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J . Phys. Chem. 1991, 95, 4038-4044
Simulation Studies of the Structure and Energetics of Sorbed Molecules In Hlgh-SMca Zeolites. 1. Hydrocarbons J. 0. Titiloye,' S. C. Parker, F. S. Stone, School of Chemistry, University of Bath, Bath BA2 7AY. England
and C. R. A. Catlow Davy Faraday Research Laboratory, Royal Institution, 21 Albemarle Street, London WlX 4BS, England (Received: jury 16, 1990)
Theoretical methods are used to study the adsorption of linear hydrocarbons, Cl-C8, in silicalite, H-ZSM-5, and siliceous faujasite. The aim is to model the behavior of sorbed species in zeolites and evaluate the influence of the zeolite structure and composition on the sorption process. The method of calculation is energy minimization using the Born model of solids with specified interatomic potentials. Atomatom potentials are used to model the zeolite and zeolitehydrocarboninteractions. The effect of relaxation both of the zeolite framework and of the molecule is investigated. The location of adsorption sites and heats of adsorption for the molecules are presented. The sorption process is controlled by the shape and volume of the available cavity and the packing ability of the molecule concerned. In silicalite and H-ZSM-5, adsorption at the straight channel is preferred to that of sinusoidal channel. The simulations show the extent to which hydrocarbons sorb more strongly in ZSM-5 zeolites than in siliceous faujasites.
Introduction Zeolites are microporous aluminosilicates with a wide range of industrial applications in catalysis, gas separation, and ion exchange. Their catalytic properties are structure dependent,' the critical process being the trapping and release of reactant and product molecules during reactions. The mechanism by which this operates is still far from being fully understood. Its main difference from that operative in other oxides is its selectivity and specificity in adsorbing or rejecting molecules based upon differences in molecular size, shape, and polarity; the usual surface area concepts of metal oxides are not often applicable. One of the uncertain aspects concerns the most favorable adsorption sites for possible reactions. The energetics of sorption associated with specific sites also need to be calculated in order to understand the thermodynamicsand sorption of zeolites. There have been various attempts to determine adsorption sites using a variety of experimental techniques.* In many cases, these techniques are only suitable for small molecules. To date, various theoretical methods have been applied in studying the sorption processes in zeolites.These include the use of static lattice, Monte Carlo, and molecular dynamic simulations: in certain cases quantum mechanical methods have also been used. A common assumption in these calculations is that the zeolite framework and/or sorbed molecule remains rigid. An important aim of this paper is to determine the magnitude of framework and of sorbed molecule relaxation as a function of molecular size. If its importance can be determined quantitatively one may gauge whether the assumption of holding the framework fixed is one that can be done without significant loss of accuracy. This paper reports simulation studies of alkanes ( C 1 4 8 ) adsorbed at infinite dilution in silicalite, (1) Breck, D. W. Zeolite Molecular Sieves; Wiley: New York. 1974. (2) (a) Stach, H.; Lohse, U.; Thamm, H.; Schinner, W. Zeolites 1986,6, 74. (b) Egerton, T. A.; Stone, F. S.J . Chem. Soc., Faraday Trans. I 1973, 69, 22. (3) Subramanian, Y.; Thomas, J. M.; Nowak, A. K.; Cheetham, A. K. Nature 1988, 331, 601. (4) Smit, B.; Ouden, C. J. J. J . Phys. Chem. 1988, 92, 7169. (5) Nowak, A. K.; Cheetham, A. K.; Pickett, S. D.; Ramdas, S. Mol. Simulation 1988, I , 67. (6) &ms,A. G.; Kwirik, M.; Kiselev, A. V.; Lopatkin, A. A,; Vasilyeva, E. A. Zeolites 1986, 6, 101. (7) Grauert, B.; Fiedler, K.; Stach, H.; Janchen, J. Proc. 8th Int. Zeolite Con/., July 1988, Amsterdam, 1988,196, 701-713. (8) Vetnvel, R.; Catlow, C. R. A.; Colboum, E.A. J. Chem. Soc., Faraday Trans. 2 1989, 85(5), 497.
