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Molecular Interactions in Nanoporous Adsorbents. Adsorption of N2 and O2 in Zeolites with Cavities or Channels: Na12A, Ca6A, NaX, and Decationated Mordenite A. M. Goulay, J. Tsakiris, and E. Cohen de Lara* Laboratoire de Dynamique de la Matie` re Condense´ e, Universite´ Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris Cedex 05, France Received June 29, 1995. In Final Form: September 14, 1995X The adsorption of two small molecules in porous crystals presenting void volumes of different shapes (cavities of ∼12 Å diameter, channels of ∼6 Å diameter) is measured in a large range of temperatures and pressures. The data analysis shows off the difference in the intermolecular forces between N2 and O2 molecules; in condensed phases the molecule-molecule interaction is repulsive and it is more repulsive for N2. The density of the adsorbed phase is compared with that of the liquid at three temperatures; that points out the confinement effect which is dominant in the channels.
I. Introduction Adsorption measurements in zeolites, which present void volumes of small dimensions,1 allow the analysis of adsorption processes with respect to the structure of the adsorbent and the properties of the adsorbates. At low coverage what is important is the host-guest interaction; differences in the adsorption amount of different molecules in the same zeolite point out the effect of the molecular quantities involved in the interaction with the crystal ions. At high coverage the interactions between molecules take place; the adsorbed phase cannot be considered as a sum of individual molecules, each of them interacting with the solid. The comparison of experimental results with theoretical isotherms which characterize the equilibrium of the guest-host system gives an idea of the nature of the adsorbed phase. Several models are commonly used for adsorption in zeolites. These adsorbents present internal surfaces and void volumes. Interpretation in terms of monolayer models (Langmuir)2 is not always justified in porous crystals. On the other hand, the model of Dubinin,3 which considers the adsorbed phase as a fluid occupying a volume, is scarcely adapted for a large range of temperatures, except maybe for small molecules such as H2.4 In fact zeolites are principally regular arrays of connected domains in which the guest molecules are enclosed. As previously mentioned for alkanes in A zeolites by Ruthven5 and in X zeolites by Stach,6 a model of adsorption in separate boxes is appropriate for these systems. Another statistical model containing a small number of parameters, i.e., the interaction of the molecule with the zeolite, the interaction between adjacent molecules, and the number of molecules at saturation in the box, has been proposed by Dupont-Pavlovsky (DP).7 As this model assumes that the guest molecules are localized on sites in a volume, it is more similar to Langmuir’s than to Ruthven’s, which considers that the enclosed molecules are mobile in the cavity. Futhermore this model is very X Abstract published in Advance ACS Abstracts, December 1, 1995.
(1) Breck, D. W. Zeolite molecular sieves; John Wiley and Sons: New York, 1993. (2) Langmuir, I. J. Am. Chem. Soc. 1918, 40, 1361. (3) Dubinin, M. M. Chem. Phys. Carbon 1966, 51. (4) Cohen de Lara, E.; Kahn, R.; Bouchaud, J. P.; Ibnass, H. Proc. Int. Zeolite Conf. Montreal 1992, 55. (5) Ruthven, D. M.; Loughlin, K. F. J. Chem. Soc., Faraday Trans. 1 1972, 68, 696. (6) Stach, H.; Lohse, U.; Schirmer, H. Zeolites 1986, 6, 74. (7) Dupont-Pavlovsky, N. The`se, Universite´ Nancy I, 1971.
