Modeling the Concentration Dependence of the Methanol Self

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J. Phys. Chem. B 2006, 110, 15926-15931

Modeling the Concentration Dependence of the Methanol Self-Diffusivity in Faujasite Systems: Comparison with the Liquid Phase D. F. Plant,†,‡ G. Maurin,*,‡ and R. G. Bell*,† The DaVy Faraday Research Laboratory, Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, United Kingdom, and Laboratoire LPMC, UMR CNRS 5617, UniVersite´ Montpellier II, Pl. E. Bataillon, 34095 Montpellier Cedex 05, France ReceiVed: May 15, 2006; In Final Form: June 7, 2006

Molecular dynamics simulations were performed to understand further the concentration dependence of the self-diffusion of methanol in the faujasite zeolite systems. The evolution of the self-diffusivity was investigated as a function of coverage for DAY and NaY systems to study the effect of both the pore confinement and the presence of the extraframework cations within the supercage. It was found that the self-diffusivity decreases with loading for DAY, whereas for NaY it passes through a maximum at intermediate coverage, in agreement with pulse-field gradient NMR and quasi elastic neutron scattering data reported in similar systems. The activation energies of the methanol diffusion corresponding to a combination of both intra- and intercage motions were evaluated as a function of the coverage. The simulated trends are interpreted on the basis of the predominant interactions which take place in both systems. Finally, the preferential arrangement of the adsorbate molecules are provided and compared with those simulated in the liquid phase. For the fully loaded materials, it was seen that the methanol molecules form a one-dimensional hydrogen-bonded chain along the channels in DAY whereas only dimers are present in NaY.

1. Introduction The diffusion of adsorbate molecules in nanoporous materials such as zeolites plays a crucial role in many industrial applications involving separation and catalysis processes.1-3 Several experimental techniques have been used to study the diffusion of various adsorbates in zeolite systems.1-4 Among them, incoherent quasi elastic neutron scattering (QENS) and pulsed-field gradient (PFG) NMR have been used to measure the evolution of the self-diffusion coefficients of different gases in silicalite and faujasite systems as a function of the loading.5-9 This self-diffusivity, which is related to the mobility of an individual molecule as it diffuses at equilibrium, generally either decreases with loading or in some cases passes through a maximum at a particular loading. It was shown, for instance, that the self-diffusivity decreases with loading for the adsorption of CO2, N2, C2H6, or CF4 in silicalite5-7 or CH4 in Y-faujasite system,10 whereas it exhibits a maximum at an intermediate loading for the adsorption of CH4 and C3H8 in silicalite.11-12 These different behaviors are controlled by a balance of attractive and repulsive adsorbate-adsorbent and adsorbateadsorbate interactions. Molecular modeling has also been applied to provide a microscopic interpretation of this experimental loading dependence of the diffusivity. The main theoretical studies have been based on molecular dynamics simulations using reliable interatomic potentials;13-15 some others have applied Monte Carlo procedures coupled with transition-state theory.16-18 The experimental trends were explained as follows. The decrease of the self-diffusivity was attributed to packing density which restricts the individual mobility, whereas the presence of a * Authors to whom correspondence should be addressed. E-mail: [email protected]; [email protected]. † The Davy Faraday Research Laboratory. ‡ Universite ´ Montpellier II.

