Kinetics of Zeolite Dealumination: Insights from H-SSZ-13 - ACS

Oct 14, 2015 - When zeolite catalysts are subjected to steam at high temperatures, a permanent loss of activity happens, because of the loss of alumin...
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Kinetics of Zeolite Dealumination: Insights from H‑SSZ-13 Malte Nielsen,†,‡ Rasmus Yding Brogaard,† Hanne Falsig,*,‡ Pablo Beato,‡ Ole Swang,†,§ and Stian Svelle*,† †

Center for Materials Science and Nanotechnology (SMN), Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway ‡ Haldor Topsøe A/S, Haldor Topsøes Allé 1, DK-2800 Kgs., Lyngby, Denmark § SINTEF Materials and Chemistry, P.O. Box 124 Blindern, 0314 Oslo, Norway S Supporting Information *

ABSTRACT: When zeolite catalysts are subjected to steam at high temperatures, a permanent loss of activity happens, because of the loss of aluminum from the framework. This dealumination is a complex process involving the hydrolysis of four Al−O bonds. This work addresses the dealumination from a theoretical point of view, modeling the kinetics in zeolite H-SSZ-13 to gain insights that can extend to other zeolites. We employ periodic density functional theory (DFT) to obtain free-energy profiles, and we solve a microkinetic model to derive the rates of dealumination. We argue that such modeling should consider water that has been physisorbed in the zeolite as the reference state and propose a scheme for deriving the free energy of this state. The results strongly suggest that the first of the four hydrolysis steps is insignificant for the kinetics of zeolite dealumination. Furthermore, the results indicate that, in H-SSZ-13, it is sufficient to include only the fourth hydrolysis step when estimating the rate of dealumination at temperatures above 700 K. These are key aspects to investigate in further work on the process, particularly when comparing different zeolite frameworks. KEYWORDS: density functional theory, steaming, CHA, microkinetics, kinetics, hydrothermal stability, catalysis

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INTRODUCTION Zeolites are microporous crystalline aluminosilicates that have a wide range of catalytic applications,1 specifically including hydrocarbon conversion processes such as methanol-to-olefin (MTO) reactions.2,3 In this type of reaction, the active site is a Brønsted acid, created by substituting a Si with an Al atom and compensating the excess charge with a proton. During MTO conversion, nonreactive species, also known as “coke”, accumulates on and within the zeolite, causing a decrease in the reactivity.4−7 The catalyst is regenerated by burning the coke. Because water is also formed in this combustion process, the zeolite catalyst is exposed to steam at high temperature. This leads to irreversible dealumination of the zeolite extraction of Al from the zeolite framework,8which permanently reduces the activity of the catalyst. Dealumination can also be used intentionally, to change the Si/Al ratio of a zeolite.9 A deeper understanding of dealumination could help to determine the most stable zeolite material toward steaming and, as studies have shown that steaming can lead to mesopore generation,10−12 identify where defects leading to mesopores are initiated. Such understanding could also explain why some T-sites apparently are resistive to steaming.13 The dealumination process can be separated into two stages: first, the hydrolysis sequence, which involves water-assisted removal of Al from the framework, and second, condensation of © XXXX American Chemical Society

the thus-formed extra-framework Al species (EFAls) in the pores and on the crystal surface with concomitant release of water.14,15 Previous theoretical works have focused on the hydrolysis stage, but so far have not addressed the kinetics of dealumination. Much effort has been put into determining the relevant reaction mechanism of the hydrolysis stage and the corresponding potential energy profile.16 A very recent work managed to establish a linear relationship between the reaction energy and the intrinsic activation energy of hydrolyzing the initial Al−O bond.17 Silaghi has investigated the full potential energy profiles of several zeolite frameworks.18 Quantative experimental work is scarce, but some studies have measured the amount of Al species in H-ZSM-5 before, during, and after steaming, in order to derive dealumination rates.14,19,20 Two investigations found initial dealumination rates to be second order in the pressure of water vapor, and derived an apparent activation energy of ∼100 kJ/mol.14,19 The second-order pressure dependence strongly indicates that the rate-determining stage of dealumination is the consumption of steam (hydrolysis), rather than its release (condensation). Therefore, we expect the hydrolysis sequence to determine the kinetics of dealumination, in agreement with the assumptions Received: July 16, 2015 Revised: October 12, 2015

