4462
J . Phys. Chem. 1988, 92,4462-4465
Relative StabllRtes of Zeolftlc Aluminosilicates G. Ooms, R. A. van Santen,* C. J. J. den Ouden, KoninklijkelShell- Luboratorium, Amsterdam (Shell Research B. V.), Postbus 3003, 1003 AA Amsterdam, The Netherlands
R. A. Jackson, and C. R. A. Catlow Department of Chemistry, University of Keele, Keele, Staffordshire ST5 5BG, Great Britain (Received: October 26, 1987)
The question is addressed as to whether there is a theoretical basis to an apparent relation that has been experimentally observed between the lattice topology and the Al/Si ratio of zeolites. Calculations are presented for three lattices formed with very different Al/Si ratios: faujasite, mordenite, and ZSM-5. The relative stabilities of these lattices are studied as a function of AI/Si ratio in the presence or absence of adsorbed water. Na+ ions are taken as the compensating ions. Two types of approaches were followed to study the changes in heat of formation as a function of alumina content. In one approach, for a certain zeolite structure the Madelung and polarization energies are calculated for fixed lattice positions. The heat of formation due to ionic bonding is calculated both for the zeolitic aluminosilicate with varying amounts of aluminum and sodium ions and for the zeolitic silica, with the same framework distances as in the aluminum-containing material. The difference between the two heats of formation is assumed to represent the contribution to the total heat of formation due to bonding stemming from the presence of aluminum and cations in a particular zeolite structure. This difference is added to the heat of formation due to covalent bonding of the silica polymorph as calculated by the extended Hiickel method. The effect of hydration on the relative stabilities is estimated by using empirical data on hydration with water. In the second approach rigid ion lattice energy minimization calculations were used, with potentials parametrized to fit a-quartz. This technique was particularly useful to determine the stability of the structures whose energy had been calculated by the method discussed earlier. The presence of aluminum ions and cations as well as hydration is found to have a considerably larger influence on the relative stabilities of zeolites than covalent contributions. The predictions for the order of stability of faujasite, mordenite, and ZSM-5 as a function of Al/Si ratio is in qualitative agreement with the results of synthesis experiments.
Introduction The use of organic bases in zeolite synthesis’ has constituted a breakthrough, enabling new zeolites to be made with lattice AI/Si ratios much lower than those obtained in the absence of organic bases. Apart from the change in Al/Si ratio there is a change in lattice structure: whereas at high Al/Si ratios structures built from even rings dominate, at lower Al/Si ratios systems containing a significant fraction of five rings can be made. In this paper we address ourselves to the question as to whether there is indeed a relation between lattice topology and Al/Si ratio found in the zeolite. Barrer2 demonstrated that for the stability of porous structures the presence of “guest” molecules in the “continuous” structure is essential. In a recent paper,3 we interpreted the difference in stability between ZSM-5 in the presence and ZSM-5 in the absence of organic cations in the mother liquor as being related to the interfacial energy of the micropore/zeolite lattice. If no aluminum is present in the zeolite lattice, this interface will be hydrophobic and adsorption of water from the mother liquor will be an endothermic process. If aluminum is present in the zeolite lattice, compensating cations will have to be present as well in the micropores and these will be solvated by adsorbed water, providing a driving force to water adsorption. Here we present calculations for three zeolite lattices: faujasite, mordenite, and ZSM-5. We will study the relative stabilities of these lattices as a function of Al/Si ratio in the presence or absence of adsorbed water. Na+ ions are taken as the chargecompensating ions. Faujasite consists of (SiO,) and (A104)- tetrahedra linked to form cuboctahedra or so-called sodalite cage units. These units (1) Barrer, R M.;Denny, P.J. J. Chem. Soc. 1961,971. Ranigan, E. M. Adv. Chem. Ser. 1973,121, 119. Rollman, L. P. Adv. Chem. Ser. 1979,173, 381. ( 2 ) Barrer, R . M.Proc. Int. Symp. Zeolites, Portorosa (1984) 1985, 1. Barrer, R. M.J . Phys. Chem. Solids 1960, 16, 84. (3) Van Santen, R. A.; Keysper, J.; Ooms, G.; Kortbeedk, A. G. T. G. Proc. Seventh Int. Zeolite Con/., Tokyo 1986, 169; Stud. Surf. Sei. Catal. 1986, 20, 169.