maximum for a given loading was interpreted by proposing that the adsorbate-adsorbate repulsions increase the diffusivity by overcoming the attraction of the adsorbate for the zeolite framework. More recently, a new computational approach reported by Beerdsen et al.19 suggested that transitions between the various adsorption sites can result in temporary local increases in diffusivity. Here, we report for the first time molecular dynamics simulations conducted to investigate the self-diffusivity of methanol in faujasite. Two different faujasite systems were selected: the “extraframework cation-free” DAY and the cation-containing NaY, to specifically investigate the influence both of the confinement effect of the zeolite pore and of the presence of the extraframework cations on the concentration dependence of the methanol self-diffusivity. Methanol is involved in several catalytic important reactions such as Mobil’s methanol to gasoline (MTG) and methanol to olefin (MTO) processes20,21 and the selective alkylation of toluene.22 Zeolite materials play a crucial catalytic role as membrane reactors in this process either by interacting with methanol molecules to form an intermediate species during the chemical reaction23 or by increasing the rate of conversion via high-separation selectivity of the products.24,25 The optimization of all these industrial processes demands a sophisticated understanding of the interactions between the zeolite surfaces and the reactant methanol molecules, including the diffusion properties of the reagent within the catalyst micropores. We use classical simulations based on interatomic potentials, as the adsorption processes are known to be entirely physical in nature under ambient conditions. The potential parameters were partly derived using ab initio cluster calculations and are reported in our previous paper.26 Both the self-diffusivity for methanol over a wide range of temperature [300-700 K] and the activation energies corresponding to the adsorbate motions within the supercages of the faujasite are evaluated as a function of loading for DAY

10.1021/jp0629543 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/20/2006

Modeling Concentration Dependence of Methanol

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TABLE 1: Self-Diffusion Coefficients in (m2 s-1) Calculated for Methanol in DAY and NaY for Loadings of 8, 16, 32, and 48 Molecules and Temperatures 350-700 K temperature /K

8 molecules/u.c.

DAY 16 molecules/u.c.

32 molecules/u.c.

48 molecules /u.c.

350 400 450 500 550 600 650 700

7.966 × 1.032 × 10-8 1.142 × 10-8 1.285 × 10-8 1.475 × 10-8 1.736 × 10-8 1.915 × 10-8 1.995 × 10-8

6.371 × 8.372 × 10-9 1.018 × 10-8 1.127 × 10-8 1.229 × 10-8 1.536 × 10-8 1.612 × 10-8 1.806 × 10-8

2.183 × 3.725 × 10-9 4.470 × 10-9 5.554 × 10-9 6.000 × 10-9 6.587 × 10-9 7.626 × 10-9 9.200 × 10-9

5.196 × 10-10 7.042 × 10-10 8.858 × 10-10 1.138 × 10-9 1.205 × 10-9 1.300 × 10-9 1.861 × 10-9 1.950 × 10-9

500 550 600 650 700

5.785 × 10-10 9.037 × 10-10 1.319 × 10-9 2.069 × 10-9 2.989 × 10-9

NaY 4.828 × 10-10 1.414 × 10-9 1.931 × 10-9 2.304 × 10-9 3.030 × 10-9

7.230 × 10-10 1.519 × 10-9 2.075 × 10-9 2.580 × 10-9 3.165 × 10-9

2.885 × 10-10 5.487 × 10-10 6.229 × 10-10 9.719 × 10-10 1.094 × 10-9

10-9

10-9

TABLE 2: Self-Diffusion Coefficients in (m2 s-1) Calculated for Methanol in Liquid Phase and Temperatures 350-700 K temperature/K

D/m2 s-1

300 350 400 450 500 550 600 650 700

1.365 × 10-9 2.103 × 10-9 3.628 × 10-9 6.150 × 10-9 8.442 × 10-9 9.226 × 10-9 9.667 × 10-9 1.068 × 10-8 1.208 × 10-8

and NaY. These simulated data are then compared and contrasted with those obtained experimentally by Grenier et al.27 using pulsed-field gradient (PFG) NMR. In addition, we made a study of the structure properties of methanol confined in the faujasite systems. This type of investigation has been intensively reported for water in various porous media such as zeolites, clays, and mesoporous molecular sieves because of interest and importance of water in geological and biological systems.28-31 It was shown, for instance, that confined water molecules form one-dimensional hydrogen-bonded linear chains in some zeolites32,33 and in carbon nanotubes.34 Here, the behavior of methanol within the supercages of both the faujasite systems studied is also compared with that found from simulations performed for liquid-phase methanol. 2. Computational Methodology Interatomic Potentials. I. Zeolite Framework. The simulation of methanol self-diffusion through the DAY and NaY systems required an accurate description of the potential between the methanol molecules and the zeolite framework, including the sodium cations, and between the methanol molecules. Furthermore, we needed a fully flexible model in which both the zeolite and the sorbate molecules were free to alter their internal configurations. The force field used to describe the zeolite framework was selected from the work of Ramsahye and Bell35 which included a partially ionic model where the atoms carry the following partial charges (in electron units): Si (+2.4), Al (+1.4), Oz (-1.2), and Na (+1.0). The short-range interactions were described by Buckingham potentials, including explicit Si-O and Al-O terms, and additional harmonic three-body terms were defined for the O-Si-O and O-Al-O intratetrahedral angles. II. Intermolecular Terms. Intermolecular potentials between the zeolite framework and methanol molecules are based on those reported by Blanco and Auerbach.36 In these potentials,

