J. Phys. Chem. B 2001, 105, 9569-9575
9569
A Simple Model for Predicting the Na+ Distribution in Anhydrous NaY and NaX Zeolites Se´ verine Buttefey,† Anne Boutin,*,† Caroline Mellot-Draznieks,‡ and Alain H. Fuchs† Laboratoire de Chimie Physique, UMR 8000 CNRS, UniVersite´ Paris-Sud, 91405 Orsay, France, and Institut LaVoisier, UMR 8637, UniVersite´ de Versailles Saint Quentin, 78035 Versailles, France ReceiVed: February 16, 2001; In Final Form: May 17, 2001
A simple model is used for predicting the way cations are distributed among the known crystallographic sites I, I′, II, and III, in NaY and NaX faujasite zeolites. This model is based on the well-known assumption that the cation distribution is dominated by the repulsive cation-cation Coulombic interactions. In the case of NaY the predicted distributions are in good agreement with the available experimental data. Monte Carlo simulations have been performed, using a simplified framework model together with the recently proposed cation-framework model of Jaramillo and Auerbach. These simulations confirm the basic assumption of the cation-filling model. They also reveal a striking sensitivity of the configuration energy to a weak deviation from the most uniform local cation spatial distribution. The existence of the extra site III′ experimentally reported in NaX is also observed in these simulations.
1. Introduction Understanding the factors that control separation properties in zeolites requires a detailed knowledge of the structure of the host materials. In aluminosilicate zeolites the presence of aluminum atoms introduces charge defects, which are compensated with some nonframework cations (sodium, potassium, barium,...). Zeolites are characterized by the fact that the number of potential cation sites observed in the structure usually exceeds the number of cations needed to ensure electroneutrality of the material. The need exists for a method that could predict the way the extraframework cations are distributed among the available sites, since this is known to play a crucial role on the adsorption and transport behavior of guest species in the host framework. A substantial number of experimental,1,9-17 theoretical,2-5 and computational6-10 studies have examined the cation distribution in the industrially important faujasite-type zeolites. Cations can occupy different types of sites in faujasite (Figure 1). Sites I are located in the hexagonal prism, which connect sodalite cages. Sites I′ are inside the sodalite cage facing site I. Sites II are in front of the 6 rings inside the supercage. Sites III are also in the supercage, near the 4 rings of the sodalite cage. Site I has a multiplicity of 16 per unit cell, sites I′ and II have a multiplicity of 32. Some cations have also been found (in the case of NaX) in the 12-ring window.9,11 These are called sites III′. Sites III and III′ are believed to be of higher potential energy than sites I, I′, and II. At low occupancy (Si:Al g 2) Na+ ions occupy sites I, I′, and II only. Even in prototypical systems such as dehydrated NaX9,11,12 or NaY13-17 the precise location of some cations remains uncertain. This is particularly true for cations occupying lowsymmetry sites with low occupancy factors. The variety of cation positions reported in the literature for the same systems might also arise from genuine differences among the samples: inhomogeneous aluminum distribution in an overall identical * Author to whom correspondence should be addressed. † Universite ´ Paris-Sud. ‡ Universite ´ de Versailles Saint Quentin.
Figure 1. Schematic view of a faujasite supercage.