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ACS Catalysis made in previous publications.17,19,20 In the present work, we will hence focus on modeling the kinetics of the hydrolysis stage of dealumination. Unless otherwise noted, we refer to this stage when using the term “dealumination” in the following. The reaction is generally very complicated to model, because it involves sequential hydrolysis of four bonds between aluminum and oxygens of the zeolite framework. These bonds can be dissociated in different orders and by different mechanisms. Furthermore, the aluminum can be in several different crystallographic positions (T-sites), depending on which zeolite framework is considered. This means that, for most zeolites, there are thousands of possible reaction pathways, and one cannot easily narrow them down. It is a daunting task to model this many reaction steps and possibilities by density functional theory (DFT); hence, it is highly desirable to investigate ways of reducing the complexity. In this work, we approach these challenges by performing calculations on the dealumination reaction on H-SSZ-13 zeolite, containing only one T-site. The focus is on high-silica zeolites, whereas low-silica zeolites should likely be addressed separately. The objective here is to extract aspects of the dealumination that are independent of the specific reaction pathway and, hence, are extendible to other zeolites. We do this by deriving the free-energy profiles of selected dealumination pathways and performing microkinetic modeling, thereby predicting initial reaction rates as a function of temperature and pressure. A correction scheme for the water reference free energy is suggested, based on water inside a zeolite. The results obtained using this scheme compare significantly better to experiments than results obtained using an ideal gas reference. This indicates that, in the kinetically relevant reference state, water is (physisorbed) inside the zeolite framework. Our data show that the hydrolysis of the first Al−O bond is kinetically irrelevant, significantly simplifying the search for dealumination pathways in future investigations. In addition, we discuss how to interpret and relate kinetic parameters obtained experimentally to the reaction mechanism.

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framework. Transition states were confirmed to have one imaginary frequency, while other states were relaxed so that no imaginary frequencies were present. Note that the free energies for the zeolite structures were calculated based only on the frequencies of the optical phonons. The three unit-cell translations were excluded by employing the acoustic sum rule when diagonalizing the Hessian. This was done using the asr = “crystal” option in the dynmat.x code. Free energies were calculated using the ASE Thermochemistry package,29 which uses the harmonic approximation for zeolite structures, and ideal gas limit for isolated molecules. Microkinetic modeling was based on the reaction free-energy profiles and done using the CatMAP code.30 The model consisted of the following steps:

H‐SSZ‐13 + H 2O → Water ads 1

Water ads i → Initial i Initial i ↔ TS i → Final i

i=1−3

Final i + H 2O → Water ads (i + 1)

Water ads 4 ↔ TS 4 → Final 4 Final 4 → Dealuminated See the Reaction Pathway section and section S1 for further details on the elementary steps. The artificial Dealuminated state was fixed at a free energy of −50 kJ/mol, independent of temperature, relative to gas phase water and the intact framework. It was verified that the exact value for the free energy of the Dealuminated state did not influence the rate, as long as it made the reaction exergonic. Hence, it can be considered a technicality of the model that does not influence the results. The concentration of the state was set to zero (0), in order to exclude a reverse reaction rate. This way, the model simulates the initial forward dealumination rate, which is the experimentally measured parameter. When implementing the model in CatMAP, one faces two technical issues. First, CatMAP is designed to simulate catalytic reactions and, hence, requires the overall model to leave the substrate unchanged. This was accomplished by defining the Dealuminated state as desorption of an artificial species, stoichiometrically equivalent to four water molecules, leaving the zeolite structure unchanged. The pressure of this species was set to 0 bar. This state definition is purely technical and does not change the characteristics of the model defined above; it still simulates the initial forward rate of dealumination. Second, CatMAP does not allow input of frequencies (in order to get free energies) of the catalyst structure. To include this, we employed the “frozen_adsorbate” and “frozen_gas” options in CatMAP (see the .mkm file in the Supporting Information). This means CatMAP will not derive thermochemical corrections to the input energies, allowing us to use free energies of the entire system as input.

COMPUTATIONAL DETAILS

Periodic DFT calculations were performed using the Quantum Espresso code21 interfaced with the Atomic Simulation Environment.22 The Grimme DFT-D2 dispersion-corrected23,24 PBE exchange correlation functional25 was applied using a plane wave basis with kinetic energy cutoff at 500 eV and charge density cutoff at 7000 eV, using only the Γ-point to sample the Brillouin zone. These parameters were based on a convergence analysis of adsorption energy of water showing convergence to 15 meV. The 36 T atom hexagonal unit cell was used. The unit cell was optimized with a plane wave energy/density cutoff of 750/7500 eV, using no symmetry constraints, where convergence to 0.01 Å in any direction was reached. The lattice parameters obtained (a = b = 13.72 Å, c = 14.82 Å) are within 1% of experimental results (a = b = 13.60 Å, c = 14.83 Å).26 After this optimization, a Brønsted acid site was created by substituting an Si with an Al and adding a hydrogen, with the hydrogen on the O1 position, since this is the energetically most stable position (see section S1 in the Supporting Information for energies and positions). Transition states were located using the nudged elastic band (NEB) method with a spring constant of 0.3 eV/Å, where climbing image was applied27 until all forces were below 0.01 eV/Å. Vibrational frequencies were calculated using the internal quantum espresso phonon code,21 which employs density functional perturbation theory for calculating the Hessian.28 The phonon calculations employed a self-consistency threshold (tr2_ph) of 10−15. All the atoms in the cell were included. This is crucial, since the reaction involves the