TABLE I: Heat of Formation Due to Covalent Bonding for Some Dealuhated Zeolites, Calculated by Using the ASED Method‘ heat of formation, kJ/mol
faujasite mordenite EM-5
a-quartz a-quartz (expt)
905 925 925 896 910
are linked via six-membered rings (Figure 1). Apart from sixmembered rings there are four-membered rings. Mordenite has a channel-like pore structure in which the basic building blocks consist of five-membered rings. A view of the mordenite structure perpendicular to the main channels is shown in Figure 2. ZSM-5 is a pentasil zeolite. It is also composed of five-membered rings and its structure is shown in Figure 3. In an earlier paper4 we described a simple quantum-chemical calculation method to obtain an estimate of the relative stabilities of zeolitic silicas. When we applied the method to dealuminated faujasite, mordenite, and ZSM-5, we found faujasite to be less stable than mordenite and ZSM-5. The differences between the calculated heats of formation of the three zeolitic silicas proved to be very small. The results of these calculations are reproduced in Table I. The absolute values of the results are different from the values given in the original paper, as more recent values for the heat of vaporization of Si (450 kJ/mol) and for the dissociation energy of O2(498 kJ/mol) were used. As these are constant terms, only the absolute values changed, the differences remaining the same. Whereas faujasite is found to be less stable than mordenite and ZSM-5, the latter two structures are found to be more stable than a-quartz. The last results indicate that the method used is too crude to allow a reliable prediction of the differences in covalent energy between these structures. Indeed recent ST03G ab initio calculationsSon silicate rings indicate that the differences (4) Ooms, G.; Van Santen, R. A. R e d . Trav. Chim. Pays-Bas 1987,106, 69. ( 5 ) Van Beest, B. W.; Van Santen, R. A. Catal. Lett., in press.
0022-3654/88/2092-4462$01 .SO10 0 1988 American Chemical Society
Stabilities of Zeolitic Aluminosilicates
The Journal of Physical Chemistry, Vol. 92, No. 15, 1988 4463
TABLE II:
Rigid Ion Parameters for Interatomic potential^'^.'^
A , eV
interaction 02-432-
A13+-02Si4+_02Na+-02-
P7
22764 1460.30 1584.167 1226.84
A
0.1490 0.2991 0.3296 0.3065
C, e V A " 27.88 0.000 52.64511 0.000
Three-Body Potential
Figure 1. Structure of faujasite.
Figure 2. Structure of mordenite.
interaction
k. eV.rad-*
On. rad
0-T-0
4.5815
1.911
= 0.0256 A3,aAp+= 0.0448 A3, and aN+ = 0.128 A3. In the second approach we used lattice energy minimization calculations to study the lattice energy as a function of aluminum content. These techniques enable the calculation of the stability of structures corresponding to minimum lattice energies.I2 This calculation may be done in two ways: either the atomic positions only are adjusted until the minimum is obtained (constant volume minimization) or, additionally, the unit parameters are adjusted to remove any remaining strains in the lattice (constant pressure minimization). In our calculations relaxation to constant pressure has been used. The technique requires the specification of a starting structure, which may be based on experimental data, if available, and a set of interatomic potentials. The following potential model is used, in which the interaction of a pair of ions i and j is described by 4i9j V(rij) = - + Aij exp(-rij/pij) - Cij/rij6 rij
Figure 3. Structure of ZSM-5.
in covalent energies are smaller than those found with the extended Huckel method. Rigid ion lattice energy minimization calculations6 predict a-quartz to be the most stable of the silica polymorphs and a difference of 40 kJ/mol between a-quartz and dealuminated faujasite. We followed two types of approach to study the changes in heat of formation as a function of alumina content. In one approach, for a certain zeolite structure the Madelung and polarization energies and the heat of formation due to ionic bonding are calculated both for the zeolitic aluminosilicate with varying amounts of aluminum and for the zeolitic silica. The difference between the two results for the heat of formation is assumed to represent the contribution to the total heat of formation of the zeolite structure stemming from the presence of aluminum ions and cations in this structure. This difference is added to the heat of formation due to covalent bonding resulting from a simple quantum chemical calculation method for zeolitic silicas in order to arrive at the total heat of formation of the zeolite structure as a function of the amount of aluminum. This procedure leads to heats of formation at zero aluminum content which are correct to within 10 kJ/mol. The work is an extension of earlier calculations of electrostatic fields and potentials not including polarization by Dempsey' and Preuss.* For the electrostatic calculations we used the method and computer program described by Piken and Van Goo19 and Van Gool and Piken.'O Formal ion charges were used. The values of the polarizabilities" were as follows: aOz-= 1.984 A3,a s i 4 + (6) Ooms, G.; Van Santen, R. A.; Jackson, R. A.; Catlow, C. R. A. Proc. "Innovation in Zeolite Materials Science", Belgium Sept. 1987; Stud. Surf. Sci. Carol. 1988, 37, 317. (7) Dempsey, E. J . Phys. Chem. 1969, 73, 3660. (8) Preuss, E.; Linden, G.; Peuckert, M. J . Phys. Chem. 1985,89, 2955. (9) Piken, A. G.; Van Gool, W. Ford Motor Co. Scientific Laboratory, Technical Report SL 68-10, 1968. (10) Van Gool, W.; Piken, A . G. J . Mater. Sci. 1969, 4, 95, 105.
