However, the values of 1/L0 increase linearly with reciprocal flow rate in accordance with eq 5 and the K values calculated in accordance with eq 5 are approximately independent of flow rate. A detailed analysis of the experimental values of L0 is presented below (see Analysis of L Values). Diffusion of C2H6 in DDR. The diffusional time constants (D/R2) derived from a series of replicate measurements with different sample quantities (DDR I) are summarized in Table 2. There is considerable experimental scatter ((20%), but there is no significant trend with sample mass, confirming the absence of any significant extracrystalline heat or mass transfer resistances. Figure 4 shows representative plots of diffusivity (for C2H6) versus the purge flow rate (F) for both He and CO2 as purge gases in samples of DDR I and DDR II. Although the data show appreciable experimental scatter it is evident that there is no significant trend with flow rate, and the time constants for He and CO2 purges are very similar. This implies that the diffusion of C2H6 is not significantly affected by the presence of CO2, even in large excess. There is a substantial difference in diffusivities between DDR I and DDR II, but differences between the two different samples of DDR I are minimal. These conclusions are supported by a direct comparison of the ZLC response curves 1384
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Figure 2. Theoretical ZLC response curves showing comparison between the exact solution (eq 1) (points) and (a) the asymptotic solution given by eq 3; (b) the approximate solution given by eq 4 (for L = 20 and 40).
measured with He and CO2 at the same temperature and purge flow rate (see Figure 5). The temperature dependence of the diffusivity is shown in Arrhenius form (D = D∞eE/RT) in Figure 6 which includes the data obtained with both He and CO2 as the purge gas. The Arrhenius parameters are summarized in Table 4. The data for DDR II are more consistent with less variation between replicate runs. For both DDR I and DDR II the diffusivities obtained with He and CO2 are essentially the same (see Figures 4 and 6) but the diffusivities for DDR II are about two to three times larger than the values for DDR I (at the same temperature). Remarkably the activation energy is also significantly larger for DDR II. This is somewhat unusual: more commonly different samples of the same zeolite show either a constant activation energy or, if the activation energy varies, the higher diffusivity is associated with a lower activation energy, as is the case for methane in DDR.8 Diffusion of C2H4 in DDR. Diffusion of C2H4 in DDR was studied less extensively and only in DDR I. The diffusivity values measured at 298 K are very close to the value reported by Hedin et al19 from PFGNMR self-diffusivity measurements. The measured diffusivities are essentially independent of flow rate,
as expected. As for C2H6, there appears to be little difference in diffusivity between the measurements with He and CO2 and between the values for the 2.4 and 5.9 mg samples. This may be seen from Figure 7 and from the direct comparison of the ZLC response curves shown in Figure 8 as well as from the Arrhenius plot shown in Figure 9. Furthermore any difference in diffusivity between C2H4 and C2H6 appears to be minimal and within the range of experimental uncertainty. Analysis of L Values: Surface Resistance. It follows from eq 5 that a plot of 1/L0 versus 1/F should yield a straight line with slope 3KVsR2/D and intercept D/kR. The intercept corresponds to the ratio of the time constants for intracrystalline diffusion and surface resistance and therefore measures the relative importance of these two resistances. A negligible intercept means no significant surface resistance and complete intracrystalline diffusion control while a large intercept would imply surface resistance control. Representative plots 1/L0 versus 1/F for C2H6 in DDR I and DDR II are shown in Figure 10. The plots all show approximate conformity with eq 5, but they show significant differences between the different samples. The behavior of DDR II and the 1385
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Table 2. Comparison of Diffusional Time Constants (103 D/R2 s1) for C2H6 in DDR I at 298 K 1.5 mg
2.4 mg
5.9 mg
He
0.81
1.2
0.85
1.0
CO2
1.2
1.3
0.89
1.0
Figure 4. Variation of experimental diffusivities for C2H6 with flow rate showing comparison of data for DDR II (], () and DDR I (2.4 mg O, b; 5.9 mg 0, 9) with He (open symbols) and CO2 (filled symbols) as carrier. The lines denote the average values.
Figure 3. Representative ZLC response curves for C2H6He in DDR II at 323 K showing (a) approach to asymptotic solution (eq 3) and (b) conformity with approximate solution (eq 4).