10-9

the short-range parts are given in the form of the Lennard-Jones 12-6 function. As described in detail in our previous article,26 both the methanol partial charge distribution and the potential between the oxygen of methanol (Om) and the oxygen of the zeolite framework (Oz) were scaled slightly. The Lennard-Jones parameters which represent the intermolecular interactions between the methanol molecules were similarly slightly adjusted from those reported in the cVff force field37 to be consistent with the changed atomic charges on methanol. III. Methanol Intramolecular Terms. Intrasorbate flexibility was described by two-body bond-stretching, three-body bondbending, and four-body torsional potentials. The corresponding parameters were obtained by slightly modifying those given by the cVff force field.37 The validity of the modified potential parameters used for describing both the interactions between methanol-methanol and the guest molecule flexibility was checked by comparing the simulated diffusion coefficient of methanol in the liquid phase at ambient temperature with those obtained experimentally. All the intra- and interatomic potential parameters are reported in our previous paper.26 Zeolite and Liquid Models. The crystal structure of the two faujasite systems was modeled as follows. The purely siliceous faujasite Si192O384 with a cubic unit cell and lattice parameter of 24.8 Å38 was considered to model the DAY zeolite. The chemical composition Si136Al56Na56O384, with Si/Al ratio of 2.4, was taken to represent NaY. The zeolite framework was built in accordance with Lo¨wenstein’s Al-O-Al avoidance rule.39 The aluminum configurations representing NaY were then selected to reproduce the experimental cation distributions as the cation is embedded close to the aluminum position. The second step consisted of modeling the distribution of the extraframework cations among the different crystallographic sites. This distribution was defined as follows, on the basis of the structure refined from X-ray diffraction data by Fitch et al.: 38 6 cations in sites SI located in the center of the hexagonal prism connecting two sodalite cages, 18 in sites SI′ in the sodalite cage in front of the 6-ring window connected to the hexagonal prism, and 32 in sites SII in the 12-ring windows of the supercages. The sites occupied were chosen randomly, with the exception that neighboring SI and SI′ sites were not allowed to be occupied. Both DAY and NaY structures were then energy-minimized with the GULP code,40 using the previous described interatomic potentials developed by Ramsahye and Bell,35 with the constraint that the cell remained cubic. These optimized structures were then loaded with 8, 16, 32, 48, 64, and 96 methanol molecules using the sorption module in the

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Plant et al.

Figure 1. Evolution of the self-diffusion coefficients (D) (a) DAY and (b) NaY zeolites at various temperatures as a function of methanol loading.

Figure 2. Arrenhius plots of ln(D) versus 1000/T for (a) 8, (b) 16, (c) 32, and (d) 48 methanol molecules per unit cell: DAY (0) and NaY (O).

Figure 3. Radial distribution functions (rdf) of H(methanol)O(methanol) for 16, 32, 48, and 64 methanol molecules per unit cell, calculated at 300 K in DAY. For comparison, the H(methanol)O(methanol) rdf calculated at the same temperature for methanol in liquid phase is reported.

