J. Phys. Chem. 1991, 95, 5881-5889
migraton of xenons is a t best small.20 A second point that is worthwhile to note is the fact that the barriers for cage-to-cage migration and for site-to-site migration depend on the adsorbate size. As the size of the adsorbate increases the barrier for cage-to-cage migration increases rapidly. Consequently for large molecules the barrier for cage-to-cage migration is expected to be greater than that for site-to-site migration. Again this depends on the size and dimensions (shape) of the guest adsorbate. Thus, for example, linear alkanes of n carbon atoms are expected to have a smaller barrier than the corresponding branched alkanes. In summary, the particles essentially pass through within a radius of 2 A from the window center. The distributions of energy and rawfor particles in the plane of the window during cage-to-cage (20) Yashonath, S.Chem. Phys. Lett. 1991, 177, 54.
5881
migration show that the particles with an energy of about -12 kJ/mol and at a distance of 1.6 A from the window center predominate. The potential becomes strongly dependent on 0 at large rawand repeats with a periodicity of 60'. The surface-mediated mode of diffusion is the predominant mode of cage-to-cage migration at least up to room temperature and low adsorbate concentrations. The particles migrate from one cage to another always keeping close to the inner surface of the cage. The barrier for the surfacemediated cageto-cage migration is small (0.5 kJ/mol). In contrast, in diffusion without surface mediation, in particular, a particle diffusing from one cage center to another, passing through the center of the window, encounters a potential well instead of a barrier. Acknowledgment. I thank the anonymous reviewers for their critical comments and helpful suggestions.
Temperature and Concentration Dependence of Adsorption Properties of Methane in Nay: A Molecular Dynamics Study Subramanian Yashonath,* Solid State and Structural Chemistry Unit, Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore, 560 01 2 India
Pierfranco Demontis: and Michael L. Klein Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323 (Received: October 30, 1990)
Molecular dynamics calculations on methane sorbed in NaY (&/A1 = 3.0) employing realistic methane-methane and methanezeolite intermolecular potential functions at different temperatures (50, 150,220, and 300 K) and concentrations (2,4,6, and 8 molecules/cage) are reported. The thermodynamic results are in agreement with the available experimental data. Guest-guest and guest-host radial distribution functions (rdfs), energy distribution functions, distribution of cage occupancy, center-of-cage-center-of-mass(coc-com) rdfs, velocity autocorrelation functions for com and angular motion and the Fourier transformed power spectra, and diffusion coefficientsare presented as a function of temperature and concentration. At 50 K,methane is localized near the adsorption site. Sitesite migration and essentially free rotational motion are observed at 150 K. Molecules preferentially occupy the region near the inner surface of the a-cage. The vibrational frequencies for the com of methane shift toward higher values with decreasing temperature and increasing adsorbate concentration. The observed frequencies for com motion are 36,53, and 85 cm-' and for rotational motion at 50 K, 95 and 150 cm-' in agreement with neutron scattering data. The diffusion coefficients show a type I behavior as a function of loading in agreement with N M R measurements. Cage-to-cage diffusion is found to be always mediated by the surface.
1. Introduction
The catalytic and separation properties of faujasites-an important class of zeolites- are well-known. The three-dimensional network of linked SO, and AIO, tetrahedra give rise to a three-dimensional structure of interconnected cavities of different sizes. Many organic molecules are adsorbed in one or more of these cavities at specific sites. The sorption properties of faujasites clearly depend on the nature of the guest and on the host-guest interaction. The study of sorption characteristics of faujasites is complicated by the presence of a large number of factors that influence the properties of the sorbatezeolite system. The Si/AI ratio, nature of the extraframework cations, presence of sorbed water molecules, temperature, and the loading or the adsorbate concentration are just some of the factors tfiat determine the properties of the gu&tzeolite system.'-) For example, a decrease in the Si/Al ratio will influence the adsorbatezeolite interaction due to the increased negative charge of the framework. Further, electroneutrality- requires . an increase in the number of cations. To whom correspondenceshould be addressed. 'On leave of absence from: Dipartimento di Chimica, Universita di Sassari, Sassari, Italy.
0022-3654/91/2095-5881$.02.50/0
These cations occupy sites that block the windows and channels, making it more difficult for the guest species to migrate from one cavity to another. In addition to these, the difficulty of characterization of the zeolite and the inherent limitations of the techniques employed complicate matters. Thus, for example, the self-diffusion coefficients for the guest species measured by different methods have yielded values that differ by several orders of magnitude.,J Adsorption of the simplest member of the hydrocarbon family in faujasites, viz. methane, has been investigated by several different techniques. Calorimetric studies on the sorption of methane in NaX and NaY have been reported.&" Measurements of (1) Ruthven, D. M. Principles of Adsorption and of Adsorption Pnmsscs; John Wiley and Sons: New 1984. (2) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieues; Academic Press: New york, 1978. (3) Fyfe, C. A.; Thomas, J. M.; Klinowgki, J.; Gobbi, G. C. Agnew. Chem., Inr. Ed. End. 1983, 22, 259. (4) Ruthen, D. M.; Loughlin, K. F.; Derrah, R. 1. Adv. Chem. Ser. 1973, No. 121, 330. (5) Karger, J.; Caro, J. J . Colloid Interface Sei. 1975, 52, 623. (6) Barrer, R. M.; Sutherland, J. W. Proc. R. Soc. London, A 1956, 237, 439.