Here qi and qj are the ionic charges and Aij, pij, and Cij the short-range potential parameters. In the calculations discussed here, ions were treated as rigid and assigned formal charges. In order to be able to simulate framework relaxation it is necessary to include an extra term in the potential to take account of the directionality of the bonding of the oxygen ions with silicon or aluminum ions. This term, which defined for each OSiO or OAlO bond, takes the form where k and Bo are constants The same parameters are those used earlier by Jackson and CatlowI3 were employed. They are listed in Table 11. Madelung and Polarization Energy Calculation
In the calculations, we started with an existing zeolite structure and used the cell constants and the coordinates of the A13+/Si4+ ions, 02-ions, and Na+ ions as given in the literature. For faujasite we used the data of Hseu,I4 for mordenite and the data of MeierI5 and of Mortier et a1.,I6 and for ZSM-5 the data of Baerlocher" and of Chao et al.'* The distribution of the AI3+ ions over the A13+/Si4+ locations is not well-known, although it is generally accepted that Lowenstein's rule precluding two aluminum ions being near-neighbors is obeyed. In our calculation the A13+ ions were smeared out over the possible A13+/Si4+ion locations, so that at those locations a fractional charge was present dependent on the Al/Si ratio. This simplification is rather drastic, but necessary due to the lack of knowledge about the positions of the A13+ ions and justified by the fact that we are interested in the difference in heat of formation due to ionic bonding of a zeolite structure (1 1) Greenwood, N . N. Ionen Kristalle, Gitterdefekte und Nichtstochiometrische Verbindungen;Verlag Chemie: Weinheim, FRG, 1973. Tessmann, J R.; Kahn, A. H.; Shockley, W. Phys. Rev. 1953, 92, 890. (12) Catlow, R. A., Mackrodt, W. C., Eds.; Computer Simulation of Solids; Lecture Notes in Physics No. 166; Springer: Berlin, 1982. (13) Jackson, R. A.; Catlow, C. R. A . Mol. Simulation 1987, 2. (14) Hseu, T. Ph.D Thesis, University of Washington, 1972; University Microfilms, no. 73-13835, Ann Arbor, MI. (15) Meier, W. 2. Kristallogr. 1961, 115, 439. (16) Mortier, W. J.; Pluth, J. J.; Smith, J. V. In Natural Zeolites Occurrence, Properties, Use;Sand, L. B., Mumpton, F. A,, Eds.; Pergamon: New York, 1978. (17) Baerlocher, C. Paper presented at the Sixth International Zeolite Conference, 1983. (18) Chao, K. J.; Lin, J. C.; Wang, Y.; Lee, G H. Zeolites 1986, 6, 35.
4464
The Journal of Physical Chemistry, Vol. 92, No. 15, 1988 01
02
Ooms et al.
A L / S L RAT IO 04
03
IONIC BONDING CONTRIBUTION TO TOTAL HEAT OF FORMATION (kJ/moL S t O z )
-2500t ZSM-5
MORDENITE
--
WITHOUT AL" AND No' W I T H pi3+ A N D N O *
-4OOOb
HEAT OF FORMATION DUE TO IONIC BONDING ( k J / m o t SLOZ)
Figure 4. Influence of Al/Si ratio on heat of formation due to ionic
200 100
FAUJASITE
0
02
01
03
Figure 5. Influence of AI/Si ratio on ionic bonding contribution to total heat of formation.
