4997
J. Phys. Chem. 1992, 96, 4997-5000 (23) Ewing, G . E. J . Chem. Phys. 1962, 37, 2250. (24) Buontempo, U.; Cunsolo, S.; Jannucci, G. J . Chem. Phys. 1973,59, 3750. (25) Maki, A. G. J . Chem. Phys. 1961,35, 931.
(26) Leroi, G. E.; Ewing, G. E.; Rmentel, G . C. J . Chem. Phys. 1%3,40, 2298. (27) Jiang, G . J.; Person, W. B.; Brown, K. G . J . Chem. Phys. 1975,62, 1201.
A Study on Hydrogen Encapsulation in Cs,.,-Zeolite
A
Jong-Ho Yoon* Department of Industrial Chemistry, Kyungpook Sanup University, 55, Hyomokdong, Donggu, Taegu, 701- 702 Korea
and Nam Ho Heo Department of Industrial Chemistry, Kyungpook National University, 1370, Sankyukdong, Pukgu, Taegu, 702-701 Korea (Received: October I, 1991; In Final Form: December 30, 1991)
The numbers of hydrogen molecules encapsulated in the cavities of Csz,5-zeoliteA were calculated with respect to pressure as well as temperature, and the results were compared with known experimental data. The calculations were performed by the combined use of the statistical theory of the radial distribution function and the theory of the perfect 3-D lattice gas. The pressures and the temperatures used for the calculations ranged from 10 to 129 atm and from 373 to 623 K,respectively. The results indicated that these two theories were enough to reproduce the pressuredependent experimental data which increase with increasing pressure at the pressures studied.
Introduction The storage (encapsulation) and release (decapsulation) of hydrogen molecules by the use of molecular sieves, such as dehydrated M,-zeolite A (M,Na12-mSi12A112048;M can be any monopositive cation) has been the subject of interest to chemists as well as physicists during the past two Since the use of hydrogen as a multipurpose fuel has been thought to be useful, the importance of the en(de)capsulation of hydrogen has been emphasized. In general, the encapsulation of hydrogen in zeolite A is possible by forcing hydrogen molecules into the cavities developed in zeolite A through the apertures of the cavities under a high-temperature (400-600 K) and high-pressure (more than 10 atm) condition followed by the quenching of the zeolite apertures to the ambient condition? The principles involved in this process are the thermal activation of the vibrational motion of the apertures and the molecular diffusion which allows molecules to be distributed in the cavities. That is, around r m m temperatures, the vibrational motion is not activated (closed) enough to allow the entrance (diffusion) of hydrogen molecules into the cavities. However, if the temperature is sufficiently raised, the aperture’s vibrational motion will be fully activated to allow the entrance of hydrogen molecules into the cavities. Since this process is reversible, the decapsulation of hydrogen molecules from the cavities becomes possible upon heating the quenched zeolite A. From the work of Fraenkel and Shabtai* in 1977, it has been known empirically that the number of hydrogen molecules encapsulated in C ~ ~ , ~ - z e o lAi t increases e almost linearly with increasing the encapsulation pressure in the log-log scale. However, detailed consideration to account for this linear relationship has not yet emerged. Most of the studies done on such a system are limited to the investigation of the state of the encapsulated hydrogen molecules in a zeolite A cavity at fairly low temperatures (10-20 K).4*S From these studies, it has been shown that the encapsulated hydrogen molecules are adsorbed on the molecules constituting the zeolite A cavity wall.e6 However, since hydrogen encapsulations in zeolite A are possible only at a high-temperature and high-pressure condition, the low-temperature results may not be directly applicable in studying high-temperature hydrogen encapsulations.
Bearing this in mind, we applied the statistical theory of the radial distribution function (rdf)’ and the theory of perfect 3-D lattice gasEto calculate the number of the encapsulated hydrogen molecules in Csz,S-zeolite A for the purpose of more detailed understanding on this phenomenon. That is, by comparing the theoretically calculated hydrogen encapsulations with known experimental data: we examined the effect of pressure as well as temperature on the hydrogen encapsulation in Csz,S-zeolite A.