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RESULTS AND DISCUSSION Reaction Pathway. The dealumination pathway consists of the dissociation of four Al−O bonds via hydrolysis to create an EFAl species, Al(OH)3(H2O). The salient feature of this pathway is the particular adsorption mode of the water molecule. Immediately prior to hydrolysis, water is bound directly to the Al in a Lewis acid−base-type interaction, rather than to the Brønsted acid site. Silaghi et al.17 have convincingly showed that this adsorption mode leads to hydrolysis mechanisms that are substantially energetically favored over those involving a disilanol defect.16 Moreover, Silaghi18 has calculated full energy profiles for the delamination of several zeolite frameworks, including CHA. Following Silaghi, the pathway consists of sequential dissociation of a bond in the following four types of states: (1) Adsorption of a water molecule on the lowest energy site (Water ads), (2) Initiation of hydrolysis (Initial), 7132

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ACS Catalysis Scheme 1. Hydrolysis of the First Al−O Bond,a Following the Mechanism of Silaghi et al.17

a

The names of the intermediates in the reaction are used throughout this article.

shows the resulting free-energy profiles of the dealumination pathways. Note that the reference free energy for water has been corrected, as will be explained in the next section. At a temperature of 723 K, we see that the additional water does not lower the free-energy barrier for hydrolysis steps 1 and 3, while it slightly lowers the barrier for hydrolysis step 2. Whether or not these pathways are favored is clearly dependent on the free energy of the reference state of water (vide inf ra), the temperature, and the water pressure. Because of the marginal influence of additional water, and to maintain simplicity, it was not included in the microkinetic model. The potential energy barriers obtained here generally are in excellent agreement with the work of Silaghi,18 except for the first hydrolysis step, where the barrier is 36 kJ/mol larger in our pathway. However, as will become evident, we have reason to be confident that our pathway constitutes a sound starting point for investigating the kinetics of the dealumination reaction. Most importantly, we are interested in investigating trends in the kinetics that are independent of the specific reaction pathway. We do this by assessing how uncertainties in calculated potential energies influence the predicted rates of dealumination (vide inf ra). As can be seen from the free-energy profile in Figure 1, formation of the EFAl species is an endergonic reaction under conditions where dealumination is known to occur. A study of Groen et al. concludes that EFAls are, in fact, created while steaming, and their data suggest significant clustering of EFAls.8 Thus, this endergonicity is clearly not true for overall material dealumination, and some driving force should be found. We identify this as an important topic for further work. The condensation of growing clusters of EFAl species inside the zeolite pores and concomitant release of water molecules should be investigated. This could include possible proton exchanges between Brønsted acid sites and EFAl species.32 Such complex investigations are clearly outside the scope of the present work and the driving force is built into the microkinetic model, as described in the Computational Details section. It was verified numerically that the results are insensitive to the exact magnitude of the driving force, as long as it ensures an exergonic reaction. Finally, we note that the results of Figure 1 support our assumption that the hydrolysis sequence is the rate-determining part of the overall dealumination process. Consider the tetrahedrally coordinated EFAL species physisorbed in the framework (the ”Final 4” state in Figure 1). Condensation of two such species can be expected to proceed through a transition state similar to TS 4, involving pentacoordinated aluminum species. Note that the calculated intrinsic free-energy barrier between ”Water ads 4” and ”TS 4” is vanishing. Hence, we expect the corresponding barrier for condensation of two EFAl species to be very small, and indeed is smaller than the 50 kJ/mol that is necessary for the first condensation to be rate-