0743-7463/96/2412-0371$12.00/0
sensitive to the intermolecular interaction and allows a rather good estimation of this quantity.8 Many investigations have been done on simple gases, such as the air gases.9-18 In this paper we have taken again a comparative study of nitrogen and oxygen in zeolites with different porosities: NaA, CaA, and NaX zeolites contain cavities of about 12 Å diameter, interconnected by windows more or less open (4, 5, and 8 Å diameter, respectively); the structure of the H-mordenite presents unidimensional channels of about 7 Å diameter with small pockets. Then the shapes of the void volumes, in which the adsorption takes place, are rather different. Futhermore the inner surfaces of the decationated mordenite are probably more homogeneous than in the A and X-types since this zeolite is more siliceous. The isotherms of N2 and O2 in four zeolites, for temperatures from 300 to 78 K and pressures from 10-3 mbar up to the atmospheric pressure, are obtained by microgravimetry; this method gives directly the adsorbed mass from which one calculates the number of molecules per unit cell at each equilibrium point. The aim of this study was not the research of a correct model but an analysis of the density of the adsorbed phase. As a matter of fact the experimental determination of the void volumes in porous adsorbents leans on the hypothesis that the adsorbed amount at saturation has the density of the liquid. This hypothesis is a rough approximation. II. Adsorbent and Adsorbate Characteristics In this part we emphasize the evaluation of the void volumes from the structural data and the densities of the two species at the coexistence of the gas and liquid phases. II.1. Adsorbents. Much information about these zeolites comes from Breck’s book.1 The anionic framework is built of SiO4 and AlO4 tetrahedra linked by an oxygen (8) Tarek, M.; Kahn, R.; Cohen de Lara, E. Zeolites 1995, 15, 67. (9) Dupont-Pavlovsky, N.; Bastick, J. Bull. Soc. Chim. 1970, 1, 24. (10) Roques, M.; Bastick, M. Bull. Soc. Chim. 1970, 4, 1252. (11) Ginoux, J. L.; Bonnetain, L. Acad. Sci. Paris, C 1971, 272, 879. (12) Roques, M.; Bastick, M. J. Chem. Phys. 1976, 66, 445. (13) Hayhurst, D. T.; Sefcik, M. D. J. Am. Chem. Soc. 1983, 333. (14) Furuyama, S.; Nagato, M. J. Phys. Chem. 1984, 88, 1735. (15) Furuyama, S.; Miyazaki, M.; Inoue, H. 1984, 88, 1741. (16) Reichert, H.; Moller, U.; Unger, K. K.; Grillet, Y.; Rouquerol, F.; Rouquerol, J.; Coulomb, J. P. Characterization of Porous Solids II; Elsiver Science Publishers B.V.: Amsterdam, 1991, p 535. (17) Llewellyn, P.; Coulomb, J. P.; Grillet, Y.; Patarin, J.; Andre, G.; Rouquerol, J. Langmuir 1993, 9, 1852. (18) Breck, D. W. Crystalline Molecular Sieves. J. Chem. Educ. 1964, 41, 678.
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Goulay et al. Table 1. Characteristics of the Adsorbents mass (g)
density (g/cm3)
crystallographic void volume (nm3)
NaA
12[(AlO2)(SiO2)]-12Na+
1705
1.52
CaA
12[(AlO2)(SiO2)]-6Ca2+
1670
1.49
NaX
86(AlO2)-106(SiO2)86Na+
13419
1.44
mordenite
[4(AlO2)-44(SiO2)]4 H+; 0.01 Na+
2882
1.73
spherical cavities R: 0.776 β: 0.150 spherical cavities R: 0.776 β: 0.150 spherical cavities R: 0.905 β: 0.150 channel + pocket 0.890
formula
atom. Monovalent or divalent exchangeable cations compensate the negative charges due to the presence of aluminum. These microporous adsorbents are mostly hydrophillic; for instance the NaA zeolite contains up to 27 H2O molecules in normal conditions of temperature and pressure; water is completely removed by dehydration treatment at 400 °C and secondary vacuum.18 The void volume of the structure can then be occupied by adsorbed molecules. We will recall some data about the zeolites which have been used in this study. Their formula and characteristics are gathered in Table 1. Structural Data. The A type zeolite is a cubic array of sodalite units (cavity β) which delimitate nearly spherical cavities (cavity R) of 11.4 Å diameter; they are connected by windows made of an eight-oxygen ring of 5 Å diameter. When the Si and Al tetrahedra are not differentiated, the formula of the pseudocell is [SiO2AlO2]1212- and the unit cell parameter is 12.3 Å containing one R cavity. We worked on pure sodium and calcium zeolites, Na12A and Ca6A, provided by Union Carbide. In NaA there are three types of cationic sites: the SI site is in the plane of the six-oxygen ring of the sodalite unit, they are all occupied by a cation; two SII sites are in each window but only one is occupied by a cation; the 12 SIII sites are in the cavity R in front of a four-oxygen ring, but only one is