J. Phys. Chem. B 2005, 109, 125-129
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Influence of Extra-Framework Cations on the Adsorption Properties of X-Faujasite Systems: Microcalorimetry and Molecular Simulations G. Maurin,* Ph. Llewellyn, Th. Poyet, and B. Kuchta Laboratoire MADIREL, UMR CNRS 6121, UniVersite´ de ProVence, Centre St Je´ roˆ me, AV. Escadrille Normandie Niemen, 13397 Marseille Cedex 20 ReceiVed: August 24, 2004; In Final Form: October 7, 2004
Isotherms and differential enthalpies of adsorption are obtained for nitrogen at ambient temperature on monovalent (Li+, Na+, K+) and divalent (Ca2+, Ba2+, Sr2+, Mn2+) substituted X-faujasite systems by microcalorimetry measurements. These experimental data are compared with those obtained by combining grand canonical Monte Carlo simulations and newly derived force fields for describing the interactions between the extra-framework cations and the adsorbates obtained from a simple model based only on the intrinsic properties of the cations. It is the first time that such good qualitative agreement is reported between experiment and simulation for a series of both monovalent and divalent cations.
1. Introduction Zeolite microporous materials are involved in a large domain of chemical science and technology including catalytic and separation processes,1 gas storage, and ion exchange.2,3 Much research effort performed both experimentally and theoretically has been thus focused on this class of materials. This is not only because of their technological importance but also because they represent model systems. Indeed, zeolite materials, which are well-ordered nanoporous materials, offer great possibilities for investigating their adsorption properties as a function of parameters such as size and shape of the pores, chemical composition of the framework (Si/Al ratio, metal-substituted aluminophosphate), and nature of the extra-framework cations. In the past few years, some experimental studies4-8 have dealt with the influence of either the nature or distribution and density of these extra-framework cations on the adsorption properties of various zeolite systems. It was clearly established that these cations play a key role in the adsorption phenomena in such materials. For instance, the lithium and calcium cationexchanged faujasites are adsorbents9,10 in the separation of air by pressure/vacuum swing adsorption procedures, whereas the barium-exchanged form is involved in the selective separation of aromatic molecules.11 Such processes are based on specific interactions of the adsorbates with the field gradient generated by the cations. Systematic studies have focused on the adsorption properties of X- and Y-faujasite systems containing various monovalent cations with respect to different adsorbates such as ethane and ethene,12 argon and nitrogen13 water vapor,14,15 or carbon dioxide and ammonia.16 They were completed by a limited number of experiments on divalent cation-exchanged zeolites.17,18 These investigations led to empirical relationships showing, for instance, that the initial enthalpy of adsorption obtained from various methodologies, including calorimetry, volumetry, and virial adsorption models, usually increases with increasing charge density of the cations or with decreasing cation size. Furthermore, some of them13,16 qualitatively analyzed the adsorption data in terms of dispersion, repulsion, polarization, and electrostatic interactions. * To whom correspondence should be addressed. E-mail: maurin@ up.univ-mrs.fr. Phone: +33 4 91 63 71 17. Fax: +33 4 91 63 71 11.