(3) Transition state (TS), and (4) Final state (Final). There are four states of each type, one for each hydrolysis step. Hence, e.g., “TS 3” refers to the transition state of hydrolysis 3. These states are shown for the hydrolysis of the first Al−O bond in Scheme 1. There are different possible hydrolysis mechanisms, and, in this study, two have been investigated (section S1). In addition, the proton of the Brønsted acid site can be located on four different O atoms. Assuming only two relevant mechanisms, the possibilities of hydrolysis order and mechanism for this simple 1-T-site framework still number in the hundreds. The first hydrolysis step has four possibilities in bond choice, times two possibilities in mechanisms. The second step has three possibilities in bond choice times two mechanisms, and so forth. This gives total number of possibilities of (4 × 2) × (3 × 2) × (2 × 2) × (1 × 2) = 384. Clearly, it is not possible to try all combinations to determine the lowest energy pathway, and a description of the specific pathway used in this work along with the possibilities explored can be found in the Supporting Information. The pathway chosen is the combination that gives the most stable transition states. We also attempted to locate pathways in which an additional water molecule was added before the Al−O bond was hydrolyzed. The idea is that additional water may catalyze the hydrolysis, as reported for SAPO-34.31 The pathways without the extra water were used as starting points in the calculations. Note that the extra water is added in the ”initial”-type states, not the ”water ads”-type states. The lowest energy pathway from many different attempts was taken (section S1). Figure 1

Figure 1. Free-energy and enthalpy profiles for the dealumination of H-SSZ-13 at a temperature of 723 K and a vapor pressure of 1 bar. The profiles represent a reaction pathway with only the needed water for hydrolysis, and a pathway with an additional water molecule. 7133

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takes a cruder, but more cost-efficient approach (vide inf ra), in order to investigate potential benefits of a more accurate calculation. Second, we acknowledge that it represents a significant challenge to model the entropy of adsorbates and the reacting zeolite structure. In this work, we employ the harmonic limit, which likely underestimates the entropy for adsorbed species at high temperatures. Piccini et al.42 investigated adsorption of small hydrocarbons in H-SSZ-13 and reported that the harmonic limit, in fact, does overestimate the free energy. This leads to an underestimation of entropy of the adsorbate, compared to both the experiment and a more thorough anharmonic calculation.42 In this work, we wish to highlight that the entropy difference between the reference and the adsorbed state is central to correctly model the kinetics, thus identifying this as a topic for further work. As a starting point, we adopt a pragmatic solution, accounting for both sources of entropy error in a corrected reference state of water. This provides a crude, yet simple alternative to employing the anharmonic correction presented by Piccini et al.42 and calculating the free energy of the water in a zeolite by first principles. We stress that the water reference free energy is the only parameter we correct in this work. All remaining free energies are used directly as obtained from the DFT calculations. We define the free energy of water in the corrected state as follows:

determining. The condensation will free water molecules and release free energy. Therefore, the transition states of the following condensation steps can be expected to be even lower in free energy than that of the first condensation step. This supports our assumption that the hydrolysis stage indeed does determine the overall dealumination rate. Water Vapor in Zeolite: The Reference State. When calculating the free-energy profile of the reaction pathway, two things are needed: the free energy of the intermediates and the reference free energy of water. The reference free energy of water is crucial for modeling dealumination, since the process involves the adsorption and reaction of four water molecules. We can illustrate this point more quantitatively by using transition state theory to relate the free energy of activation to the reaction rate:33 r=

⎛ −ΔG† ⎞ kBT exp⎜ ⎟ h ⎝ RT ⎠

(1)

where r is the rate, kB the Boltzmann constant, T the temperature, R the gas constant, and ΔG† is the free-energy difference between the initial state and the transition state (ΔG† = ΔH† − TΔS†). With the objective of comparing theory and experiment, we use the dealumination rate measured by Ong et al.20 to arrive at an estimated ΔG† value of 246 kJ/mol for the process at 723 K. On the other hand, we consider the reaction profile discussed in the previous section, but calculated using the commonly employed ideal gas reference state31,34−38 for water. By considering the states with the largest free-energy difference (Water ads 1 and Initial 4), defining the predicted free energy of activation,39 we obtain values of ΔG† = 376 kJ/ mol, ΔH† = −81 kJ/mol, and −TΔS† = 457 kJ/mol. It is apparent that the free energy of activation is grossly overestimated by theory. This overestimation is too large to be explained by errors in DFT, leaving the question if some basic assumption of the model is wrong. Since the entropy term dominates, it is reasonable to assume that we overestimate the entropy of activation by this model. We see two reasons for such overestimation. First, Jiang et al. have argued that one should consider the physisorbed state as the reference state when investigating kinetics of reactions in porous materials.40 Water physisorbed in a zeolite pore is spatially constrained, compared to an ideal gas (Figure 2), which should lead to a reduced entropy. Hence, using the ideal gas phase water will overestimate the entropy cost of adsorbing water. Ideally, the free energy of water vapor inside the zeolite would be calculated by first-principles using a combination of DFT and molecular dynamics (MD), as Asthagiri et al. did for water in the liquid phase.41 This work