occupied; this NaIII cation is then less coordinated to the framework19 and acts often as the more attractive adsorption site for the molecules. The effective diameter of the window aperture is smaller than 5 Å because of the presence of Na cation in the eight-oxygen ring; it is equal to 4 Å. In Ca6A there are four cationic sites;20 three of them are similar to the SI site of NaA but on both sides of the sixoxygen plane: one CaII and one CaIII are inside the sodalite unit, three CaI are outside, i.e., in the large cavity; only one cation, CaIV, occupies a window per unit cell. The NaX zeolite is a diamond-like array of sodalite units. The unit cell (25 Å parameter), built of 192 SiO2 or AlO2 tetrahedra, contains eight cavities connected through the 12-oxygen rings (8 Å in diameter). The internal diameter of the cavity is about 12 Å. The cationic sites are inside the hexagonal prisms which link two sodalite units, adjacent to the six-oxygen rings and in the cavity.1 The mordenite, provided by Zeocat, has a large Si/Al ratio and most of the exchangeable cations are protons. The unit cell parameters are 18.12, 20.30, and 7.47 Å. The structure of the framework looks like a channel system.21 The main channel is parallel to the c axis; its aperture is 6.7 × 7.0 Å2, corresponding to a 12-oxygen ring. They are interconnected by passages parallel to the b axis having a minimum diameter of 2.9 Å. In fact this represents small pockets of 3.8 × 4.7 Å2 aperture connected to each other by a very narrow aperture. (19) Yanagida, R. Y.; Amaro, A. A.; Seff, K. J. Phys. Chem. 1973, 77, 805. (20) Firor, R. L.; Seff, K. J. Am. Chem. Soc. 1978, 100, 3091. (21) Meier, W. M. Z. Kristallogr. 1961, 115, 439.
In short these zeolites are quite different. The A type presents rather independent cavities with inhomogeneous surfaces; the cations act as adsorption sites with different interactions with the adsorbates, depending on their crystallographic sites. On the contrary mordenite with almost unidirectional channels is more homogeneous with respect to the adsorbates (very few exchangeable cations). Evaluation of the Void Volume. The void volume is estimated by the maximal amount of adsorbed molecules. It depends first on the adsorbed species which can or cannot penetrate into the small pockets or into the β cages. However this determination depends strongly on the nature of the adsorbed phase; generally this latter is considered as a liquid but this assumption is not always relevant. Thus, for our study, the main problem is the knowledge of the geometrical void volume of these porous crystals. In A-type zeolite the cavities are well delimitated; the volume of the R cage is a spherical volume of about 776 Å3 and that of the β cage is about 150 Å3. These volumes do not account for the presence and the number of exchangeable cations and can be slightly different for NaA and CaA. For instance according to Breck1 the number of adsorbed water molecules in NaA and CaA is respectively equal to 27 and 30 per unit cell. In X-type the window aperture is rather large compared to the dimension of the cavity; therefore the image of a spherical cage is less appropriate than for the A-type. The approximate volume of the R cage is 905 Å3. The number of water molecules per unit cell is equal to 264, i.e., 33 for one R cage and one β cage, then slightly larger than for A zeolites.1 In mordenite the irregular section of the small pockets makes the estimation of the void volume difficult. At the maximum this volume is equal to 890 Å3. We will see that the adsorption amount measured with N2 and with O2 at saturation leads to different values of the void volume which are different from the value given by water content. II.2. Adsorbates. The two diatomic molecules N2 and O2 have similar physical quantities, almost the same dimension and mass (Table 2); at first sight the only noticeable difference is the value of their quadrupolar moment. It acts on the interaction with the adsorbent, this interaction being larger for N2 than for O2. Nevertheless in the liquid state, respectively at 77 and 93 K, their densities are quite different; therefore the mean volume occupied by each molecule in this phase is different; the molecules O2 are closer to each other than the molecules N2. Figure 1 presents the densities of both species (calculated from the international tables22), in the gas phase and in the liquid phase at different temperatures at the point corresponding to the coexistence of both phases (the critical temperatures are equal to 125 K for N2 and (22) International critical table III, 203.
