A microscopic approach using molecular dynamics

IL NUOVO CIMENTO DOI 10.1393/ncb/i2008-10724-2

Vol. 123 B, N. 10-11

Ottobre-Novembre 2008

Ca-Na cation exchange in zeolite A: A microscopic approach using molecular dynamics simulations ´lez(2 ) and R. Sale(1 ) G. B. Suffritti(1 )(∗ ), P. Demontis(1 ), J. Gul´ın-Gonza (1 ) Dipartimento di Chimica, Universit` a di Sassari - Via Vienna 2, I-07100, Sassari, Italy ecnico José A. Echevarr`ıa (ISPJAE) (2 ) Instituto Superior Polit´ Departamento de F`ısica, Marianao Grupo de Matem´ atica y F`ısica Computacionales, Universidad de las Ciencias Inform´ atica(UCI) - Carretera a San Antonio de los Ba˜ nos, Km 21/2, La Lisa La Habana, Cuba (ricevuto il 15 Dicembre 2008; pubblicato online il 13 Febbraio 2009)

Summary. — Molecular dynamics computer simulation technique was applied to the study of Ca-Na cation exchange in hydrated zeolite A, one of the most widely exploited cation exchange processes in practical applications. The exchange can occur only by breaking and reconstructing the coordination shell of the cations, so that some steps of the mechanism show a high activation energy, even if the overall energy difference between the starting and the final states of the process is relatively small. Therefore, special procedures such as umbrella sampling must be used to force the system to overcome the energy barriers. The cation exchange appeared to follow a highly coordinated mechanism, and a complete exploration of the free-energy hypersurface is required to obtain quantitative results. In this paper some interesting qualitative features of the cation exchange process are anticipated. PACS 82.75.Jn – Measurements and modeling of molecule migration in zeolites.

1. – Introduction Ion exchange is one of the most outstanding phenomena involving zeolites, and one of the most exploited for practical applications, including detergents and waste water remediation from heavy and/or radioactive metals [1,2]. However, many details of water and ion mobility and dynamics in microporous structures are still not completely clarified. For instance, the microscopic mechanism of the water and ion diffusive processes and their correlation are mostly unknown. In order to complement and explain experimental results, one of the possible issues is the use of computer simulations. Molecular (∗ ) E-mail: [email protected] c Societ` a Italiana di Fisica

1553

1554

´ G. B. SUFFRITTI, P. DEMONTIS, J. GULÍN-GONZALEZ

and

R. SALE

Dynamics (MD) technique [3, 4] is one of the most widely applied to study complex dynamical phenomena at atomistic scale, and revealed itself suitable and fruitful in the investigations of the processes involving molecules and ions adsorbed in microporous materials and in zeolites. In cation exchange usually bond breaking and making do not occur, so that classical MD with usual intermolecular potentials can be applied. This kind of potentials, in general, depend on the interparticle distances and are pair additive, with short-range repulsive terms, medium-range dispersion potential functions most often depending on inverse power of distance (r−n , with n ≥ 6) and long-range Coulombic terms representing the interactions between charges, dipoles and sometimes higher-order multipoles and possibly including polarization effects. However, MD simulations of ion exchange are surprisingly rare [5-7], because of the high-energy barriers that ions must overcome, as both a solvation shell and a coordination shell of framework atoms must be disrupted by a concerted mechanism in order to make the exchange possible. Indeed, in hydrated zeolites the coordination shell of exchangeable cations includes both the closest oxygen atoms of the framework and the water molecules that can fit in the available remaining free space. For a detailed discussion see ref. [8]. In the first of the papers reporting MD simulations of ion exchange [5] the substitution of one Na cation with one ammonium cation in gmelinite, in the presence of a few water molecules, was considered, using the Car-Parrinello MD method. The exchange occurred without any relevant energy barrier in some picoseconds. The other two papers [6, 7] report the results of a series of classical MD simulations in the same model. The system contained two plane membranes made of adjacent a-cages (see next section) containing Na cations. Initially, water molecules filled the space between the membranes, while on the outer side of the membranes an aqueous solution of CaCl2 or LiCl in ionic form was present. Both by applying an extra pressure to the CaCl2 or LiCl solution and by performing equilibrium MD simulations the evolution of the system led some Ca or Li cations to enter into the membranes and remain there, while some Na cations were extracted from the membranes and were solvated by the pure water present between them. No detail of the mechanism of the exchange was given, nor the energy barriers and the kinetics involved in the process were derived. In this laboratory a sophisticated potential model was developed for MD simulations of water and cations adsorbed in zeolites, which proved to yield good results in the reproduction of structural, vibrational and dynamical properties of different zeolites [8-12] and in particular of hydrated zeolite Na-A [13]. This model was applied to the study of the Ca-Na cation exchange process in zeolite A, which resulted to be complex and multifarious. The detailed and complete study of this process is still in progress, but some interesting general features appeared, which are described in this paper. 2. – Method and model The structure of hydrated zeolite Na A, Na96 [Al96 Si96 O384 ] · 224 H2 O, belongs to the cubic symmetry group F m3c [14] and is illustrated in fig. 1. The frameworks of zeolites are often described by using a simplified scheme in which the T O4 tetrahedra are represented by points corresponding to the T -sites: for instance, a hexagonal planar structure made of six corner-sharing tetrahedra is schematized by a hexagon, which is called six-membered ring, or more synthetically six-ring. In particular, the framework of zeolite A can be described in terms of β-cages, which are schematized as cubooctaedra consisting in of six four-membered rings separated by eight adjoining six-membered rings. The framework is built by a simple cubic lattice of β-cages connected through the square faces with each other. Larger a-cages involving 48 T sites are thereby generated. In other