G H2O = Hideal gas + dHads − T (Sideal gas − C)

(2)

where dHads is the experimental asymptotic limit of adsorption enthalpy of water in H-ZSM-5, as a function of adsorbed water molecules43 (∼42 kJ/mol). This enthalpy correction reflects that water is physisorbed in the zeolite, assuming it to be independent of framework. We correct the gas-phase entropy using the constant C, so the final rate of dealumination calculated in the Kinetics section of this work is the same as that measured experimentally at a temperature of 723 K and a vapor pressure of 1 bar in the zeolite H-ZSM-5.20 We chose the work of Ong et al.20 for this correction, because they express the rates in easily comparable units, which is a point that should not be underestimated. We chose an investigation of H-ZSM-5, since no quantitative experimental results have been reported for H-SSZ-13. This way, we arrive at an entropy correction of C = 114 ± 11 J/(mol K). The uncertainty reflects the maximum variation in the correction when using experimental rates from refs 19 and 14, respectively, in place of ref 20. Note that eq 2 maintains the temperature dependency of the Sideal gas. This is done to approximate the temperature dependency of the entropy of the remaining translation and rotations in the corrected reference state. Figure 3 shows a diagram comparing entropy and free energy at a temperature of 723 K and a vapor pressure of 1 bar for the gas phase, our corrected reference state, and the liquid phase of water. The liquid water reference energy is calculated as G liq,H2O = Hideal gas + dH vap − TS liq

(3)

The entropy value is given as Sliq = 70 J/(mol K),44 and dHvap = 41 kJ/mol.44 Here, dHvap is the enthalpy of vaporization; note that it is vitually equal to the asymptotic adsorption enthalpy in the zeolite. As can be seen from Figure 3, the correction roughly corresponds to removing two degrees of translational freedom,

Figure 2. Sketch of water in three different states. Gas phase (shown in green), a state where it is confined in a zeolite (shown in orange) and a state adsorbed on a Brønsted acid site (shown in purple). 7134

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corrected reference state. This will be discussed further below, in relation to the predicted kinetics of dealumination. As also seen, independent of the reference chosen, the first hydrolysis step is never rate-limiting and the corrected energy profile is between those using gas-phase and liquid-phase reference states. Kinetics. Using the free-energy profile shown in Figure 4 and the reaction steps discussed in the Reaction Pathway section, we conducted microkinetic modeling of the dealumination reaction. Doing this type of modeling, we assume that diffusion limitations of water do not influence the kinetics of the reaction. We did this using the corrected water reference and the gas-phase reference, respectively. The Computational Details section shows the elementary steps included in the model. We stress that we model the initial rate of reaction; this is done by setting the concentration of the dealuminated species to zero. Figure 5 shows the predicted rate per Al atom, at steady state, as a function of temperature and pressure. It is clear that the

Figure 3. (a) Plot of entropy and (b) free energy of water at 723 K in gas phase, the corrected reference state (eq 2), the liquid phase (eq 3), and the adsorbed state (Figure 2). For the gas-phase reference, the entropy is divided in translational (Trans), rotational (Rot), and vibrational (not labeled due to the small value) contributions. For the free energy, zero is defined by the enthalpy of gas-phase water.

compared to the gas phase, which intuitively makes sense when thinking of motion along a zeolite pore. It is also seen that water adsorbs spontaneously using the corrected reference state, while it is endergonic using the gas-phase reference state. This is also evident in Figure 4, which shows the free-energy

Figure 5. Plot of the logarithm of the rate of dealumination as a function of temperature and pressure, using (a) the corrected water reference and (b) the gas-phase reference.

absolute rate is strongly influenced by the choice of water reference state. By construction, the correction ensures that the calculated rates are closer to experimental values. More importantly, using the corrected reference results in an intuitively pleasing picture, where the dealumination rate increases with temperature and pressure. On the other hand, using the gas-phase water reference causes a constant or even, at some pressures, declining rate as a function of temperature for temperatures above 600 K. We stress that the only difference between the two models is the reference state of water. Having derived the rate of dealumination, we now turn to investigate the species along the reaction pathway that determine the rate. Initially, we will simply consider the relative free energies of the transition states, before moving on to an analysis using the degree of rate control. It turns out that, at a temperature of 723 K, transition states TS 2, TS 3, and TS 4 are within 5 kJ/mol of each other, in terms of free energy. This is too close to conclude which one is rate-determining within the error of DFT. On the other hand, the free energy of TS 1 can be increased by as much as 63 kJ/ mol, before the rate of dealumination is altered by more than 1%. In other words, even a barrier of 112 + 63 = 175 kJ/mol will not make the first hydrolysis step rate-determining. Such a high barrier is unlikely, considering that the work of Silaghi et al.17 reported intrinsic energy barriers of 76−120 kJ/mol for the first hydrolysis step in a series of zeolite frameworks. Conversely, it seems highly unlikely that the free energies of TS 2−4 could be as low as to reduce the free energy of activation by 63 kJ/mol (to make TS 1 rate-determining), as it

