Combining the Monte Carlo Technique with 29SI NMR Spectroscopy

F-34095 Montpellier Cedex, France, and CDROM2, Theoretical Study of the .... Yunier Garcia-Basabe , A. Rabdel Ruiz-Salvador , Guillaume Maurin , L...
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J. Phys. Chem. B 2001, 105, 9157-9161

9157

Combining the Monte Carlo Technique with 29SI NMR Spectroscopy: Simulations of Cation Locations in Zeolites with Various Si/Al Ratios G. Maurin,† P. Senet,‡ S. Devautour,† P. Gaveau,† F. Henn,*,† V. E. Van Doren,‡ and J. C. Giuntini† L.P.M.C. UMR 5617, UniVersite´ Montpellier II, Place E. Bataillon, F-34095 Montpellier Cedex, France, and CDROM2, Theoretical Study of the Matter, Department of Physics, UniVersity of Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium ReceiVed: May 10, 2001; In Final Form: June 27, 2001

For the first time, the monovalent cation positions in a zeolite, i.e., mordenite, with increasing Si/Al ratios are calculated from combination of Monte Carlo techniques and 29Si NMR spectroscopy. For each Si/Al ratio, a combination of solid-state 29Si NMR and Monte Carlo simulations is used and leads to the proposal of a realistic structural model where the aluminum atoms are distributed among the four possible crystallographic sites. Then, the positions of the cations stabilizing the mordenite lattice are obtained by using Monte Carlo simulated annealing. The populations of the sites occupied by the cations and their variations with the Si/Al ratio predicted by the model are in very good agreement with those measured by thermally stimulated current spectroscopy on Na-mordenites.

1. Introduction Zeolites play an important role in catalysis1 and in electrochemistry2 because of their surface and ion exchange properties, related to the specific network of channels and cages formed by their structures. Although their crystalline structures are well defined, the substitution of Si by Al atoms induces chemical disorder. The problem which consists of characterizing this disorder has not yet been resolved, even though it plays a crucial role in their reactivities. To perform our calculation, we have chosen a given zeolite, i.e., a mordenite, as a typical example since it exists for a large Si/Al ratio domain. Na-mordenite is an aluminosilicate zeolite with an ideal composition of Na8Al8Si40O96, nH2O.3 The framework has a porous structure, which consists of main channels parallel to [001], having a slightly elliptical cross section with 12 TO4 tetrahedron units (T ) Si, Al) and connected with small side channels parallel to [010], with 8 TO4 cross section, called side-pockets. In the Cmcm space group, the T atoms can occupy four nonequivalent crystallographic sites noted T1, T2, T3, and T4 (Figure 1). The anionic character of the lattice due to the substitution of silicon by aluminum is neutralized by extraframework cations localized in different sites I, II, III, IV, and VI4 (Figure 1) which can be easily exchanged. The Si/Al ratio is an important feature of the mordenites related to their thermal stability5 and the strength of their acid sites.6 Further, the knowledge of the locations of the counterions is a key point since it influences the adsorption and the catalytic properties of mordenites.7 The number of sites available to these extraframework cations and their occupancies depend also on the Si/Al ratio. This problem is not resolved yet because it needs a detailed microscopic description of the distribution of the Al * Author to whom correspondence should be adressed. F. Henn, L.P.M.C. UMR 5617 CNRS, CC003, University of Montpellier II Sciences et Techniques du Languedoc, Place E. Bataillon, F-34095 Montpellier cedex 05, France. Phone: +33 4 67 14 48 55. Fax: +33 4 67 14 42 90. E-mail: [email protected]. † Universite ´ Montpellier II. ‡ University of Antwerpen.