nominal composition,9 presence of H+ ions, small amount of residual water molecules, or impurity cations in the sample. This very important point is fully discussed in ref 12. Although theory and computer simulations have helped in corroborating the experimental findings, a general modeling of cation occupancy in faujasite, taking into account the nature of the cation and the Si:Al ratio, is still lacking. Previous theoretical work has mostly used energy minimization which are equivalent to zero K calculations and yield minimized structures that can only be compared with low-temperature diffraction studies.6-9 We have performed here Monte Carlo simulations of cation distributions in models of NaY and NaX, using a recently proposed force field for cations in zeolites.10 This method is of special interest for generating the statistically averaged information (at finite temperature) that is required for such systems. Based on a simple assumption that has been assumed by zeolite chemists for long, namely that cations, in selecting among similar chemical sites, would prefer to be relatively distant to avoid intercationic repulsions, we derive a “cation filling model” through which we are able to predict cation distributions in dehydrated NaY and NaX whatever the Si:Al ratio is. The
10.1021/jp0105903 CCC: $20.00 © 2001 American Chemical Society Published on Web 09/11/2001
9570 J. Phys. Chem. B, Vol. 105, No. 39, 2001 predicted distributions compare rather well with the available experiments, and this is very encouraging, considering the very simple assumptions of the model. The theoretical approach presented here supports most of the experimental and modeling results previously obtained in faujasite.1-17 It is meant as a first step toward the general modeling of cation distribution and redistribution upon adsorption in cationic zeolites. The remainder of the paper is organized as follows. In Section 2, we discuss the computational methodology. In Section 3, we present the results of the Monte Carlo simulations for Na48Y, the “cation filling model”, the predicted cation distribution for NaY and NaX, and the comparison of the predictions with available experiments. Concluding remarks are given in Section 4. 2. Computational Methodology Our goal is to formulate a coherent rationale for cation distributions in faujasite. We have thus used, to begin with, a very simple structural model in which the framework atoms are fixed and only the cations are allowed to move. Several Monte Carlo (MC) simulations with a fixed number of cations have been performed. Long enough MC runs make it possible, in principle, to perform a proper averaging of the different instantaneous cation arrangements; thus allowing a direct comparison between the simulation averaged quantity and the corresponding experimental observable. In aluminosilicate zeolites, however, the thermodynamic averaging problem is getting somewhat more complicated because of the existence of two tetrahedrally coordinated atoms (T atom: Si or Al) in the framework. In all but the Si:Al ) 1 case, aluminum atoms will be asymmetrically arranged in the simulation box (one unit cell in our case). The use of periodic boundary conditions leads to a replication of this arrangement in all three directions of space. This is unphysical, since in a real crystal the asymmetry would be averaged over space. Thus, to compute a reliable quantity in the thermodynamic limit, one would also have to perform an average over a large number of different aluminum atom arrangements in the simulation cell. This double averaging (over cation and aluminum atom arrangements) is a tedious task. A way to overcome this problem is to consider a unique average T atom in the simulations. This has been done quite often in previous studies of adsorption in zeolites,18-22 and we have used this assumption again here. By doing this we are aware that our model will miss some of the details of the cation-framework interaction. Our strategy is first to provide a certain basic understanding in the simplest cases. More sophisticated models will be developed in the future in order to predict cation distributions more accurately. A. Faujasite Model. The framework structure of dehydrated faujasite was taken from the experimental neutron diffraction studies of Fitch et al.15 The crystalline structure is described in the Fd3m space group and the cubic lattice parameter is 24.8536 Å. Cation site III positions, as experimentally observed in NaX, were taken from the work of Mellot.23 The structural parameters of the model are given in Table 1. The same, rigid, framework structure has been used throughout this work. One unit cell of faujasite was used as the simulation box, with periodic boundary conditions in all three directions. Different systems/materials have been studied, their Si:Al ratio ranging from 3 to 1. The corresponding number of sodium cations per unit cell ranged from 48 (Si:Al ) 3) to 96 (Si:Al ) 1). For each system the T-atom partial charge was adjusted in the way described below and the number of cations was adjusted accordingly. B. Atomic Charges. Partial charges on the oxygen and T atoms have been taken from the work of Mortier and co-
Buttefey et al. TABLE 1: Framework Structure of Dehydrated Faujasite Obtained by Neutron Diffraction Experiments of Ref 15a atom
position
x/a
y/a
z/a
Si/Al O(1) O(2) O(3) O(4) Na(II) Na(I′) Na(I) Na(III)a
192i 96h 96h 96h 96h 32e 32e 16c 48f
-0.0543 0 -0.0021 -0.1764 0.1786 0.2345 0.0507 0 0
0.0354 -0.1061 -0.0021 0.1764 0.1786 0.2345 0.0507 0 0
0.1247 0.1061 0.1418 -0.0335 0.3182 0.2345 0.0507 0 0.209
a
Site III is taken from ref 23.
