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Shape Selectivity in Adsorption on the All-Silica DD3R W. Zhu,* F. Kapteijn, J. A. Moulijn, M. C. den Exter,† and J. C. Jansen† Industrial Catalysis, DelftChemTech, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received October 25, 1999 The adsorption of ethane, ethene, propane, and propene on the all-silica DD3R has been investigated using the tapered element oscillating microbalance, TEOM. Single-component adsorption isotherms are for the first time reported at temperatures in the range from 303 to 473 K and at pressures up to 500 kPa. At high temperatures, the Langmuir isotherm appropriately describes the equilibrium adsorption data for ethane, ethene, and propene on the all-silica DD3R with energetically uniform sites. For the propene data below 340 K, a dual-site Langmuir model was used. Thermodynamic properties, like the isosteric heat and entropy of adsorption, have been determined. Only minor differences exist between the adsorption of ethane and ethene. Transient adsorption experiments reveal that the eight-ring windows of the all-silica DD3R are accessible to propene molecules, while they exclude propane molecules. The high shape selectivity for propene suggests that the all-silica DD3R might be effective as an adsorbent for the separation of propene and propane mixtures.
Introduction Porous tectosilicates can be divided into two classes, clathrasil and zeolite, according to the classification proposed by Liebau and co-workers.1,2 The name “clathrasil” was first introduced by Gies et al.3 for a class of porous tectosilicates. Clathrasils are clathrate compounds with 3-dimensional 4-connected host frameworks of silicacontaining cagelike voids between the [SiO4] tetrahedra. Decadodecasils 3R (DD3R) is a member of the clathrasil family possessing topologically different frameworks. Gies4,5 did pioneering work on the synthesis and structural identification of the clathrasil DD3R. The crystal structure of the clathrasil DD3R is built by corner-sharing [SiO4] tetrahedra that are connected to pseudohexagonal layers of face-sharing pentagonal dodecahedra ([512] cages). These layers are stacked in a ABCABC sequence and are interconnected by additional [SiO4] tetrahedra that form six-membered rings between the layers. Thus, two new types of cages arise, a small decahedron, [435661] cage, and a large 19-hedron, [435126183] cage; see Figure 1, the latter housing the 1-aminoadamantane template molecule during the synthesis. A detailed description of the clathrasil DD3R structure can be found in the literature.4 On thermal treatment of the clathrasil DD3R up to ca. 773 K, the template molecules can be decomposed and the fragments are driven out of the cages, transforming the clathrasil to a phase possessing zeolitic properties. An optimum procedure for the clathrasil DD3R crystallization that ensures the phase purity of DD3R has been * To whom correspondence should be addressed. Telephone: +31(0) 15 2784356. Fax:+31(0) 15 2784452. E-mail: w.zhu@ tnw.tudelft.nl. † Applied Organic Chemistry and Catalysis. (1) Liebau, F.; Gies, H.; Gunawardane, R. P.; Marler, B. Zeolites 1986, 6, 373. (2) Liebau, F. Zeolites 1983, 3, 191. (3) Gies, H.; Liebau, F.; Gerke, H. Angew. Chem., Int. Ed. Engl. 1982, 21, 206. (4) Gies, H. Z. Kristallogr. 1986, 175, 93. (5) Gies, H. J. Inclusion Phenom. 1984, 2, 275.
Figure 1. Building units and framework of the DD3R. After Gies.4
developed by Den Exter.6 The synthesis was scaled up to batches of 20 g. A complete removal of the template led to the pure silica sample, referred to as all-silica DD3R. One unit cell of the all-silica DD3R has the chemical formula Si120O240, and consists of six decahedra, nine dodecahedra, and six 19-hedra.4 The silica host framework can completely be constructed by linking decahedra and dodecahedra through common faces. The interlayer sixmembered rings with a maximum pore diameter of 0.28 nm expand the distance between two [512] layers and give rise to [435126183] cavities. These cavities or cages are interconnected through eight-membered rings with a free cross diameter of about 0.45 nm. Thus, a 2-dimensional (6) Den Exter, M. J. Exploratory Study of the Synthesis and Properties of 6-, 8- and 10-ring Tectosilicates and Their Potential Application in Zeolite Membranes. Ph.D. Thesis; TU Delft Press: Delft, The Netherlands, 1996; Chapters 3-4.