bonding. and its dealuminated version. Using Van Gool's computer program we calculated the Madelung energy and the polarization energy of the zeolite structure. Next we subtracted the ionization energies, the heat of vaporization of Al, Si, and Na, and the dissociation energy of 02,and found the cohesive energy with respect to the elements, called heat of formation due to ionic bonding of the structure. The calculation was repeated, but with the A13+ ions and Na+ ions removed from the structure. The difference between the two results for the heat of formation due to ionic bonding was assumed to represent the contribution to the heat of formation due to the presence of aluminum and sodium ions in the structure. The total heat of formation of the structure was finally found by adding this contribution to the heat of formation due to covalent bonding resulting from the quantum chemical ASED method applied to the dealuminated structure. In the following step of the calculation of the concentration of aluminum and sodium ions was changed. For faujasite we started with an Al/Si ratio of 0.416 and decreased this ratio to zero. The aluminum ions were theoretically replaced by silicon ions via increasing the charge at the A13+/Si4+ion locations. The order of removing Na+ ions did not have a significant influence on the results. For mordenite we started with a Al/Si ratio of 0.166, decreased it to zero, and increased it to 0.416. Taking care that the addition of Na+ ions was done in accordance with the symmetry properties of the unit cell, we found that the order of the addition again did not significantly influence the results. For ZSM-5 we started with a ratio of zero and increased it to 0.416. In this way the influence of the presence of aluminum and sodium ions on the total heat of formation was studied for the three zeolites. In the last step of the calculation procedure the influence of hydration on the total heat of formation, as described in the Appendix, was taken into account. Results with and without the effect of hydration will be presented. A . Results without Hydration of Cations. Figure 4 gives the heat of formation due to ionic bonding for faujasite, mordenite, and ZSM-5 with and without the presence of A13+and Na+ ions. The results for the case without AI3+and Na+ ions depend on the Al/Si ratio, as the cell constants depend on it. After each calculation for a case with A13+ and Na+ ions we removed these ions, kept the values of the cell constants depending on the Al/Si ratio the same, and repeated the calculation. The difference between the solid and dotted curves in Figure 4 represents the ionic bonding contribution to the total heat of formation of the zeolite structure due to the presence of aluminum and sodium ions in the structure. These contributions are given in Figure 5. The total heat of formation of the zeolites consists of the covalent bonding contribution taken from Ooms and Van Santen4 and the ionic bonding contribution given in Figure 5. The results for the total heat of formation are given in Figure 6. At an Al/Si ratio between 0 and 0.2 the mordenite and ZSM-5 curves in Figure 6 coincide, as in that region the covalent bonding contribution and the ionic bonding contribution are the same for both zeolite structures. From Figure 6 it can be concluded that the presence of aluminum and sodium ions in the zeolite structure has a sig-
04 A L/S L RATIO
A L / S t RATIO
0
02
01
0 3
04
-6001
-
,
-1oooF
O
O
b
TOTAL HEAT OF FORMATION ( k J / m o l SLOZ)
Figure 6. Total heat of formation as a function of AI/Si ratio. 0
01
02
03
Al/St 04
RATIO
: l L ZSM-5
MORDENITE
-800
FAUJASITE
-1000 TOTAL HEAT
OF FORMATION (kJ/mol StOz)
Figure 7. Total heat of formation as a function of AI/Si ratio with effect of hydration.
nificant influence on the total heat of formation. B. Results with Hydration of Cations. In the final step of this calculation the effect of hydration of the cations was taken into account. This contribution was calculated with eq 1-6 of the Appendix and added to the results of Figure 6. Figure 7 gives the final results for the total heat of formation. It can be concluded that the influence of hydration of cations is also considerable. Results of Lattice Energy Minimization Calculations
The relative lattice energies of faujasite, mordenite, and ZSM-5 have been compared at varying AI/Si ratios. These calculations used an average charge corresponding to the Al/Si ratio. For the framework and cation positions the same data were used as earlier. The framework and cation positions were allowed to relax under constant pressure. Figure 8 shows the computed lattice energies for faujasite and mordenite as a function of Al/Si ratio. These detailed lattice energy calculations agree rather well with the approximate calculations discussed earlier. At Al/Si ratios larger than 0.2 the lattice energy of mordenite starts to decrease when compared to that of faujasite. It appears that convergence of the calculations is only possible for a finite range of Al/Si ratios. This is shown in Figure 9. Calculations on ZSM-5 do not converge for Al/Si ratios larger than 0.1, mordenite 0.5, and faujasite 0.8. Also indicated in the figure are the maximum values of the Al/Si ratios for which those structures can directly be ~ynthesized.~The correspondence is quite reasonable.
The Journal of Physical Chemistry, Vol. 92, No. 15. 1988 4465
Stabilities of Zeolitic Aluminosilicates
with the results of synthesis experiments.
