Developing a Thermodynamic Model for the Interactions between

Article pubs.acs.org/JPCC

Developing a Thermodynamic Model for the Interactions between Water and Cu in the Zeolite SSZ-13 Florian Göltl,*,† Alyssa M. Love,† and Ive Hermans*,†,‡ †

Department of Chemistry, University of WisconsinMadison, University Avenue 1101, 53706 Madison, Wisconsin United States Department of Chemical and Biological Engineering, University of WisconsinMadison, 1415 Engineering Drive, 53706 Madison, Wisconsin United States

‡

S Supporting Information *

ABSTRACT: The Cu-exchanged zeolite SSZ-13 is an efficient catalyst in the selective catalytic reduction of nitrous oxides in the presence of ammonia, and understanding the nature of the active sites under realistic conditions is important in rationalizing its activity. Especially the interactions between Cu and water have drawn significant amounts of attention in recent years. In this work we develop a thermodynamic model for the water coordination of Cu based on static calculations and present occupational probabilities and phase diagrams for different Al distributions at different temperatures and water pressures. We find that only at high temperatures and low pressures is the bare Cu cation the most stable species and that the cation is solvated at lower temperatures and higher pressures. In the following we compare our results to experimental and theoretical work in this field and find good agreement. This work shows that it is possible to construct an accurate thermodynamic model for water interactions with Cu in zeolites and it will be interesting to see how a similar methodology can be applied to elucidate different problems in the future.

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INTRODUCTION

However, these measurements were performed for materials pretreated under vacuum at elevated temperatures. McEwen et al. realized that, as soon as ambient conditions were encountered, water would bind to Cu and change the coordination of these sites significantly10 and over time more and more evidence was found that, at low temperatures and typical water pressures, the Cu cation is fully solvated and does not form bonds with framework oxygen atoms.19−25 However, the coordination of the ions would change when the temperature was increased until, eventually, all water would desorb.21,25 These findings were supported by a theoretical, force-field based study by Psofogiannakis et al.26 and a very detailed, combined experimental and theoretical study by Paolucci et al.,20 which both use molecular dynamics to model the interactions between water and Cu at various temperatures. Despite our improved understanding of the process of hydration of Cu in SSZ-13 provided by the studies mentioned above, some questions still remain open. Up until today it is not clear in what way the distribution of Al influences the hydration process and whether it is connected to the preferential occupation of the different sites in the material. Also the requirements for the formation of six-ring Cu or eight-ring Cu− OH species have not been addressed in detail. Finally, a

NOx are environmental pollutants that are byproducts in the combustion of gasoline. These emissions are strictly regulated, and their removal is one of the major challenges of automotive exhaust aftertreatment systems, especially for lean-burn diesel engines, where the removal has to take place in an oxidative environment.1 A system with particular promise as a catalyst for this application is Cu-exchanged SSZ-13. This zeolite shows high activity in the selective catalytic reduction of NOx in the presence of NH3, which is paired with high stability over a wide temperature range.2−5 After being patented in 2008,6 it is already applied in several diesel trucks today. Due to these favorable properties this system has been studied intensively over the last years and one of the questions, which attracted much attention, was the nature of the active sites. In this system, Cu can exist as either CuI or CuII.2,7−13 For CuII, two different coordination environments, one as single Cu atom in the six-ring and one as Cu−OH in the eight-ring of the framework, were identified.2,8,14,15 The presence of these sites was furthermore linked to the distribution of Al atoms,16 which activate the framework and are associated with a negative charge of one. At low Si/Al ratios, where many Al pairs in sixrings exist, Cu in the six-ring is supposed to be dominant, whereas in materials with high Si/Al ratios, where distances between two Al atoms are large, Cu−OH should be preferred.14,16−18 © 2017 American Chemical Society

Received: January 9, 2017 Revised: February 21, 2017 Published: February 28, 2017 6160