0 1991 American Chemical Society
5882 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
TABLE I: Guest-Cuest and Guest-Host Intermolecular Parameters CI. kJ mol-' 7740
A, IO3
atom C
H
(a) GuestGuest C.. kJ mol-' A* 89 956
A6
Cjn.kJ mol-' AIo 1 058 552
(b) Guest-Host B, lo6 kJ mol-' A'* kJ mol-' A6
Si
0
Na
Si
0
Na
0 0
1.7159 0.5802
0.5547 0.1506
0 0
1.0169 0.1118
0.6985 0.0758
Yashonath et al. and TabiszzSqz6is used in the present study. This is one of the best potentials available for methane. Potential parameters were obtained by fitting the solid- and gas-phase properties of methane. There are five interaction sites coinciding with the atomic positions. The dispersion interaction acts only between the carbon sites and is of the form
where
- r2)/rz] forr > 5.18 A
exp[-(5.18
self-diffusion coefficients have been reported by NMR and uptake technique^'*^*'*^^ Neutron timwf-flight experiments on methane adsorbed in faujasites at room temperature are a~ailab1e.l~ Several theoretical treatments of this system and also the more general problem of adsorption in zeolites have been reported in recent times. Kiselev and co-workers have proposed an intermolecular potential function and have obtained by direct numerical integration thermodynamic properties at infinite dilution for methane adsorbed in NaX.I6+I7 Rowlinson and co-workers have obtained equilibrium properties by grand canonical ensemble Monte Carlo and other methods for simple adsorbates in fauja~ i t e s , ' and ~ J ~more recently a study of the energetics and mobility of methane in NaY at different temperatures has been simulated by the Monte Carlo method.20 Recent studies on the effect of geometry on the sorption characteristics and also a molecular dynamics study in silicalite have been reported.21-22Preliminary molecular dynamics (MD) results on methane in NaY and benzene in NaY were reported by us r e c e r ~ t l y . ~ ~ - ~ ~ In this paper we present extensive molecular dynamics calculations on adsorption of methane in faujasite at different temperatures and sorbate concentrations (loadings). In the next section we present details of the intermolecular potential and computational procedures. Results of the calculations are presented and discussed in the last section.
2. Intermolecular Potential Functions The methane-methane interaction was modeled by a realistic potential. The methanezeolite interactions were modeled in terms of a short-range dispersion and repulsion and a long-range Coulombic part. 2.1. Guest-Cuest Interactions. There are several potentials in the literature for modeling liquid and solid methane. The modified Righini-Maki-Klein (RMK) potential of Meinander (7) Neddenriep, R. J. J. Colloid Interface Sei. 1968, 28, 293. (8) Habgood, H. W. Can. J. Chem. 1964, 12, 2340. (9) Stach, H.;Lohse, U.; Thamm, H.; Schirmer, W. Zeolites 1986,6,74. (IO) Dzhigit, 0. M.; Kiselev, A. V.;Rachmanova, T. A. Zeolites 1984,4, 389. (1 I ) Ruthven, D. M.;Derrah, R. 1.; Loughin, K. F. Can. J. Chem. 1973, 51, 3514. 1121 Ruthven. D. M.ACS Svmo. Ser. 1977. No. 40. 320. (13) Caro, J.;'Karger, J.; PfGfe;, H.; Schollner, R. Z. Phys. Chem. (Leipzig) 1975, 256, 698. ( 1 4) Kareer, J.; Pfeifer, H.Wiss. Forrschr. 1979, 29, 344. (1 5) Stockmeyer, R. Zeolires 1984, 4, 81 (16) ~ N SA. ,G.;Kiselev, A. V.;Lopatkin, A. A,; Quang Du, P. J . Chem. Soc., Faraday Trans. 2 1978, 74, 361. (17) Kiselev, A. V.;Quang Du, P. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1. (18) Woods,G. B.;Panagiotopoulos, A. Z.; Rowlinson, J. S. Mol. Phys. 1988, 63, 49. (19) Rowlinson, J. S. Proc. R. Soc. London, A 1985, 402, 67. (20) Yashonath, S.; Thomas, J. M.; Nowak, A. K.; Cheetham, A. K. Nature 1988, 331, 601. (21) (a) Politowicz, P. A.; Kozak, J. J. Mol. Phys. 1987, 62, 939. (b) Derouane, E. G. Chem. Phys. Letr. 1987, 142, 200. (22) June, R. L.;Bell, A. T.; Theodorou, D. N. J . Phys. Chem., in press. (23) Yashonath, S.; Demontis, P.; Klein, M.L. Chem. Phys. Lerr. 1988, 153, 551. (24) Demontis, P.; Yashonath, S.; Klein, M.L.J . Phys. Chem. 1989, 93, 5016. I
forr 5 5.18A
The short-range repulsive part is A charge of -0.572)e) was placed at the carbon site and +0.1431el at each of the hydrogens. The short-range potential parameters are listed in Table Ia. 2.2. Guest-Host Interaction Potentials. The short-range interaction between the methane and the zeolite has been modeled by means of a potential of the Lennard-Jones form Aim
4ia = --
ria
6
+ -Bia ria
12
i = Si, 0, Na; a = C, H
(3)