TABLE 2: Partial Charges of T and Oxygen Atoms in NaY and NaX, the Partial Charge of Sodium Is Equal to +1 Si/Al ratio
cation number/ unit cell
T atom (|e|)
oxygen atom (|e|)
3 2.9 2.85 2.75 2.7 2.6 2.55 2.5 2.4 1.2 1
48 49 50 51 52 53 54 55 56 86 96
1.396 1.392 1.388 1.3837 1.3796 1.3756 1.3715 1.3674 1.363 1.24 1.2
-0.823 -0.8235 -0.824 -0.8247 -0.825 -0.826 -0.8263 -0.827 -0.8275 -0.8433 -0.85
ref [24]
[24]
workers.24 These calculations have been performed in two cases corresponding to the Si:Al values of 3 and 1, using the Electronegativity Equalization Method. We have used a linear interpolation method to obtain the atomic partial charges for different intermediate values of Si:Al (see Table 2). The atomic charge on the sodium cation was fixed at a value of +1. C. Cation Force Field. The total potential energy U of the system is calculated as
U ) UCF + UCC
(1)
where the cation-framework potential energy UCF has the following form:
UCF )
∑
C,F)O
[
CO
a
exp(-b rCO) CO
( )] cCO
6
+
rCO
∑ C,F∈T,O
qCqF rCF
(2)
in which an exp-6 repulsion-dispersion term acts between the cations (C) and the oxygen (O) atoms of the framework, and a Coulombic term acts between the cations and all the framework atoms. The cation-T atom repulsion-dispersion interaction is not taken into account here. The cation-cation energy UCC contains a Coulombic term only:
UCC )
∑
C,C′
qCqC′ rCC′
(3)
This force field was proposed by Jaramillo and Auerbach (JA).10 We have recently compared several cation force fields and shown that this one was doing the best job in reproducing the cation location in NaY.25 The JA sodium-oxygen a, b, and c parameter values used here are given in Table 3. It should be pointed out that the potential used here is not strictly equivalent
Na+ Distribution in Anhydrous NaY and NaX Zeolites
J. Phys. Chem. B, Vol. 105, No. 39, 2001 9571
TABLE 3: Sodium-Oxygen a, b, and c Parameter Values (JA potential10) parameter
value
aco bco cco
6.1 × 107 K 4.05 Å-1 7.652 × 105 K Å6
to JA’s since we are using an average T-atom while JA have distinguished Si and Al atoms in their molecular dynamics simulation.10 Thus the partial charges borne by the framework atoms are slightly different from one work to the other. We will show later on in this paper that the initial and modified JA force fields yield much the same results for cation location in NaY. Ewald sums were used to calculate the long-range Coulombic terms. The Ewald parameter R was equal to 0.19 Å-1 and the k vectors were such that k ∈ [-3,3]. D. Monte Carlo Simulations. Several NVT simulations were performed (T ) 298 K, or otherwise mentioned) for materials having an Si:Al ratio ranging from 3 to 1. Random translational displacement of cations were adjusted so to obtain an acceptance rate of ∼50% (maximum displacement of 0.3 Å). Equilibrium was typically reached after 105 moves. A further 106 production steps were performed to average quantities. As we will see below, metastable cation distributions have been obtained in the simulations. Depending on the initial configuration, standard NVT simulation at T ) 298 K will or will not converge spontaneously, in a finite MC run, to the most stable configuration. This kind of problem is often encountered in the simulation of particles with strong (.kT) interaction energy. This is why a standard MC simulated annealing procedure was used to search for the global minimum, starting from configurations at high temperature (1500 K) and progressively cooling the system to 298 K. Each cation distribution annealing consisted of at least 100 independent energy minimizations. In some cases the existence of numerous low-energy local minima in the energy landscape may prevent the system from reaching a lower energy minimum. This was found to happen for Na56Y where the path from the local minima to the lower energy minimum includes numerous cooperative as well as local rearrangements. To overcome this problem we have supplemented the standard MC annealing (which uses microscopic displacements) with a site-to-site hopping procedure. Starting from the configurations obtained at 298 K from simulated annealing, the MC simulations were carried on at this temperature using long distance jumps between sites I, I′, and II. The combination of these two methods presumably generated a relaxation of the system to the most stable state. At finite temperature the equilibrium cation distribution corresponds to a free energy minimum. However, since the number of cations is lower but of comparable magnitude than the number of available sites, the entropy contribution to free energy is presumably small as compared to the potential energy. This has been tested in detail in Na56Y (see next section). This leads to the conclusion that the cation distribution found at the potential energy minimum also corresponds to a minimum in free energy. 3. Results and Discussion We have studied faujasite models with Si:Al ranging from 3 to 1. We begin with a description of the case in which Si:Al ) 3 . This corresponds to NaY with 48 sodium cations per unit cell. We call this model Na48Y. On the basis of the results
Figure 2. Schematic view of the cation location in faujasite showing the smallest distances between crystallographic sites.