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Table 2. Molecular Constants of the Adsorbatesa
N2 O2 a
m (g)
σ (Å)
Size L (Å)
l (Å)
octopole Θ (10-26 esu)
28 32
3.8 3.5
4.34 4.18
3.39 3.27
-1.4 -0.4
polarizability a| (10-24 esu) a⊥ (10-24 esu) 2.38 2.35
1.45 1.21
dliq (g/cm3)
dsol (g/cm3)
Tc (K)
Pc (bar)
0.808 (77 K) 1.149 (93 K)
1.026 (21 K) 1.426 (21 K)
126 154.6
33.5 50.1
σ is van der Waals diameter, L and l are length and width, d is density, and Tc and Pc are critical temperature and pressure. Table 3. Experimental Parameters of the Isotherm Measurements
NaA
CaA NaX mordenite
Figure 1. Densities of the vapor and liquid phases of N2 and O2 versus absolute temperature: N2, (]) gas, ([) liquid; O2, (O) gas, (b) liquid.
155 K for O2). One can notice that in the gas phase, at a given temperature, there are less O2 molecules per unit volume than N2 molecules and it is contrary in the liquid. How can these thermodynamic quantities of the molecules in the bulk be correlated to the behavior of the sorbed phase? III. Experimental Section The sorption amount with respect to temperature and pressure is measured by a gravimetric method. The variation ∆m of the mass mz of the dehydrated adsorbent is measured when the adsorbent is in contact with the gas at pressure p and temperature T. The isotherms are a set of curves n ) fT(p). The number of adsorbed molecules per unit cell is given by
n)
∆m Mz mz Mmol
where Mz and Mmol are respectively the mass of the unit cell and the mass of the molecule. The microbalance is a MTB 10-8 Setaram, to which a cryostat with two compartments for the two baskets has been attached. The cryostat is symmetrical and allows the sample to be heated up to 750 K for dehydration and cooled to 50 K for adsorption measurements. Thermocouples, for temperature regulation and measurements, are sealed in the bottom of the tubes. The temperature gradient has been measured at different temperature and pressure conditions for both gases; the accuracy of the sample temperature is about 2°. The pressure is measured with a Penning gauge for the dehydration treatment, with a Barocell gauge from 10-3 up to 25 mbar and with a sensitive manometer (membranovac) up to 1000 mbar for gas adsorption. Measurements have been also done in a dewar containing pur liquid nitrogen (and not liquid air) and the real temperature of the sample is 78 K. The zeolites are in powder form; the grain sizes are about 2 µm for the A type zeolite and 25 µm for the mordenite. The powder is sightly compressed in order to avoid any loss of powder during the pumping. The mass of hydrated zeolite is about 100 mg; the microbalance is ordered to provide sensitivity from 10-2 to 0.2 mg for the low and high coverage, respectively. Before each cycle, the dehydration treatment is performed under secondary vacuum (10-6 mbar) at 650 K during 16 h. The loss
N2 O2 H 2O N2 O2 H 2O N2 O2 H 2O N2 O2 H 2O
temp range (K)
time for equil at the lowest T (min)
nmax
301-193 78 301-78 273 300-78 243-78 273 300-78 243-78 273 293-78 293-78 273
50 no adsorption 40 10 15 15 10 40 40 10 15 20 10
12.3 25.5 13 13.7 28 13.9 16.4 31 19 21.2 26.7
of water gives an order of magnitude of the volume accessible to adsorption. In order to determine more precisely the saturation amount for all the samples, the isotherms of H2O have been measured at 273 K in the whole pressure range. Table 3 presents the temperature range of the isotherms, the time needed to reach the adsorption equilibrium at the lowest temperature, and the saturation amount when it is reached. As a matter of fact this time for N2 in NaA is very long at 193 K; it is then difficult to perform isotherms at lower temperatures because of the temperature regulation. At 78 K, the diffusivity of N2 in NaA is completely hindered, meanwhile O2 continues to diffuse easily in this zeolite; the Na cations in the window aperture impede totally the intracrystalline diffusion of N2.10-18 This fact has been used to verify the quantity which can be condensed in the intergrain volume. We present now the experimental results and their analysis.