Theory The two most important thermodynamic factors making hydrogen encapsulation in Cs,,,-zeolite A cavities possible are temperature and pressure. In principle, by raising or lowering temperature one may open or close the apertures of zeolite A cavities to allow or to prohibit the entrance of hydrogen molecules, respectively. On the other hand, pressure plays a role by forcing hydrogen molecules into the cavities. Hence, the number of hydrogen molecules encapsulated in Csz,S-zeolite A cavities (hydrogen encapsulation) should be a function of both pressure and temperature. According to the theory of statistical mechanics, the maximum number of molecules contimed in a finite volume can be calculated, by making use of rdf.’ That is d
N =p
g(r)47rP dr
+1
where d is the radius of the zeolite cavity, r the intermolecular separation, N the maximum number of molecules encapsulated in a cavity, p the number density, and g(r) the radial distribution fimction (rdf). In eq 1, the fmt term counts the maximum number of neighboring molecules distributed around a probe hydrogen molecule in a cavity. The second term, 1, comes from the contribution of the probe molecule itself. For gaseous hydrogen, rdf may be written asI3
Here, U(r) is the intermolecular potential, k the Boltzmann constant, and T the temperature in absolute scale. As can be seen in eq 2, rdf is independent of pressure. For the potential function
0022-3654/92/2096-4997%03.00/0 0 1992 American Chemical Society
Yoon and Heo
4998 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 3.5
,
TABLE I: Maximum Hydrogen E~psulptioas4 A (At 623 K)
press., atm 10 30 80 100 129
0
I
I
1.5
0.5 0.0
L 20
40
60
80
100
120
140
Pressure ( a h )
Figure 1. Maximum hydrogen encapsulation at 623 K.
between hydrogen molecules in eq 2, we chose the Lennard-Jones type potential
U(r) = 4e((u/r)12- ( u / r ) 6 )
(3)
where c and u stand for the depth of the potential well and the intermolecular separation at which V(r) = 0, respectively. Next, in order to calculate the total hydrogen encapsulation in the actual three-dimensional array of cavities in zeolite A, one must take into account the fractional coverage (e) of zeolite A cavities at a given pressure and temperature. In fact, because of the inherent molecular dynamics (thermal motions) of hydrogen molecules, not all the cavities are filled completely. Since at high enough temperatures the hydrogen molecule behaves essentially as a noninteracting free gas, the hydrogen encapsulation problem becomes very similar to the one-component perfect 3-D lattice gas8 problem. According to this theory, we may express the fractional coverage of zeolie A cavities as8 0 = S / B = 1 - exp(-pr/kT)
P,
1.17 X 3.49 X 9.10X 11.28 X 14.38 X
A-3
temp, K
p,
373 398 423 473 523 573 623
14.97 X 14.06 X 13.25 X 11.89 X 10.79 X 9.87X 9.10 X
N+4
Na
(/v8)
(/va
1.081 1.241 1.630 1.781 1.996
1.006 1.018 1.046 1.057 1.073
2.087 2.259 2.676 2.838 3.069
lo4 lo-’ lo4 lo4 lo4 lo4 lo4
Na (/va)
(/v&
N8
N a + N8 ( / v a + v&
2.043 1.978 1.921 1.825 1.748 1.684 1.630
1.064 1.061 1.059 1.055 1.052 1.049 1.046
3.089 3.039 2.980 2.880 2.800 2.733 2.676
TABLE Ik F r ~ ~ t iCoverages o~l A (At 623 K) press., atm a-cage 10 30 80 100 129
0.0873 0.2398 0.5186 0.5990 0.6923
0.0180 0.0529 0.1358 0.1669 0.2098
B (At 80 atm)
a-cage
@-cage
373 398 423 473 523 573 623
0.7051 0.6815 0.6593 0.6182 0.5814 0.5483 0.5186
0.2164 0.2043 0.1935 0.1749 0.1596 0.1468 0.1358
0.8
0.6
D P)
e 6
U
-0 0.4 0
F 0
0
0.2
In general, zeolite A has an aluminosilicate structure and is
fi;
~~
temp, K
LL
characterized by two types of polyhedra known as a-(26-hedron) and @-(14-hedron)cages. The a- and @-cageshave the cavity volumes of 776 and 155 A3,respectively.” C&5zeolite A is known to have one a-cage and one @-cageper unit cell. Both cavities are known to have hydrogen encapsulation a b i l i t ~ . ~ . ~ In order to calculate the maximum numbers of the encapsulated hydrogen molecules in the cavities (using eq l), we placed the probe hydrogen molecule at the centers of the cavities. As mentioned earlier, the interactions between the encapsulated hydrogen molecules and the cavity wall molecules were neglected. Further, the cavities were regarded as perfect spheres, for simplicity. The radii 5.7 and 3.3 A for a-and @-cages,respectively, were calculated from the cavity volumes mentioned above. For the hydrogen Lennard-Jones potential function, we used the erg and u = 3.275 tential parameters e = 5.1084 X For the pressure dependence of hydrogen encapsulations, we used pressures from 10 to 129 atm at the fixed temperature of 623 K. While, for the temperature-dependent calculations, we
+ v8)
V, = 776 A’ and V, = 155 A’.