The potential parameters A and B were taken from an earlier Monte Carlo work on methane in faujasiteZ0since the results obtained in that study were satisfactory. The Coulomb contribution was included by assigning charges 1.151e1, -0.70)eJ,and 1.001el to Si, 0,and Na atoms, respectively. The charges assigned are based on M O calculations and result in a Coulomb contribution of about 20% to the total guest-host interaction energy, the exact value of the contribution depending on the position and orientation of the guest in the a-cage. No distinction was made between A1 and Si atoms as far as the interaction potential is concerned. However, the presence of aluminum is taken into account indirectly since the charges assigned to the framework atoms depend on the Si/Al ratio as also the number of extraframework cations. The short-range potential parameters are given in Table Ib. We obtained a value of 21 kJ mol-' for a single static molecule adsorption energy which compares well with the earlier estimate of 23 kJ mol-'.I6 The discrepancy of 2 kJ mol-' can be accounted for by the polarization energy of the guest species due to the host lattice. However, the induction energy term is not included in calculating ( V ) , since it is a many-body term and this would significantly increase the computational time. For a single guest molecule this contribution is known to be about 10% of the adsorption energy. 2.3. Computational Details. The recent neutron measurements of Fitch et aLZ7find the faujasite in the cubic space group Fd3m with a = 24.85 A. Throughout the present study we have used this structure for faujasite. The zeolite lattice is assumed to be rigid. In order to overcome the problem of partial occupancy of extraframework cations, we have assumed the Si/AI ratio to be 3.0. For this Si/AI ratio there are 48 Na cations that occupy sites SI and SI1 completely. The resulting unit cell composition is Na48(Si+Al) 1920384. The MD calculations were performed in the microcanonical ensemble (N,V,E)on one unit cell of faujasite consisting of eight supercages. Periodic boundary conditions were imposed. At the start of the simulation for the 300 K run methanes were uniformly distributed with N / 8 molecules in each cage. Simulations for temperatures below 300 K were performed by choosing the equilibrated 300 K configuration as the starting configuration unless stated otherwise. The host provides a highly inhomogeneous but time-invariant field in which the guest species move. The (25) Righini, R.; Maki, M.;Klein, M. L.Chem. Phys. Lcrr. 1981,80, 301. (26) Meinender, N.; Tabisz, G. C. J. Chem. Phys. 1983, 79, 416. (27) Fitch, A. N.; Jobic, H.; Renouprez, A. J. Phys. Chem. 1986,90,311.
The Journal of Physical Chemistry, Vol. 95, No. 15. 1991 5883
Adsorption Properties of Methane in NaY
1
0 1
g(r) 0 1
0 1
0
2
4
6
8
1
0
2
4
6
r(i)
-
"
8
1
0
1M K
1 .
4
6
0
rt8)
1
0
lMKl
150 K J
I
/
g(r) 0
2
r(%)
220 K
220 K
0
8 1 0 2 4 6 0 8 10 12 r(%) r(A) Figure 1. Atom-atom radial distribution functions between the guest and the zeolite: C-Si, C-O, C-Na, H-Si, H-O, and H-Na at different temperatures near 300, 220, 150 and 50 K, for methanes adsorbed in a-cage of NaY zeolite at n = 6 molecules/cage. 2
4
6
r(i)
8 1 0
2
4
equations of motion of the methanes were integrated by using a predictor-corrector algorithm with a time step of 1.0 fs. Quaternions were employed for the orientational degrees of freedom." The system was thermalized for 10-20 ps, and properties were calculated over trajectories of 25-45 ps. Four runs were carried out a t nominal temperatures of 50, 150, 220, and 300 K with n = 6 molecules/cage and four runs near 300 K with n = 2,4,6, and 8 methanes/cage. A cutoff distance of 9 A was used for the guest-guest interaction and 12 A for the guest-host interaction in all the runs. The Coulomb interaction was calculated by employing the Ewald sum. 3. Results and Discussions 3.1. Thermodynamic Properties. The average temperature, ( T ) ,the total potential energy of interaction, (U), the guest-guest interaction energy, (U ), guest-host interaction energy, (Ugh), and the isosteric heat sorption obtained from the MD trajectories are listed in Table 11 for runs at different temperatures and different concentrations. The total potential energy (U)= (U&! + (U,) equals the sum of guest-guest and guest-host contributions. The values reported are accurate to within the limits shown in parentheses. The contribution from the guest-guest interaction is significant at low temperatures and at high loadings. The isostcric heat of sorption was obtained from qsl = -( U)+ RT exact at infinite dilution and approximate at higher loadings. The calculated value of the isosteric heat of sorption is 15.5 kJ mol-' for NaY (Si/AI = 3.0) at 324 K. Experimental measurements" at this temperature yield values in the range 17.6-18.8 kJ mol-' while Bezus et aI.I6 obtained 15.2 kJ mol-' in their calculations for NaX @/AI = 1.3) at this temperature. At least part of this discrepancy is due to the different value of the Si/AI
I#
(28) Nose, S.;Klein,
M.L. Mol. Phys. 1983, 50, 1055.