CA-NA CATION EXCHANGE IN ZEOLITE A: A MICROSCOPIC APPROACH ETC.

1555

Fig. 1. – (Colour on-line) A schematic representation of the zeolite A structure. The α-cage is the large empty one. The truncated polyhedra at the corners are β-cages, accessible to water but usually not to ions. The vertices of the polyhedra are occupied by Si (green) and Al (blue) atoms, alternatively, connected by bridges containing O atoms (white). Na (red) ions are located near the hexagons (six-membered rings) or in the windows connecting a-cages. The unit cell contains eight a-cages.

words, the framework is constructed of α-cages by the sharing of the eight-membered rings. The T sites are alternatively occupied by Si and Al atoms, resulting in a complete Si/Al ordering with Si/Al = 1. For the simulations we started from the XRD structure reported in [14]. As shown in figs. 1 and 2, there are three sites that can be occupied by exchangeable Na ions. Sites I are in the centre of the six-membered rings, and are all occupied by NaI ions. Sites II lie in the plane of the eight-membered rings (i.e. the windows connecting adjacent α-cages) slightly off-centre forming a square 1.8 ˚ A in side. Only one site II per ring is occupied by NaII ions. Finally, sites III are located over the center of fourmembered rings and the NaIII ions lie inside the α-cage about 1.7 ˚ A from the plane of the ring. Only one NaIII ion per α-cage is present. It is worth to note that the positions of sites II and III are those found for dehydrated zeolite Na A [15], as in [14] they were not resolved, but from the simulations it resulted that in the hydrated form they are located within a few hundredths of ˚ A from the coordinates of the same ions in the dehydrated zeolite. The positions of water molecules are less precisely defined, but it appears that β-cages contain four molecules, whose oxygens are located at the vertices of a distorted tetrahedron with four edges of 2.9 ˚ A. The remaining water molecules are contained in the α-cages. In order to the Ca-Na exchange can occur, a Ca cation coming from a solution in contact with the external surface of the a crystal of zeolite Na A must enter in one α-cage through one eight-membered window. As neither sites II nor site III are usually occupied by Ca cations in Ca exchanged zeolite A (at least in the dehydrated form) the incoming Ca cation should replace one Na cation in site I (coordinated to six-membered rings). Therefore the simulations were devised to follow this process. In particular,

1556


and

R. SALE

Fig. 2. – (Colour on-line) One anhydrous α-cage. Ca ions are red, NaI cations are yellow and the NaIII ion is black.

the MD simulation box (figs. 1-3) consisted of one crystallographic cell (a = 24.555 ˚ A) including eight α-cages. NaI ions (coordinated to six-membered rings) and NaIII ions (coordinated to four-membered rings) were left in their crystallographic positions, while NaII ions, which usually are located in the eight-membered ring windows connecting the cages, were substituted by half a number of Ca ions, in order to conserve the electric neutrality of the system. Overall the considered extraframework species per unit cell were

Fig. 3. – One fully hydrated α-cage (24 water molecules). Ca ions are red and all Na cations are yellow.