obtained for Na48Y, we derive a simple way of “filling” the faujasite framework with sodium cations, thus predicting the cation distribution for all materials ranging from Na48Y to Na64Y. We then test these predictions against experiments and simulations. Finally we extend the suggested “cation filling model” to the more complicated NaX case and discuss the limitation of our model. A. Cation Distribution in Simulated Na48Y. The most stable state found by simulated annealing corresponds to the complete filling of sites I (16 cations) and II (32 cations). No sodium cations were found in sites I′ and III. This will be termed a {16,0,32,0} cation distribution. It must be stressed that other stable local minima have been found in addition to the global minimum, but at higher energies. The nature of these metastable states is discussed below. The average interaction energy of a sodium cation with each individual adsorption site (I, I′, II, or III) has been computed at 10 K. As expected, site III is a less stable location for an individual sodium cation (interaction potential energy of -15000 K). Site I′ is the most stable cation-framework site (-55000 K), followed by site I (-52000 K) and site II (-45000 K). The fact that site I′ is not occupied in Na48Y simply means that the cation distribution is dominated by the Coulombic cation-cation interaction term UCC rather than the cation-framework UCF energy. Cations will then primarily arrange themselves in order to minimize UCC, and this corresponds to a full occupancy of sites I and II in the case of our model Na48Y (the distances between each pair of sites are indicated in Figure 2). As mentioned above, the most stable {16,0,32,0} configuration was not always found in finite MC runs. Numerous metastable states exist, which were identified, in the simulated annealing procedure, as local minima of the potential energy surface of the system. In these local minima, sites II were almost always fully occupied and the remainder of the cations were distributed among sites I and I′. This can be explained by considering the way adjacent I and I′ sites are occupied. It is usually supposed that adjacent sites I and I′ are not simultaneously occupied,4,5 and we explain this fact by the high repulsive energy experienced by the two cations. For a pair of monovalent cations separated from each other by 2 Å, the Coulombic energy amounts to 8300 K. This energy decreases by ∼5500 K when the cation separation increases up to 5.73 Å (the actual distance between sites I and II). Moreover each site I in the hexagonal prism has two adjacent I′ sites (Figure 2). The term “linked group” used by Barrer4 can be applied to this trimer of adjacent (I′-I-I′) sites. In several MC configurations, we found both sites I′ occupied in one of these linked groups, with the site I in the middle being empty. This situation is quite stable in a MC “timescale”, since a translational move of a cation from site I′ to site I will not happen unless the cation in the opposite site I′ is also displaced. This latter move will rarely take place since most surrounding sites II will be occupied and
9572 J. Phys. Chem. B, Vol. 105, No. 39, 2001
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TABLE 4: Predicted Cation Distributions in NaY (The simulation results are shown in italic and the experimental results are shown in bold) cation Si/Al number/ ratio unit cell 3 2.9 2.85 2.75 2.7 2.6 2.55 2.5 2.4 2.35 2.3 2.25 2.2 2.15 2.1 2.05 2.0
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
this work I I′ II 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32
I
experiments/simulation I′ II other sites
ref
9.3
13.7
25.3
3.5
[17]
7.04 4.0 7 8.0 7.1
13.76 17.6 17 18.88 18.6
29.44 32.0 25 30.08 32.2
3.76 1.4 7 0.04
[16] [14] [10] [13] [15]
empty site I′ will often have adjacent sites I occupied. Then a change of the occupancy of the linked group becomes highly improbable and the whole configuration is trapped in a metastable state. To confirm this explanation, we found that different initial configurations such as {16,32,0,0}, {15,1,32,0}, or {15,2,31,0} spontaneously transformed during an MC run at 298 K into the most stable {16,0,32,0} state, provided that only one of the I′ site in each linked group was occupied in the initial configuration. Conversely, initial configurations in which these two I′ sites were occupied got trapped in metastable states. In summary, the cation distribution in Na48Y can be understood in terms of a minimization of the cation-cation Coulombic interactions. Metastable states are found, which are related to some cations being locally trapped in (I′-I-I′) linked groups. The actual time scale associated with the trapping of these states is not known. What we describe here is presumably related to the sluggish and cooperative