DOI: 10.1021/acs.jpcc.7b00254 J. Phys. Chem. C 2017, 121, 6160−6169

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The Journal of Physical Chemistry C

ring of the structure,16 while also a CuII position in the eightring is reported, which is typically associated with a CuII−OH site.14,20 Following this concept, we optimize the positions of CuII in the six-ring and eight-ring for all 2 Al configurations. In consecutive steps we bind up to six water molecules to CuII. In agreement with the reports of CuII−OH in the literature, we allow water to split for all configurations in the eight-ring, which leads to five different scenarios, four of which include a CuII−OH group and a proton binding to an activated O atom, and one with adsorbed water. For the configuration with one Al atom in the unit cell, we focus on an OH group and bind up to five additional water molecules to it. In a consecutive step we calculate the temperature dependent Gibbs free energies at finite temperature G(T) of the optimized molecular and zeolite structures by performing a full vibrational analysis and correcting energies from static structure optimization by zero-point vibrational corrections and the vibrational and translational contributions to the entropy. To obtain the stabilization of the different hydration states, we use

connection between a thermodynamic model based on most commonly used, static density functional theory calculations and molecular dynamics based calculations, has not been established. In this work we derive such a thermodynamic model based on static density functional theory calculations for the interactions between water and Cu atoms in SSZ-13. In a first step we define the input parameters for our model, followed by discussing the structures and occupations of different sites for a large temperatures and pressure window. We furthermore show that our model is successful in reproducing trends previously published in the literature. Finally, we compare our results to experimental measurements and show how our data can be used to calculate temperature and water pressure dependent IR spectra.

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THE SYSTEM AND THEORETICAL METHODS SSZ-13 is a zeolite in the chabazite structure. The unit cell of the purely siliceous form contains 12 SiO4 tetrahedra (T-sites), which are linked by the O atoms and form a double six-ring structure (Figure 1). When the unit cells are connected, a

Cu Cu + zeo + nH 2O ΔGCu (T ) − G2H + zeo + nH2O(T ,p) = G

− (n − 1)μH2O(T ,p) −

1 O2 μ (T ,0.2) 2

(1)

II

for Cu sites in two-Al configurations and Cu Cu − OH + zeo + nH 2O ΔGCuOH (T ) − GH + zeo + nH 2O(T ,p) = G

− nμH2O(T ,p) −

1 O2 μ (T ,0.2) 2

(2)

for CuII−OH site in the one-Al configuration. In these equations the superscript G denotes the studied structures and μ is the temperature and pressure dependent chemical potential of the respective molecules in the gas phase. Furthermore, the term “zeo” refers to the zeolite structure for the given Al distribution. While we leave the water pressure p as a variable, we keep the oxygen pressure fixed. Finally we use the calculated ΔG(T,p) values to construct a thermodynamic model of hydration. In a first step it is possible to calculate occupational probabilities for each Al configuration as

Figure 1. Primitive unit cell of SSZ-13 (left) and schematics of the six different possibilities to distribute two or one Al atoms in the unit cell (right). In the ball and stick model, Si atoms are displayed in yellow and O atoms are displayed in red. In the schematic representation a line corresponds to Si−O−Si and red dots mark Al positions.

Cu

P

medium-sized pore is formed, which is connected to its neighboring pores by eight-rings.11 The framework is activated by substituting Si T-sites by Al T-sites, where Al has one less valence electron, which in turn leads to a negative charge of one electron. Even though all T-sites in the chabazite structure are symmetrically equivalent, understanding the position of Al in the material is still challenging. At realistic Si/Al ratios, which are very often below 11, more than one Al atom will be present in the unit cell. In previous work, some of us have pointed out the similarities between the positioning of Al in zeolites and the presence of defects in solids.16−18 Therefore, a distribution of local Al configurations will be present. In this work we will therefore focus on all six possibilities to distribute one and two Al atoms in one unit cell, which are displayed in Figure 1.18 The charge introduced by the Al atoms has to be compensated for by positive charge at a cation. In this study we focus on CuII, which can compensate for the presence of either two Al atoms in one unit cell or, when present as CuII− OH, one Al atom in the unit cell.18,20 In the literature it was shown that the bare CuII cation is most likely located in the six-

e−ΔG X +nH2O(T , p)/ kBT (T ,p) = Z

X + n H 2O

(3)

with Z=

∑ X = Cu,CuOH

∑ e−ΔG n

Cu X + nH2O(T , p)/ kBT

(4)