1557

72 Na+ , 12 Ca2+ and a variable number of water molecules (40, 120 160 and 224), in order to verify if incomplete hydration shells would favour the exchange process. Periodic boundary conditions and the minimum image convention were adopted. We used the cell parameters and the atomic coordinates of hydrated zeolite Na A as a starting point, because Ca2+ -water and Ca2+ -framework oxygens distances are similar to those for the Na+ cations, although energetics is obviously different. The simulations reported in the present paper were finished, when we became aware of structural data of hydrated zeolite Na-Ca A, reporting slightly different cell parameters and positions of the cations [16]. In particular, the difference of cell parameters with respect to those used in the simulations appears to be negligible (less than 0.2%), but diffraction experiments show that Ca cations can be located in three different sites, all of them in the α-cage near the centre of the six-membered rings, at about 0.2, 1.1 and 2.1 ˚ A, respectively, over the plane of the six-membered rings. We verified that in completely exchanged zeolite these locations are reasonably reproduced, but not their population. Therefore, a more detailed analysis of the new experimental data should be performed, and the results illustrated in the following must be verified against the new experimental data and must be considered as preliminary. On the other hand, the differences most probably are not as large as to affect the qualitative features of the results. In order to ensure realistic thermalization and to account for possible deformations caused by the interactions with cations and water and to include lattice deformations and vibrations in the simulated system, a flexible zeolite framework model developed in this laboratory as well [12, 17] has been used. To simulate flexible water molecules, a sophisticated electric-field–dependent empirical model [8, 12] developed in this laboratory was adopted. Moreover, new empirical potential functions had been elaborated for representing and Ca2+ -water interactions, as the ones previously proposed for simulating aqueous solutions containing sodium ions did not reproduce satisfactorily the structure of water and the hydration energies in zeolites. Details of the potential models (including all the interactions involving the framework, water and Na cations) are reported in the Supporting Information of [8] and [13]. Ca2+ -water and Ca2+ -framework interactions are still unpublished and are reported in the present paper. They were obtained by fitting analytical potential functions to ab initio calculations and verified by comparison with structural and vibrational data of scolecite, a Ca-exchanged fibrous zeolite [18]. The final form of the Ca2+ -water potential function reads (1)

VCaO (r) =

CCaOf 1 qCa qOf + ACaO exp [−bCaO ] − S(σ, r), 4πε0 r r2

where S(σ, r) is a switching function given by

(2)

S(σ, r) =

1

if r < r0 = 0.4 nm exp −σ(r − r0 )2 if r ≥ r0 = 0.4 nm

which is necessary because the r−2 term does not become negligibly small at the cell boundaries. The form of the switching function ensures that in r0 both the potential and its first derivative are continuous. As in our previous simulations [8,13], water and cations were assumed to interact with Si and Al atoms via a Coulomb potential only, because the oxygens of the framework are


1558

and

R. SALE

Table I. – Values of the parameters included in eqs. (1)-(3). Energies are obtained in kJ/mol if the distances are in units of ˚ A. Interaction 2+

Ca -O Ca2+ -H Ca2+ -Of Charges

A

b

C

σ

2.597963 × 10 4.895 × 105 1.2004285 × 108

3.51 6.79 6.00

1422.56 209.2 17761.08

0.5 0.5 -

qCa2+ /e

qCa2+ /e

qO /e

qH /e

qOf /e

qSi /e

qAl /e

2.0

1.0

−0.65966

0.32983

−1.03

1.85

1.27

5

interposed between, so that they should screen the short-range interactions. Finally, the potential functions between Ca2+ and the oxygens of the framework were represented by (3)