Since the past few years, molecular simulation of adsorption phenomena has been intensively introduced in order to establish a correlation between the microscopic behavior of the zeolite/ adsorbate system with the macroscopic properties which are measured experimentally, such as isotherms and enthalpies of adsorption.18 The grand canonical Monte Carlo technique is particularly adapted to calculate these equilibrium thermodynamic properties.18,19 Furthermore, various other theoretical methods have been applied for studying the adsorption process in zeolites, including energy minimization, Monte Carlo, and molecular dynamic simulations, in order to gain deeper information on the organization of the adsorbate molecules in the host structures.19 They rely on the accurate interatomic potentials needed to reproduce as accurately as possible the interactions between the adsorbate and the zeolite framework and between the adsorbate molecules themselves. Although several theoretical studies have been reported on the adsorption properties of exchanged zeolites,20,21 only some attempts have been performed to model the adsorption properties of zeolite systems as a function of the nature of the extra-framework cations.5,8,22-24 The most significant work performed by Beerdsen et al.22,23 showed that both the selectivity and the capacity of adsorption of alkanes in MFI zeolites strongly depend on the type and distribution of the extra-framework cations. Nowadays, several efforts are focused on the development of new semiempirical force fields to describe the interactions between the adsorbate and the zeolite framework, which allows a better transferability of the parameters to any zeolite structure.25 In this paper, our aim is to investigate the interactions of a quadrupolar gas (nitrogen) on a series of X-faujasites containing various divalent (Ca2+, Ba2+, Sr2+, Mn2+) and monovalent (Li+, Na+, K+) cations at ambient temperature by combining microcalorimetry and molecular simulation approaches. From an experimental point of view, microcalorimetry, which is a powerful tool for investigating the interactions of adsorbates and adsorbent,26 provides a significant contribution because of the very limited existing experimental data for divalent cations in the case of nitrogen adsorption. From a theoretical standpoint, we follow an original approach based on grand canonical Monte Carlo simulations, which consists of deriving new semiempirical
10.1021/jp0461753 CCC: $30.25 © 2005 American Chemical Society Published on Web 12/04/2004
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TABLE 1: Physicochemistry Characteristics of the Investigated X-Faujasite Systems samples equivalent BET surface area (m2 g-1) pore volume (cm3 g-1)
CaX
BaX
812
LiX
877
NaX
472
850
598
732
764
0.272
0.304
0.204
0.324
0.216
0.268
0.298
Figure 1. Structure of the faujasite framework and description of the main crystallographic sites for the extra-framework cations.
Lennard-Jones (LJ) parameters for Na+ by fitting both the isotherm and the evolution of the differential enthalpy of adsorption for NaX/N2 and NaX/Ar systems up to 50 bar at 300 K. The second step consists of defining the LJ parameters for the various investigated cations from those obtained for Na+ by a simple model only on the basis of intrinsic properties of the extra-framework cations (i.e., polarizability and ionic radius). This approach will be detailed in the computational part of this paper. The originality of this method is to avoid time-consuming ab initio calculations and further fitting procedures for deriving accurate interatomic potentials. From these new interatomic potentials, the simulation of the adsorption properties of the various X-faujasite/N2 systems are reported, including both the differential enthalpies at low coverage and isotherms of adsorption in the low-pressure domain. These simulated data are compared and contrasted with those measured experimentally in order to test the transferability of our derived force fields. Furthermore, a direct comparison between experiment and simulation is given at high pressure up to 40 bar for a typical divalent substituted CaX/N2 system in order to extend the validity of our interatomic potentials to a wide range of pressures. To the authors’ knowledge, it is the first time that such a nice agreement between experiment and simulation is obtained for the adsorption properties involving a series of both monovalent and divalent cations. 2. Experimental Section Materials and Characterization. The structure of the Faujasite system used in this investigation consists of large cavities (supercages) which have roughly spherical symmetry and diameters around 12.5 Å with window sizes of 7.4 Å (Figure 1). Each cavity is connected to four others in a tetrahedral arrangement. The structure also contains sodalite cage units linked together by double six rings.27 The monovalent and divalent extra-framework cations preferentially occupy different crystallographic sites named I, I′, II, and III28 and depicted in Figure 1. The various samples investigated in this work (LiX, NaX, KX, CaX, BaX, SrX, and MnX) were supplied by Air Liquide. The base material was NaX powder (Si/Al ) 1), and the different divalent and monovalent cation-substituted forms of