6
TABLE 11: Results of Molecular Dynamics Calculation for Methane in NaY as a Function of Temperature and Concentration4 n, molecules/
cage
( T)
8 6 4 2 6 6 6
313.4 306.3 312.4 323.9 226.1 154.3 53.8
(U)
-13.72 -13.35 -12.78 -12.82 -14.45 -16.16 -19.19
(0.15) (0.20) (0.21) (0.33) (0.16) (0.12) (0.04)
(u)gh
(u),
-11.33 -11.68 -11.60 -12.26 -12.72 -14.43 -17.14
-2.39 -1.67 -1.18 -0.56 -1.73 -1.73 -2.05
91t 16.33 15.90 15.38 15.51 16.33 17.44 19.64
OAll temperatures in K and energies in kJ mol-].
ratio. In the case of ethane adsorbed in faujasite the value of the zero heat of sorption changes by 3.43 kJ mol-I on going from a Si/Al ratio of 1.3 to 3.0. The neglect of the induction interaction between the guest and the host is expected to contribute about 10%. 3.2. Dependence on Temperature. 3.2.1. Structure and Energetics. The guest-zeolite rdfs C-Si, C-O, C-Na, H-Si, H-O, and H-Na at nominal temperatures of 300, 220, 150, and 50 K are shown in Figure 1. Several interesting observations can be made regarding the rdfs. At 300 and 220 K,the absence of peaks in the rdfs suggests a more fluidlike behavior of the adsorbates. We shall present other evidence supporting this conclusion. This is in agreement with results of the neutron time-of-flight experiments.I5 It was found that a fluid-phase model yielded good agreement with the neutron experiment for motion of methane a t room t e m p e r a t ~ r e . 'The ~ peaks are just beginning to appear at 150 K. By 50 K prominent peaks begin to appear in the C-Si, C-O, and C-Na (C-zeolite) as well as the H-Si, H-O, and H-Na (H-zeolite) rdfs. Energy minimization was performed to obtain the coordinates of methane sorbed at the minimum-energy site.
Yashonath et ai.
5884 The Journal of Physical Chemistry, Vol. 95, No. 15, 195'I
We found that there are six minimum-energy sites in any given a-cage. There are four six-membered rings which form part of the inner wall of the a-cage. Any two six-membered rings are connected through three four-membered rings. The position of the adsorption site is in the center of the middle four-membered ring. The C-Si distances for the methane sorbed in the minimum-energy site are 3.6 and 3.7 A, and C-O distances are 3.2, 3,8, and 3.9 A. The dominant peaks in the C-Si and C-O sitesite rdfs are at these positions, suggesting that the minimum-energy site is significantly populated at 50 K. It is also clear from Figure 1 that the C-Na and H-Na are more significantly structured than the other rdfs, and C-Si shows greater structure than C-O. This is a consequence of the geometry of the faujasite structure and the presence of a larger number of oxygen than silicon and the presence of larger number of silicon atoms in comparison with the sodiums and more number of oxygens relative to silicons. This leads to the methane encountering a variety of oxygen C-O and H-0 distances in comparison with C-Si and H-Si distances. Similarly, the C-Si and H-Si distances are more uniformly distributed in comparison with C-Na and H-Na. At low temperatures this shows up rather well due to the localization of methane near the adsorption site resulting in peaks in the rdf at specific distances in preference to others. Unfortunately, there are no reports of neutron structure investigations at low temperature in the literature. The guest-guest rdfs, viz. C-C, C-H, and H-H, are shown in Figure 2. The main peak in the C-C rdf shows significant increase only when the temperature is decreased from 150 to 50 K when the molecules are largely localized. The C-H and H-H rdfs, however, show no significant peaks at all tem eratures including 50 K. The well-defined first peak near 4 at 50 K in the C-C rdf is partly due to the decrease in the translational mobility and increase in the dimer and higher n-mers lifetimes at 50 K. The absence of structure in the C-H and H-H indicates that the methanes are either randomly oriented in different directions or undergo rotational motion. The absence of orientational correlations between the methanes is not surprising in view of the fact that the mean distance between the centers of mass (com) of methanes is large, and the average density at 6 molecules/cage is roughly 50% of the normal liquid density. We note that the plastic crystal or the orientationally disordered (James-Keenan) phase of methane persists down to about 20 K.29 The influence of the zeolite on the guest, however, is significant and the structured nature of the H-zeolite rdfs suggests that the presence of zeolite influences strongly the rotational motion of the methane. We note that sharp peaks exist near 50 K, at a distance as large as 1 1 A, in all rdfs in Figure 1. This suggests that at 50 K a solid-phase model should be more appropriate in place of a fluid-phase model and that the absence of well-defined features in the C-H and H-H rdfs is due to static rather than dynamic disorder. The behavior of adsorbed methane at room temperature is, however, best explained in terms of a fluid-phase model. Again, this is in agreement with the conclusions reached by Stockmeyer on the basis of the neutron scattering measurements.lS These results along with the energy distribution function and the center-of-mass-center-of-cage (com-coc) rdP3 suggest that the translational diffusion is progressively reduced on going from 300 to 50 K. At 50 K, the molecules seems to be localized at least within the time scale of the present study. The com-coc r d f 3 and the above results suggest that mobility, if any, at 50 K is confined to motion parallel to the surface at about 1 A from the inner surface of the a-cage. The results obtained here are in reasonable agreement with the neutron and IR study of Cohen de Lara and co-workers for methane adsorbed in NaA zeolite which imply that, at low temperatures, the methane is largely bound to a specific site.s32 At higher temperatures, but below 300 K, the molecules are close to the walls of the a-cage and spend longer times near
w
(29) James, H. M.; Kecnan, T. A. J . Chem. Phys. 1959, 31, 12. (30) Cohen de Lara, E.; Kahn, R. J . Phys. (Purls) 1981,12, 1029. (31) Kahn, R.;Cohen de Lara, E.; Moiler, K. D. J. Chem. Phys. 1985,83,
2653.