VCaOf (r) =

CCaOf 1 qCa qOf + ACaO exp [−bCaO ] − . 4πε0 r r6

The interactions between cations were represented by Coulombic repulsion. The evaluation of the Coulomb energy was performed using the efficient method proposed by Wolf et al. [19] and extended in our laboratory to complex systems [20]. For ambient conditions zeolite A the cut-off radius was Rc = 12.2775 ˚ A, equal to one half of the side of the simulation box and, correspondingly, the damping parameter was α = 2/Rc = 0.1629 ˚ A−1 . The values of the parameters are reported in table I. The charges assigned to the atoms were similar to those corresponding to the Mulliken populations reported in many quantum calculations on clusters and zeolites, approximately one half of the formal ionic charges, except for the exchangeable cations, which retained a full charge. A first series of simulations was carried out at low hydration, in view of the results of Benco et al. [5], hoping that the incomplete hydration shells would favour the exchange. The simulations, at different water content (40, 120 and 160 molecules per u.c.) and at temperatures ranging from 300 to 750 K, lasted at least 1 ns. As no exchange was observed even at high temperature, to find the possible reaction paths we considered the experimental conditions (fully hydrated zeolite, loaded with 224 molecules per u.c.) and we adopted the umbrella sampling procedure, consisting in a forced exploration of the energy landscape undergone by the ions. Fictitious harmonic potentials holding the ions around a chosen distance from the exchange sites (the six-membered rings) were applied and for each distance MD simulations lasting 150 ps were performed at room temperature, in order to let the system to relax and find the average energy corresponding to that configuration. A set of 15 different distances, starting from the plane of the eight-membered ring and ending in the centre of the closest six-membered ring (the exchange sites) was chosen. Once the ion exchange site was reached, the system was allowed to relax without any constraint to verify that the final configurations were stable. 3. – Results and discussion It was found first that even using strong harmonic potentials it is not possible to force the Ca cations to reach their final positions (the centre of six-membered rings) if these positions are occupied by Na cations.


1559

Fig. 4. – (Colour on-line) An example of the first kind exchange: Step 1: Na cations move into the α-cage and are settled near the centre of a four-membered ring (blue arrow).

Therefore, a first series of umbrella sampling simulations were performed by applying the fictitious potential to Na cations to remove them from these positions while holding the Ca cations in their starting point near the eight-membered windows. Then, by holding the Na cations at some different distances from their preferred positions, the Ca cations were forced to move stepwise into the centre of six-membered rings. This procedure was aimed at exploring as large as possible regions of the energy landscape of the process, in order to find eventually the reaction coordinate, at least approximately, as the exchange involves certainly a concerted motion of the ions. The analysis of the simulations is still in progress, and another series of calculations is needed to obtain a complete view of the process. Indeed, once Ca cations have reached their final positions (the centre of six-membered rings) the Na cations are still away from their final positions, near the centre of the eight-membered windows, from which they can eventually diffuse through the crystal and eventually reach its external surface. Thus, further umbrella sampling simulations will be necessary to bring the Na Cations near the windows. The analysis of the series of umbrella sampling simulations performed so far led to distinguish two kinds of exchange processes, depending on the behaviour of the Na cations subjected to the fictitious potentials forcing them to leave their preferred positions. In the first series of cases, the Na cations were pushed into the α-cage, but, as they are preferentially coordinated to the surface of the framework, they were trapped at the centre of the four-membered ring adjacent to their starting six-membered ring. These positions are those occupied by NaIII cations, thus corresponding to energy minima. A different fate of the NaII cations is observed. Some of them are forced to sink into the small β-cages and cross them to emerge in an adjacent α-cage, but in this case they need to displace somehow another NaII cation, well settled on the surface of a neighbouring α-cage. Both processes are strongly energy demanding. They are illustrated in figs. 4-7. The water molecules that are present in all simulations (24 in alpha-cages and 4 in the small β-cages) have been not yet considered. They are mostly coordinated to the ions,

1560


and

R. SALE

Fig. 5. – Step 2: Ca cations move into the α-cage and are settled near the centre of a sixmembered ring.

with nearest-neighbours interaction energy of about 80 kJ/mol and 200 kJ/mol for Na [8] and Ca [21] cations, respectively, for each molecule. Therefore, they play an essential role in hindering or favouring the motion of the ions. For instance, in order to remove a Na cation from its preferred position, one must overcome the coordination energy to the framework and arrange the surrounding water molecules so that a new coordination shell is formed. In turn, when a Ca cation is moved to its target six-membered ring, its hydration shell must be rearranged so that a new coordination shell including some framework oxygen atoms can be formed. These rearrangements occur obviously through

Fig. 6. – An example of the second kind exchange: Step 1: Na cations move into the β-cage.