Table 1. Parameters Derived from Representative ZLC Response Curvesa
a
L
K0
K
D/R2 (s1)
15
120
110
0.0015
49
140
103
0.0014
78
150
215
112
0.0014
48
57
207
155
0.0008
system
F (mL/sec)
L0
C2H6He
0.097
14
DDR II
0.292
37
348 K
0.973
C2H6He
0.083
D/kR
0.005
DDR I
0.25
85
120
344
180
0.0009
(5.9 mg)
0.50
128
0.0035
232
485
189
0.0010
298 K
0.83
185
546
585
165
0.0008
Note: The response curves for DDR II are shown in Figure 3.
5.9 mg sample of DDR I (shown in Figure 10 a and b) is very similar. The intercepts are essentially constant (invariant with temperature) implying that the activation energies for surface resistance and intracrystalline diffusion are the same. This suggests that the surface barrier probably originates from complete blockage of a significant fraction of the pore entrances (rather than from partial obstruction of all the pore entrances). In contrast, for the 2.4 mg sample of DDR I, the intercept decreases regularly with temperature, as shown in Figure 10c, implying a higher activation energy for the surface resistance. Such behavior
might suggest partial obstruction of the pore entrances, leading to a higher energy barrier at the crystal surface. In all cases, the intercepts are relatively small (D/kR∼ 0.003 0.005), implying that the contribution of surface resistance is minor except at the higher flow rates. To put this into context, the half- time for surface resistance control is given by tsurf = (R/3k) ln 2 while the half time for internal diffusion is given by tdiff = 0.03(R2/D) so the ratio tdiff/tsurf ≈ 0.13(kR/D). With D/Rk = 0.003 this gives tdiff/tsurf ≈ 40 so, by normal criteria, the system would be considered to be diffusion controlled. Nevertheless, even this small contribution from surface resistance leads to a significant variation of the apparent K value with flow rate, as may be seen from the data shown in Table 1. The analysis of the data for the 2.4 mg DDR I sample is summarized in Table 3. The differences in surface resistance between the samples, particularly the two samples of DDR I, suggest that the surface resistance is probably affected (or even determined) by the sample history rather than by the original synthesis. The obvious suspect would be surface coke deposition. The experimental data for C2H4 are less consistent, with greater differences between replicate measurements. As a result the plots of 1/L0 versus 1/F were too scattered to provide any useful information. Henry Constants. The dimensionless Henry constants derived from the L0 values are plotted in van’t Hoff form (K = K∞exp( ΔU/RT)) in Figure 11. The K values for the two samples of DDR I are essentially the same and very similar to the values derived from the equilibrium isotherms for C2H6 on DDR reported by Zhu et al. The values for DDR II are slightly larger. The parameters K∞ and ( ΔU) correlating the temperature dependence are given in Table 4 which includes also the kinetic parameters. 1386
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Figure 7. Diffusivity data for C2H4 in DDR I showing comparison of data for two different samples (2.4 mg and 5.9 mg) with He and CO2 purge.
Figure 5. Comparison of experimental ZLC response curves for C2H6 (at the same temperature and purge flow rate) with He and CO2 as the carrier gas. (a) DDR I at 323 K; (b) DDR II at 348 K.
Figure 8. Direct comparison of experimental ZLC response curves for C2H4 at 348 K showing similarity between data for He and CO2 carriers.
Figure 6. Arrhenius plot showing temperature dependence of diffusivity for C2H6 in two different samples of DDR crystals (DDR I and DDR II). Data for CH4 in the same DDR samples are indicated for comparison.
Since it was not possible to derive reliable K values for C2H4 from plots of 1/L0 versus 1/F the values included in Figure 11
Figure 9. Arrhenius plot showing temperature dependence of diffusivity for C2H4 in DDR I. (5.9 mg Δ, 2; 2.4 mg 0). The line shows the average values for C2H6 in DDR I (see Figure 6). 1387
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Table 3. Analysis of L0 Values for Ethane in DDR I (2.4 mg Sample) T (K)
Int.= D/kR
k/R (s1)
slope
D/R2 (s1)
K
273 298 323 348 373
0.0033 0.004 0.0022 0.0014 0.0009
0.185 0.31 0.64 1.52 3.0
0.0008 0.001 0.00063 0.00051 0.00039
0.00061 0.00124 0.0014 0.00213 0.0027
312 192 107 57 34
Figure 11. van’t Hoff plot showing variation of dimensionless Henry constant (K) with temperature. Measurements with different samples of DDR I are indicated by different symbols. The dashed line indicates the values calculated from the equilibrium isotherms presented by Zhu et al.4
Figure 10. Plots of 1/L0 versus 1/F for ethane in (a) DDR II; (b) DDR I (5.9 mg); (c) DDR I (2.4 mg) Open symbols, He; filled symbols, CO2.