(32) Cohcn de Lara, E.; Nguyen Tan, T. J . Phys. Chem. 1976,80, 1917.
4-
2
An.
1
I
2L 1
1-
21.
r
I
2
m
0.
-
150K
220K
321
0. 321 0.
300 K
/
34-H 21
50K ,
I
23 t
2L 3
I 2b LtcLlFd 1
0'
2
4
6
8
10 12
r IA, Figure 2. Atom-atom rdfs between guest and guest: C C , C-H,and H-H are depicted as a function of temperature.
the adsorption site with decrease in temperature. Thus, methane preferentially occupies regions close to the wall below 300 K. These are in excellent agreement with the results of neutron and IR studies of Cohen de Lara.3*32 The distribution of the number of molecules per cage is shown for n = 6 molecules/cage, at different temperatures in Figure 3. At high temperatures it is found that the distribution can vary widely from 2 or 3 molecules/cage to 9 or 10 molecules/cage. At lower temperatures the width of the distribution decreases becoming largely concentrated around n = 6 methanes/cage. The asymmetric nature of the distribution at lower temperatures is possibly due to the long relaxation times and the relatively short lengths of the MD run (20-30 ps). These distributions are similar to that obtained for xenon in faujasite by Wood et a1.I8 3.2.2. Dynamid Properties. The strong attraction exhibited by the surface over the guest as shown by the energy distribution function and the coc-com r d f 3 suggests that the motion of methane in the supercages to a good approximation has some two-dimensional character. However, it is difficult to obtain an exact value for the dimensionality of motion. Also, this is not true at higher temperatures, and further the pulsed field gradient NMR
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5885
Adsorption Properties of Methane in NaY
150 K 0.40
0.40
1
220K
300 K 040
0.20 Frequency (c")
Figure 4. Power spectra obtained from Fourier transformation of the com vaf of methane in sodium-Y zeolite at different temperatures. Two peaks are observed at low temperatures.
0 2 4 6 8 1 0 1 2 molecules /cage Figure 3. Distribution of cage occupancy at different temperatures. TABLE III: Diffusion Coefficients Obtained from Molecular Dyimmica Calculation at Different Temperatures D, IO9 m2 s-I T,K 50 1.3 150 2.1 220 3.3 300 13.3
measurements of Karger and Pfeifer suggest that the motion is actually threedimensional. The "dimensionality" of the adsorbate is actually a function of temperature. The self-diffusion coefficients were calculated from the usual Einstein relation
D
( u2)/67
(4)
which is an approximation. Here, u2 is the mean-square displacement of the molecules in time 7.33 The values of D thus obtained are listed in Table 111. At 300 K the error in the reported value of D is less than 0.15 X 10-9. At low temperatures, the value of D reported is less accurate due to the relatively short run length. Hence, we have not tried to calculate the energy of activation from values reported in Table 111. The value of D at 220 and 300 K is large enough to suggest that the methanes are mobile, and a fluid-phase model might be appropriate. This is in agreement with the neutron scattering studies at room temperature, the results of which support a fluid-phase m~del.'~J' (33) Allen, M. P.; Tildesley, D. J. Computer Simulurion of Liquids; Clarendon Prw: Oxford, 1987. (34) Stookmeyer, R.: Monkmbusch, M.Be?. Bumen-Ges. Phys. Chem. 1980,84, 1072.
The power spectra obtained by Fourier transformation of the a m velocity autocorrelation function (van is shown in Figure 4 for various temperatures. A band is observed at room temperature near 30 cm-I. At 220 K, the band appears at 35 cm-' with a faint shoulder near 75 cm-I. At 150 K,the band appears at 40 cm-I with a somewhat more distinct shoulder at 80 cm'l. At 50 K, the power spectrum has a sharp peak just above 53 cm-I and two shoulders at 36 and 85 cm-I. The bands show a shift toward higher frequencies with decrease in temperature. The bands at 36,53, and 83 cm-I essentially characterize the com vibration of the methane at low temperatures probably sorbed near the minimum-energy site. In this connection, the findings of the neutron scattering measurements of S t ~ k m e y e r ' on ~ *methane ~ adsorbed in NaA at 7 K are noteworthy. They found that for n = 1 molecule/cage the com motion of methane showed maxima at frequencies 5 7 , and 10 meV corresponding to 42,63,and 84 cm-I. In view of the close structural similarity of the supercages in dimension and shape in NaY and NaA, these frequencies are likely to be similar for methane in N a y . The angular vaf for rotation around the com is shown in Figure Sa for methane at 150 K. The vaf suggests that the methane undergoes essentially free rotational diffusion at this temperature. On decreasing the temperature to 50 K,the vaf changes markedly, indicating constrained reorientational motion (Figure 5b). The power spectrum obtained by Fourier transformation of the angular vaf at 50 K is shown in Figure 5c. There are two bands, one near 95 cm-I and another at 150 cm-I, the latter being more prominent. Figure 5c suggests that the rotational diffusion coefficient, D,,,,, is nonzero even at 50 K. This is in agreement with the conclusions reached earlier on the basis of the rdfs. Note that the 95-cm-l band overlaps with the high-frequency band of the power spectrum for the com motion of methanes. We have not been able to assign the bands to specific types of motion of the methane. The power
5886 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Yashonath et al.