Figure 4. Free-energy profiles at a temperature of 723 K and a vapor pressure of 1 bar. Profiles are shown for three different water references (gas, corrected, and liquid), depicted in Figure 3 and described by eqs 2 and 3. See the Computational Details section for a discussion of the red dealuminated state.

profiles of the dealumination reaction for the three different water reference states. By considering the profile calculated with the gas-phase reference state, it is clear that even if one excludes the activation barriers for the individual hydrolysis steps, the predicted free energy of activation still grossly overestimates the experimental value derived above. In other words, using the gas-phase reference, the free-energy barrier of the hydrolysis sequence is mainly determined by the freeenergy penalty associated with adsorption of four water molecules. Therefore, we find it likely that this free-energy penalty is overestimated. As discussed above, we correct this overestimation by considering water in the physisorbed reference state (eq 2). Note that, since the correction is defined per water molecule, the later transition states in the hydrolysis sequence are stabilized more than the earlier. As a result, TS 2−4 have almost equal free energy when using the 7135

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Figure 6. Dealumination reaction order in vapor pressure as contour lines and the step with the highest degree of rate control by colors, shown as a function of temperature and pressure, using (a) the corrected new water reference and (b) the gas-phase reference.

two when TS 4 begins to be rate-limiting, and toward three where TS 4 is completely rate-determining. Using the gas-phase reference in Figure 6b, it is only at very low temperatures that TS 4 is not completely dominant. The reaction order goes toward four instead of three, because water does not adsorb at high temperatures with this reference. Hence, the difference between the initial and rate-limiting state is indeed four adsorbed water molecules. We stress that the model cannot be trusted to exact values, but believe that trends are meaningful. Hence, moving from low to higher temperatures, the free energy of the later hydrolysis steps will increase due to a larger entropy cost of adsorbing water. This causes the reaction order to increase with temperature. In the present model of H-SSZ-13, the last hydrolysis step will be rate-determining above 700 K, and the reaction order will be approximately three (Figure 6a). If a favorable initial state with two water molecules is found, the reaction order would, however, decrease to two. Comparison to Experimental Work. We are now in a position to compare the predictions of the models to available experimental results in order to identify which reference state produces the best agreement. Since no quantitative kinetic measurements of H-SSZ-13 exist, we compare to experiments on the dealumination of H-ZSM-5. In addition to comparing the measured rates to the modeled rates, the apparent activation energy and reaction order, with regard to vapor pressure, will also be compared. Since we have assumed that diffusion limitations are insignificant, we will not go into detail about the flow rate of steam in the experiments. Before comparing, we would like to estimate how the rate is affected by changes in the potential energy profile of the reaction. Such sensitivity analysis is of particular importance when trying to extract aspects that are independent of the exact dealumination pathway and maybe even of the zeolite framework. This way, we seek to show that our results would not change significantly if we had considered another of the 384 possible pathways. In H-SSZ-13, the T-site is in a position that is accessible to a water molecule from many angles, whereas, in H-ZSM-5, some of the 12 T-sites are far less accessible. This could potentially increase the barriers of especially the first hydrolysis steps, since these states could be highly restricted by the framework. Silaghi et al. obtained barriers for the first hydrolysis, varying by 44 kJ/mol among a range of frameworks and T-sites,17 so an uncertainty of ±20 kJ/mol seems just. Thus, when comparing our model of H-SSZ-13 to results on HZSM-5, error bars were produced by the maximum and minimum rate given by the following procedure: varying the

would correspond to an increase in dealumination rate by 4−5 orders of magnitude. Hence, it seems unlikely that the first hydrolysis can be rate-determining for the dealumination of common zeolite frameworks. It is instructive to consider how the reaction order reflects which hydrolysis step is rate-determining: this is derived based on the data in Figure 5 and shown in Figure 6. The ratedetermining species are conveniently identified using the degree of rate control.39,45−48 It is defined as