transport dynamics observed by Jaramillo and Auerbach in dry NaX and NaY by MD simulations.10 The model dependence of the results obtained here deserves a comment. Indeed, it must be pointed out that the use of a much deeper potential well for the cation-oxygen interaction would lead to a stabilization of at least some of the cations in site I′. This point has been examined in a previous work25 and we believe that the order of magnitude of the cation-oxygen well depth is realistic enough so to mimic reasonably well the NaY behavior. In the next section, we examine how these results can be used to understand the way cations distribute in NaY systems with decreasing Si:Al ratio (i.e., increasing cation number). B. A Simple Model for “Cation Filling” in NaY. Starting from Na48Y in which all sites I and II are occupied, it is obvious that the additional cations will try to occupy sites I′. Sites III are higher in energy and will be occupied later on. This has been shown experimentally.13-17 Keeping in mind that the cation distribution among sites I, I′, and II is dominated by the cationcation Coulombic repulsion, we focus on the peculiar local arrangement of a (I′-I-I′) linked group described above (see Figure 2). Placing one cation in a site I′ will push the adjacent cation in site I toward the opposite site I′. The new configuration for Na49Y is then expected to be {15,2,32,0}. We use this simple argument over again for each additional cation, and predict the
Figure 3. Potential energy histogram of the 12870 possible configurations of the {8,16,32,0} distribution in Na56Y. The energy scale was shifted so that the most stable configuration corresponds to an energy of 0 K.
cation distribution for all systems ranging from Na48Y to Na64Y. These are listed in Table 4. In summary, we have derived a simple model for “cation filling” in dry NaY based on the well-known assumption that cation distributions are dominated by the Coulombic repulsive interaction between cations. We will now test the prediction listed in Table 4 against the available experiments and against molecular simulation. C. Test of the Cation Filling Model. The available experimental cation distributions are given in Table 4. Except for the data of Marra et al.,17 the agreement between predicted and observed distributions is good, considering the spread in experimental data. In all cases, sites II are almost fully occupied. The site I occupancy seems to decrease with decreasing Si:Al ratio, while the site I′ occupancy increases, in agreement with our predictions. A more conclusive test of our model would be brought by experimental data on a system having a cation concentration close to Na64Y in order to see whether the site I occupancy tends to vanish at high cation concentration. The fact that real NaX materials show almost no site I occupancy provides a clue in favor of our model. The Na56Y case can be compared to both experimental data obtained on samples having a rather similar cation concentration (Na55-57Y) and the MD simulation of Jaramillo and Auerbach.10 The agreement between simulations and experiments is good. The MD simulation seems to slightly underpredict the site II occupancy. Using the combination of MC annealing methods described above in Section 2D, the global minimum we obtained is the {8,16,32,0} distribution, in agreement with the filling model prediction. A simple MC annealing (not supplemented with site-to-site jumps) led to configurations very similar to the one described in the work of JA.10 We thus suggest that the {8,16,32,0} distribution does correspond to the global potential energy minimum of Na56Y. It should also be reminded here that, although the JA cation potential model was used in both simulation works, the framework models differ from one another (see above, section 2C). The {8,16,32,0} distribution of the model Na56Y system has been studied in some details. Because of the partial occupancy of sites I and I′, a given distribution can be obtained through a large number of local arrangements. Given the fact that we
Na+ Distribution in Anhydrous NaY and NaX Zeolites
J. Phys. Chem. B, Vol. 105, No. 39, 2001 9573
TABLE 5: Predicted Cation Distributions in Na86X, Na96X Compared to JA Simulation (ref 10) and Experiments (refs 9, 11, 12) (Experiments of refs 9,12 and simulations of ref 10 assume distinct Si and Al positions. Experiments of ref 11 and this simulation work assume average Si/Al positions and charges) Na86X
total
III III′a III′b III′c
Na96X
this work
experiment [11]
experiment [12]
0 32 32 0
1 31 32 0
2.9 29.1 31.0 0
0 32 32 0
I I′ II II′ total III
Na92X
simulation [10]
18 22
4 86
7 1 14 0
22 86
0 10.6 8.6 10.6
29.8 92.8
Figure 4. Schematic view of the intersection between 4 (I′-I-I′) linked group of sites which takes place in a sodalite cage.