1561

Fig. 7. – Step 2: Ca cations move into the α-cage and are settled near the centre of a sixmembered ring.

concerted mechanisms, which are difficult to visualize. Simplifying schemes to describe such mechanisms are under study. However, we were able to describe, at least in part, the role of water molecules, by considering what happens around the lines connecting the ions. Indeed, the exchange process brings the cations close together and one or more water molecules are driven by intermolecular forces to interpose between ions in order to lower they repulsion. Some examples are given in figs. 8-13.

Fig. 8. – The role of water molecules: first kind exchange, step 1. The view is from the plane of the 8-membered window. Initially, Ca cation (grey) is out of the α-cage; the Na cation (black), initially in the 6-membered ring, is shifted to the 4-membered ring. A water molecule substitutes the Na cation near the centre of the 6-membered ring.

1562


and

R. SALE

Fig. 9. – The role of water molecules: first kind exchange, step 2. The Ca cation (grey) entered in the α-cage, the Na cation (black) is still in the 4-membered ring. A water molecules remains near the centre of the 6-membered ring.

4. – Conclusions and perspectives We obtained preliminary results, which enable to sketch the possible reaction paths of the exchange process. It appears to be complex and highly coordinated. In particular, some main features of the process were evidenced. First, as expected, the exchange occurs via a concerted motion of the ions. When pushed by an incoming Ca cation, Na cations can move to an adjacent four-membered ring or inside the β-cages.

Fig. 10. – The role of water molecules: first kind exchange, step 3. The view is from over to the 6-membered ring. The Ca cation (grey) comes closer to the 6-membered ring and coordinates to the water molecule, which is still near the centre of the 6-membered ring. Na cation (black) remains in the 4-membered ring.


1563

Fig. 11. – The role of water molecules: first kind exchange, step 4. The Ca cation (grey) settles itself in the 6-membered ring, Na cation (black) remains in the 4-membered ring. A bridge of two water molecules is formed between the cations.

Fig. 12. – The role of water molecules: second kind exchange, step 1. The view is from inside the α-cage. Initially, Ca cation (grey) is in the 8-membered window, the Na cation (black) is near the 4-membered ring, but inside the β-cage. Some water molecules are interposed between the ions.

Water plays an essential role in driving the motion of the cations and in stabilizing some configurations. In particular, at least one water molecule is interposed between the cations, so that electrostatic repulsion is screened. Work is in progress to complete the exploration of the energy landscape (including the path of the displaced Na cations to the cage windows) and to find a reasonable reaction coordinate in order to estimate the freeenergy barriers (via thermodynamic integration [22]) with reasonable accuracy. Once the relevant elements determining the reaction coordinate will be found, it will be possible to explore the possibility of using the metadynamics technique [23] to refine the knowledge of the free-energy landscape. Finally, one could attempt to derive the kinetic constants, by simulating the reactive trajectories (starting from the transition state onward and backward in time) and by computing the suitable correlation functions. ∗ ∗ ∗ This research is supported by the Italian Ministero dell’Istruzione, dell’Universit` ae della Ricerca (MIUR), PRIN funding, by Universit` a degli studi di Sassari and by Istituto

1564


and

R. SALE

Fig. 13. – The role of water molecules: second kind exchange, step 2. The Ca cation (grey) moved to the centre of the 6-membered window, the Na cation (black) is pushed inside the β-cage. One water molecule is interposed between the ions.