IV. Experimental Results and Data Analysis IV.1. Isotherms. Figure 2 presents the isotherms of N2 and O2 respectively in NaA, CaA, NaX, and Hmordenite. The curves have the shape of type I from the Brunauer classification.23 The slope at origin increases when T decreases; at 78 K the saturation is reached very rapidly with pressure (the vapor pressure of O2 at 78 K is 220 mbar). As said before, we cannot obtain adsorption equilibrium for N2 in NaA below 193 K. At 78 K one can notice a slight slope of the palier which can be attributed to a small condensation outside of the porous grains. In order to verify this assumption, we have carefully measured the gain in weight of NaA cooled at 78 K in the presence of N2, from p ) 0 to the liquefaction pressure (Figure 3). One can see that this quantity corresponds to a very small number of molecules per unit cell (0.2-0.4) when nitrogen is condensed in the intergrain intervals. As the grains of NaA and CaA have the same shape, the same amount of condensation occurs for CaA; one can then substract this spurious effect from the isotherms in CaA. In the mordenite, which is synthesized in large crystals, the desorption presents a hysteresis which is not seen in A and X zeolites. As this hysteresis starts at p/ps ≈ 1/2, it can be attributed to the intergrain condensation.24 At the highest temperatures, in all (23) Brunauer, S. Adsorption of Gases and Vapors; Physical Adsorption; Princeton University Press: Princeton, NJ, 1965; Vol. I. (24) Everett, D. H. Langmuir, 1990, 6, 1729.
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Figure 2. Isotherms of N2 and O2 in NaA, CaA, NaX, and H-Mordenite.
zeolites, the number of adsorbed N2 molecules is larger than the one of O2. For instance in CaA at 192 K there are two molecules O2 at the higher pressure; meanwhile
at the same temperature there about six molecules of N2. On the contrary at low temperature there are more adsorbed O2 molecules; for instance in CaA at 105 K the
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K(T) ) (2.44 × 10-8)
Tr
[
exp(-Tr′/2T)
M3/2 (1 - exp(-Tr′/T)
[
]
2
×
exp(-Tt′/2T)
(1 - exp(-Tt′/T)
Figure 3. Isotherms of N2 in CaA and NaA at 78 K versus p/ps.
amount of O2 reaches 12 molecules and the one of N2 is less than 11. When the adsorbed phase is dense, the same feature as in the liquid occurs, the molecule O2 occupies a smaller volume than N2. The experimental data are analysed in terms of thermodynamic models. In each case we tried to fit the whole temperature range with the same set of parameters. IV.2. Thermodynamic Data Obtained from the Models. In none of these systems was a fluid phase model such as Dubinin’s3 adapted. We present here the two models which have been applied. The Langmuir model,2 one of the most common models, was conceived for surface adsorption. We remind only the basis and the general equation. The model considers that each molecule can be adsorbed on a site, defined by its multiplicity N and an interaction energy Φ; the equation gives the ratio of occupied sites, Θ ) n/N, with respect to pressure at a given temperature. In the general expression the surface may present different types of sites si. The total number of adsorbed molecules is then equal to
n)
Kip
Qi Ki ) Koi exp RT
∑i ni 1 + K p i
ni and Qi are respectively the multiplicity and the interaction energy of the site i. This model contains three parameters for each type of sites. The second model is derived from the Dupont-Pavlovski model.7 Considering that the rate of interchange between molecules adsorbed into adjacent cavities is small, the system can be satisfactorily described as an assembly of identical and independent boxes, each being able to contain up to a maximum number m of indistinguishable molecules, i.e., m adsorption sites. All the molecules have identical interaction energy with the adsorbent, Ua, and the interaction between two molecules, Ui, is independent of their distance. The calculation is presented in the Appendix. This model contains four parameters: m, Ua, Ui, and νe (external frequency). The expression of the isotherms is the following: m
n)
m
∑ l)0 with
[ [
[( [(
lClm pK(T) exp - Ua + ∑ l)0 Clm pK(T) exp - Ua +
) ]] ) ]]
(l - 1) Ui /kT 2
l
(l - 1) Ui /kT 2
l
]
3
T-7/2