should discard the physically unrealistic local arrangements in which adjacent I and I′ sites are occupied, there remain 12870 possible arrangements for this single {8,16,32,0} distribution in Na56Y! Each of these configurations has been generated and its potential energy computed. Much to our surprise, the energy distribution obtained for these different arrangements is spread over more than 70000 K (Figure 3). The potential energy of a given configuration crucially depends on the occupancy of the I′ cation sites in the sodalite cages, since it is now the I′-I′ distance which is the closest possible distance between two cations. As sketched in Figure 4, a sodalite cage can be viewed as the meeting point of 4 (I′-I-I′) linked groups of sites. Depending on how these linked groups are populated, a sodalite cage will contain from 0 to 4 cations located in site I′. The most stable arrangement was found to correspond to a uniform occupation of 2 site I′ cations in each of the 8 sodalite cages of the unit cell. The less stable configuration is such that 2 sodalite cages contain 4 cations, 4 cages contain 2 cations, and the remaining 2 cages contain none. Again, the cation-cation Coulombic energy minimization is the crucial factor for determining not only which of the distributions will be the most stable one, but also which among all possible arrangements, for a given distribution, corresponds to the true global energy minimum. Finally, having computed all the possible local configurations of the {8,16,32,0} distribution in Na56Y, it was possible to
0 10 18 0
28 92
this work
simulation [10]
experiment [9]
0 32 32 0
3 29 32 0
0 32 32 0
31 32
1 96
0 5 27 0
32 96
0 0 32 0
32 96
compute the free energy of each configuration, from the knowledge of its degeneracy. This enabled us to check that the entropy contribution to free energy was negligibly small as compared to the potential energy. It is clear that some of the results obtained here are very much model dependent. Our model corresponds to an ideal, highly symmetrical and homogeneous system with Si/Al positions with averaged charge. A real faujasite crystal would also inevitably contain local defects and heterogeneities. This would presumably prevent it from reaching the most stable configuration predicted for the ideal material. In view of the observed sensitivity of the configuration energy to a weak deviation from the most uniform local cation spatial distribution, it is not surprising that the filling model predictions and molecular simulations do not quite match experiments. This may also explain why the precise location of a certain proportion of cations remains unclear in the experiments. D. Extension of the Filling Model to NaX Models. Going back to the Na64Y model, in which all sites I′ are occupied (Table 4), we predict that a further increase in cation number (beyond 64 cations/unit cell) will lead to site III occupancy since cations can no longer be located at site I, due to the “cation filling” argument developed above in Sections 3A and 3B. We have performed MC NVT simulations and MC annealing for two systems of interests Na86X and Na96X for which experiments9,11,12 and simulation10 data were available. The cation distributions obtained are listed in Table 5. The cation distributions for Na86X and Na96X are expected to be {0,32,32,22} and {0,32,32,32}, respectively. This is known from experiments, and the present cation filling argument, as well as the MC simulations, support these results, as long as we do not discriminate between different kinds of site III. In the experiments the site I occupancy is extremely low and sitesI′ and II are almost fully occupied. We thus conclude that the cation filling model can reasonably be extended to high cation content faujasites. We now examine in more details the cation locations observed in the MC simulations of the Na86X and Na96X models. In all simulations, cations in the initial configurations were placed in the site I, II, and III locations described above in Section 2A. The positions spontaneously reached by the cations after convergence of the MC runs at 298 K are shown in Figure 5. Several interesting features can be seen in these cation distance distributions. While the site II location is unchanged from the initial positions taken from the works of Fitch15 and Mellot,23 we observe a small displacement of the site I′ position (0.2 Å), a larger displacement for the site III position (∼1 Å), and the occurrence of two extra locations for site I′ and site III, respectively.