Figure 1. Representation of the unit cell of mordenite. Description of the different extraframework cation sites and the four inequivalent tetrahedral positions for aluminum and silicon atoms T1, T2, T3, and T4.

atoms in the zeolitic framework for the different Si/Al ratio which is difficult to extract from the available experimental data. Indeed the atomic scattering factors of Si and Al are too close in X-ray diffraction. Therefore the discrimination of the chemical nature of the T atoms can only be obtained indirectly by considering the slight difference between the Si-O and Al-O bond lengths and the Si-O-Si and Al-O-Si angles. Such a careful analysis of XRD data leads to a preferential occupation of the sites T3 and T4 by Al in the space group Cmcm. Although there are some attempts to predict the distribution of Al atoms by using other techniques, such as 29Si NMR data,9 or theoretical calculations (simulated annealing techniques),10-12 they are difficult to apply to zeolites with high aluminum contents. The previous attemps13,14 to predict the positions of Al atoms among the four nonequivalent crystallographic tetrahedral sites of mordenite, principally concern dealuminated samples, for which the reported results are dispersed and do not provide a complete and comprehensive description at a microscopic level. Dealu-

10.1021/jp011789i CCC: $20.00 © 2001 American Chemical Society Published on Web 08/28/2001

9158 J. Phys. Chem. B, Vol. 105, No. 38, 2001

Figure 2.

27Al

Maurin et al.

MAS NMR spectra of Na-mordenites with Si/Al ) 5.5, 6.8, 7.9, 11.4.

minated samples generally contain extraframework Al in an amorphous phase that complicates the description of the Al distribution. In this work, the variations of the populations of the cation sites have been simulated and compared to those measured by TSC for crystalline samples obtained by direct synthesis, i.e., without using dealumination processes.8 From a microscopic point of view, these crystals are chemically disordered because of the large possible number of coexisting Al distributions for a given Si/Al ratio. A microscopic description of the variations of the cation locations with the Si/Al ratio is thus only possible through a statistical description of the mordenite lattice. We present here such a model by combining 29Si NMR measurements and Monte Carlo simulations. The number of sites and their occupations rate calculated by the present microscopic model are in very good agreement with the TSC data8 on Namordenites, and with the cation site populations measured by XRD4,15 for Si/Al around 5 which is the only one available. The experimental 29Si NMR data are presented in Section 2. The Monte Carlo modelization is developed in Section 3. Concluding remarks are presented in Section 4. 2. Experimental Section The mordenite samples characterized by Si/Al ratios varying from 5.5 to 12 have been synthesized8 by a direct synthesis without any dealumination treatment. Solid-state 29Si NMR of aluminosilicates is used to characterize the average coordination of Si to Al16,17 in the second coordination shell, i.e., the populations of Si-nAl with n ) 0, 1, 2, 3, and 4. We also study 27Al NMR to check if octahedral coordinated aluminum could be found in this symmetry or not.

29Si

magic angle spinning (MAS) spectra were obtained on a Bru¨ker ASX 400 spectrometer. The conical rotor was spun at a rate of 3 kHz and the spectra were recorded at 79.5 MHz. Time intervals between pulse sequences were 10 s with π/4 pulses (4 µs). Chemical shifts were measured from tetramethylsilane (TMS). 27Al (MAS) NMR spectra were recorded at 104, 25 MHz with a spinning rate of 13 kHz. Chemical shifts were measured with respect to Al(H2O)63+ as an external reference. Pulse width was 1 µs (π/12 pulses) and the time interval between pulse sequence was 1.5 s. Figure 2 shows 27Al MAS NMR spectra of four representative samples with Si/Al ratios equal to 5.5, 6.8, 7.9, and 11.4, respectively. All spectra consist only of one peak at 50 ppm which is due to tetrahedral coordinated Al sites in the network.16 In contrast to dealuminated mordenites,16 no peak at 0 ppm, corresponding to octahedral coordinated Al sites, is observed. Therefore the Si/Al ratio of the framework calculated from 27Al NMR intensities corresponds here perfectly to the Si/Al ratio obtained by chemical analysis. This result is clearly different from those obtained for dealuminated mordenites16 where there is a strong deviation between the two Si/Al ratios. 29Si MAS NMR spectra of the same four representative mordenites (Figure 3) show a shoulder and two strong peaks at -99 ppm, -106 ppm, and -112 ppm, respectively. The following assignments are generally accepted. The shoulder at -99 ppm and the peak at -112 ppm correspond, respectively, to Si atoms with 2 and 0 Al atoms in the second coordination sphere.17 The fractions of Si-3Al and Si-4Al are not detected and are neglected. The peak at -106 ppm is due both to the contributions of Si-1Al and of Si-OH defect groups appearing during synthesis. One decomposes therefore its relative intensity

Monte Carlo Technique with

29Si

Figure 3.