At low pressure this equation tends to the Henry law, n ) K′p. The curves, given by the generalized Langmuir equation, are shown in Figure 2. In almost all cases three types of sites are necessary to fit the whole range of temperature (Table 4); this makes the results less interesting since it is easy to adjust with such a number of parameters. Nevertheless this analysis shows that in a given zeolite (i) the same number of adsorption sites is found for N2 and O2 and (ii) the energy is always larger for N2 than for O2. The second model of interacting molecules in adjacent domains is adequate for the adsorption in the decationated mordenite as shown in Figure 4 (the curves are drawn in logarithm coordinates): it is only acceptable for NaX; in this zeolite the cations are located inside the anionic framework. In CaA and NaA, which present strong adsorption sites such as the NaIII and the Ca cations, the fit cannot be done for the whole temperature range. This model gives interesting data concerning the interaction between molecules (Table 5); this energy Ui is repulsive and the repulsion is smaller for O2 than for N2; as previously, the interaction with the zeolite is larger for N2 than for O2; the external frequencies are very low and slightly larger in the more attractive adsorbant. The number of sites in both zeolites is larger for O2 than for N 2. In any case the curves at 78 K can be adjusted with the same parameters as those used for the highest temperatures. This probably reflects a change in the nature of the condensed phase. IV.3. Saturation Amount. The accessible volume is estimated from the number of molecules adsorbed at saturation, with H2O at 273 K, N2 and O2 at 78 K, and from the density of the corresponding liquid. On Figure 5 we report the isotherms in terms of volume of the liquids and the calculated free volume of the unit cell (cf. II.1); the results for the three species are different. The volume measured with N2 is always greater than the one with O2. In A and X zeolites, it is smaller than the R cavity volume and that obtained from the water content; H2O can penetrate into the β cages but both N2 and O2 cannot. In the mordenite the content of water is smaller than those of N2 and O2 and seems to tend to the calculated free volume of the unit cell; on the contrary the saturation amount of N2 and O2 is larger than the calculated volume. V. Discussion As commonly noticed it is difficult to find a model which fits large temperature and pressure ranges. Models give only a simplified image of the adsorbed phase. In none of these systems was a fluid phase model such as Dubinin’s appropriate; on the contrary models with localized sites allow a rather good representation of the experimental results. The molecules N2 and O2 in these zeolites are then slightly mobile; they have a large interaction with the solid and a small repulsive interaction between them. The data analysis shows that the DP model cannot be applied when the attraction of the inner surface is strongly inhomogeneous like in CaA and NaA; H-mordenite and NaX present a more homogeneous space for the adsorbed
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Table 4. Parameter Values from the Langmuir Model NaA CaA mordenite
N2 O2 N2 O2 N2 O2
n1
Q1 (kJ/mol)
Ko1 109 (bar-1)
n2
Q2 (kJ/mol)
Ko2 109 (bar-1)
n3
Q3 (kJ/mol)
Ko3 109 (bar-1)
5 5 2 2 5 5
18.9 11.0 18.8 13.6 14.9 13.2
0.25 0.48 2.6 0.55 8.0 6.6
4.5 5 5 7 7
11.3 17.3 13.1 12.0 12.2
0.08 0.08 0.10 1.0 1.1
3 3 4 4
11.8 9.6 11.8 10.9
0.35 0.43 0.1 0.7
Figure 4. Fit of the isotherms in H-mordenite from the Dupont-Pavlovski model (- - -, various temperatures; - - -, 78 K). The different marks are the experimental points. Table 5. Parameter Values from the Dupont-Pavlovski Model NaX mordenite
N2 O2 N2 O2
m
Ua (kJ/mol)
Ui (kJ/mol)
νe (cm-1)
13 15 16 18
24.7 17.3 17.5 15.6
-0.90 -0.12 -0.50 -0.23
5.0 5.5 4.4 4.0
molecules. The most interesting effect appears in the comparison of the two species N2 and O2. In all cases when the saturation is reached, the number of O2 molecules is larger than that of N2, meanwhile there are more adsorbed N2 molecules than O2 at high temperatures. In order to analyze this change from high to low temperatures, the isotherms of both molecules are drawn, in logarithm coordinates (Figure 6). This figure shows that in fact the crossing is related to the adsorption amount, corresponding to a number of molecules per nm3 larger than 8. At low coverages in agreement with the gas densities (Figure 1) and also with the interaction of the molecules with the zeolite, the number of N2 molecules is larger than that of O2. At pressures corresponding to high coverages (around 8 to 10 molecules per unit cell) the molecule-molecule interactions promote the oxygen molecules to condense in the zeolites; this can be compared to the fact that the density of the liquid oxygen is larger than that of nitrogen (Figure 1). Nevertheless if we come back to the evaluation of the void volume from the number of molecules measured at 78 K and the density of the corresponding liquids (Figure 5), one sees that the adsorbed volume of nitrogen is larger. If we assume that the adsorbed phase of oxygen has the same density as in the liquid, this infers that nitrogen is more condensed than in the liquid. On the contrary, if we assume that the adsorbed phase of nitrogen has the same density as in the liquid, then we may suppose that the oxygen molecules are less attracted by the inner surfaces.