e
Calculations and Results
lo4 lo-’ lo4 lo-’ lo-‘
+ N8
Na (/va)
B (At 80 atm)
(4)
where S and B are the number of zeolite A cavities occupied by hydrogen molecules and the total available number of zeolite A cavities, respectively. p and T represent the pressure exerted by hydrogen molecules and the cavity volume, respectively. As can be seen in eq 4, the fractional coverage is a function of both pressure and temperature. Here, the hydrogen molecule is treated as a free gas. Considering the temperature range used (373-623 K), which is usually employed in this kind of work, we believe that this assumption is good enough. At this point, one should notice that in two-dimensional cases eq 4 can be reduced to the familiar Langmuir adsorption isotherm.8 Combining eq 1 and 4, we calculated the total hydrogen encapsulations in 1 g of C~,,~-zeoliteA.
A*’
0
0
D I
0.0;
20 1
40
I
I
1
60 BO 100 Pressure ( a h )
1
120
I 0
Figure 2. Fractional coverage at 623 K.
fixed the pressure at 80 atm and varied the temperature from 373 to 623 K. The number densities ( p ) of hydrogen molecules at the bulk states needed were calculated numerically by inverting the well-known van der Waals gas equation
p = - - pRT 1- p b
ap2
(5)
where a and b are the van der Waals coefficients and R is the gas constant. The van der Waals coefficients for hydrogen gas used were a = 0.244 Lz atm/mo12 and b = 0.0266 L/mol.” The
A))
0
o : Experiment 0 : Theory
A (At 623 K) ~~
-m
6.0
5
5.0
I
6 4.0
~
~
press., atm
0 0
0.568 X 1.775 X 4.986 X 6.278 X 8.115 X
10
30 80
D
1
theory
100
129
lo4 lo4 lo4 lo4 lo4
~~~
experiment' 1.11 x 10-4 2.51 X 5.67 X 6.63 X 8.71 X
lo4 lo4 lo4 lo4
B (At 80 atm)
temp, K 373 398 423 413 523 573 623
1.0 0
0.0
I
I
20
40
I
I
I
60 80 100 Pressure (atm)
I
120
140
Figure 3, Hydrogen encapsulation ( n ~ at ) 623 K.
t
: Experiment : Theory
J 8.0
theory 8.437 X 7.902 X 7.430 X 6.629 X 5.980 X 5.440 x 4.986 X
lo-' lo4 loa lo-' lo4 10-4 lo4
experiment' 4.67 X 5.39 x 6.00 X 6.27 X 6.02 x 5.78 x 5.67 x
lo4 10-4 lo4 lo4 104 lo4 104
'The data sets were recalculated through the van der Waals equation by use of the data sets in ref 9 in which the data are given in STP volumes.
D
encapsulated hydrogen (nT) increases linearly with increasing pressure. According to the theories used here, this linear relationship seems to be due to the combined effect of the maximum hydrogen encapsulation ability (N) and the fractional coverage
r
(el. , _
Temperature (K)
Figure 4. Hydrogen encapsulation (nT) at 80 atm.
calculated maximum hydrogen encapsulation abilities in both cavities have been tabulated in Table I and plotted in Figure 1 with respect to pressure. The fractional coverages were calculated by eq 4. The pressure-dependent results were tabulated in Table IIA and plotted in Figure 2. Assuming that the number of hydrogens distributed in zeolite A is proportional to both the maximum hydrogen encapsulation capacity and the fractional coverage of the cavities, we multiplied the two factors to give the total hydrogen encapsulation in 1 g of C ~ ~ , ~ - z e o lA i t eas In eq 6,nT and nlgzstand for the mole number of the hydrogen molecules encapsulated in 1 g of Cs2yzeolite A and the mole number of Cs2,S-zeoliteA molecules contained in its mass of 1 g, respectively. The subscripts a and 8 stand for the a- and 8-cages, respectively. The calculated nT's are given in Table I11 and plotted in Figures 3 and 4 together with the known experimental data.9 One thing to note here is that all the integrals, involving the rdf, were calculated numerically by the trapezoidal rule with the integral interval of 0.01 A.