I-106

ppm

29SI

NMR Spectroscopy

J. Phys. Chem. B, Vol. 105, No. 38, 2001 9159

MAS NMR spectra of Na-mordenites with Si/Al ) 5.5, 6.8, 7.9, 11.4.

in two contributions

I-106ppm ) ISi-1Al + ISi-OH

(1)

where ISi-1Al and ISi-OH are the relative intensities of the peaks Si-1Al and Si-OH. On the other hand, the Si/Al ratio is related to the Si-nAl relative intensities by 4

()

∑ ISi-nAl

Si

Al

) framework

i)1

0.25 × (2 × ISi-2Al + 1 × ISi-1Al)

(2)

in which ISi-2Al is the relative intensity of the Si-2Al peak at 4 ISi-nAl ) 100. ISi-1Al can be therefore -99 ppm and ∑n)0 calculated from eq 2 and ISi-OH deduced from eq 1. The Si-nAl distributions calculated using eqs 1 and 2 are presented in Table 1. The Si-nAl distribution varies with the Si/Al ratio as shown in Figure 4. In this Figure, the contributions of Si-OH and of Si-0Al have been added. We observe that the contribution of Si-2Al is almost constant whatever the Si/Al ratio and that the Si-0Al proportion increases with respect to Si-1Al. 3. Computational Methodology In a first step, we define the (Si,Al) mordenite lattice by a representative ensemble of 100 Al distributions constructed by

TABLE 1: Experimental Si-nAl Distribution Determined from Eqs 1 and 2 Si/Al ratio

Si-2Al (contribution -99 ppm)

Si-1Al (contribution -106 ppm)

Si-0Al (contribution -112 ppm)

Si-OH (contribution -106 ppm)

5.5 6.1 6.8 7.9 8.5 9.7 11.4 12

6.2 7.2 6.4 5 7.6 5.9 6.0 4.6

60.2 54.1 46 40.6 32.0 29.4 23.1 24.1

33.6 35.6 40.8 48.7 48.1 46.9 49.8 49.7

0 3.1 6.8 5.9 12.3 17.8 21.1 25.6

combining the 29Si NMR data presented above and Monte Carlo simulations for each Si/Al ratio. In the second step, we evaluate the average locations of the extraframework cations by a Monte Carlo simulated annealing18 for each Si,Al lattice as defined previously. Finally, the equilibrium cation sites and their occupancies are then compared to experiment. The calculations are performed using periodic boundary conditions and crystallographic unit cell of mordenite with space group Cmcm. The simulation cell contains n Al atoms, 48-n Si atoms, and 96 O atoms with n varying from 4 to 8. Two models of Monte Carlo simulations of Al distributions are used which are based on the connectivity of the lattice. The first model is the Soukoulis’ model,19 which only takes into account the

9160 J. Phys. Chem. B, Vol. 105, No. 38, 2001

Maurin et al.

Figure 4. Relationship between Si-nAl distribution and Si/Al ratio in mordenite. Solid lines with solid symbols are assigned to experimental results, dash lines with open symbols correspond to Monte Carlo simulated results.