Although this procedure allows insights about the hydration process for each separate Al configuration, in a realistic zeolite, several Al configurations exist and will be accessible, as long as a certain mobility of the cations is assumed. It is therefore also possible to calculate the occupational probabilities for a situation where more than one Al configuration is present, by simply adding an additional summation in eq 4 over the considered Al configurations.

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RESULTS Structures. In this work we study 14 different structures for the five two-Al configurations and 6 structures for the one-Al configuration and we find that in most of them the structural changes upon hydration follow a similar trend. To keep the 6161


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The Journal of Physical Chemistry C discussion tractable, we will only discuss the hydration for one of the typical two-Al configurations (2Al-C,; the structures are displayed in Figure 2) in detail and explicitly mention the deviations in behavior for the other configurations in the following. Additionally, we believe that displaying and

discussing all bond lengths and energies for all structures would be excessive and we provide relative stabilities and the structural files of all calculated configurations in the Supporting Information sections S1 and S2. As already discussed in detail previously, the Cu atom is initially 4-fold coordinated close to the center of the six-ring, leading to a slight strain in the six-ring. When a water molecule is added, it inserts itself into one of the Cu−O bonds. This allows Cu to move closer to the Al atom and form three bonds to framework O atoms. At the same time the water molecule forms a hydrogen bond to the O atom Cu was bonded to previously. When another H2O is added, it binds on top of Cu, leading to an almost 4-fold-planar coordination of Cu with two water molecules and two framework O atoms and a fifth bond to a framework-O perpendicular to this plane. The added water molecule forms a hydrogen bond with an activated O atom (an O atom next to Al). When a third H2O molecule is added, another bond between Cu and framework-O is broken and additional hydrogen bonds between water and framework-O atoms are formed. For four water molecules, all bonds between Cu and the framework are broken and the Cu atom shows a square-planar coordination with four water molecules. This complex is stabilized by hydrogen bonds over the six-ring of the structure. Interestingly, the fifth water molecule does not bind directly to the Cu atom but forms a hydrogen bond to one of the other water molecules and the framework and only the sixth water molecule binds directly to the Cu atom again. In the eight-ring, Cu initially forms two bonds with activated framework O atoms. When now adding an H2O molecule, we find that adsorbing it to Cu is energetically significantly preferred over splitting it into a Cu−OH complex and an H added to one of the activated O atoms. This trend holds true for all eight-ring structures. Similar to the six-ring case, the first adsorbed water forms two hydrogen bonds to the activated O atoms on the other side of the eight-ring. When a second water molecule is added, Cu is again square-planarly coordinated to two water molecules and two activated framework O atoms. The two water molecules form hydrogen bonds to either one or two framework O atoms. When a third water molecule is added, it again binds directly to the Cu and a full square-planar coordination of Cu with water molecules is encountered as soon as a fourth water molecule is added. However, hydrogen bonds stabilize this Cu−H2O complex in a different position than for the six-ring configuration. The fifth water molecule binds directly to Cu, whereas the sixth water molecule is hydrogen bonded to another H2O and water. The general trends for all the other structures are fairly similar. The main differences are that for 2Al-A the splitting of water into Cu−OH and H is preferred for the adsorption of one water molecule, a situation that is also encountered for 1AlF, where the formation of H2O is not possible by construction. Generally speaking, Cu tends to form a square-planar coordination, with either framework or water bonds. At the same time, water binds to Cu via the O atom and tries to establish hydrogen bonds to preferentially activated O atoms. When a fifth and sixth water molecule is added, the interactions between Cu and water seem to be weakened and water can either take its position in an octahedral coordination or form a hydrogen-bond network with other water molecules and the framework. In the case of 1Al-F, one of the square-planar positions is taken by an OH group instead of water. Although for up to three water molecules Cu still binds to the framework, this bond is lost for four or more molecules. It is therefore not