9574 J. Phys. Chem. B, Vol. 105, No. 39, 2001
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Figure 5. Computed distance distributions between the observed cation locations and the known crystallographic sites in Na86X and Na96X.
The extra site I′ is located at ∼ 0.7 Å away from the initial site I′ toward the hexagonal prism. It is very weakly occupied in the simulations. The existence of such an extra site I′ has been reported by Olson.11 Two types of site III are observed in
the simulations and sketched in Figure 6. The first one lies in the middle of a 4-ring. The second one is close to the 12-ring window. It corresponds quite well to the site III′ location reported by Vitale et al.9 It then turns out that several features
Na+ Distribution in Anhydrous NaY and NaX Zeolites
Figure 6. Sites III and III′ observed in this work.
TABLE 6: Distances between Cations and Oxygen Atoms Obtained in This Work Compared to Experimental Results (refs 9,12) distance/Å
this work
experiment [9]
experiment [12]
d(I′-O) d(II-O) d(III-O) d(III′-O)
2.14 2.4 2.37 2.26
2.241 2.364
2.266 2.355
2.58
2.44
of the real NaX faujasites are reproduced by MC simulations using a very crude model for the faujasite structure. The relative occupancy of site III and III′, however, is not satisfactorily reproduced in the simulations. Neither do we obtain the secondary sites III′a, III′b, and III′c reported by Olson11 and obtained in the MD simulations of Jaramillo and Auerbach.10 We note that the experimental data of Olson11 disagree with those of Vitale et al.9 and Zhu and Seff.12 In a fourth crystallographic report of the crystal structure of NaX, Lecomte et al.29 found two III′ positions that are different from the previous determinations. The reasons for this substantial disagreement have been discussed in detail by Zhu and Seff.12 These authors have shown that the discrepancies between the different investigations can be reconciled if the data collection temperatures, the qualities of the diffraction data, and the presence of impurity ions are considered. In any case, these secondary III′i sites can obviously not be obtained in the simulations as long as the silicon and aluminum atoms are not distinguished in the faujasite framework model. This was also thought to be true in general for the existence of site III′. It is then interesting to point out that a model with an average T-atom is capable of predicting the existence of such a site, and also reproduces fairly well the experimental Na-O distances (see Table 6). 4. Conclusion and Prospects A simple model has been derived for predicting the way cations are distributed among the sites I, I′, II, and III, in NaY and NaX faujasites. This model is based on the well-known assumption that the cation distribution is dominated by the repulsive cation-cation Coulombic interactions. The theoretical approach presented here supports most of the results obtained previously. Monte Carlo simulations, using a simplified framework model together with the recently proposed cationframework model of Jaramillo and Auerbach,10 have confirmed the basic assumption of the cation filling model. They have also revealed a striking sensitivity of the configuration energy to a weak deviation from the most uniform local cation spatial distribution. They have finally been able to reproduce the existence of the extra site III′ experimentally reported in NaX. The next step is now to examine the effect of explicitly