Discussion We have calculated the hydrogen encapsulations in 1 g of Cs2,5-zeolite A with respect to pressure as well as temperature. The results indicated that the combined use of the statistical theory of rdf and the theory of the 3-D lattice gas seemed to be good enough to reproduce the pressure-dependent experimental data at the pressures studied. As can be seen in Figure 3, the pressure-dependent hydrogen encapsulation data show good agreement between the theory and the experiments at all pressures examined. The average error between these two data sets was found to be +lo% (see also Table IIIA). Also, one can easily find that the mole number of the
As can be seen in Tables IA and IIA and in Figures 1 and 2, both the maximum numbers of the distributed neighboring moleculm and the fractional coverages in the a-cage are roughly an order of magnitude greater than those in the @-cage. Thus, one notices easily that the a-cages are the major cavities in controlling the hydrogen encapsulation in Cs2,,-zeolite A. Since in both a- and @-cages the general tendencies are the same, hereafter discussions will be confined to the major a-cage. From eq 1, one finds that the change of N, corresponds to the change in the number of distributed neighboring molecules in the cavity. Since the number of neighboring molecules changes linearly with pressure, N,,also changes linearly with pressure. This can be seen in Figure 1. The best fit derived from Figure 1 was N , = 0 . 0 0 7 7 ~ 1.008. At the same time,, as shown in Figure 2,the fractional coverage is proportional to a fractional power of p. The best-fit result gave 8, = 0.03 19p0.816.Since in Figures 1 and 2 the increments with respect to pressure are similar, one may state that N, and ea are equally important factors for the increase of the hydrogen encapsulation with respect to pressure. In other words, both encapsulation pressure and fractional average are the major factors in inducing the hydrogen encapsulation. Nonetheless, the multiplication of these two factors was linearly dependent on p (see Figure 3). The power fitting results based on the e vsp plot (see Figure 3) obtained were nT = 0.0512p1.043 and 0.172p0.798 for the theory and the experiment, respectively. These results perfectly agree with Fraenkel and Shabtai's2 result which states that e is linearly dependent on p in the log-log scale. Further, Nu is a function of intermolecular potential (Le., rdf) between guest molecules. Hence, if there exists any attractive interaction between guest molecules, Nu will increase due to the increased distribution of neighboring molecules to increase nT. Similarly, 0, is a function of intermolecular potential between guest and host molecules. Therefore, any attractive interaction between guest and host molecules will give rise to an increase in nT even further (for example, CH4).3 In contrast to the pressure-dependent study, the temperaturedependent study showed rather poor agreements between theory and experiment, particularly at the first three low-temperature data points (373, 398, and 423 K). This can be seen in Table IIIB and in Figure 4. Though, at the present time, the definitive reason for the deviations is not given, we are speculating that the deviations are likely due to the incomplete hydrogen encapsulat i o n ~ .That ~ is, at the low temperatures, the vibrational motion of the apertures may not be activated fully; thus, it is more difficult
+
J . Phys. Chem. 1992, 96, 5000-5007
so00
for hydrogen molecules to enter (diffuse) into the cavities so that the lower the temperature, the longer the time to attain the pressure equilibrium between the inside and outside of the cavity. Since all the temperature-dependent experimental data were obtained by taking 15 min of encapsulation time? we cannot exclude the possibility of incomplete hydrogen encapsulations at the low temperatures. According to the time-dependent hydrogen encapsulation study in Cs2,,-zeolite A done by Heo et the time required for the pressure equilibrium at the low temperatures is at least 180 min. However, at higher temperatures, the hydrogen encapsulation, which decreases with increasing temperature, can be found both in theory and in experiment. However, if we assume that our formalism is correct, the hydrogen encapsulation would increase exponentially with decreasing temperature (see Figure 4).
One additional remark here is that in both pressure- and temperature-dependent studies, the theoretically calculated values always underestimated the experimental data (except for the first four low-temperaturedependent data). We believe that this may be due largely to the neglect of attractive interactions between guest hydrogen and the host Cs2,5-zeolite A molecules in our theoretical model. Nevertheless, we have been able to successfully functionalize the hydrogen encapsulation process without including any interaction between the host and the guest molecules at least with respect to pressure. This suggests that the major physical process responsible for the hydrogen encapsulation at high temperatures seems to be the molecular diffusion.
We feel that experiments covering wider ranges of pressures and temperatures are needed to gain a more detailed understanding of this phenomenon. Such experiments are in preparation.
Acknowledgment. N. H. Heo acknowledges the financial support from the Korea Science and Engineering Foundation. Re&@ NO. HZ,1333-74-0; CS,7440-46-2.