Figure 2. Optimized structures for the adsorption of up to six H2O molecules to Cu centers in SSZ-13 with the 2Al-C Al configuration. The left-hand column displays structures where Cu is initially bonded in the six-ringl the right-hand column displays structures where Cu is initially located in the eight-ring of the structure. The green dot represents the number of H2O molecules adsorbed to the structure. We find that Cu gets more and more solvated with increased amounts of water and loses its direct bonds to the framework. Si atoms are displayed in yellow, O atoms are displayed in red, Cu in blue, and Al in blue-gray and H in white. 6162


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Figure 3. Occupation statistics for different water coordinations of Cu in Al configuration 2Al-C between 300 and 800 K and partial water pressures between e−10 and 1 atm. The corresponding structures are displayed in Figure 2. We see that several water coordinations show high occupancies for the given temperature range, but we also find sites that show very low probabilities. This indicates the possibility of the occupation of several Cu hydration states and locations at a given temperature and pressure. Dark blue corresponds to an occupation of 0; red, to an occupation of 1.

energy and highest occupational probability, at a given water pressure and temperature, is displayed. We can immediately see that the trends observed for 2Al-C hold for the other 2Al sites as well. In all configurations with 2Al in the unit cell, Cu in the six-ring is preferred at high temperatures and low pressures. However, the domain size varies dramatically. It is largest for 2Al-A and smallest for 2Al-B and 2Al-E with 2Al-C and 2Al-D in between. When temperature is reduced and pressure increased, in most of the cases Cu is coordinated with one water molecule. It can be located in either the six-ring (2Al-B and 2Al-C) or the eight-ring (2Al-D and 2Al-E). Configurations 2Al-A, 2Al-B, and 2Al-C also show occurrences of Cu coordinated to two water molecules in either the six-ring (2Al-A) or eight-ring (2Al-B and 2Al-C). Only 2Al-E shows also the presence of three water-coordinated Cu in the six-ring. Interestingly, the sum of the total areas of the phase diagrams for these nonsolvated Cu species are fairly similar in size and the phase boundaries only vary by about 50 K. At lower temperatures, Cu is solvated with most often five or six water molecules bonded to it. For 1Al-F we only find two possible occupations, one being Cu−OH without water and the second Cu−OH with five water molecules. So far, each local Al configuration was treated separately. However, a realistic material consists of unit cells with different local Al distributions and Cu will be able to diffuse between them. To take this into account, we now couple the different Al configurations, by summing over all of them in eq 4 and use eq

possible anymore to speak of Cu with respect to the ring structure. In the following, we will just call it Cu(H2O)x. Occupational Probabilities, Phase Diagrams, and Encountered Cu Sites. In a next step we address the hydration state of Cu under different conditions, using eq 3 for a temperature window of 300−800 K and partial water pressures between e−10 and 1 atm. We again focus on Al configuration 2Al-C and all the different occupational diagrams are displayed in Figure 3. As expected, we find Cu located in the six-ring and no water molecules bonded to it at high temperatures and low pressures and a fully hydrated Cu(H2O)6 complex at high water pressures and low temperatures. However, in the region in between, we find different coordinations, mainly Cu in the eight-ring coordinated to two or five water molecules and also, in far smaller temperature and pressure windows, Cu in the six-ring with one H2O and in the eight-ring with four water molecules. We also find regions where sites only show a very small occupation for Cu in the eight-ring with one adsorbed water molecule, or Cu in the sixring with three adsorbed water molecules. These data actually indicate that there is a high chance that for large regions of the investigated pressure and temperature space, more than one coordination state of Cu is present. Though such a detailed analysis is highly informative as a proof of concept, it is not very easily accessible. Therefore, we also present phase diagrams for all the studied Al configurations in Figure 4. Here, only the Cu coordination with the lowest 6163