10.1021/la9914007 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/16/2000
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pore system is formed parallel to (001), with the cavities in a hexagonal arrangement, where each cavity is connected with three other cavities. The [435126183] cavity has a free volume of about 0.35 nm3 and a free cross diameter of 0.875 nm by assuming a spherelike cage. The adsorption of hydrocarbons on porous materials is an important subject that has received considerable attention in recent years. Apart from the traditional interest from the standpoint of separation, the understanding of adsorption, from a theoretical point of view, is of utmost importance. The size of the adsorbate molecule plays an important role because it will limit the range of pores and/or windows for which they are accessible. Matching the diameter of the pore aperture of microporous materials with the critical dimensions of gas molecules might lead to higher separation factors. Selectivity can be reached by differences in strength of adsorption or by steric hindrance of the molecule to be adsorbed in the pore system. Considering the critical diameters of small hydrocarbons, the all-silica DD3R with eight-ring windows might meet these requirements. Moreover, in heterogeneous catalysis a tailored contribution of shape selectivity and activity can lead to high-precision chemical conversion. However, up to now there have been very few data concerning the adsorption properties of light hydrocarbons on the all-silica DD3R. In this paper, we present adsorption data of ethane, ethene, propane, and propene on the all-silica DD3R measured by the inertial microbalance technique, TEOM.7 An interpretation of the difference in the adsorption behavior of propane and propene is given, based on their critical-molecular diameters. The conventional and dualsite Langmuir isotherm models have been used to describe the adsorption data. Furthermore, thermodynamic properties, like isosteric heat and entropy of adsorption, are presented to characterize interactions between adsorbate and adsorbent. Experimental Section Adsorption. A Rupprecht & Patashnick TEOM 1500 mass analyzer was used in an experimental setup designed for measurement of equilibrium and transient adsorption on microporous materials. A detailed description of the TEOM apparatus is given elsewhere.7 On the basis of the operating principle, the TEOM yields information about mass changes rather than absolute sample masses. The total mass change measured consists of the amount adsorbed and the mass change caused by the change of the gas density in the tapered sample tube. The change in the gas density depends on the type of gas and the operating conditions. To correct for the mass change caused by the change in the density of the gas phase reference experiments have been performed. In a reference experiment the response of the TEOM is measured without adsorbent. Two different reference experiments were performed with either 55 mg quartz wool or without sample, but no significant difference in the mass change was observed between these two reference runs. In addition, the relationship between the mass change in the reference runs and the partial pressure of the adsorbing gas is almost linear. No exact correlation, however, was found for different gases to be able to rely on a kind of master curve for this correction. The TEOM technique has several advantages for measurements of adsorption properties on microporous materials: (1) A well-defined gas phase is observed due to the high gas flow of feed with carrier gas through the adsorbent bed. This improves the external mass and heat transfer for microporous materials and also results in a fast response to gas phase changes. (2) A high-mass resolution is found across the entire range: a low system standard deviation and a stable baseline. These (7) Zhu, W.; van de Graaf, J. M.; van den Broeke, L. J. P.; Kapteijn, F.; Moulijn, J. A. Ind. Eng. Chem. Res. 1998, 37, 1934.
Langmuir, Vol. 16, No. 7, 2000 3323 properties are scarcely influenced by a change in experimental conditions, resulting in accurate and reproducible measurements. (3) Experimental conditions can be varied over a wide range of pressure and temperature, relevant to practical operations. A sample of 48.7 mg of the all-silica DD3R crystals was used for the adsorption experiments. Quartz wool was used at the top and the bottom of the sample bed to keep the adsorbent particles firmly packed, which is essential for a stable measurement. The isotherms were obtained by a stepwise increase of the partial pressure of the feed gas at fixed temperatures. The partial pressure of the feed gas was determined by its fraction of the total molar-feed-flow rate through the sample bed and the total pressure. A mixture of helium and the sample gas was used to create partial pressures below 1.013 × 105 Pa and pure adsorbate gas was used for pressures above 1.013 × 105 Pa. The isotherm data were accurately measured in different pressure ranges with a range of (0-1) × 105 Pa and (1-5) × 105 Pa. It is necessary because of the importance of the data in the low-pressure region for accurate determination of the Henry law constant. The temperature range covered was from 303 to 473 K. Six temperature levels were used for each adsorbate to enhance the accuracy of thermodynamic properties derived. Most experiments were repeated, and both adsorption and desorption experiments were performed to confirm reversibility. Prior to the experiments the crystals were outgassed in the following way. After a temperature rise with a rate of 10 K‚min-1 in situ in a helium flow of 200 cm3‚min-1, the sample was heated at 573 K for 24 h in order to remove adsorbed impurities. Helium was obtained as an ultrahigh purity gas (>99.999%). The gaseous adsorbates such as ethane, ethene, propane, and propene were 3.5 grade (>99.95%). All-Silica DD3R. The all-silica DD3R crystals had been synthesized in-house.8 The template inside the clathrasil DD3R crystals was removed by calcination at 973 K for 6 h. The apparent density of the all-silica DD3R was 1.714 g‚m-3 and the adsorption of N2 indicated an accessible microporous void volume of 0.15 cm3‚g-1. The crystal size is in the range of 5-10 µm, as determined by SEM.