4
E
h
\
L
1 L
0.10-
al
n L
al
n
E,
--w 0.05C.
l.O0u 2 4
Z
time Ips)
0.00
-220
1
I
I
-17.0
-12.0
-7.0
-2.0
3.0
Energy, k J /mol
Figure 7. Energy distribution function N(E)for the interaction between methane and sodium-Y zeolite at n = 2,4,6, and 8 molecules/cage at 300 K. The ordinate is in units of the number of molecules per kJ mol-'.
Od
t
a 8.0 3
fime(ps)
4
2/cagc ----cage ... .. . . . . 6/41cope
w cogc
5
0
Frequency lcmi 1)
Figure 5. Angular vaf for methane in sodium-Y at (a) 150 and (b) 50 K. (c) Power spectrum obtained by Fourier transformation of the angular vaf shown in (b) for methane in sodium-Y at 50 K. 1
50 K
I
O b
100
I
zoo Frequency
1
I
I
300
LOO
(ern-')
Figure 6. Power spectrum obtained by Fourier transformation of the hydrogen vaf for methane in sodium-Y at 50 K. See text for discussion.
spectrum obtained by Fourier transformation of the hydrogen velocity autocorrelation function is shown in Figure 6. The figure shows two prominent bands a t about 50 and 150 cm-I and one small band near 100 cm-I. The 5O-cm-' band corresponds to the vibration of the com motion while the 150-cm-' band corresponds to the librational motion of the methanes. The lOO-cm-' band has contributions from both motion of the com and the rotational motion about the com of the methanes a t the adsorption site. 3.3. Dependence on Concentrationat 300 K. 3.3.1. Structure and Energetics. The energy distribution function indicating the distribution of the energy of interaction between a methane and the zeolite at n = 2,4,6, and 8 molecules/cage is shown in Figure
0.0 0
2.0
4.0 r
6.0
(A)
Figure 8. (a) Center-of-cage to center-of-mass (coc-com) radial distribution function for methane in sodium-Y at n = 2, 4, 6, and 8 molecules/cage and near 300 K. (b) The total number of molecules, n(r), in the eight cages within a distance r from the center of the cage is shown as a function of r. The curves were obtained by integrating g(r). 7. The energy distribution function is bimodal with a shoulder near -17 kJ mol-' and a maximum around -1 1 kJ mol-I. The -1 7 kJ mol-' band is essentially due to molecules in close proximity of the adsorption site. Molecules with energy around -1 1 kJ mol-' are highly mobile and delocalized and cannot be assigned to any local region in the cr-cageaMThe energy distribution function for n = 8 molecules/cage shows a small shoulder near -3 kJ mol-'. This may be either due to the methane near the cage center or due to methanes near window center crossing over from one cage to another. An anomaly is also observed for the low concentration
The Journal of Physical Chemistry, Vol. 95, NO. 15, 1991 5887
Adsorption Properties of Methane in NaY C-Si
1-
0.
41 cage
+age
1-
g(r) 0 -
61cage
6/cage
-
1 -
0
81cage
I
2
l
l
I
l
8/cage
l
6,8 10 0 2 4 6 , 8 10 12 d l r(A) r (A) Figure 9. Atom-atom rdfs between the guest and the zeolite at different loadings and near 300 K. Only C-Si, C-O, and C-Na are shown. The Hzeolite. atom-atom rdfs show little change. Note the presence of slightly sharper features at lower loadings.
0
4
6
8 10
0
2
of 2 molecules/cage; the band near -1 1 kJ mol-' is significantly weaker than that observed for higher concentrations. We also find that the curve shows somewhat greater intensity on the higher energy side between -1 5 and -22 kJ mol-'. Thus, for low loadings, the fraction of molecules occupying the region in the cage with a higher interaction with the surface is higher and the number of molecules populating the energy range of magnitude -12 to -7 kJ mol-' is smaller. The coc-com rdf at different loadings is shown in Figure 8a. The error in the determination of the cage g(r) near the cage center is large since this region is very sparsely populated and the volume under consideration is small. The integrated curve, n(r),indicating the total number of molecules in all the eight cages from the center of the cage up to a radial distance r is shown in Figure 8b. The fraction of molecules that are not near the surface, i.e. those with r < 4 A, is 0.22 for n = 2 molecules/cage and 0.26 or more for n = 4.6, and 8 molecules/cage. This and the anomaly observed in the energy distribution function for n = 2 molecules/cage suggest that the fraction of molecules occupying the higher energy region are the same as those near the inner surface of the a-cage. A consequence of this is the increase in U from -12.30 kJ mol-' (n = 2 molecules/cage) to -1 1.3 kJ mol-' = 8 molecules/cage). This decrease of 1 kJ mol-' in is, however, compensated by a decrease in U, from about -0.6 to -2.4 kJ mol-' (see Table 11). Thus, the guest-guest interaction, We, compensates for the loss in ugh due to the decrease in population near the surface for n = 4 molecules/cage, and a t still higher concentrations the gain in U, more than offsets the loss in U h. Interestingly, the population of the central region ( r < 3 A! of the cage is very small 5% (for n = 8 molecules/cage) as compared to the volume ratio of 13%. At lower loadings ( n = 2 molecules/cage) the fraction near the cage center ( r < 3 A) is practically zero. Some of the typical guest-host and guest-guest rdfs are shown in Figures 9 and IO,respectively, as a function of different loadings at 300 K. The C-C rdf shows a significant increase in correlation near 4 A with increase in concentration. This could in part be due to the significant number of dimers formed at higher loadings. The distribution and lifetime of dimer and higher n-mers in methane in silicalite system have been r e p ~ r t e d . ' ~This should result in an increase in U,. From Table I1 we find this is indeed true. The C-H,on the other hand, showed little increase in intensity wen though a distinct shoulder appears near 3 A. The H-H (not shown in the figure) also shows little change. This is understood easily, since, as we saw in the previous section, molecules undergo essentially free rotational diffusion at 300 K. The observed peaks (see Figure 9) in the C-Na rdf is a result of considerable time spent by the methanes in the vicinity of the minimum-energy site (21 kJ mol-'). The fact that C-O and C-Si rdfs do not show any prominent peaks follows from the same
4
2Lch-l
1
61cage
2 1
00
~~~
2
&
r6(A) , 8
10
12
2
4
6 8 r (AI
10
12
3 2 1
thn
(35) Demontis, P.;Suffritti, G . B. J. Phys. Chrm. 1990. 91, 4329.