KX
SrX
MnX
zeolite X were prepared by following a conventional ionexchange technique using various aqueous salt solutions, distilled water washing, and drying procedures.29 These cationexchange treatments were repeated in order to obtain the higher degree of exchange. The various samples were then carefully characterized. The chemical analysis were performed by using electron dispersive spectroscopy (EDS) and showed that each sample is characterized by Si/Al ) 1, which means that the framework composition remained unaltered during the cation-exchange process. These analyses further indicated a degree of cation exchange close to 100% for both LiX and KX, 95% for CaX and SrX, and 85% for BaX and MnX. Powder X-ray diffraction revealed the samples to be highly crystalline, and the so-obtained diffractograms showed all the characteristics peaks closely matching those predicted in the literature for low silica X (LSX) faujasite systems.30 Furthermore, the morphology and texture of each exchanged solid examined by scanning electron microscopy (SEM) remained unchanged by comparison with those observed for the parent NaX sample. Finally, the micropore volumes and surface areas of the investigated samples (Table 1), determined by nitrogen adsorption at 77 K, are in agreement with those reported in the literature.17 Microcalorimetry Measurements. Prior to each adsorption experiment, the sample is outgassed using sample-controlled thermal analysis (SCTA).31 The samples were thus heated using SCTA conditions, under a constant residual vacuum pressure of 0.02 mbar up to a final temperature of 450 °C, which was maintained until the residual pressure was less than 5 × 10-3 mbar. The adsorption at 300 K up to 1 bar was carried out by means of a Tian-Calvet type isothermal microcalorimeter built in-house. The experiments were performed using a highresolution quasiequilibrium procedure of gas introduction32 on approximately 1 g of sample. This apparatus allowed us to obtain both the isotherms and the pseudodifferential enthalpies of adsorption at low coverage for each X-faujasite/N2 systems. Additionally, the argon and nitrogen adsorption properties were investigated at 300 K up to 50 bar for NaX and CaX systems. In this case, a point-by-point adsorbate dosing procedure detailed elsewhere33 was used to evaluate both the isotherms and pseudodifferential enthalpies of adsorption. For the low-pressure experiments up to 1 bar, gas nonideality was not taken into account for both nitrogen and argon. However, the nonideality behavior was considered for the experiments up to 40 bar and leads to a maximum of 5% difference in the calculated amount adsorbed. 3. Computational Methodology The crystal structure of the X-faujasite systems with the various monovalent and divalent cations was modeled as n+ follows. The chemical composition Si96Al96M96/n O384 (with n+ + + + 2+ 2+ 2+ M ) Li , Na , K , Ca , Mn , Sr , or Ba2+) was considered in order to reproduce the Si/Al ratio of 1 of the investigated samples. The framework was built with a strictly ordered alternation of aluminum and silicon atoms in accordance with the Lowenstein’s Al-O-Al avoidance rule.34 The second step consisted of modeling the distribution of the extraframework cations among the different crystallographic sites.
Adsorption Properties of X-Faujasite Systems
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For NaX zeolite, the distribution defined by Vitale et al.35 was selected corresponding to 32 Na+ in sites I′ located in the sodalite cage in front of the 6-ring window connected to the hexagonal prism, 32 Na+ in sites II, and 32 Na+ in sites III, 6-ring and 4-ring windows of the supercages, respectively (Figure 1). The distributions of the extra-framework cations for LiX36 and KX37 provided by recent reinvestigation of these crystal structures include the occupation of sites I′, II, III, and III′ for Li+ and sites I, I′, II, III, and III′ for K+. For the divalent cations, we started from a diffraction refinement of the dehydrated CaX faujasite38 where the 48 Ca2+ extra-framework cations are distributed as follows: 16 Ca2+ cations in site I locations in the center of hexagonal prisms, which connect the sodalite cages, and 32 Ca2+ in site II locations. This distribution of the extra-framework cations was also used to model a first approximation of BaX,39 SrX, and MnX faujasite systems. The total energy of the zeolite framework and adsorbed molecules (E) is expressed as the sum of the interactions energy between the adsorbate and the zeolite (EAZ) and that between the adsorbates (EAA).