Appendix Method for Calculating the Hydration Energy. In our cal-
0
0.20
040
060
080
I00
AL/SL RATIO
Figure 8. Lattice energy as function of AI/Si. 4XIMUM ALLOWABLE AL/SL RATIO
0EXPERIMENTAL EZZ PREDICTED
ZSM5
MORDENITE
1 FAUJAS ITE
Figure 9. Experimental and predicted maximum allowable AI/Si ratios.
Analysis of the cation positions in the various structures indicates that the strong decline of mordenite and ZSM-5 stability with decreasing Si content is due to the unfavorable interaction between the interchannel cations at high cation concentration in the narrow pores of these zeolites.
Discussion An important conclusion of our studies is that the presence of aluminum ions and cations and hydration have a considerably larger influence on the relative stabilities of zeolites than differences arising from purely topological factors. If during the synthesis process zeolites are formed with an AI/Si ratio larger than 0.2 the stability decreases in the following order: faujasite > mordenite > ZSM-5. If zeolites are formed with an Al/Si ratio below 0.2, mordenite and ZSM-5 are of equal stability; faujasite is less stable. It is difficult to predict the Al/Si ratio of zeolites formed during the synthesis process, as for such a prediction not only the heat of formation of the zeolites must be known but also the heat of formation of all other components of the synthesis process. The necessary data for such a detailed study are not available. Yet we believe that some rough indications based on Figures 6 and 7 are possible. Without hydration (organic ions block entrances to the pores) zeolites with a very low Al/Si ratio tend to be formed. With hydration of cations the situation is more complex, as the curves of Figure 7 have several minima. If in that case faujasite is formed, it is likely to have an Al/Si ratio of about 0.4; if mordenite or ZSM-5 is formed, their Al/Si ratio will probably be about 0.15 or 0. These results are in qualitative agreement
culations we have limited ourselves to the case that the cations present inside the channels and cages of zeolites are Na+ ions. The locations and number of Na+ ions in a unit cell of faujasite, mordenite, and ZSM-5 are given in Mortier’sig review. The hydration of such cations gives a contribution to the total heat of formation of the zeolites. A simple method has been developed to calculate this contribution. First the volume of a unit cell of faujasite, mordenite, or ZSM-5 was calculated. Knowing the porosity of these zeolites we determined their pore volume per unit cell and from this we calculated the maximum number of water molecules present in a unit cell. The result is as follows: for faujasite 236 water molecules, for mordenite 25, and for ZSM-5 60. For faujasite and mordenite these numbers are in very good agreement with the experimental data as given in Mortier’~’~ review paper; there are no data about the possible water content of ZSM-5. Next we calculated for faujasite and mordenite the value of the ratio of the maximum number of water molecules to the maximum number of Na+ ions in a unit cell; this value is for both zeolites very close to 3. Therefore we assumed that each Na+ ion can hydrate three water molecules; if more water molecules per Na+ ions are present no further contribution to the heat of formation occurs. So for faujasite (Na,A1,Sil,z-x0384)-240H20 there is a continuously growing contribution to the heat of formation, if x runs from 0 to 80; after that the contribution is constant. For mordenite (Na&l$&+x09,)-24Hz0 there is an increasing contribution from x = 0 to x = 8; for ZSM-5 (Na,A1,Si96-,0i92)~60H20 there is a contribution from x = 0 to x = 20. As the hydration energy is equal to about 420 kJ/mol of Na, we find that for faujasite it is given by (x/192) X 420 kJ/mol of S O 2 , for mordenite by (x/48) X 420 kJ/mol of S O 2 , and for ZSM-5 by (x/96) X 420 kJ/mol of S O 2 , in which x/192, x/48, and x/96 are the Al/Si ratios for the three zeolites. A second, negative, contribution to the heat of formation due to hydration comes from the heat of evaporation of water, when during the synthesis stage it goes out of the solution and into the zeolite structure. As the heat of evaporation is about 42 kJ/mol of H 2 0 , we find that for faujasite it is (240/192) X 42 = 52.5 kJ/mol of Si02,for mordenite (24/48) X 42 = 21 kJ/mol of S O 2 , and for ZSM-5 (60/96) X 42 = 26.25 kJ/mol of SOz. In conclusion the net hydration energy is given by the following relations: faujasite Uhydr
=
(&
X
- 52.5 kJ/mol of S i 0 2
420)
Uhydr = 122.5 kJ/mol of Si02
for 0 6 x 6 80 (1)
> 80
for x
(2)
mordenite Uhydr=
(d x
420)
- 21 kJ/mol Of si02
for 0
20
(6)
(19) Mortier, W. J. Compilation of Extra Framework Sites in Zeolites; Butterworth: London, 1982.