Cerius2 program.41 Prior to the molecular dynamics simulations, all the generated structures were optimized using GULP to provide lowest energy starting configurations. The liquid methanol system was simulated using 205 methanol molecules distributed within a cubic simulation box of cell length 24.20 Å, which was the cell parameter of our model dealuminated zeolite DAY structure. This is equivalent to the density of methanol at standard temperature and pressure.42 Molecular Dynamics Simulation. The interatomic potentials described above for modeling the systems were implemented in the DL_POLY program,43 using an NVT ensemble with the Evans isokinetic thermostat.44 We selected the optimized structures obtained from the minimization procedure as starting

configurations, and the minimized cell dimensions were kept fixed during the molecular dynamics (MD) runs. All components of the system (adsorbate and adsorbent) were treated as fully flexible during the MD simulation. A time step of 1 fs was selected, with simulations runs at loadings of 8, 16, 32, 48, 64, and 96 molecules per unit cell; in other words, an average of 1, 2, 4, 6, 8, and 12 molecules per supercage, respectively. The simulations spanned a range of temperatures between 300 and 700 K, each for 106 steps (i.e., 1 ns), following 50 000 steps of equilibration. A short-range cutoff of 8.50 Å was used, while electrostatic interactions were evaluated using the Ewald method. The trajectory was recorded every 200 steps during the production stage, and radial distribution functions were recorded every 500 steps. The mean square displacements (MSD) of the methanol molecule for each loading and at the different temperatures were evaluated by means of the following classical equation:

MSD(t) ) 〈∆rj (t)〉 ) 2

1

N

1

N

∆rj (t) ) ∑(rj(t) - rj(0))2 ∑ N j)1 N j)1 2

where N corresponds to the number of methanol molecules considered in the computation of the MSD, and we used multiple time origins to improve the statistics of the calculation. The self-diffusion coefficients evaluated at low and intermediate loadings were obtained by fitting the MSD plots as a function of the time in the region 0-200 ps, assuming

Modeling Concentration Dependence of Methanol

J. Phys. Chem. B, Vol. 110, No. 32, 2006 15929

Figure 4. Typical arrangements of the methanol molecules in DAY for (a) 8, (b) 32, and (c) 64 methanol loadings at 300 K.

the following Einstein relation:

MSD(t) ) A + 6Dt The activation energies corresponding to the self-diffusion processes were then evaluated from the linear least-squares fit to the Arrhenius plots of ln(D) ) f(1000/T). 3. Results and Discussions The values of the self-diffusion coefficients extracted as described above are reported in Table 1 for low and intermediate loadings in a wide range of temperature for both NaY and DAY systems. The same methodology was also applied to methanol in the liquid phase, and the calculated values are shown in Table 2. A major feature of the data presented in these tables is that all the calculated self-diffusion coefficients generally increase in the order NaY < DAY < liquid phase, although, at low loading, diffusivities are higher in DAY than for the liquid system. The difference between NaY and DAY is much clearer in the Figure 1a and 1b reporting the diffusivity values as a function of temperature and loading for both systems. When one compares these calculated values with those obtained experimentally by PFG NMR spectroscopy for NaX,27 the diffusivity for a given loading is at least 1 order of magnitude lower than those for NaY. Such behavior is consistent with those recently observed for the adsorption of CO2 in these systems.45 This trend suggests that both the confinement effect induced

by the zeolite framework and the presence of the extraframework cation strongly affect the self-diffusivity of the methanol molecules. Furthermore, figure 1a and 1b illustrates two different methanol self-diffusion behaviors for NaY and DAY as a function of the loading. For NaY, it can be observed that the self-diffusion coefficients at all temperatures tend to reach a maximum for 32 methanol/u.c., which in turn corresponds to a loading of 1 methanol molecule per extraframework cation at the accessible SII sites, before decreasing at higher loading. This trend is explained by a collective cation-adsorbate motion which enhances the diffusivity of the methanol molecules up to the point that the average number of methanol molecules around each cation exceeds 1. Above this loading, steric hindrance becomes dominant and the self-diffusivity decreases. This typical behavior has already been established from pulsedfield gradient NMR measurements performed on a NaX/ methanol system, where it was reported that the self-diffusivity at constant temperature passes through a maximum at intermediate methanol loading levels.27 Similar diffusivity behavior has been observed in silicate zeolites upon the adsorption of methane, propane,12 and 2-butene46 and was interpreted in a different way by suggesting that repulsion between the adsorbate molecules is responsible for the increase of the diffusivity. By contrast, the self-diffusion coefficients for DAY decrease continuously when the loading increases. Increased adsorbate