E ) EAZ + EAA
(1)
EAZ and EAA are both written as sums of pairwise additive potentials of the form
eij ) 4ij
[( ) ( ) ] σij rij
12
-
σij rij
6
+
qiqj rij
(2)
where the first term is the repulsion-dispersion LJ potential, with ij and σij corresponding to the parameter sets for each interacting pair that is obtained from i and σi of each species by using the Lorentz Berthelot mixing rule (i.e., a geometric combining rule for the energy and an arithmetic one for the atomic size: ij ) (ij)1/2 and rij ) (ri + rj/2)). The second term is the Coulombic contribution between point charges qi and qj separated by distance rij. For nitrogen, we used the three-point charge model,40 where the two outer sites separated by a distance of 1.098 Å have a charge of q ) -0.4048 e, and the third midpoint has a point charge of -2q. The N and σN LJ parameters were given values of 0.00314 eV and 3.318 Å, respectively.40 The neutral spherical model was selected for argon with the following LJ parameters: Ar ) 0.0103 eV and σAr ) 3.403 Å.41 Furthermore, considering that the polarizabilities of silicon and aluminum atoms are much lower than those of oxygen atoms, the repulsion-dispersion term of the zeolite may be assigned only to oxygens of the framework (O) and extra-framework cations (M). The calculation thus only requires the knowledge of the LJ parameters (O, σO) and (M, σM) for modeling the adsorbateadsorbent repulsion-dispersion interactions by using the mixing rule. In addition, the charges carried by each atom of the faujasite framework are required to calculate the total energy E (equation 2). In this way, the optimization of the (O, σO) and (Na+, σNa+) LJ parameters and the atomic charges of the zeolite framework were obtained from the best agreement between experimental and simulated adsorption properties of both NaX/ N2 and NaX/Ar systems. The initial (O, σO) and (Na+, σNa+) LJ parameters were taken from the literature,42 and the partial charges on silicon and oxygen of the faujasite framework system were fixed at the usually considered values43 (i.e., +2.4 e and -1.2 e, respectively). The charges on aluminum and sodium cations were allowed to change in order to take into account the partial charge transfer from the framework, with the constraint of a global charge of zero for the faujasite system.
TABLE 2: Ionic Radius44 and Polarizability45 for Each Investigated Monovalent and Divalent Cation type of cation
radius Rc/Å
polarizability R/Å3
Li+ Na+ K+ Mn2+ Ca2+ Sr2+ Ba2+
0.73 1.16 1.52 0.89 1.14 1.32 1.49
1.20 1.80 3.83 2.64 3.16 4.24 6.40
Once this first step is reached, the LJ parameters for the other extra-framework cations were then deduced from those for Na+ using the following relationships:
σMn+ )
Mn+ )
RMn+
σNa+
(3)
( )( )
(4)
RNa+
RMn+ RNa+
2
σNa+ 6 σMn+ Na+
where R and R correspond to the cation radius and polarizability, respectively, summarized in Table 2. Absolute adsorption isotherms were then computed using a grand canonical Monte Carlo calculation algorithm which allows displacements (translations and rotations), creation, and destruction. These simulations consist of evaluating the average number of adsorbate molecules whose chemical potential equals those of the bulk phase for a given pressure and temperature. All these simulations were performed at 300 K using one unit cell of faujasite with typically from 3 × 106 to 5 × 106 Monte Carlo (MC) steps. The evolution of the total energy over the MC steps was plotted in order to control the equilibrium conditions. The zeolite structure was assumed to be rigid during the sorption process. This assumption is not so drastic, because the flexibility of the lattice influences more significantly the diffusion properties.46 The Ewald summation was used for calculating electrostatic interactions, and the short-range interactions were calculated with a cutoff distance of 12 Å. Furthermore, as it is wellestablished experimentally and theoretically that nitrogen and argon cannot access the sodalite cages, dummy atoms with appropriate van der Waals radii were placed in these cages. This was done in order to avoid any introduction of adsorbates into this space, thus leading to accessibility only for gas in the supercages. The calculations of the differential enthalpies of adsorption at zero coverage ∆adsh˙ θ)0 at 300 K were performed through the fluctuations over the number of particles in the system and from fluctuations of the internal energy U47 by considering very low pressure and switching off the adsorbateadsorbate interactions
∆adsh˙ ) RT -
〈U‚N〉 - 〈U〉〈N〉 〈N2〉 - 〈〈N〉〉2
(5)
4. Results and Discussion The first step was to adjust the (O, σO) and (Na+, σNa+) LJ parameters and the partial charges on aluminum and sodium in order to yield good agreement with our experimental adsorption data for both NaX/N2 and NaX/Ar systems. Figure 2 reports the experimental and simulated isotherms and differential enthalpies of adsorption for the two systems. We observe a nice qualitative agreement in the whole range of pressures up to 45 bar. The resulting potential parameters are O ) 0.0197 eV, σO ) 2.708 Å and Na+ ) 0.004 34 eV, σNa+ ) 1.746 Å, and the
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Figure 2. Isotherms (a) and differential enthalpies (b) of adsorption for NaX/N2 and NaX/Ar at 300 K up to 45 bar: (0) simulation, (O) experiment.