Theoretical Section Molecular Dimensions and Adsorbent Pore Systems. Knowledge of the dimensions of adsorbate molecules is crucial to understanding molecular exclusions as well as shape and size selectivity on microporous materials. Transient diameters or Lennard-Jones potential constants, σK, have been employed to determine the accessibility of molecules to channels and/or apertures on microporous materials. The transient or collision diameter is the intermolecular distances of closest approach for two molecules colliding as the potential is equal to zero.9 By assuming that the molecule is effectively spherical, one observes that the minimum equilibrium diameter of a molecule, rmin, is given by a Lennard-Jones 12-6 potential, i.e., rmin ) 21/6σK. Webster et al.10 pointed out that transient diameters do not take into account molecular orientation, and this orientation is crucial in determining whether a molecule will fit into a small pore of fixed size. In addition, for large, nonspherically symmetrical molecules, transient diameters cannot be used directly in determining whether the molecule can enter a pore. A better criterion of molecular exclusion is to use the critical dimensions of adsorbate molecules, based on the molecular structure and effective van der Waals radii of extreme atoms. The structural diameter, σS, which can be calculated from bond lengths and angles, is defined as the (8) Den Exter, M. J.; Jansen, J. C.; van Bekkum, H. In Zeolites and Related Microporous Materials; Weitkamp, J., Karge, H. G., Pfeifer, H., Ho¨lderlich, W., Eds.; Elsevier: Amsterdam, 1994. (9) Breck, D. W. Zeolite Molecular Sieves-Structure, Chemistry, and Use; John Wiley and Sons: New York, 1974; Chapter 8. (10) Webster, C. E.; Drago, R. S.; Zerner, M. C. J. Am. Chem. Soc. 1998, 120, 5509.
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Table 1. Characteristic Diameters of the Adsorbate Molecules Studied adsorbate
σK (nm)a
σS (nm)b
σC (nm)c
ethane ethene propane propene
0.38 0.39 0.43 0.45
0.206 0.178 0.280 0.265
0.372 0.344 0.446 0.431
a Transient or collision diameter.9 b Structural diameter defined as the diameter of the smallest cylinder that can be drawn around the molecule in its most favorable conformation through the centers of the extreme binding atoms.11 c Critical diameter calculated by the summation of the structural diameter and the effective van der Waals radii of the two extreme hydrogen atoms.
diameter of the smallest cylinder that can be drawn around the molecule, in its most favorable conformation, through the centers of the extreme binding atoms.11 For the hydrocarbons, ethane, ethene, propane, and propene, the effective van der Waals radii of the two extreme hydrogen atoms must be taken into account. The van der Waals radius of hydrogen is about 0.12 nm.12 By subtraction of its atomic radius, 0.037 nm,13 the net contribution to the critical diameter is about 0.166 nm. Table 1 shows the three characteristic diameters of the hydrocarbon molecules studied. In contrast to the transient diameter, the alkene molecule has a smaller critical diameter than that of the corresponding alkane with the same carbon number. The cross section of a methyl group is circular while that of a methylene group is more elliptical. In addition, a double bond can decrease the curvature of the molecule. Therefore, it is reasonable to expect that the alkene molecule has a smaller critical diameter, compared to that of the corresponding alkane. Adsorption Isotherms. On the basis of the critical diameters of the light hydrocarbons studied, one may assume that the adsorption only takes place inside the 19-hedron cavities, entering via eight-membered rings of the all-silica DD3R. For the regular structure it is instructive to express the adsorbate location in terms of molecules per unit cell. The number of adsorbed molecules per unit cell, c (muc), is given by
c)
mads Muc ms Mmol
(1)
where Muc and Mmol are respectively the molar weight of the unit cell and the molar weight of the adsorbate, and mads and ms represent the adsorbed mass of the adsorbate and the mass of the adsorbent used, respectively. The number of molecules per unit cell is converted into that of molecules per cavity by dividing the number of cavities per unit cell, i.e., 6. This corresponds with a loading of 0.832 mol‚kg-1. Adsorption isotherms provide a quantitative measure of the heterogeneous equilibria involved in the adsorption of a gas by a solid. A generalized description of heterogeneous equilibria uses the Langmuir equation that can be derived from transient, thermodynamic, or statistical mechanical considerations,14,15 and is often found to be satisfactory for zeolites due to compensation effects.16 If (11) Ruthven, D. M.; Derrah, R. I.; Loughlin, K. F. Can. J. Chem. 1973, 51, 3514. (12) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: New York, 1960; p 260. (13) Huggins, M. L. J. Am. Chem. Soc. 1953, 75, 4126. (14) Langmuir, I. J. Am. Chem. Soc. 1918, 40, 1361. (15) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley and Sons: New York, 1984. (16) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieves; John Wiley and Sons: New York, 1978.