TABLE 2: Relative Populations of Si-nAl Units in Mordenites for Different Si/Al Ratios 29Si NMR binomial Monte Carlo Monte Carlo Model 1 Model 2 Si/Al Si-nAl experiment distribution

n)0 n)1 n)2 n)3 n)4

33.6 60.2 6.2 0.0 0.0

41.0 41.0 15.3 2.6 0.1

37.3 46.7 14.7 1.3 0.0

30.0 60.0 10.0 0.0 0.0

5.5

n)0 n)1 n)2 n)3 n)4

38.7 54.1 7.2 0.0 0.0

47.3 38.9 12.0 1.7 0.1

44.3 44.0 11.0 0.7 0.0

39.0 53.7 7.3 0.0 0.0

6.1

n)0 n)1 n)2 n)3 n)4

47.6 32.0 7.6 0.0 0.0

54.0 36.0 9.0 1.0 0.0

51.5 40.2 7.8 0.5 0.0

47.6 47.6 4.8 0.0 0.0

6.8

n)0 n)1 n)2 n)3 n)4

60.4 31.8 7.4 0.0 0.0

61.0 32.1 6.3 0.6 0.02

59.0 35.5 5.2 0.3 0.0

60.5 32.5 7.0 0.0 0.0

8.5

n)0 n)1 n)2 n)3 n)4

70.9 23.1 6.0 0.0 0.0

68.3 27.3 4.1 0.3 0.0

66.8 30.0 3.2 0.0 0.0

70.4 22.7 6.9 0.0 0.0

11.4

Loewenstein20 rule, which prohibits Al-O-Al bonds. It leads to Si-nAl population close to a binomial distribution21 for all Si/Al which agrees qualitatively with experiment (see Table 2). A more sophisticated model (Model 2) which consists in Model 1 with constrain imposed by the 29Si NMR data17 reproduces well the experimental results as it is observed in Table 2 and in Figure 5 where theoretical and experimental Si-nAl populations are represented as a function of Si/Al ratio. Because the model is based only on the connectivity, it cannot predict preferential occupation of sites T3 and T4 observed in XRD. To include this bias, only the Al configurations generated by Model 2 which contain a majority of T3 and T4 sites are selected for the calculations of the positions of the extraframework cations since these crystallographic sites are occupied preferentially by Al atoms whatever the Si/Al ratio.22-25 One selects thus 100 representative Al configurations obtained by Model 2 to represent the mordenite lattice for each Si/Al ratio.

Figure 5. Evolution of the number of sodium ions Na+ per unit cell, as a function of the Si/Al ratio. (a) Theoretical mean populations obtained from the average of our sample space. (b) Comparison between theoretical predictions and experimental data (XRD and TSC). Experimental sites I and main channel sites (sites IV and sites VI) are represented by solid circles and triangles, respectively. Theoretical sites (I, II) and sites (IV, VI, III) are represented by open circles and triangles, respectively.

Packing and structure optimization procedures26-28 have been applied to find the locations of extraframework cations in various zeolites as faujasite. In these calculations, a low number of initial cation configurations are generated and the lattice energy is optimized without the influence of the temperature. More sophisticated simulation strategies are then needed to overcome these shortcomings. Here, the minimum energy distribution of the cations is obtained, for the various Si/Al ratios, by simulated annealing using the Monte Carlo Metropolis algorithm18 implemented in a parallel code. The framework is rigid and non-polarizable and periodic boundary conditions are used with the crystallographic positions of the Cmcm unit cell. The energy of the crystal cell is represented by the sum of pair Coulomb potentials between all the atoms (cations and atoms of the framework) and pair Born Mayer repulsive potential between the sodium cations and the oxygen atoms of the lattice. The pair potential parameters are those obtained by Kramer et al.29, which are based on a fit to ab initio potential-energy surface of molecular clusters and on experimental bulk data. The mordenite is assumed to be semiionic with atoms carrying on the following partial charges: Si (+2.4), Al (+1.4), O (-1.2), and Na (+1). The Ewald summation30 is used for the Coulomb interactions and the shortrange interactions are calculated with a cut-off of 10 Å. Each annealing consists of 30000 independent Monte Carlo steps/ cation. 20000 steps initiate each energy minimization at 1200