TABLE 3: Lennard-Jones Parameters for Each Investigated Monovalent and Divalent Cation type of cation
σ/Å
/eV
Na+ Li+ K+ Mn2+ Ca2+ Sr2+ Ba2+
1.746 1.098 2.288 1.339 1.715 1.987 2.243
0.00434 0.03121 0.00388 0.04591 0.00743 0.01108 0.01220
TABLE 4: Differential Enthalpies of Adsorption at Low Coverage for the Various Monovalent-Divalent X-Faujasite/ N2 Systems Obtained Both Experimentally and Theoretically at 300 K differential enthalpy of adsorption at low coverage ∆adsh˙ θ ) 0 (kJ mol-1) type of zeolite LiX NaX KX MnX CaX SrX BaX
experiment
simulation
24.80 ( 0.15 19.00 ( 0.11 14.00 ( 0.08 30.00 ( 0.18 27.00 ( 0.16 26.00 ( 0.16 21.00 ( 0.13
23.6 19.2 14.1 30.1 26.5 26.0 20.8
partial charges carried by the aluminum and sodium are +1.7 and +0.7 e, respectively. The second step consisted of defining the LJ parameters for each cation from Na+ using eqs 3 and 4, and the data are reported in Table 2. The corresponding LJ parameters are summarized in Table 3. It has to be mentioned that the next calculations involving divalent cations include charges of 1.7 and 1.55 e for cations and aluminum atoms, respectively, assuming the same magnitude of charge transfer from the framework as in the case of the monovalent cations. On the basis of these derived LJ parameters, the differential enthalpies of adsorption at low coverage (∆adsh˙ θ)0) were computed for monovalent and divalent substituted X-Faujasite/ N2 systems and were contrasted with those measured experimentally. Table 4 shows that our simulations reproduce well the general trend consisting of a decrease of ∆adsh˙ θ)0 with increasing ionic radius. Furthermore, the calculated values are very close to the experimental ones for each X-faujasite. This good qualitative agreement between experiment and simulation reveals a nice transferability of the LJ parameters derived with our simplified model for each cation. Figure 3 show the isotherms of adsorption obtained for nitrogen in divalent cation-substituted X faujasites both experimentally and theoretically at 300 K in the pressure range 0-1 bar. The simulations indicate that the affinity of adsorption in this low-pressure domain increases in the order MnX > CaX > SrX > BaX, thus following the increase of the differential
Figure 3. Isotherms of adsorption for the various divalent substituted faujasites/N2 systems at 300 K in the pressure range 0-1 bar obtained both experimentally (continuous lines) and theoretically (dashed lines).