Figure 2. Adsorption isotherms of ethane on the all-silica DD3R. Lines are the Langmuir isotherm model fits.
the average number of molecules inside the 19-hedron cavity is e1, interaction only takes place between adsorbate and adsorbent. Thus, the isotherms might be described by the conventional Langmuir model, eq 2,
c ) csat,1
K1p 1 + K1p
(2)
where csat,1 is the saturation concentration of the molecules adsorbed per unit cell, K1 is an equilibrium constant, p is the equilibrium pressure of the adsorbate, and the subscript 1 represents the adsorption process at loadings up to one molecule per cavity. This model implies that all adsorption sites are equivalent and that each site only contains a single molecule that does not interact with any neighboring molecule. When the number of molecules per cavity exceeds one, interaction between adsorbates will occur. This probably leads to deviations from the Langmuir model. In view of the free volume, the 19-hedron cavity is capable to accommodate more than one molecule. The adsorption of the second molecule will be energetically different. To describe this adsorption at higher loadings, a dual-site Langmuir (DSL) model is proposed. This model takes into account implicitly interactions between adsorbates, which give rise to a pseudo-second-adsorption site.
c ) csat,1
K2p K1p + csat,2 1 + K1p 1 + K2p
(3)
with the subscript 2 referring to the adsorption at the second “site”. Results Isotherms. The isotherm data of ethane, ethene, and propene adsorbed on the all-silica DD3R are presented in Figures 2-4. The isotherm data of propane on the allsilica DD3R are not presented, because the uptake was relatively slow and the equilibria were far from reached after 6 h at a temperature between 303 and 473 K and pressures up to 5 × 105 Pa. The obtained loadings of propane were more than 10 times smaller than those of propene. A transient uptake of propane and of propene is given in Figure 5, illustrating these observations. The isotherms of ethane, ethene, and propene adsorbed on the all-silica DD3R exhibit a type-1 adsorption isotherm, according to the Brunauer classification, over the temperature and pressure range studied, as shown in Figures 2-4. Both the Langmuir model and the DSL
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Table 2. Adsorption Isotherm Parameter Values Estimated for Ethane, Ethene, and Propene adsorbate
a
K1 (10-5 Pa-1)
std deva (muc)
csat,1 (muc)
ethane
303 338 373 408 438 473
9.577 ( 7.598 ( 0.003 5.908 ( 0.002 5.224 ( 0.003 4.298 ( 0.005 3.801 ( 0.007
2.759 ( 1.565 ( 0.002 0.780 ( 0.001 0.500 ( 0.001 0.312 ( 0.001 0.212 ( 0.001
0.069 0.005 0.002 0.002 0.002 0.002
ethene
303 338 373 408 438 473
9.302 ( 0.067 7.792 ( 0.030 5.888 ( 0.036 5.161 ( 0.048 4.222 ( 0.055 3.819 ( 0.155
2.794 ( 0.079 1.247 ( 0.014 0.772 ( 0.012 0.488 ( 0.010 0.303 ( 0.007 0.208 ( 0.014
0.126 0.038 0.033 0.029 0.020 0.034
propene
303c 338c 303 338 373 408 438 473
3.575 ( 0.215 4.527 ( 0.137 8.716 ( 0.165 6.898 ( 0.168 5.579 ( 0.001 5.420 ( 0.001 5.291 ( 0.001 5.140 ( 0.001
Standard deviation:
csat,2 (muc)
K2 (10-5 Pa-1)
T (K)
0.037b
0.041b
5.767 ( 0.194b 3.685 ( 0.088
x∑n(ccat-cexp)2/(n-j), for j fitting parameters;
Figure 3. Adsorption isotherms of ethene on the all-silica DD3R. Lines are the Langmuir isotherm model fits.
Figure 4. Adsorption isotherms of propene on the all-silica DD3R. Lines are the Langmuir isotherm (solid) and the dualsite Langmuir isotherm (dashed) model fits.
model, see eqs 2 and 3, were used to fit the isotherm data, as indicated in Figures 2-4. At high temperatures, the Langmuir model gives a good description of the isotherm data. For the adsorption of propene at 303 and 338 K, deviations from the Langmuir model are observed at high loadings. The DSL model gives a significantly better description. If the DSL model is used to fit the results
260.7 ( 117.9 29.48 ( 2.04 13.51 ( 1.56 10.27 ( 1.63 7.693 ( 0.003 3.330 ( 0.001 1.810 ( 0.001 0.980 ( 0.001 b
3.299 ( 0.257b 0.660 ( 0.087
0.076 0.048 0.505 0.464 0.001 0.001 0.001 0.001
Standard deviation. c Results for the dual-site Langmuir model.