Monte Carlo Technique with

29SI

NMR Spectroscopy

K followed by system cooling to 300 K. The final cation equilibrium positions have been checked by analytical and numerical evaluation of the derivatives of the potential energy with respect to the cation displacements. The first derivatives are always zero and the Hessian is positive define, thus confirming that the equilibrium positions have indeed been found. The theoretical mean populations of the cations obtained from the average of 100 selected representative Al configurations for each Si/Al ratio are reported in Figure 5a. We find that the cations, for each Si/Al ratio, are principally localized on the crystallographic sites I (in side pockets) and sites IV and VI (main channels)4 in agreement with XRD data available for Na mordenite with Si/Al around 5.4,15 However other sites, sites II and sites III, are also occupied by a slighter fraction of the cations (almost 10% for each site). These sites are not detected neither by X-ray diffraction for Si/Al varying from 5 to 5.5 or by thermally stimulated current (TSC) within the experimental error bars. Therefore, the occupation of sites II and III is certainly overestimated in the present simulation. This is due to necessary limitations of our model in which we recall that the framework is kept rigid and that the polarizabilty of the lattice is treated in a mean field approach by using pair potentials. In addition, the present calculations are performed for a perfectly dry material. The impact of these various approximations deserves further work. However, it is worth noting that residual water molecules are always present in experimental partially hydrated samples. Water is known to stabilize sites I and IV. By performing simulations in a dry crystal, we neglect this effect. This can affect the distribution of cations in sites II and III which are in the close neighboring of sites I and IV, respectively. This is probably because residual water molecules, which are always present in experimental partially hydrated samples, stabilize sites I and sites IV neighbors of sites II and III, respectively.31 Consequently, the cations which are found most stable in sites II and III in our simulations, appear to be, in experimental conditions, more stable in sites I and IV, respectively, due to the presence of residual water molecules in their coordination sphere.31 Therefore, to compare our results with the experimental data obtained by XRD and TSC, we add the small fraction of cations occupying sites II and III to the population of the sites I and of the main channel sites (sites IV and VI), respectively. The comparison with experimental data, XRD for the ratio Si/Al ) 515 and TSC for ratio varying from 5.5 to 12, is reported in Figure 5b. We observe in general a nice agreement between our predicted populations and the experimental data for all Si/Al. It is worth noting that there is also a slight difference between the total number of cations in the experimental samples and in the theoretical calculations because of slightly different Si/Al ratios studied due to the limited size of the unit cell of the simulation. The site I, which has been previously mentioned as the deepest one in energy32 remains always the most occupied site. However, for 8 Al/cell, corresponding to an Si/Al ratio equal to 5, our simulation predicts that the populations of the cations in the main channel are higher than the population of the cations in the side pockets as measured in XRD. 4. Conclusion We have developed a Monte Carlo model to predict the locations of extraframework cation in mordenites of arbitrary Si/Al ratio. The locations of the cations are in agreement with available X-ray diffraction data available for Si/Al around 5. Our calculations extend the conclusions of this experimental