H-ZSM-5, and siliceous faujasite zeolites. These allow us to study the effects on sorption of framework geometry, of protonation, and of hydrocarbon chain length. As noted above, there are three main complementary simulation methods used in the studies of sorption in zeolites. These are energy minimisation (EM), Monte Carlo (MC), and molecular dynamics (MD). The energy minimization method computes the structure and thermodynamic stability of zeolites. In addition, it is used to locate the lowest energy site for sorbed species. Monte Carlo simulation, as well as locating the sorption site, is used to determine sorption equilibria and various thermodynamic functions at higher temperatures. The molecular dynamics approach yields detailed dynamical information on, e.g., diffusion processes and gives the extent to which intramolecular vibration and framework motion assist sorption and diffusion processes. However, the computer time requirement for MC and MD calculations make them less favorable for investigating larger molecules. A clear advantage of the energy minimization method is its ability to handle large sorbed molecules. Moreover, in MC and MD, zeolite frameworks are often held rigid and the effect of ionic polarization of the zeolite lattice is neglected. Energy minimization on the other hand has the advantage of being able to include straightforwardly the effect of polarization and can explicitly relax both molecule and zeolite frameworks during the minimization. This is the method that has been chosen for the present work.
Method In the calculations the energy is determined by summing the interaction energy between all atoms by using defined potentials. The defect simulation code CASCADE (Cray Automatic System for Calculation of Defect Energies) developed by Leslie9 may be adapted for predicting the sites and energetics of sorbed molecules. The molecule to be sorbed is introduced into the zeolite cavity surrounded by approximately 240 framework atoms (region I). The sorbed molecule and region I are then surrounded by a region I1 which extends to infinity, but in which the atoms are held rigid. Efficient energy minimization procedures then locate the lowest energy configuration of the molecule and of the surrounding lattice allowing the atoms in region I to relax to equilibrium. Thus, as noted, an important feature of this technique is that the zeolite framework and hydrocarbon molecule are allowed to relax. (9) Leslie, M. Technical Memorandum of SERC Daresbury Lab. No DL/SCI/TN 31T. 1982.
0022-365419112095-4038$02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95. No. 10, 1991 4039
Sorbed Molecules in High-Silica Zeolites TABLE I: Interatomic Potentials Used for Zeolite/HydrocarbonO Interaction (a) Buckingham Potential atoms
A, eV 1283.907 AI3+-O2-/OHO 1460.30 02-***02-/OH0 22764.0 02-** *OHH 262.537
Si4+-02-/OH0
p,
A
0.32052 0.299 12 0.149 0.348
C, eV A6 10.66158 0.0 27.88 0.0
(b) Lennard-Jones Potential atoms A. eV AI2 B. eV Ab ,,+C***02-/OH0 1 1825.61 5 17.661 H**02-/OH0 1557.522 5.574 ,&* *OHH 2854.57 1 5.844 H***OHH 3.553 0.1 10
ref 10 10 10 8 ref 12 12 12 8
(c) Morse Potential
Db,eV
atoms OHO-OHH &-H
5.896 4.7 13 3.819
sp3c-Gp3
atoms H-,,+C-H
02-A13+-02-
cy,
A-l
2.277 1.77 1.92
ro, A 0.948 1.10 1.53
(d) Three-Body Potential K,eV rad-2 eo,deg 3.428 106.4 3.854 110.0 4.045 110.5 2.09724 109.47 2.09724 109.47
ref 8 13 13 ref 13 13 13 10 10
OThe full listing of the charges on the adsorbates is available from the authors.
The heat of adsorption (q,J of the molecule in the zeolite is calculated as follows qst = -p(Z
W Figure 1. (a, top) Zeolite ZSM-5; showing the straight channels ( b axis). (b, bottom) Silicalite framework showing the substitution of Si-0 with an AI/OH complex at the channel intersection to represent H-ZSM-5.