J. Phys. Chem. B, Vol. 105, No. 39, 2001 9575 distinguishing silicon from aluminum T-atoms on the cation distributions.26 This work raises a certain number of questions. How can the cation filling model be generalized to other cationic zeolite frameworks and how should it be modified for treating divalent cations? Can we think of a possible extension of the filling model to predict site III and III′ occupations in NaX? How can we model physically meaningful defects and heterogeneities that may be encountered in real zeolite crystals in a simple way so that we could understand, and predict, the way the cation distribution departs from the ideal situation? All these, and other questions, remain for future works. This work should also help in modeling the cation redistribution that is suspected to occur in faujasite upon adsorption of highly polar fluids such as water27 or HFCs.28 Acknowledgment. We thank the Institut Franc¸ ais du Pe´trole for financial support through a BDI/CNRS grant for S.B. and for a generous allocation of computer time. References and Notes (1) Mortier, W. J. Compilation of Extraframework Sites in Zeolites; Butterworth Scientific Ltd.; Guildford, U.K., 1982. (2) Dempsey, E. J. Phys. Chem. 1969, 73, 3660. (3) Sanders, M. J.; Catlow, C. R. A.; Smith, J. V. J. Phys. Chem. 1984, 88, 2796. (4) Barrer, R. M. Zeolites 1984, 4, 361. (5) Smolders, E.; Van Dun, J. J.; Mortier, W. J. J. Phys. Chem. 1991, 95, 9908. (6) Newsam, J. M.; Freeman, C. M.; Gorman, A. M.; Vessal, B. Chem. Commun. 1996, 16, 1945; Gorman, A. M.; Freeman, C. M.; Kolmel, C. M.; Newsam, J. M. Faraday Discuss. 1997, 106, 489. (7) Mellot, C. F.; Cheetham, A. K., C. R. Acad. Sci. Paris 1998, 1 (II), 737. (8) Herrero, C. P.; Ramirez, R. J. Phys. Chem. 1992, 96, 2246. (9) Vitale, G.; Mellot, C. F.; Bull, L. M.; Cheetham, A. K. J. Phys. Chem. 1997, 101, 4559. (10) Jaramillo, E.; Auerbach, S. M. J. Phys. Chem. 1999, 103, 9589. (11) Olson, D. H. Zeolites 1995, 15, 439. (12) Zhu, L.; Seff, K. J. J. Phys. Chem. B 1999, 103, 9512. (13) Eulenberger, G. R.; Shoemaker, D. P.; Keil, J. G. J. Phys. Chem. 1967, 71, 1812. (14) Jira`k, Z.; Vratislav, S.; Bosa`cek, V. J. Phys. Chem. Solids 1980, 41, 1089. (15) Fitch, A. N.; Jobic, H.; Renouprez, A. J. Phys. Chem. 1986, 90, 1311. (16) Van Dun, J. J.; Dhaeze, K.; Mortier, W. J. J. Phys. Chem. 1988, 92, 6747. (17) Marra, G. L.; Fitch, A. N.; Zecchina, A.; Ricchiardi, G.; Salalaggio, M.; Bordera, S.; Lamberti, C. J. Phys. Chem. B 1997, 101, 10653. (18) Smirnov, K.; Lemaire, M.; Bre´mard, C.; Bougeard, C. Chem. Phys. Lett. 1994, 179, 445. (19) Mellot, C. F.; Davidson, A. M.; Eckert, J.; Cheetham, A. K. J. Phys. Chem. B 1998, 102, 2530. (20) Demontis, P.; Yashonath, S.; Klein, M. L. J. Phys. Chem. 1989, 93, 5016. (21) Lachet, V.; Boutin, A.; Tavitian, B.; Fuchs, A. H. J. Phys. Chem. B 1998, 102, 9224. (22) Lachet, V.; Buttefey, S.; Boutin, A.; Fuchs, A. H. PCCP 2000, in press. (23) Mellot, C. F. Ph.D. Thesis, Universite´ Pierre et Marie Curie, 1993. (24) Uytterhoeven, L.; Dompas, D.; Mortier, W. J. J. Chem. Soc. Faraday Trans. 1992, 88, 2753. (25) Buttefey, S.; Boutin, A.; Fuchs, A. H. Mol. Sim., submitted. (26) Mellot-Draznieks, C.; Buttefey, S.; Boutin, A.; Fuchs, A. H. Chem. Commun., submitted. (27) Pichon, C.; Me´thivier, A.; Simonot-Grange, M.-H.; Baerlocher, C. J. Phys. Chem. B 1999, 103, 10197. (28) Grey, C. P.; Poshni, F. I.; Gualtieri, A. F.; Norby, P.; Hanson, J. C.; Corbin, D. R. J. Am. Chem. Soc. 1997, 119, 1981. (29) Porcher, F.; Souhassou, M.; Dusausoy, Y.; Lecomte, C. Eur. J. Mineral. 1999, 11, 333.