References and Notes (1) Gregory, D. P. Science 1973, 12, 228. Verziroglu, T. N. Hydrogen Energy; Prenum Press: New York, 1975. (2) Fraenkel, D.; Shabtai, J. J . Am. Chem. Soc. 1977,99,7074. Seff, K. Acc. Chem. Res. 1976, 9, 121. (3) Zhang, S.-Y.; Talu, 0.;Hayhurst, D. T. J . Phys. Chem. 1991,95, 1722 and references therein. (4) Nicol, J. M.; Eckert, J.; Howard, J. J. Phys. Chem. 1988, 92, 7117. (5) de Menoval, L. C.; Raftery, D.; Liu, S.-B.; Takegosci, K.; Ryoo, R.; Pine, A. J. Phys. Chem. 1990, 94, 27. (6) Goldfard, D.; Kevan, L. J . Phys. Chem. 1986, 90, 2137. (7) For example, see: Mquarrie, D. A. Srarisrical Mechanics; Harper and Row: New York, 1976, Chapter 13. ( 8 ) Hill, T. L. Statistical Mechanics; McGraw-Hill Book Co.: New York, 1956; p 402. (9) Heo, N. H.; Rho, B. R.; Kim, D. H.; Kim, J. T. Hwahak Konghak 1991, 29, 407. (10) Rees, L. V. C.; Berry, T. Proc. Con/. Mol. Sieves 1969, 149. (11) Heo, N. H. Ph.D. Thesis, University of Hawaii at Manoa, 1987. Breck, D. W. Zeolite Molecular Sieves; Structure, Chemistry, and Use; John Wiley & Sons: New York, 1974; p 428. (12) Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley & Sons: New York, 1954. (1 3) Weast, R. C. Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1989.
Acidic Properties of Alumina-Supported Metal Oxide Catalysts: An Infrared Spectroscopy Study Andrzej M. Turek,+ Israel E. Wachs,* Zettlemoyer Centerfor Surface Studies and Department of Chemical Engineering, Lehigh University, Bethlehem. Pennsylvania 18015
and Elaine DeCanio Research and Development Department, Texaco Inc., Beacon, New York 12508 (Received: October 8, 1991)
The infrared spectra of the hydroxyl region and that of surface chemisorbed C 0 2 species for Re207/A1203,Cr03/A1203, M&3/,4@, V20s/A1203,Ti02/A1203,and Nb05/A1203catalytic systems have been investigated. A sequential consumption of the alumina OH groups upon deposition of the supported metal oxide has been found for all the investigated catalytic systems. A possible relationship between Bronsted acidity and a new low-frequency band in the hydroxyl region observed at high loadings of the supported metal oxide systems is postulated. The various chemisorbed C 0 2surface species formed on the uncovered parts of the exposed surface of alumina are identified. Furthermore, the applicability of the infrared C 0 2 chemisorption technique as a general method to determine the monolayer coverage for alumina-supported metal oxides has been confirmed because CO2 adsorption is suppressed as monolayer coverage is approached. Infrared pyridine chemisorption data for selected alumina-supported metal oxide catalysts are quantified, and a simple model for the Bransted acid site is proposed. Comparison with the molecular structures of the surface metal oxide overlayer, determined by Raman spectroscopy, reveals that there is no correlation between the surface metal oxide structures and the corresponding surface hydroxyl chemistry, Br~lnstedacidity, and C 0 2 chemisorption.
Introduction Alumina-supported metal oxide catalysts are widely used in various catalytic processes. Molybdenum-based catalysts are well-known as very efficient hydrodesulfurization Molybdena/alumina, tungsta/alumina, and rhenia/alumina are all metathesis catalysts after induction with olefin a t room temperature&* or following a very mild reduction in H2? Chromia/alumina catalysts are used for the conversion of parafins to On leave from the Faculty of Chemistry, Jagiellonian University, ul. M. Karasia 3, 30 060 Cracow, Poland. To whom correspondence should be addressed.
olefinic hydrocarbons, in hydrodealkylation of aromatics, and to some extent in catalytic reforming.’O Vanadia/alumina catalytic systems are being examined as candidates for selective catalytic reduction of NO, by ammonia.” In many cases the catalytic activity and selectivity of these catalysts may be related to their acidity. The acidic properties of multicomponent metal oxide systems are usually determined by means of appropriate probe molecules acting as titrants or adsorbents.12 When the adsorption method is combined with infrared measurement of the adsorbed molecules, useful information about the type and concentration of surface acid sites can be obtained.” To avoid steric limitations, rather
0022-3654/92/2096-5000$03.00/00 1992 American Chemical Society