Figure 5. Uncorrected mass uptakes of single components, propane and propene, and their mixture in flowing He. T ) 373 K, p(total) ) 1.013 × 105 Pa, ms ) 48.7 mg. The mass change caused by the change in the density of the gas phase is on the order of 10-5 g under the same conditions.
obtained at a high temperature, the parameters of one of the two terms become very small. The adsorption parameters obtained from the fits are listed in Table 2. The various results, presented in Table 2 and Figures 2-4, show that the temperature and the molecular dimension have a pronounced effect on the adsorption of the light hydrocarbons on the all-silica DD3R. In the further analysis, fitted model isotherms were used for the estimation of thermodynamic adsorption properties. Thermodynamic Properties. From the isotherm data a number of thermodynamic properties have been derived. The Henry law constant, KH, quantifies the extent of adsorption of a given adsorbate by a solid. The magnitude of KH depends on both the properties of the adsorbate and solid. As a first estimation of the Henry law constant, its value can be obtained from the estimated parameter values in the conventional Langmuir model, KH ) K1csat,1. An alternative way of representing the equilibrium data to extract the Henry law constant makes use of the virial form of the thermodynamic equilibrium relation.17 (17) Barrer, R. M.; Lee, J. A. Surf. Sci. 1968, 12, 354.
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p)
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c 3 4 exp 2A1c + A2c2 + A3c3 + ... KH 2 3
(
)
(4)
where KH is the Henry law constant, c the amount adsorbed, p the equilibrium pressure, and Ai the virial coefficient. It is evident that ln(p/c) vs c should approach linearity at low loadings, thus providing a straightforward extrapolation to determine the Henry law constant KH. The KH values obtained in this way, at the different temperatures, can be described with the integrated form of the van’t Hoff equation:
(
KH ) KH0 exp
)
-∆U0 RT
(5)
The observed linearity of the lnKH vs 1/T plots, Figure 6, leads to the internal energy for adsorption at zero coverage, ∆U0, summarized in Table 3. The isosteric heat of adsorption is defined by eq 6.18 st
Q [∂ ∂Tln p] ) RT c
Table 3. Summary of Derived Thermodynamic Adsorption Parameters and Physical Properties of the Adsorbates
(6)
2
So Qst can be obtained from a plot of ln p against the reciprocal of the temperature. Figure 7 shows the results of the isosteric heat of adsorption as a function of the amount adsorbed. Extrapolation then gives the isosteric heat of adsorption for the limiting case of adsorption at zero coverage, Qst 0 , and presented in Table 3. The calculated isosteric heat of adsorption at zero coverage is independent of the temperature. If Qst and the differential adsorption enthalpy are assumed to be identical by neglecting any small temperature dependence, the differential molar entropy, S h ads, of adsorbates in the adsorbed phase can be calculated by eq 7.16
S h ads ) S0g(298.15) +
Figure 6. ln KH vs 1/T plots for the studied adsorbates by the all-silica DD3R.
T Q dT 0 + R ln( ) Cp ∫298.15 T p T
p
adsorbate
KH0a (10-9 mol‚kg-1‚Pa-1)
-∆U0 (kJ‚mol-1)
Qst 0 (kJ‚mol-1)
Rb (10-24 cm3)
νc (10-12 s-1)
ethane ethene propene
2.22 1.06 1.58
24.74 26.71 32.94
24.76 24.29 36.02
4.43 4.25 6.26
2.29 2.46 2.23
a Preexponential factor for the van’t Hoff relationseq 5; b Polarizability.30 c Approximate mean frequencies of molecules in adsorbed state, calculated relative to Ar on KCl,27 using -∆U1 ) 6.66 kJ‚mol-1, m1 ) 39.91 × 1.662 × 10-24 g, and ν1 ) 1 × 1012 s-1 in eq 14.
st
(7)
Here S0g(298.15) is the standard molar entropy of the gas phase at T ) 298.15 K and p0 ) 1.013 × 105 Pa. Cp is the molar heat capacity of gaseous adsorbates at constant pressure, and T and p are the equilibrium pressure and temperature. S0g and Cp are obtained from the literature.19 Values of S h ads were determined at each of the experimental temperatures for ethane, ethene, and propene and were plotted as a function of the amount adsorbed. Results are illustrated for ethane and propene in Figures 8a and b. S h ads increases with temperature and decreases with increasing loadings. The curves of S h ads at different temperatures never intersect and follow parallel courses. Discussion Shape Selectivity. The critical diameters of both ethane and ethene are smaller than the free cross diameter of the eight-membered ring and their molecules easily enter the 19-hedron cavities. Under the same conditions, for the adsorption of ethane and ethene, there is no significant difference in the amount adsorbed on the allsilica DD3R. (18) Ross, S.; Olivier, J. P. On Physical Adsorption; John Wiley and Sons: New York, 1964. (19) Rossini, F. D.; Pitzer, K. S.; Arnett, R. L.; Braun, R. M.; Pimentel, G. C. Selected values of physical and thermodynamics properties of hydrocarbons and related compounds; Carnegie Press: Pittsburgh, PA, 1953.