elcage
3
0 3 2 1
-0 3
3
" 2
1
0 3 2 1
0 0
Figure 10. Atom-atom rdfs of C C and C-H for methane in sodium-Y at near 300 K. The appearance of the 4-A peak at higher loadings is attributed to the formation of dimers and higher sized clusters inside the
a-cages.
argument as stated in section 3.2.1 while discussing the guest-host rdfs obtained as a function of temperature. The guest-zeolite rdfs C-Si and C-Na show on careful observation more well-defined features at lower concentrations. At higher concentrations the features become rather diffuse and tend to disappear. At lower concentrations as indicated by the energy distribution function, the number of methanes with -22 < Cr, < -1 7 kJ mol-' is greater. This suggests that a larger fraction of methanes are near the adsorption site a t lower loadings. The methanes away from the site of minimum energy are more mobile.*O This results in a g(r) that is more diffuse at higher concentrations. Thus, one expects that a t still higher loadings of greater than 8 methanes/cage the
Yashonath et al.
5888 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
0.40
0.20
0.20
o.oo l
2
'
4
8
6O
110
methanes per cage
Figure 12. Self-diffusion coefficients at 300 K and n = 2, 4, 6, and 8
methanes/cage: molecular dynamics ( 0 )and pulsed gradient NMR results36(H).
,.bot
0.20
-
8 /cage
I
n
O.LO/
0.20
0
0
100
200
300
40
Frequency (cm'l)
n
0'
@/cape
2 1, 6 8 10 12 moleculedcage
Figure 11. Distribution of cage occupancy at different loadings for near 300 K.
peaks will become significantly more diffuse since the region near the cage surface and the minimum-energy site is already densely populated and the additional methanes, therefore, are likely to occupy the regions of the cage not in the proximity of the adsorption site. The distribution of cage occupancy is shown in Figure 1 1. The distribution always peaks around the mean value of n. At all concentrations, it is found that the cages have significant population only in the range of (n - 3, n + 3 ) molecules/cage. At n = 8 methanes/cage as many as 11 methanes have been found to reside simultaneously in one a-cage. 3.3.2. Dynamical Properties. The self-diffusion coefficients at various concentrations of the guest species are shown in Figure 12. The selfdiffusion coefficients" have been measured by pulsed NMR, and these are also shown in Figure 12. The values reported by us reproduce the trend observed in NMR studies. However, the NMR values are always lower than the calculated values. Given the fact that the NMR data is for NaX with lower value of Si/AI, this is to be expected since a lower Si/Al leads to a higher heat of adsorption. The value obtained for D at 2 methanes/cage is 3.5 X 10" m2 s-l. At higher loadings (n = 8 methanes/cage), however, the calculated value agrees well with the NMR measurement. Although the overall agreement is quite good, the incorrect dependence on loading may be related to neglect of induction effects. The vibrational spectra for the com motion of methane is shown in Figure 13 as a function of concentration. At 2 methanes/cage, (36)Karger, J.; Pfeifer, H.Zco/trc# 1987, 7, 90.
\
OO
100
200
300
A00
Frqurncy 1cm-l)
Figure 13. Power spectra obtained from Fourier transformation of the com of methane in sodium-Y near 300 K at different loadings: n = 2 and 8 molecules/cage. A small shift toward higher frequency is observed with increase in concentration of methane.
there is a low-frequency mode near 20 cm-'. At higher concentrations the main peak shifts to higher frequencies (45 cm-l for n = 8 molecules/cage), and the high-frequency tail gains in intensity. The shift toward higher frequencies with increase in concentration, though small, is significant. It is clear that the presence of neighboring guests results in a higher vibrational frequency. 3.3.3. Cageto-Cage Diffupion. Diffusion of methane from one cage to another is observed to take place frequently a t room temperature. The mechanism of this diffusion is interesting and is important from the point of view of the overall diffusion of methane in the N a y . To understand the mechanism of this migration and to learn the role played by the surface in cageto-cage migration, we have plotted the c m o m distance just before, during, and immediately after a molecule migrates from one cage to another. Here rl is the we" distance for the parent cage in which the methane is residing just before migrating to
J. Phys. Chem. 1991,95, 5889-5895
.