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Figure 5. (a) Typical arrangement of the methanol molecules in the liquid phase at 300 K. (b) Distribution of the molecules around one methanol consistent with the rdfs reported in Figure 3.

concentration leads to a reduced volume for the individual molecules in the supercage and consequently to reduced translational mobility. This trend is in good agreement with data, both observed and simulated, in the purely siliceous silicalite system.5-7,47 These two different behaviors exhibited in DAY and NaY emphasize the role played by the extraframework cations in methanol diffusivity. Inspection of the trajectories clearly shows that in both systems the diffusive process involves displacements throughout the pore structure combining both intra- and intersupercage motions. It was thus estimated that the residence time of the methanol molecule in one supercage, for a given loading of 32 methanol molecules/u.c., ranges from 50 to 80 ps when the temperature goes from 600 to 500 K. For high methanol loading, the poorly linear evolution of the MSD plots for 64 and 96 methanol molecules/u.c. in NaY did not allow us to evaluate the self-diffusion coefficients. Furthermore, in DAY, upon loading of more than 64 methanol molecules/u.c., we observed the complete absence of diffusive behavior even at high temperature, with the motions of the methanol molecules restricted to oscillation around their mean spatial positions because of steric hindrance arising from packing of the methanol molecules present in the pore. This observation also indicates that the energy barrier for methanol molecules to pass each other with loading close to the saturation is much higher than kT. This result is in very good agreement with those recently reported by Demontis et al. for water adsorption in Li-ABW zeolites.33 Activation energies, characteristic of the diffusive processes in NaY and DAY, were derived from linear least-squares fits to the Arrhenius plots reported in Figure 2. As can be seen, these energies are much lower in DAY than in NaY whatever the loading. This difference can be interpreted as follows. In NaY, the activation energy is mainly governed by a strong

Plant et al. interaction between the methanol molecules and the Na+ extraframework cations which requires traversal of a high-energy barrier for the adsorbate molecules to move across the faujasite supercage. By contrast, in DAY, interactions between the methanol and the zeolite framework are much weaker. It is notable that the activation energies we obtain for NaY are within the same order of magnitude or slightly lower than those previously measured by pulsed-field gradient NMR technique for equivalent methanol loadings in similar NaX systems (0.17 eV vs 0.18 and 0.175 eV vs 0.23 eV for 32 and 48 methanol molecules/u.c., respectively27). This observation is consistent with the difference observed for the values of the diffusivity in the two faujasite systems. In addition, we observe a different trend in the calculated activation energies for DAY and NaY as a function of loading. For NaY, these values decrease because of an attenuation of the dominant methanol/Na+ interactions by the increasing number of surrounding adsorbate molecules, whereas for DAY, they increase slightly because of greater interaction between methanol molecules. Figure 3 reports the radial distribution functions (rdfs) calculated at 300 K in DAY for loadings from 8 to 64 methanol/ u.c., which are compared with those evaluated in the liquid phase. This figure clearly shows the existence of hydrogen bonding between the adsorbate molecules with characteristic peaks ranging from 2.1 to 2.2 Å, the extent of hydrogen bonding increasing with the methanol loading. This behavior is significantly different from that previously reported in NaY,26 where hydrogen bonding was only seen at higher loading. It can be also observed that these peaks are slightly shifted from those we calculate for the methanol in the liquid phase (1.8 Å) which means that at high loading the adsorbate molecules within the supercage interact with weaker hydrogen bonds. The arrangement of the methanol molecules in DAY is typically illustrated in Figure 4. At low loading, it can be observed that the methanol molecules preferentially interact with the formation of small-size clusters, dimers, or trimers (Figure 4a and 4b) with hydrogen bond length consistent with those reported in the rdfs (Figure 3). At high loading, it was possible to observe a linear arrangement and ordering at higher loading. Figure 4c shows a cut-away side view of the zeolite channel with a single linear chain formed by methanol molecules. Here, we highlight only one chain (clarifying the picture), as other chains are also present at this high loading aligning themselves parallel to the pore channel with other methanol chains The length of these types of chains are continuous throughout the unit cell, therefore around 24 Å. The strength of interaction between the individual molecules remains constant, with interaction distances oscillating about 2 and 2.5 Å. This results in the linear formations being stable. The chains possess a steady linear diffusion along the direction of the chain, comparable to a single file diffusion. This geometry, different from those we recently reported in NaY26 where the presence of extraframework cations favors the formation of small-size methanol clusters, predominantly dimers, is very similar to those reported for water in some zeolites systems. Recently, it was reported that zeolites such as Li-ABW33 and bikitaite,32 which exhibit parallel straight channels, show hydrogen-bonded linear chains of water molecules running along the axis of the channels. Furthermore, the confinement effect due to the faujasite supercage induces slight changes in the arrangement of the methanol molecules compared with those observed in the liquid phase. In this latter system, branched-chain hydrogen bond structures were indicated by our simulation (Figure 5a) with typical Hm-