Xi =

1 ∂r r ∂ Gi kT

(4)

where Xi is the degree of rate control for the ith intermediate or transition state, r is the turnover frequency of a given species, and Gi is the free energy of the ith intermediate. It is not always possible to define a single rate-determining step, but, for the sake of simplicity, the species having the highest degree of rate control is depicted as being rate-determining. As the vapor pressure decreases or increases, the free energy of activation for the reaction will change. Assuming an ideal gas, the change in the free energy of activation ΔG† when going from pressure p1 to p2 can be expressed by ⎛p ⎞ Δ p → p (ΔG†) = Δn H2ORT ln⎜⎜ 2 ⎟⎟ 1 2 ⎝ p1 ⎠

where ΔnH2O is the difference in the number of adsorbed water molecules from the lowest energy state to the rate-limiting transition state. Because ΔnH2O enters directly in this difference, the reaction order can be linked to the difference in number of water molecules between the initial (lowest free energy) state and the rate-limiting transition state. In our model, the most stable initial state has one water molecule adsorbed at the Brønsted acid site and we have not found states favoring the adsorption of additional water molecules. As seen on Figure 6a, using the corrected reference, at low temperatures and pressures, the reaction order is close to one, where the rate-limiting step is TS 2. Indeed, there is one additional molecule adsorbed in TS 2, compared to the initial state. Approaching the region where TS 3 begins to be ratelimiting, the reaction order increases to two, as TS 3 has one more water molecule adsorbed than TS 2. Note that, in this region, the three transition states are almost iso-energetic, and the rate control is divided between all three steps, with TS 3 exhibiting the largest value. The reaction order increases above 7136

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Research Article

ACS Catalysis free energy of a transition state by ±20 kJ/mol, then recalculating the reference entropy of water, according to eq 2; thus, the rate at 723 K and 1 bar again matches the rate of Ong et al.20 All of the attempted transition states were varied, and those giving maximum and minimum rates compose the error bars. We start out by comparing the modeled apparent activation energy with experimental results. Figure 7 shows the results of

As can be seen, our model underestimates the dealumination rates measured by Masuda et al.14 The data point in Figure 8a at 773 K, 1 bar, is so close to the conditions to which we have fitted the rate, that the significant discrepancy in rate must be due to differences in the materials of the studies of Ong et al.20 and Masuda et al.14 Especially since our model accounts fairly well for the temperature dependence of the rate (Figure 7), the 50 K difference should not cause a deviation of orders of magnitude. Furthermore, our model overestimates the reaction order, as we get an order of 3.2 and the reported experimental reaction order here is 1.5. Here, the model using the gas-phase reference is not included, since it is already established that it would result in an even higher reaction order than using the corrected reference. Figure 8b compares our model to the results of Sano et al.,19 showing better agreement than in Figure 8a. The reaction order of the model (3.4) is again above the experimentally reported one (1.5−2). We note that the data from Sano et al.19 match well with the data of Ong et al.,20 while the data from Masuda et al.14 are somewhat different. As previously explained, the reaction order can, in a simple picture, be seen as a measure of the difference in number of water molecules adsorbed in the initial state before the reaction and the rate-limiting step. Hence, we attribute the overestimated reaction order in our model to one of the following explanations. First, we model H-SSZ-13, which could be sufficiently different from H-ZSM-5, that the second or third hydrolysis steps are rate-limiting in the latter but not in the former. Second, there could exist an initial state with more than one water molecule adsorbed and, thus, a reaction pathway with more water molecules adsorbed in the first hydrolysis steps. Both would decrease the difference in water molecules between the initial and rate-limiting transition state, decreasing the reaction order. However, as we have seen in Figure 7, a late rate-determining step results in a significant reduction in the activation energy. Hence, we find it most likely that the second and/or third hydrolysis steps are rate-determining in the dealumination of H-ZSM-5 under the experimental conditions. Finally, as a consequence of using physisorbed water as the reference state, we assume that the loading of water inside the zeolite is dependent linearly on the partial pressure of water outside the zeolite. Clearly, a sublinear dependence will reduce the predicted reaction order. At this stage, we conclude that using the corrected reference state for water gives far better results than using the conventional gas phase as reference. The reaction order

Figure 7. Dealumination rate at a vapor pressure of 0.05 bar (as employed by Sano et al.19). The derived apparent Arrhenius activation energies are shown in the plot. The results from the model using the gas-phase reference have been multiplied by a factor of 1012 for easier comparison of the temperature dependency. Error bars were derived on the basis of potential energies, as described in the text. The experimental data are extracted from Figure 3 in the work of Sano et al.19 The details of how we have obtained the rate from the experimental data can be seen in section S2 in the Supporting Information.

our model, compared to those of Sano et al.19 As can be seen, the apparent activation energy obtained from the model using the corrected water reference (124 kJ/mol) matches quite well with that obtained experimentally (105 kJ/mol). In contrast, the model with the ideal gas-phase water reference derives a negative apparent activation energy (−66 kJ/mol). Moving to the reaction order, Figure 8 shows a comparison of the experimental and modeled results. The method for calculating error bars causes small errors close to the conditions that have been fitted. Conversely, if these variations change the reaction order, e.g., by moving up an early transition state to be rate-limiting, a significant difference will be observed at pressures far from 1 bar. This is the case in Figure 8a, as an increase in free energy of TS 2 decreases the reaction order, producing a significant error bar at low pressures.