Figure 7. Isosteric heat of adsorption as a function of the amount adsorbed.
It is interesting to note the difference in the adsorption behavior between propane and propene, as shown in Figure 5. The critical diameters of both propane and propene are comparable to the free cross diameter of the eight-ring window (see Table 1). For propane, the mass uptake recorded with the TEOM shows that the amount adsorbed is much lower than that of propene under the same conditions. Figure 5 also shows the mass uptake of binary mixture of propane and propene, which is the same as that of propene at the same partial pressure. This indicates that the presence of propane hardly affects the adsorption of propene. Apparently, the eight-ring windows exclude propane molecules. The small amount adsorbed is probably caused by adsorption on the external surface of the DD3R crystals. The critical diameter of a propene molecule is slightly smaller than that of propane. The isotherm data show that the eight-ring windows of the 19-hedron cavities are accessible to propene molecules. At 303 K and a pressure
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over 4 × 105 Pa, a maximum amount adsorbed, about 8.9 muc, seen in Figure 4, was obtained. The uptake of propene, shown in Figure 5, indicates that its equilibrium adsorption takes a long time. Such a phenomenon can be interpreted in terms of the accessibility of the cavities through the eight-ring window, since the critical diameter of propene molecule is close to the free-cross diameter of the eight-ring window. Also the orientation of the propene molecule to enter the eight-ring window and to move to the next cavity will play a role. The different adsorption behaviors between propane and propene on the all-silica DD3R have been interpreted by means of simulations with the program Cerius2. The simulation results indicate energy barriers of 30.35 and 89.20 kJ‚mol-1 for propene and propane, respectively, as the molecules are forced through the eight-membered ring window.20 For a propane molecule, the angle between two C-C bonds will increase from about 113 to 125°, resulting in the internal deformation of the molecule, if the molecule is forced to pass through the window. Cryogenic distillation has been the dominant technology utilized for light alkene/alkane separations for many years. Although distillation is reliable and essentially unchallenged in this application, the necessary low temperatures and high pressures make it an energy-intensive separation scheme.21 The transient experiments for the adsorption of propane and propene reveal a high selectivity for propene on the all-silica DD3R. So, the all-silica DD3R is effective as a shape-selective adsorbent for the separation of propane/propene mixtures. Its potential application in separation is being further investigated. Isotherms. The isotherm data of both ethane and ethene are well described by the Langmuir model over the temperature and pressure range studied. Especially, for propene, deviations from the Langmuir model have been observed at 303 and 338 K and the higher-pressure range, at which the amount adsorbed exceeds 6 muc (see Figure 4). The molecular dimensions increase in order of ethene, ethane, and propene. The deviation from the Langmuir model also follows the same order. A plausible reason is that interactions between adsorbates result in the deviation from the Langmuir model as the number of molecules residing the 19-hedron cavity exceeds one. Obviously, increasing molecular dimensions can significantly enhance such an interaction. Adsorption Affinities. For many applications of microporous materials, the equilibrium constants for the various processes are of prime concern. The Henry law constants of ethane and ethene on the all-silica DD3R are almost identical. At the same temperature, the value of the Henry law constant for propene is larger than that of either ethane or ethene, as shown in Figure 6. This indicates that propene molecule has a stronger affinity to the adsorbent, compared to ethane and ethene. The isosteric heat of adsorption for the adsorbates studied as a function of the amount adsorbed is presented in Figures 7. At loadings below 1 muc, the observed linearity of the Qst vs c plots leads to the isosteric heat of adsorption at zero coverage, given in Table 3. The isosteric heat of adsorption at zero coverage increases in order of ethene, ethane, and propene. The all-silica DD3R is hydrophobic and stable to high temperatures. It provides a nonpolar structure for adsorption of relatively small gas molecules. For the nonspecific interactions involved,