Modeling Concentration Dependence of Methanol Om distances ranging from 1.84 to 1.94 Å. This typical geometry is in good agreement with those usually reported in the literature.48 Finally, Figure 5b provides a good illustration of the calculated rdfs reported in Figure 3. It clearly shows that in addition to the hydrogen-bonding distance of 1.94 Å, the nearest neighbor Hm-Om distances (non-H-bonded) can be around 3.5 Å and the next nearest neighbor distances are in the region of 4.5-5.0 Å. The Hm-Om pair distribution function for liquid methanol (Figure 3) appears very similar to those previously reported by several authors using a six-site model for methanol.49,50 4. Conclusions Molecular simulations of methanol self-diffusion in DAY and NaY zeolites have been carried out using a fully flexible zeolite force field and have been compared with the results obtained for the liquid phase. It was observed that the diffusivity of the molecules increases in the order NaY < DAY < liquid phase and exhibits different behaviors as a function of loading, with a constant decrease and a maximum at intermediate coverage for DAY and NaY, respectively. The activation energies of this diffusive process corresponding to a combination of both intraand intersupercage motions are much higher in NaY than in DAY. This difference is ascribed to the strong intermolecular interaction between methanol oxygen and the extraframework cations which predominantly governs the transport properties in NaY and favors the formation of adsorbate dimers around the cations at higher loading. By contrast, in DAY, the formation of multiple hydrogen-bonded chains connected in parallel through the 12-ring windows is observed. This arrangement differs slightly from those found in our simulation for the liquid phase which exhibits branched-chain hydrogen bond structures. References and Notes (1) Ka¨rger, J.; Ruthven, D. Diffusion in Zeolites and Other Microporous Materials; John Wiley & Sons: New York, 1992. (2) Keil, F.; Krishna, R.; Coppens, M. O. ReV. Chem. Eng. 2000, 16, 71. (3) Auerbach, S. M. Int. ReV. Phys. Chem. 2000, 19, 155. (4) Jobic, H. Curr. Opin. Solid State Mater. Sci. 2003, 6, 415. (5) Chong, S. S.; Jobic, H.; Plazanet, M.; Sholl, D. S. Chem. Phys. Lett. 2005, 408, 157. (6) Jobic, H.; Skoulidas, A. I.; Sholl, D. S. J. Phys. Chem. B 2004, 108, 10613. (7) Papadopoulos, G. K.; Jobic, H.; Theodorou, D. N. J. Phys. Chem. B 2004, 108, 12748. (8) Valiulin, R.; Kortunov, P.; Ka¨rger, J.; Timoshenko, V. J. Chem. Phys. 2004, 120, 11804. (9) Ka¨rger, J.; Valiullin, R.; Vasenkov, S. New J. Phys. 2005, 7, 15. (10) Jobic, H.; Be´e, M.; Kearley, G. J. J. Phys. Chem. B 1994, 98, 4660. (11) Van den Begin, N. G.; Rees, L. V. C. In Zeolites: Facts, Figures, Future; Elsevier: Amsterdam, 1989.

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