J. Phys. Chem. B, Vol. 105, No. 38, 2001 9161 study to mordenites with various Si/Al ratios for which less direct experimental data are available. The predicted locations of nonframework cations and their occupancies are in very good agreement with TSC experiments for all Si/Al ratios. These results prove that the present methodology can provide a realistic structural model of Al distribution in chemically disordered system. The present model could be easily applied to other zeolites or aluminosilicate glasses. It is also the first step toward the calculation of the activation barrier of the detrapping of the cation from its site which is also experimentally measured by TSC. Acknowledgment. P. SENET thanks the Flemish Scientific Fund of Research (F.W.O.-Flanderen) for his support. References and Notes (1) Gottardi, G.; Galli, E. Natural Zeolites; Springer-Verlag: Berlin, 1985; p 223. (2) Mortier, W. J.; Pluth, J. J.; Smith, J. V. Natural Zeolite Occurrence Properties; Pergamon Press: New York, 1978; p. 53. (3) Meier, W. M. Z. Kristallogr. 1961, 115, 439. (4) Mortier, W. J. Compilation of Extraframework Sites in Zeolites; Butterworth: Guildford, 1982. (5) Klinowski, J.; Thomas, J. M.; Anderson, M. W.; Fyfe, C. A.; Gobi, G. C. Zeolites, 1983, 3, 5. (6) Chumbhale, V. R.; Chandwadkar, A. J.; Rao, B. S. Zeolites 1992, 12, 6663. (7) Vitale, G.; Bull, L. M.; Morris, R. E.; Cheetham, A. K.; Toby, B. H.; Coe, C. G.; MacDougall, J. E. J. Phys. Chem. 1995, 99, 16087. (8) Pamba, M.; Maurin, G.; Devautour, S.; Vanderschueren, J.; Giuntini, J. C.; Di Renzo, F.; Hamidi, F. Phs. Chem. Chem. Phys. 2000, 113 (11), 4498. (9) Itabashi, K.; Okada, T.; Igawa, K. Proceedings of the 7th International Zeolite Conference; Murakami, Y., Ward, J. M., Eds.; 1986, 369. (10) Herrero, C. P. J. Phys. Chem. 1991, 95, 3282. (11) Li, B.; Sun, P.; Jin, Q.; Wang, J.; Ding, D. J. Mol. Catal. A 1999, 148, 189. (12) Ding, D.; Li, B.; Sun, P.; Jin, Q.; Wang, J. Zeolites 1995, 15, 569. (13) Stoica, A. D.; Tarina, V.; Russu, R.; Gheorghe, G. Zeolites 1992, 12, 706. (14) Ripmeester, J. A.; Najid, A.; Hawkins, R. E. J. Inclusion Phenom. 1983, 1, 193. (15) Coughlan, B.; Carrol, W. M.; McCann, A. J. Chem. Soc., Faraday Trans. 1977, 73, 1612. (16) Sawa, M.; Niwa, M.; Murakami, Y. Zeolites 1990, 10, 532. (17) Ding, D.; Sun, P.; Jin, Q.; Li, B.; Wang, J. Zeolites 1994, 14, 65. (18) Metropolis, N.; Rosenbluth, A.; Rosenbluth, M.; Teller, A.; Teller, E. J. Chem. Phys. 1953, 21, 1087. (19) Soukoulis, C. M. J. Phys. Chem. 1984, 88, 4898. (20) Lowenstein, W. Am. Mineral. 1954, 39, 92. (21) Mikowsky, R. J. Zeolites 1983, 3, 90. (22) Alberti, A.; Davoli, P.; Vezzalini, G. Z. Kristallogr. 1986, 175, 249. (23) Takaishi, T.; Kato, M.; Itabashi, K. Zeolites 1995, 15, 21. (24) Olson, D.; Bisio, A. Proceedings of the 6th International Zeolite Conference; Butterworths: Guildford, U.K., 1984; p 717. (25) Debras, G.; Nagy, J. B.; Gabelica, Z.; Bodart, P.; Jacobs, P. A. Chem. Lett. 1983, 199. (26) Vitale, G.; Mellot, C. F.; Bull, L. M.; Cheetham, A. K. J. Phys. Chem. 1997, 101, 4559. (27) Lignie`res, J.; Newsam, J. M. Microporous Mesoporous Mater. 1999, 28, 305. (28) Grillo, M. E.; Carrazza, J. J. Phys. Chem. 1996, 100, 12261. (29) Kramer, G. J.; Farragher, N. P.; Van Beest, W. H. Phys. ReV. B 1991, 43, 5068. (30) Allen, M. F.; Tildesley, D. Computer Simulation of Liquids; Oxford Science Publications: Oxford, 1987. (31) Shiokawa, K.; Ito, M.; Itabashi, K. Zeolites 1989, 9, 170. (32) Devautour, S.; Vanderschueren, J.; Giuntini, J. C.; Henn, F.; Zanchetta, J. V.; Ginoux, J. L. J. Phys. Chem. 1998, 102, 3749.