We can invert the problem and start from the geometrical volume calculated from the crystallographic data. Even if the volume is approximated, its value in each zeolite is the same for both molecules (Table 1). Table 6 gives the number of molecules per nm3 at three temperatures in the liquid (at the corresponding pressures) and in the adsorbed phase. This number is obtained from the gravimetric measurements and the void volume of each adsorbent (for A and X zeolites we consider only the R cavity). The density of the adsorbed phase of N2 is similar or slightly larger than in the liquid phase. This is noticeable at 125 K; in the zeolites, at this temperature with a gas pressure of 1 bar, the molecules are more condensed than in the liquid which is obtained at 32 bar. On the contrary for O2, the density in the zeolites is rather smaller than in the liquid, especially in A-zeolite. This may be related to the interaction with the host which is larger for N2 than for O2 (Tables 4 and 5). Because of this interaction, the thermal motion of the enclosed molecules is restricted; this is equivalent to a lowering of the temperature. Furthermore we observe that both molecules are more condensed in the channel system of the mordenite than in the spherical cavities of A and X zeolites, despite the fact that the initial heat of adsorption is smaller in mordenite. This points out that the confinement effect is larger in small sized volumes. VI. Conclusions Isotherm measurements in a large temperature range of N2 and O2 sorbed into NaA, CaA, NaX, and H-mordenite have shown the confinement effect in different shaped volumes on molecules with similar sizes. The aim of this study was not to find the right adsorption model for the experimental results but to bring out the main effects on these systems. A model is not a real picture of the microscopic state of the sorbed molecules; it gives only an overall description of the nature of the sorbed phase and
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Figure 5. Intracrystalline void volume calculated from the adsorbed volume of H2O (293 K) and N2 and O2 (78 K) versus p/ps. Solid line shows volume estimated from structural data.
Figure 6. Effect of the molecular interaction: comparison of the isotherms of N2 and O2 versus ln(p). Table 6. Comparison of the Densities in the Liquid and Adsorbed Phases no. of N2 molecules/nm3 78 K
105 K
125 K
no. of O2 molecules/nm3 78 K
liquid 17.3 14 9.2 22.5 (ps/bar) (1.03) (10.5) (32.5) (0.22) in CaA 17 15.2 ≈11.5 17.4 in NaA 17.4 in NaX 15.4 14.9 ≈13.5 ≈19 in mordenite ≈19.5 15.1 12.9 ≈22.5
105 K 135 K 20 (4) 15.5 12.9 14.4 18.5
15.4 (23) 12.2 9.5 8.8 ≈15.2
average values of the interaction energies. Simulations of thermodynamic quantities and dynamic behavior are more convenient for detailed information on one particular system,25 but a simulation needs to be ruled by experimental observations. This comparative analysis has pointed out that those small molecules in cavities and in channels (of around 12 and 6 Å diameter, respectively) are slightly mobile since adsorption models with localized sites fit the results whereas the fluid phase model does not. In zeolites presenting strong energetic sites, the same number of sites is found for N2 and O2. In the others the model of adsorption in boxes shows that the intermolecular interaction is repulsive and the repulsion is larger between the N2 molecules. Therefore, as in the liquid phase the (25) Boutin, A.; Pellenq, R. J.-M.; Nicholson, D. Chem. Phys. Lett. 1994, 219, 484.
mean value occupied by N2 is larger than the one of O2. In all cases the interaction with the adsorbent is always larger for N2 than for O2, in agreement with the values of their molecular properties involved in the interaction energy. In any case the equilibrium points measured at 78 K could be adjusted with the same parameters of the models which fit the highest temperature isotherms. That probably reflects a change in the nature of the condensed phase and this assumption deserves to be studied by numerical simulations such as Monte Carlo or Molecular Dynamics methods. Concerning the determination of the zeolite porosity, the main ambiguity comes from the fact that it is generally evaluated under the assumption that the adsorbed phase has the same density as the liquid phase. This assumption is not valid in such volumes in which almost all the molecules are in contact with the surface and in which their external motions are strongly restricted by the geometry of the container. How can we use the concept of liquid in a space like the mordenite channels, the diameter of which is hardly larger than the length of the enclosed molecule. Even if the crystallographic geometry of the void volumes cannot be exactly determined, the saturation amounts measured for nitrogen show that these molecules are more condensed in the mordenite channels than in the liquid phase and also in the spherical cavities of A and X zeolites. This point can also be verified by numerical simulations.