were estimated directly from the ZLC response curves at the lowest purge flow rate (5 mL/min) at which the effect of surface resistance is minimal. These values are very close to the values for C2H6. This is consistent with the equilibrium data of Zhu et al.4 which show that the Henry constants for C2H4 and C2H6 in DDR are essentially the same.
’ DISCUSSION The substantial difference in both diffusivity and diffusional activation energy between the original (untreated) DDR I sample and the treated DDR II sample means that the sample
treatment must have caused a significant modification of the internal structure rather than simply a modification of the external surface. The precise structural difference between the samples is unclear but a minor change in the critical dimensions of the distorted 8-ring windows is an obvious possibility. Another possibility is the removal of intracrystalline (nonframework) barriers such as have been observed in some samples of MFI19 and zeolite X.20 However, far more detailed studies would be required to establish the structural difference between these samples. The diffusional and equilibrium behavior of ethane and ethylene are very similar and do not appear to reflect the slightly smaller critical diameter of the ethylene molecule. For DDR I the equilibrium constants for both ethane and ethylene agree well with the isotherm data of Zhu et al.,4 and the ethylene diffusivity data are consistent with the self-diffusivity of ethylene (at 300 K) measured by PFGNMR.21 The DDR sample used in those studies was not subjected to any treatment and were presumably similar to DDR I. The pattern of behavior shown by the C2 species is quite different from that shown by CH4. Our previous study of the diffusion of methane in DDR8 showed that the diffusivity is substantially enhanced and the equilibrium constant is correspondingly reduced in the presence of an atmosphere of CO2. That pattern of behavior is to be expected from transition state theory as a consequence of competitive adsorption. In contrast, for both ethane and ethylene in both DDR samples, both the diffusivity and the equilibrium constant appear to be essentially unaffected by the presence of CO2. That result implies that the adsorption of C2 hydrocarbons and CO2 is noncompetitive. A similar result was reported by Guimaraes et al.22 who showed that the 1388
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Table 4. Summary of Kinetic and Equilibrium Parameters for C2H6 and CH4 in DDR D∞ (m2 s1)
E (kJ/mol)
K∞
ΔU (kJ/mol)
DDR II
2.6 1010
17.5
0.025
24.0
DDR I (5.9 mg)
1.75 1011
12.7
0.025
22.0
D/kR
C2H6
DDR I (2.4 mg)
0.0047 0.0028 0.0010.0033
Zhu4
0.026
22.5
CH4 DDR II
2.2 109
17.0
0.116
13.1
0
CH4 in DDR I8
2.2 108
25.5
0.116
13.1
0
Table 5. Comparison of KD (m2 s1) for Methane and Ethane in DDR II T (K) 298 373
(KD)CH4
(KD)C2H6
5.25 10
11
9 1011
7.23 10
11
5.3 1011
diffusivity of C4C10 linear alkanes in silicalite was not affected by the presence of CO2. For those systems such a result is not unexpected since the linear paraffins are located preferentially in the straight channel segments whereas CO2 molecules prefer the channel intersections, thus making adsorption noncompetitive. However, in DDR both the C2 hydrocarbons and CO2 may be expected to be competitively adsorbed within the large cages leading to a competitive adsorption situation. The equilibrium isotherms at higher loadings show clearly that CO2 occupies the large cages since the saturation capacity corresponds closely to the quotient of the specific micropore volume and the molecular volume of CO2.23 However, the isotherms for ethane and ethylene provide some tentative evidence that these molecules may prefer the window sites. The saturation capacities for both ethane and ethylene in DDR, derived from the isotherms of Zhu et al.4 correspond to approximately 1.5 molecules per cage. Each cage contains three windows (shared with the adjacent cage) so if the C2 hydrocarbons preferentially occupy the window sites the apparent saturation limit of 1.5 molecules per cage and the noncompetitive adsorption of CO2 would be explained. It is surprising that, for ethane, the higher diffusivity adsorbent (DDR II) also has a higher diffusional activation energy than DDR I, whereas for methane the activation energy shows the expected trend, being smaller for DDR II. It is also surprising that the diffusional activation energies of methane and ethane in DDR II are essentially the same (see Table 4). Even more surprising is the observation that the diffusional activation energy for DDR I is substantially smaller for ethane than for methane (12.7 vs 25.5 kJ/mol). This suggests, somewhat counterintuitively, that the energy barrier to intracrystalline diffusion of ethane is not determined by the molecular diameter. Both these observations could be considered as consistent with the preferential occupation of the windows by the C2 hydrocarbons since the energy barrier would then correspond to the higher energy region in the center of the cage which would be much less sensitive to small differences in molecular diameter. Of course any such hypothesis is highly speculative and would require validation by either detailed experimental studies or molecular simulations. From a practical perspective it is interesting to consider the product KD since this determines the permeance of a DDR