+ mol) + p(Z) + p(mo1)
+
where P(Z mol) is the potential energy of the zeolite with adsorbate at equilibrium, p ( Z ) is potential energy of the zeolite crystal alone, and p(mo1) the self-energy of the isolated molecule. The potential energy is given by
The first term represents the long-range electrostaticinteraction for the zeolite lattice and the adsorbates; qi and qj are the charges on the atoms i and j , separated by a distance rw For the zeolite lattice, formal charges +4, +3, and -2 were used for silicon, aluminum, and oxygen ions, respectively. The use of and justification for formal charges has been discussed elsewhere.1° The charges on the adsorbates are deduced from Mulliken population analysis using a quantum mechanical calculation with the SV 3-21G basis set." The second term is a two-body potential for the short-range interaction while the last term is a three-body potential representing the bond bending forces in the zeolite and in the adsorbate. The short-range intramolecular interaction of the zeolite lattice is represented by a Buckingham potential (B) of the form
bij = A exp(-rij/d
- c/$
The exponential term represents the repulsive component and the last term is the dispersive attractive component. The flexibility of the adsorbate geometries was represented by a Morse potential (M) given by
bij = Db [{1 - exp[-a/ (rij - rO) 1)*I - Db
Dbis the dissociation constant for the bond between atoms i and j, ro is the equilibrium bond distance, and a is a constant. (10) Jackson, R. A.; Catlow, C. R. A. Mol. Simulation 1988, 1, 207. (1 1 ) GAMESS (General Atomic and Molecular Electronic Structure Systems) code developed by Guest and Kendrick (Manchester University).
Figure 2. Faujasite zeolite structure showing the large cavity and the sodalite cages.
The bond bending force in the zeolite crystal and in the adsorbate is evaluated as where K is the bond bending force constant, eois the equilibrium bond angle, and 8 is the bond angle at a t o m j between atoms i, j, and k. The potential for the interaction of the framework with the adsorbate follows Bezus et a1.6 and is represented by a Lennard-Jones (L) potential of the form
6v = A/(rv)12 - B/(r$ where A and B are constants of repulsion and attraction due to dispersion forces, respectively. Our model also includes the effects of polarizability on the oxygen atoms which are described by using the shell model (see ref 10) which describes the polarizable atom in term of a core and shell connected by harmonic spring. The interatomic potentials used in the calculation are summarized in Table I. We first investigated the purely siliceous zeolite silicalite (Figure la) which has a three-dimensional channel defined by ten-membered ring openings with straight channels parallel to [OlO] and
4040 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991
Titiloye et al.
TABLE II: Heats of Adsorption of Sorbed Molecules in Zeolites (Q,,,
kJ mol-')" mol
CH4 C2H6
C3H8 n-C,H,o n-C5H 12 n-C6H I4 n-C7H16 n-C8H18
silicalite calc expt 22.7 20.9 36.5 29.0 50.6 63.4 53.0 78.6 83.8 75.0 101.2 118.5
H-ZSM-5 calc 23.7 41.7 66.9 77.4 92.2 100.5 101.8 130.8
expt 37.5 65.0
faujasiteb calc expt 20.3 25.7 21.3 40.2 27.0 44.7 38.0 57.9 43.0 60.9 55.0 67.4 67.6 68.0
"Experimental values from ref 2a, extrapolated to zero coverage. bUS-Ex Y form with AI/Si ratio of about 0.01
intersecting this channel at right angles is a sinusoidal channel along [ 1001. Next, to model H-ZSM-5 (the Al-substituted and protonated form of silicalite), we adopted the procedure successfully developed by Vetrivel et a1.8 where the Si4+at the channel intersection is substituted by AI3+and a proton H+is added to the oxygen atom bridging the T2 and T8 sites, thus preserving the neutrality of the crystal (Figure 1b). We then studied faujasite (Figure 2) in a completely siliceous form, similar in nature to the reported US-Yof Stach et a1.2 We chose initially to model the siliceous analogue of faujasite as this allows us to separate the effects of framework geometry on sorption from that of aluminum and the counterions. We are then in a position to investigate both the effects of framework and of A13+concentrations. The initial equilibrium geometries for the hydrocarbon molecules are obtained from the optimized configurations obtained by ab initio quantum mechanical calculations, using the SV 3-21Gbasis set." For all three zeolites, calculations were performed for the adsorption of linear hydrocarbons with special attention being paid to the extent of framework relaxation.