Nazionale per la Scienza e Tecnologia dei Materiali (INSTM), which are acknowledged. This work makes use also of results produced by the Cybersar Project managed by the Consorzio COSMOLAB, a project co-funded by the Italian Ministry of University and Research (MUR) within the Programma Operativo Nazionale 2000-2006 “Ricerca Scientifica, Sviluppo Tecnologico, Alta Formazione”’ per le Regioni Italiane dell’Obiettivo 1 (Campania, Calabria, Puglia, Basilicata, Sicilia, Sardegna) - Asse II, Misura II.2 “Societ` a dell’Informazione”, Azione a “Sistemi di calcolo e simulazione ad alte prestazioni”. More information is available at http://www.cybersar.it.

REFERENCES [1] Towsend R. P. and Coker E. N., in Introduction to Zeolitic Science and Practice. Studies in Surface Science and Catalysis, edited by van Bekkum H., Flaningen E. M., Jacobs P. A. and Jansen J. C., Vol. 137 (Elsevier, Amsetrdam) 2001, pp. 467-519. [2] Zagorodni A. A., Ion Exchange Materials. Properties and Applications (Elsevier, Amsterdam) 2007. [3] Allen M. P. and Tildesley D. J. (Editors), Computer Simulations in Chemical Physics (Kluwer, Dordrecht) 1994. [4] Demontis P. and Suffritti G. B., Chem. Rev., 97 (1997) 2845. [5] Benco L., Demuth T., Hafner J. and Hutschka F., Microporous Mesoporous Mater., 42 (2001) 1. [6] Murad S., Jia W. and Krishnamurthy M., Mol. Phys., 102 (2004) 2103. [7] Murad S., Jia W. and Krishnamurthy M., Chem. Phys. Lett., 369 (2003) 402. [8] Cicu P., Demontis P., Spanu S., Suffritti G. B. and Tilocca A., J. Chem. Phys., 112 (2000) 8267. [9] Demontis P., Stara G. and Suffritti G. B., J. Phys. Chem. B, 107 (2003) 4426. [10] Demontis P., Stara G. and Suffritti G. B., J. Chem. Phys., 120 (2004) 9233.


1565

[11] Demontis P., Stara G. and Suffritti G. B., Microporous Mesoporous Mater., 86 (2005) 166. ´ lez J. and Suffritti G. B., J. Phys. Chem. B, 110 (2006) [12] Demontis P., Gul´ın-Gonza 7513. ´lez, Jobic H., Masia M., Sale R. and Suffritti G. B., [13] Demontis P., Gul´ın-Gonza ACS Nano, 2 (2008) 1603. [14] Gramlich V. and Meier W. M., Z. Kristallogr., 133 (1971) 143. [15] Pluth J. J. and Smith J. V., J. Am. Chem. Soc., 102 (1980) 4704. [16] Leardini L., Caratterizzazione cristallochimica di zeolite idrofiliche sottoposte a cicli di disidratazione - reidratazione. Potenziali applicazioni in sensoristica ambientale (Crystallochemical characterization of hydrophilic zeolites undergone to dehydration rehydration cicles. Possible application for environmental sensors), Ph. D. Thesis, Dipartimento di scienze della terra, University of Ferrara, Italy (2008). [17] Demontis P., Suffritti G. B., Bordiga S. and Buzzoni R., J. Chem Soc. Faraday Trans., 91 (1995) 525. [18] Gottardi G. and Galli E., in Natural Zeolites (Springer-Verlag, Berlin) 1985, pp. 35-56. [19] Wolf D., Keblinki P., Phillpot S. R. and Eggebrecht J., J. Chem. Phys., 110 (1999) 8254. [20] Demontis P., Stara G., Spanu S. and Suffritti G. B., J. Chem. Phys., 112 (2001) 8267. ¨ m M., J. Phys. Chem. A, 102 (1998) [21] Pavlov M., Siegbahn Per E. M. and Sandstro 219. [22] Frenkel D., in Proceedings of International School of Physics “Enrico Fermi”, Course XCVII, edited by Ciccotti G. and Hoover W. G. (SIF, Bologna and North-Holland, Amsterdam) 1986, p. 169. [23] Iannuzzi M., Laio A. and Parrinello M., Phys. Rev. Lett., 90 (2003) 238302.