membrane. Table 5 shows a comparison of the KD values for methane and ethane in DDR II, calculated from the data given in Table 4. It is clear that the values for methane and ethane are very similar suggesting that a DDR membrane will show similar permeances for these species.
’ CONCLUSIONS The results from this study lead to some important conclusions having both practical and theoretical implications. The usefulness of the ZLC technique and its ability to distinguish between internal and surface resistance to mass transfer is convincingly confirmed. The value of the asymptotic analysis which can yield an accurate value for the diffusional time constant, even in the presence of surface resistance, is also confirmed. However, to avoid errors in this approach a very stable baseline is necessary. The proprietary treatment to which sample DDR II was subjected clearly induces a significant structural change although the nature of this change is not clear. Ethane and ethylene appear to behave very similarly in DDR but the difference in the patterns of behavior between CH4 and the C2 hydrocarbons is striking. Whereas the data for methane show no evidence of surface resistance in either of the DDR samples studied, the C2 hydrocarbons show clear evidence of a small but significant contribution from surface resistance. Both the kinetic and equilibrium data imply that the C2 hydrocarbons are adsorbed noncompetitively with CO2 whereas CH4 and CO2 are clearly adsorbed competitively. This, together with the anomalous differences in activation energy between methane and ethane or ethylene, might be explained by preferential occupation of the window sites by the dumbbell shaped C2 molecules but any such hypothesis is obviously speculative. From the practical point of view the data suggest that as a result of the compensation between diffusivity and equilibrium the permeances of methane and ethane in a DDR membrane will be very similar. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We are grateful to Drs. Harry Deckman and Peter Ravikovitch (ExxonMobil Research) for helpful discussions and assistance 1389
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Industrial & Engineering Chemistry Research with all aspects of this work. The financial support provided by NSF through the GOALI program is gratefully acknowledged.
’ NOTATION c sorbate concentration initial value of c at which sample is equilibrated co D intracrystalline diffusivity pre-exponential factor (in Arrhenius expression) D∞ E diffusional activation energy F purge flow rate k surface rate constant K dimensionless Henry constant (for CH4) apparent value of K (Derived from L0 without taking K0 account of surface resistance) pre-exponential factor (in van’t Hoff expression) K∞ L dimensionless parameter defined in eq 2 apparent value of L derived directly from ZLC resL0 ponse curve R equivalent radius of DDR crystals; gas constant t time T absolute temperature volume of DDR crystals Vs ΔU internal energy of adsorption
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(16) Wloch, J. Effect of Surface Etching of ZSM-5 Zeolite Crystals on Rate of Hexane Sorption. Microporous Mesoporous Mater. 2003, 62, 81. (17) Chmelik, C.; K€arger, J. In Situ Study of Molecular Diffusion Phenomena in Nanoporous Solids. Chem. Soc. Rev. 2010, 39, 4864. (18) Tzoulaki, D.; Schmidt, W.; Wilczok, U.; K€arger, J. Formation of Surface Barriers on Silicalite-1 by Residual Water Vapor as probed with iso-butane by Interference Microscopy. Microporous Mesoporous Mater. 2008, 110, 72. (19) Vasenkov, S.; K€arger, J. Evidence for Intracrystalline Transport Barriers in MFI Zeolites. Microporous Mesoporous Mater. 2002, 55, 139. (20) Feldhoff, A.; Caro, J.; Jobic, H.; Ollivier, J.; Crause, C. B.; Galvosas, P.; K€arger, J. Intracrystalline Transport Resistances in Nanoporous Zeolite X. ChemPhysChem 2009, 10, 2429. (21) Hedin, N.; DeMartin, G. J.; Roth, W. J.; Strohmaier, K. G.; Reyes, S. C. PFGNMR Self-Diffusion Measurements for small Hydrocarbons in High Silica DDR, CHA and LTA Structures. Microporous Mesoporous Mater. 2008, 109, 327. (22) Guimaraes, A. P.; Moeller, A.; Staudt, R.; de Azvedo, D. C. S.; Lucena, S. M. P.; Cavalcante, C. L. Diffusion of Linear Paraffins in Silicalite Studied by the ZLC Method in presence of CO2. Adsorption 2010, 16, 29. (23) Vidoni, A. Ph.D. Thesis, University of Maine, Orono, ME, 2011.