0 0.0
4.0
8.0 p1
Figure 14. The center-of-cage to centersf-mass (coc-com) distance just before, during, and after cage-to-cagediffusion of methane near 300 K. The w e a m distance for the parent cage is r,. Here, the parent cage is cage where the methane is residing before cage-to-cage diffusion. The coc-com distance for the daughter cage into which the molecule has migrated is given by r,.
a neighboring cage. The me" distance between the methane and the daughter cage into which the molecule has migrated is r2. Figure 14 shows a plot of r , against r2 for several Occurrences of the cage-to-cage migration. It is observed that r, and r, are always greater than or equal to 3.5 A. Thus, the molecules always remain close to the inner surface of the parent cage as well as the daughter cage. The picture indicated by Figure 14 is that of a molecule skating on the surface of an a-cage. A detailed study of this has been recently carried out on xenon in fa~jasite.~'It is clear that surface diffusion plays the dominant role in cageto-cage migration of this molecule. 3.4. Conclusiom. The calculated thermodynamic, equilibrium, and transport properties and frequency spectra are in good (37)Yashonath, S.J. Phys. Chem., in press.
5889
agreement with the experimentally available data. The guest preferentially occupies the region near the inner surface of the a-cage. This seems to be a general characteristic of adsorption in faujasites irrespective of the guest.I8 The positions of the h n d s in the power spectra obtained by Fourier transformation of the com velocity autocorrelation function show a shift toward higher frequency with (a) decrease in temperature and (b) increase in concentration. There are three bands a t 36, 53, and 85 cm-' for the power spectra for the com motion and two bands at 95 and 150 cm-' for the power spectra for the rotational motion about the com at 50 K and n = 6 molecules/cage. At higher loadings there is an increase in the population near the cage center. At lower loadings, especially n = 2 molecules/cage, the methanes seem to occupy preferentially certain regions near the cage surface < -17 leading to a significant number of guests with -22 < Ugh kJ mol-', i.e. in the proximity of the adsorption site. As a consequence of this, the C-Na rdf shows well-defined structures in the rdfs at low loadings which disappear at higher loadings. Cage-to-cage migration takes place by a sort of skating type of motion with the guest always near the inner surface of the a-cage. After this manuscript was submitted we found that a detailed study relevant to the present study of model systems and methane and xenon in faujasite has been studied by the grand canonical Monte of other related studies have also Carlo m e t h ~ d . ~ A~ Jnumber ~ appeared in print recently.40 Acknowledgment. The research outlined herein was supported, in part, by the US.National Science Foundation and the donors of the Petroleum Research Fund, administered by the American Chemical Society. M.L.K. thanks the John Simon Guggenheim Memorial Foundation for the award of a Fellowship. (38) Woods.G. B.;Rowlinson, J. S. J. Chem. Soc.,Faraday Trans. 2 1989, 85,765. (39) Rowlinson. J. S.: Woods.G . B. Phvsica A 1990. 164. 117. (40)Titiloye, J.'O.; Parker, S.'C.; StoneiF. S.;Catlow, C. R.A. J. Phys. Chem. 1991, 95,4038.
Predicting Molecular Structures of Surface Metal Oxide Species on Oxide Supports under Ambient Conditions Coutam De0 and Israel E . Wachs* Zettlemoyer Center for Surface Studies, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania I801 5 (Received: August 20, 1990)
The molecular structures of the two-dimensional vanadium oxide overlayers on different oxide supports (MgO, A1203,ZQ, TiO,, and SO2) were determined with Raman spectroscopy under ambient conditions. The surface vanadium oxide molecular structures were found to depend on the net pH at which the surface possesses zero surface charge (point of zero charge, pzc). The net surface pH at pzc is determined by the specific oxide support and the surface coverage of the acidic vanadium oxide overlayer. Under ambient conditions the surface of the oxide support is hydrated and the surface vanadium oxide overlayer is essentially in an aqueous medium. Hence, the structure of the vanadium oxide overlayer follows the vanadium(V) oxide aqueous chemistry as a function of net pH at pzc and vanadium oxide concentration. The influence of calcination temperature and preparation methods as well as the addition of acidic and basic promoters upon the surface vanadium oxide molecular structures can also be understood and predicted from this model. The net surface pH at pzc was also successfully used to predict the molecular structures of surface rhenium oxide species, surface chromium oxide species, surface molybdenum oxide species, and surface tungsten oxide species on various oxide supports under ambient conditions.
Introduction Many recent studies have demonstrated that two-dimensional metal oxide overlayers are formed when one metal oxide component (Le., Re20,, Cr03,Moo3, W03, V,05,etc.) is deposited on a second high-surface-area metal oxide substrate (Le., A1203, TiO2,S O 2 , ~ t c . ) . ' - ~The molecular structures of these surface 0022-3654/91/2095-5889302.50/0
metal oxide species have been extensively investigated over the past decade because of their importance in numerous catalytic (1) Haber, J. In Surface Properties and Catalysis by Non-Metals; Bonnelle, J. B., Delmon, B., Devoune, E., Eds.; Reidel: Dordrecht, The Netherlands, 1983: p 1.
0 1991 American Chemical Society