the adsorption potential is almost entirely the product of dispersion forces,16 where the adsorbent-adsorbate interaction is proportional to the polarizability of the adsorbate.22 The polarizabality increases with increasing molecular dimensions, as shown in Table 3, which accounts for the fact that the isosteric heat of adsorption at zero coverage increases with increasing molecular dimensions. The derived Qst as a function of the amount adsorbed shows different trends at loadings below 6 muc. For ethane and ethene, Qst gradually increases with increasing loadings, which is generally behavioral for homogeneous adsorbents and nonspecific interaction. On the other hand, for propene, Qst slightly decreases in a linear trend up to six molecules per unit cell, although the change in the isosteric heat of adsorption at low loadings is small. Similar observations have been made for the adsorption of H2O in the all-silica DD3R.23 Both molecules have a permanent dipole, so it is suggested that this behavior be due to specific interactions. However, a clear interpretation cannot be given on the basis of the results. In view of the wide range of loadings over which this trend is present, a surface heterogeneity is not a probable explanation. The results in Figure 7 indicate that the DD3R shows reasonable energetic homogeneity, at least toward the small adsorbate molecules. The Qst tends to sharply rise with increasing adsorption at loadings above 6 muc, shown in Figure 7, which is not only ascribed to molecule-molecule interactions within the 19-hedron cavities of DD3R but also due to the more confined packing, up to 1.5 molecules per cavity. The differential molar entropy in the adsorbed phase, S h ads, gradually decreases with increasing loadings, and the same trend for all three adsorbates as a function of the amount adsorbed has been observed, as illustrated in parts a and b of Figure 8. The sigmoid form of the curves is expected for type I isotherms. Barrer24 pointed out that the adsorption entropy is a characteristic function of the amount adsorbed. For energetically uniform adsorbents, S h ads decreases continuously as c increases, while for energetically heterogeneous adsorbents, S h ads often increases as c increases. According to this concept, the allsilica DD3R can be considered as an energetically uniform adsorbent as well. If the adsorbed molecules are oscillators, then S h ads can be written as the sum of a configurational part, S h c, and a thermal part, S h th:16
(20) Ten Horst; et al. Delft University of Technology, to be published 1999. (21) Safarik, D. J.; Eldridge, R. B. Ind. Eng. Chem. Res. 1998, 37, 2571.
(22) Richards, R. E.; Rees, L. V. C. Langmuir 1987, 3, 335. (23) Den Exter, M. J.; Jansen, J. C.; Van Bekkum, H.; Zikanova, A.; Dubsky, J.; Kocirik, M., Collect. Czech. Chem. Commun. 1997, 62, 981. (24) Barrer, R. M. J. Colloid Interface Sci. 1966, 21, 415.
S h ads ) S hc + S h th
(8)
The S h th gives the differential entropy of the three vibrational degrees of freedom, associated with the movement of the molecule about its mean position over the adsorption site. The differential configurational entropy, S h c, arises from the number of distinguishable configurations of adsorbate molecules on adsorption sites. For the Langmuir isotherm, eq 2, S h c is given by eq 9,
S h c ) -R ln
(
)
( )
c θ ) -R ln csat,1 - c 1-θ
(9)
where θ corresponds to the fraction of sites covered. Equations 8 and 9 were used to evaluate S h th, as a function of the amount adsorbed at 303 K in Figure 9. At loadings lower than 6 muc, S h th is approximately independent of c,
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Zhu et al.
Table 4. Entropies for the Adsorption of Ethane, Ethene, and Propene on the All-Silica DD3R at θ ) 0.5 adsorbates
T (K)
h V (eq 11) 3S (J‚mol-1‚K-1)
St3d(g) (J‚mol-1‚K-1)
S h th (J‚mol-1‚K-1)
h V (eq 16) 3S (J‚mol-1‚K-1)
∆S(3V)a (J‚mol-1‚K-1)
ethane
303 338 373 408 438 473
51.05 53.75 56.19 58.41 60.17 62.08
151.57 153.84 155.89 157.75 159.23 160.82
138.88 148.05 163.91 171.64 177.96 186.95
60.32 65.71 77.73 81.56 84.50 89.52
9.27 11.96 21.54 23.15 24.33 27.44
ethene
303 338 373 408 438 473
49.25 51.95 54.39 56.61 58.36 60.27
150.71 152.98 155.03 156.89 158.36 159.96
128.16 135.50 153.60 160.00 165.11 172.49
58.92 63.53 78.83 82.37 84.99 89.42
9.67 11.58 24.44 25.76 26.63 29.15
propene
303 338 373 408 438 473
51.68 54.38 56.82 59.04 60.80 62.71
155.76 158.03 160.08 161.95 163.42 165.02
182.73 199.17 211.23 218.39 224.40 231.31
70.77 82.13 89.08 91.10 92.71 94.46
19.09 27.75 32.26 32.06 31.91 31.75
a
∆S(3V) ) 3S h V (eq 16) - 3S h V (eq 11).