378
Langmuir, Vol. 12, No. 2, 1996
Goulay et al.
Acknowledgment. We are grateful to Dr. R. Kahn for helpful discussions. Appendix The model is derived from the Dupont-Pavlovski model.7 The system is described as an assembly of identical and independent boxes, each being able to contain up to a maximum number m of indistinguishable molecules. The average number n of molecules per box, at a given temperature T, versus pressure p is found by applying the principles of statistical thermodynamics m
n)
lalZl ∑ l)1 m
alZl ∑ l)1 where Zl is the partition function of l molecules enclosed in a box, l ∈ {1,m}, and the activity of the sorbate, a, is equal to a ) exp(µads/kT) with µ the chemical potential. The partition function depends on the assumptions concerning the state of the adsorbed molecules: (i) all the molecules have identical interaction energy with the adsorbent Ua; (ii) the interaction between two molecules Ui is independent of their distance. The number of configurations is equal to
Clm )
UT ) lUa +
( )
qtr V mkT ) N N 2πp2
and qrot )
l
We introduced two modifications, one in the chemical potential and the other in the partition function. As our measurements are done in a large range of temperatures (then several are above the critical temperature), we used the total expression of µgas. The partition function Q of a system of N molecules can be expressed in terms of the partition function q of one molecule
The activity is then
N N ) q qtrqrotqvib
( )
1 m p 2πp2
3/2
(kT)5/2
1 T p2 with Tr ) σ Tr 2Ik
q′tr ≈
and
m
n)
( (
) )
2
exp(-T′r/2T)
1 - exp(-T′r/T)
3
exp(-T′t/2T)
1 - exp(-T′t/T)
∑ l)0 m
[ [
[( [(
lClm pK(T) exp - Ua +
∑ l)0
p ps
∂ ln Q q ) -kT ln ∂N N
)
with T′t ) hνt/k ) T′r ) hνr/k. The isotherm equation becomes
The saturation pressure is taken as reference in the chemical potential of the gas
µgas ) RT ln
3/2
we obtain
) ]]
(l - 1) Ui /kT 2
l
where q′tr, q′rot, and q′vib are the translational, rotational, and vibrational partition functions of the adsorbed molecule. The internal vibration is slightly perturbed by the adsorption (q′vib ≈ qvib); on the contrary rotations and translations are greatly hindered and replaced by lowfrequency external vibrations (νr and νt). Starting from the expressions for a perfect gas of diatomic molecules (with σ ) 2 for symmetric molecules)
l(l - 1) Ui 2
Zl ) Clm exp - Ua +
a)
[
) ]]
[(
Nq′tr q′rotq′vib (l-1) exp - Ua + Ui /kT qtrqrotqvib 2
q′rot ≈
and then the partition function is given by:
µgas ) kT
alZl ) Clm
m! l!(m - l)!
Dupont-Pavlovski considers that the adsorption energy of the l molecules is equal to
[ [(
where qtr, qrot, and qvib are the translational, rotational, and vibrational partition functions of the gas. As the adsorbed species are diatomic molecules, their vibrational and external motions are taken into account in the expression of Zl
Clm pK(T) exp - Ua +
) ]] ) ]]
l
(l - 1) Ui /kT 2
l
(l - 1) 2
Ui /kT
with
K(T) ) (2.44 × 10-8)
Tr
[
exp(-T′r/2T)
]
2
× M3/2 (1 - exp(-T′r/T) exp(-T′t/2T)
[
]
(1 - exp(-T′t/T)
3
T-7/2
In order to reduce the number of parameters, we took ν1 ≈ νt ) νe and then tried to adjust the experimental results in the overall range of temperature with four parameters: m, Ua, Ui, and νe. LA950525I