’ REFERENCES (1) van den Bergh, J. Ph.D. Thesis, University of Delft, Delft, The Netherlands, 2010. (2) van den Bergh, J.; Zhu, W.; Gascon, J.; Moulijn, J. A.; Kapteijn, F. Separation and Permeation Characteristics of a DD3R Zeolite Membrane. J. Membr. Sci. 2008, 316, 35. (3) van den Bergh, J.; Tihaya, A.; Kapteijn, F. High Temperature Permeation and Separation Characteristics of an all-silica DDR Membrane. Microporous Mesoporous Mater, 2010, 132, 137. (4) Zhu, W.; Kapteijn, F.; Moulijn, J. A.; den Exter, M. C.; Jansen, J. C. Shape Selectivity in Adsorption on All-Silica DD3R. Langmuir 2000, 16, 3322. (5) Krishna, R.; van Baten, J. M. Segregation Effects in Adsorption of CO2 Containing Mixtures and their Consequences for Separation Selectivities in Cage-Type Zeolites. Sep.Purif. Technol. 2008, 61, 414. (6) Krishna, R.; van Baten, J. M. A Molecular Dynamic Simulation of the Diffusion Characteristics of Cavity Type Zeolites with 8-Ring Windows. Microporous Mesoporous Mater. 2011, 137, 83. (7) Jee, S. E.; Sholl, D. S. CO2 and CH4 Transport in DDR Zeolite: Insights from Molecular Simulations. J. Am. Chem. Soc. 2009, 131, 7896. (8) Vidoni, A.; Ruthven, D. M. Diffusion of Methane in DDR Zeolite. Microporous Mesoporous Mater. Sept 2011, submitted for publication. (9) Vidoni, A.; Ruthven, D. M. ZLC Diffusion Masurements: Combined Effect of Surface Resistance and Internal Diffusion. Chem. Eng. Sci., in press. (10) Eic, M.; Ruthven, D. M. New Experimental Technique for Measurement of Intracrystalline Diffusivity. Zeolites 1988, 8, 40. (11) K€arger, J.; .Ruthven, D. M. Diffusion in Zeolites and other Microporous Solids; John Wiley: New York, 1992; pp 328333. (12) Ruthven, D. M.;.Brandani, S.; Eic, M. Measurement of Diffusion in Microporous Solids by Macroscopic Methods. In Molecular Sieves; Karge, H. G., Weitkamp, J., Eds.; Springer-Verlag: Berlin, Germany, 2008; Vol 7, pp 4584. (13) Ruthven, D. M.; Brandani, S., Measurement of Diffusion in Porous Solids by ZLC Methods. In Recent Advances in Gas Separation by Microporous Ceramic Membranes; Kanellopoulos, N. K., Ed.; Elsevier: Amsterdam, The Netherlands, 2000; pp 187212. (14) Hufton, J. R.; Ruthven, D. M. Diffusion of Light Alkanes in Silicalite. Ind. Eng. Chem. Res. 1993, 32, 2379. (15) Brandani, S.; Ruthven, D. M. Analysis of ZLC Desorption Curves for Gaseous Systems. Adsorption 1996, 2, 133–143. 1390
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