Figure 9. Differential thermal entropy of adsorption as a function of the amount adsorbed at 303 K.
expressed as the sum of three terms16,25
S h th ) 3S hV + S hI + S hR
(10)
where 3S h V is the differential vibrational entropy of the adsorbed molecule as a whole; S h I, the differential entropy associated with the internal vibrational and rotational degrees of freedom; and S h R, the differential rotational entropy of the adsorbed molecule as a whole. Following the procedure described by Barrer25 and h V can be estimated by the equation Eberly,26 3S
Figure 8. Differential entropy of adsorption as a function of the amount adsorbed. Points correspond to the data calculated from eq 7: (a) ethane; (b) propene.
indicating homogeneous adsorption, approaching Langmuir assumptions. For all the adsorbates investigated, at loadings above 6 muc, a pronounced decrease of S h th is seen. Here, more than one molecule is forced into the 19hedron cavities. Therefore, the molecules will lose more degrees of freedom. h ads are identical for θ ) 0.5, It is noted that S h th and S where the configurational contribution vanishes. This is also defined as the standard state of adsorption for the Langmuir model. For polyatomic hydrocarbon molecules, the thermal entropy of the adsorbed phase can be
hV 3S
) 3(1S h V) ) 3R
hν hν {kT ) - 1] [exp(kT hν ln[1 - exp((11) kT)]} -1
The quantity ν is the vibrational frequency of the hydrocarbon molecule as a whole in its intracrystalline environment. The estimation of this vibrational frequency follows the procedure previously described by Barrer.25 For argon adsorbed on potassium chloride, Orr27 calculated the potential energy-distance curve for an argon atom situated over the center of a KCl lattice cell. If the region (25) Barrer, R. M.; Bultitude, F. W.; Sutherland, J. W. Trans. Faraday Soc. 1957, 53, 1111. (26) Eberly, P. E., Jr. J. Phys. Chem. 1963, 67, 2404. (27) Orr, W. J. C. Trans. Faraday Soc. 1939, 35, 1247.
Shape Selectivity in Adsorption
Langmuir, Vol. 16, No. 7, 2000 3329
round the minimum was plotted on a large scale, the value of the restoring force per unit displacement, f, could be obtained by fitting the potential energy-distance curve using eq 12,
1 -Φ ) f(r - re)2 2
(12)
where Φ is the total potential energy, r the distance of the atom in any position above the surface, and re the equilibrium distance. Since
ν)
xmf
1 2π
(13)
where m is the reduced mass of the oscillator and, as a reasonable assumption, the restoring force is proportional to the energy of adsorption, then ν will be directly proportional to the square root of the energy of adsorption.16,28 Equation 14 was used to derive approximate mean frequencies for hydrocarbons on the all-silica DD3R.
ν1 ) ν2
x
f1m2 ) f2m1
x
∆U1m2 ∆U2m1
(14)
where ∆U is the energy of adsorption. The calculated mean frequencies are included in Table 3. The sum of SI(g) + SR(g) in the gas phase can be obtained by subtracting the three-dimensional translational entropy,29 St3d(g), from the standard entropy of the gaseous hydrocarbon
St3d(g) ) R ln(M1.5T2.5) - 9.61
(15)
where M is the molar weight (g‚mol-1) and T is the temperature (K). By assuming that the internal vibrational and rotational entropy remains unaltered upon adsorption, one observes that the differential vibrational h V, can be estimated entropy of the adsorbed molecule, 3S (28) Hill, T. L. Adv. Catal. 1951, 4, 211. (29) Kemball, C. Adv. Catal. 1950, 2, 233. (30) CRC Handbook of Chemistry and Physical, 76th ed.; CRC Press: New York, 1995.
by eq 16,
hV 3S
)S h th - [S0(g) - St3d(g)]
(16)
S0(g)
where is the standard molar entropy in the gaseous phase at the standard pressure of 1.013 × 105 Pa. So, h V: from an average there are two ways to estimate 3S vibrational frequency, eq 11, and from the differential thermal entropy, eq 16. Summary calculations of the entropy of ethane, ethene, and propene in the adsorbed phase at θ ) 0.5 are included in Table 4. As can be seen, there is a considerable discrepancy between the differential vibrational entropy calculated by eq 11 and that by eq 16. This difference changes little over the temperature range studied. This difference is interpreted as that the adsorbed molecules still possess some translational mobility inside the 19-hedron cavities. Eberly26 gave a similar interpretation on the adsorption of cyclohexane on Na-mordenite. Conclusions The adsorption isotherms of ethane, ethene, and propene on the all-silica DD3R have been accurately measured using the TEOM technique over a wide pressure and temperature range relevant to practical applications. At loadings below 6 muc, the Langmuir model gives a good description of the amount adsorbed inside the 19-hedron cavities, which can be considered as energetically uniform sites for adsorption due to interaction between adsorbate and adsorbent only. For propene below 340 K, a dual-site Langmuir model better represents the adsorption data. Thermodynamic properties such as isosteric heat and entropy of adsorption have been determined, which are in agreement with the physical picture of the localized adsorption on a homogeneous adsorbent. A high adsorption selectivity for propene over propane on the all-silica DD3R has been found. This shape-selective adsorption can been explained from the slight difference in the critical-molecular diameter. The all-silica DD3R, which is hydrophobic and stable up to high temperatures and has a relatively high capacity for the adsorption of propene, might be effective as a selective adsorbent for the separation of propane and propene. LA9914007