Figure 8. Dealumination rate of our model compared to the experimental rate from (a) Masuda et al.14 at 773 K and (b) three differently synthesized H-ZSM-5 samples from Sano et al.19 at 873 K. The derived reaction orders are indicated next to the fitted lines. Error bars were derived on the basis of potential energies, as described in the text. Section S2 in the Supporting Information details how the results were extracted from the paper by Sano et al.19 7137

DOI: 10.1021/acscatal.5b01496 ACS Catal. 2015, 5, 7131−7139

Research Article

ACS Catalysis comes closer to that obserevd via experiment, and the temperature dependence is in satisfactory agreement with the experiment. We also note that a model employing a reference state with only corrected entropy and an uncorrected enthalpy resulted in poor agreement with experimental results (see section S3 in the Supporting Information). This adds confidence to employing the physisorbed state, where both enthalpy and entropy is corrected (eq 2), as the reference state. Altogether, the results of this paper strongly suggest that water is physisorbed inside the zeolite in the reference state relevant for dealumination kinetics. When considering the dealumination that happens during regeneration of a zeolite catalyst, the fact that water is formed within the zeolite further justifies the use of physisorbed water in the zeolite as the reference state.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +45 22754776. E-mail: [email protected] (H. Falsig). *Tel.: +47 22855454. E-mail: [email protected] (S. Svelle).

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Notes

CONCLUSION In this work, we have modeled the dealumination of zeolite HSSZ-13 by water vapor. A special focus has been put on the kinetics of the reaction, because little research in this area exists. The reference state of water is a key issue to address, since the adsorption of an ideal gas-phase water molecule in a zeolite causes an unrealistically high loss of entropy. We employed an empirically corrected reference free energy, simulating water in the state of steam inside the zeolite pores. In this state, water has lost entropy, corresponding to two translational degrees of freedom, compared to the ideal gas reference used conventionally. Using the corrected reference state, we obtain significantly improved agreement with experimental kinetics measured in H-ZSM-5. Current efforts go into improving this empirical approach by a more accurate first-principles description of the state of water inside the zeolite. The model predicts that hydrolysis of the first bond does not affect the rate of dealumination in H-SSZ-13, nor is it likely to do so in any other zeolite. The rate-limiting step will move toward the final hydrolysis with increasing temperature; in HSSZ-13, it becomes the rate-determining step above ∼700 K and 1 bar. These insights can simplify the calculation of rates in other frameworks, since not being required to investigate the first barrier in detail greatly decreases the number of possible pathways. Since it is only necessary to consider the initial and final states of the first hydrolysis step, not the mechanism and transition state, the number of possible pathways is decreased by at least a factor of 2 (as we have investigated two mechanisms). Furthermore, it saves the effort of locating the transition states, which is much more computationally demanding than locating intermediates. At high temperatures and low pressures, there is a good possibility that considering only the fourth hydrolysis in the model will give the right reaction rate, since this step will move toward becoming ratedetermining. The microkinetic model can be used to predict the dealumination rate at other pressures or temperatures than already tested, but for a more-thorough validation of the model, the dealumination rate of H-SSZ-13 would need to be quantified experimentally. Finally, it is highly desirable to experimentally measure dealumination on several different zeolites, to address differences between frameworks.

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XYZ files, vibrational frequencies, and potential energies for all species in the reaction and a script solving the microkinetic model (ZIP) A more thorough description of the reaction pathway modeled; details of the extraction of data from articles; and a comparison of the reference used here and one that is corrected only on the entropy (PDF)

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was received via the European Industrial Doctorates project “ZeoMorph” (Grant Agreement No. 606965), part of the Marie Curie actions (No. FP7-PEOPLE2013-ITN-EID). The authors thank the Norwegian High Performance Computing program for a generous grant of computing resources, under Project No. nn4683k, and the staff at the USIT center for support. The authors thank Ms. Ingelin Pedersen Olsbye for the drawing of Figure 2.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.5b01496. 7138

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