Result and Discussion Silicalite. In silicalite there are two channels capable of hosting hydrocarbons, namely the straight and sinusoidal channels, respectively. For a molecule to sorb in these channels it must first enter via a ten-membered ring window. In this study the molecules are placed at the center of the straight channel, ten-membered ring as a starting point. The energy minimization program adjusts the internal geometry of the hydrocarbon molecule and zeolite framework and also relaxes the molecules with respect to the zeolite framework until the internal energy is at a minimum. In all the cases considered, the molecule drifts away from the center of the straight channel into the intersection of the two channels. If we consider methane, the initial and final positions for the molecule are shown in Figure 3 viewed along the b axis (straight channel view). Note that the molecule moves closer to the zeolite wall in its final position. Figure 4, a and b, differs from Figure 3 in that the molecule is viewed through the sinusoidal channel, clearly showing the drift of the molecule to the channel intersection. On going to the higher alkanes, C3-C8, the extent of molecular movement is now controlled by the length of the molecule; this results in a tight packing of the adsorbate inside the zeolite cavity. Figure 5 illustrates propane. A careful observation of Figure 5 showing initial and final adsorbed positions of propane illuminates this packing mechanism. The calculated heats of adsorption for hydrocarbons on silicalite at 0 K are shown in Table I1 and are compared with the experimental values of Stach et aL2 (extrapolated to zero coverage) measured at about 300 K. The calculated heats are approximately linear with the number of carbon atoms in the molecules as depicted by Figure 6. However, they are consistently larger than the experimentalvalues. This is because we have considered only the energy of the lowest energy site, whereas at 300 K the molecules will be distributed over a range of sites which will have the effect of reducing the average sorption energy. This discrepancy could be explored by Monte Carlo simulations where the molecule samples statistically a wide range of configurations. However, as noted above, the simulation then becomes so com-
Figure 3. Methane molecule adsorbed in silicalite (straight chan view): B, before minimization; F, final position after minimization. In this and subsequent figures, zeolite frameworks are shown in the skeletal solid fragment while the sorbed molecules are represented with the ball model.
putationally expensive that relaxations of both molecule and framework are usually neglected. Indeed it is one of the aims of this paper to determine where framework relaxation is negligible and to verify where the dynamic simulation, e.g., Monte Carlo will be useful. The approximately linear relationship between the heats of adsorption and molecular size given by the calculation is to be expected because of the regular increment of CH2 in the homologous series of n-alkanes. In recent simulation studies using Monte Carlo by June et al.14 linear alkanes adsorbed in silicalite (12) Kiselev, A. V.; Lopatkin, A. A.; Shulga, A. A. Zeolites 1985,5,261. (13) Osguthorpe, P.D.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Robert, V. A.; Hagler, A. T. Proteins: Struct. Funct. Genet. 1988, 4, 31.
Sorbed Molecules in High-Silica Zeolites
Figure 4. Same as Figure 3, but viewed along the a axis (sinusoidal channel).
were observed to reside mainly in the channels avoiding the channel intersections. This is contrary to the results of the present work where channel intersections are the most preferred sites and molecules even preferred the straight channel to the sinusoidal channel. In the MC calculations, the zeolite lattice was rigid and the adsorbates geometries were only partially flexible. This assumption coupled with the neglect of the long-range contributions could well account for the differences in the preferred sites predicted for the molecules and for calculated heats of sorption reported. (14) June, R.L.;Bell, A. T.; Theodorou, D.N.J. Phys. Chem. 1990.94, 1508.
The Journal of Physical Chemistry, Vol. 95, No. 10, 1991 4041
Figure 5. Propane molecule adsorbed in silicalite (viewed through sinusoidal channel): B, before minimization; A, after minimization.
H-ZSM-5. In simulating H-ZSM-5, we substitute silicon in the vicinity of the channel intersection with an aluminum ion and compensating protons as described earlier in Figure lb. The calculated heats of adsorption are shown in Table 11. We first noticed that the lower alkanes, C 1-C2, achieved energy minima as in silicalite by migrating to the channel intersection and there was little change in their calculated heats. However, the higher alkanes found a slightly different pathway, which is reflected in their heats of adsorption being higher than those of silicalite, with the exception of heptane, C7, where the change in heat of adsorption is very small. The effect of substituting the A13+ion and the proton for Si4+was noticed in the closeness of the molecule to the framework atoms when compared to silicalite. Figure 7,
Titiloye et al.
4042 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991
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