Figure 4. Isotherms of adsorption for the various monovalent substituted faujasites/N2 systems at 300 K in the pressure range 0-1 bar obtained both experimentally (continuous lines) and theoretically (dashed lines).
enthalpy of adsorption at low coverage. We observe experimentally a similar general trend; however, the adsorption affinities for CaX and SrX are close to each other. This relative discrepancy between experiment and simulation could be due to some additional adsorption sites for SrX (i.e., textural defects created during the cation exchange process) or to the approximated model used in the simulation to represent the distribution of the extra-framework cations. Similar behaviors are obtained for the monovalent substituted faujasites in Figure 4 where the adsorption affinity increases in the order LiX > NaX > KX. This simulated trend is in agreement with the experimental data reported for NaX and KX faujasites. However, a relative deviation is observed for the quantities of adsorbed gas determined experimentally and theoretically in the cases of both the monovalent and divalent forms. Finally, to test the validity of the interatomic potentials over a wide range of pressures, the isotherms and differential
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Figure 5. Isotherms (a) and differential enthalpies (b) of adsorption for the CaX/N2 system at 300 K in the pressure range 0-40 bar: (0) simulation, (O) experiment.
enthalpies of adsorption were simulated for a typical system (i.e., CaX/N2 at 300 K) up to 40 bar and compared with those measured experimentally. These results are reported in Figure 5. We can observe a very good agreement between experiment and simulation for both isotherm and differential enthalpy, which testifies to a good transferability of the LJ parameters even at high pressure. 5. Conclusions Microcalorimetry measurements performed for nitrogen on X-faujasite systems containing monovalent and divalent cations showed that the differential enthalpies of adsorption at low coverage increases in the sequence LiX > NaX > KX and MnX > CaX > SrX > BaX, respectively. This trend was confirmed by grand canonical Monte Carlo simulations which gives very good qualitative accordance with the experimental values. A qualitative agreement between experiment and simulation was also obtained for the adsorption affinities. The originality of this work was the derivation of new force fields for describing the interactions between extra-framework cations and adsorbates followed by the validation of their transferability to zeolite systems, with direct comparison with our own experimental data. This work is a significant contribution, as it reports for the first time such a good accordance between adsorption measurements and simulations for both monovalent and divalent cationsubstituted zeolites. Furthermore, the modeling approach described in this paper elaborated from a simple model can be envisaged as a predictive tool in order to easily evaluate the adsorption properties of cation-substituted zeolite systems as a function of the intrinsic properties of the cations. References and Notes (1) Corma, A. J. Catal. 2003, 216, 1-2, 298. (2) Ackley, M. W.; Rege, S. U.; Saxena, H. Microporous Mesoporous Mater. 2003, 61, 25. (3) Froment, G. F.; Jacobs, P. A. Top. Catal. 2000, 13, 444, 347. (4) Salla, I.; Salagre, P.; Cesteros, Y.; Medina, F.; Sueiras, J. E. J. Phys. Chem. B 2004, 108, 5359. (5) Macedonia, M. D.; Moore, D. D.; Maginn, E. J.; Olken, M. M. Langmuir 2000, 16, 3823. (6) Aguilar-Armenta, G.; Hernandez-Ramirez, G.; Flores-Loyola, E.; Silva-Gonzalez, R.; Tabares-Munoz, C.; Jimenez-Lopez, A.; RodriguezCastellon, E. J. Phys. Chem. B 2001, 105, 1313. (7) Siporin, S. E.; McClaine, B. C.; Davis, R. J. Langmuir 2003, 19, 4707. (8) Savitz, S.; Myers, A. L.; Gorte, R. J. Microporous Mesoporous Mater. 2000, 37, 33. (9) Fitch, F. R. U.S. Patent 1995, 467. (10) Coe, C. G. U.S. Patent 1992, 813. (11) Neuzil, R. W. U.S. Patent 1971, 3, 558, 730. (12) Bezus, A. G.; Kiselev, A. V.; Sedlacek, Z.; Pham Quang, Du. J. Chem. Soc., Faraday Trans. 1 1971, 67, 468. (13) Barrer, R. M.; Stuart, F. R. S.; W. I. Proc. R. Soc. 1959, 464. (14) Dzhigit, O. M.; Kiselev, A. V.; Mikos, K. N.; Muttik, G. G.; Rahmanova, T. A. J. Chem. Soc., Faraday Trans. 1 1971, 67, 458.
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