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Figure 4. Phase diagrams for the six different Al configurations for temperatures between 300 and 800 K and partial water pressures between e−10 and 1 atm. For all six Al configurations we find Cu in the least hydrated state for high temperatures and low water pressures and solvated at low temperatures and high water pressures. However, the regions in the phase diagram vary in size and between them the number of water molecules per unit cell varies dramatically with the given Al distribution.

3 to calculate occupational probabilities. In subsequent steps we then reduce the number of allowed Al configurations to imitate their full occupancy. The corresponding phase diagrams are displayed in Figure 5. We find that, as long as all Al configurations are available, mainly Cu in the 2Al-A configuration, either without adsorbed water or with five water molecules in the unit cell, is available. However, in a rather narrow temperature range of 50−100 K, Cu in 2Al-B coordinated to one or two water molecules is preferred. A similar trend is observed, when Cu in the 2Al-A configuration is removed. Now Cu in the 2Al-D configuration is dominant at the extremes (i.e., high temperature, low water pressure or low temperature, high water pressure) and Cu 2Al-B is dominant in the intermediate regions, which are significantly extended. We also find an entropically driven change between nonhydrated Cu in 2Al-D and 2Al-B. When either the 2Al-B or 2Al-D configuration is now eliminated, the phase diagram switches to

Cu atoms in the other one, with one significant difference being a region of Cu in the eight-ring coordinated to two water molecules in 2Al-C, when 2Al-B is not allowed. When both of them are removed, Cu only occupies 2Al-C configurations, and when 2Al-C is also removed, it goes to the 2Al-E configuration, indicating that CuOH in the 1Al-F configuration is least stable at any time.

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DISCUSSION

The results obtained in this work clearly show that the Al distribution influences the number of water molecules in the unit cell and the water coordination of Cu at different water pressures and temperatures. On a qualitative level, the results obtained in this work clearly indicate that Cu prefers squareplanar water coordination and additional water molecules can either bind to this complex to complete an octahedral coordination or optimize energies by forming a hydrogen6164


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Figure 5. Phase diagrams for the six different Al configurations for temperatures between 300 and 800 K and partial water pressures between e−10 and 1 atm. The green X denotes the Al distributions that were not considered.

less stable than Cu(H2O)5 for 2Al-A at all conditions in our model. Such differences are expected, because we did not include the structures in our model (CuOH(H2O)6), they occupy only a very small temperature window (CuOHH2O), or they can access a large multitude of local configurations (Cu(H2O)6 in 2Al-A), where single water molecules possibly shift between being hydrogen bonded and interacting with Cu, a situation that cannot be captured by our simplified model. Furthermore, we find Cu(H2O)2 more stable than CuH2O for 2Al-A. Quantitatively, we find significant differences. For 1Al− F, our model gives a transition temperature between solvated and nonsolvated Cu around 450 K, whereas the model of Paolucci et al. leads to about 400 K. For 2Al-A, this phenomenon is even more pronounced, because we find a far narrower window of about 500−550 K for the Cu(H2O)2 configuration compared to 450−650 K for Cu(H2O) by Paolucci. The higher solvation temperature in our model indicates that the harmonic approximation underestimates the

bond network between the Cu(H2O)4 complex and the framework. A similar study has been performed by Paolucci et al. using molecular dynamics simulations to calculate entropic contributions for two of the studied Al distributions (2Al-A, 1Al-F).20 That way they were able to capture the mobility of the Cu(H2O)n complexes, which has already been highlighted by Psofogiannakis et al. using force fields.26 Our approach neglects this physically correct diffusional behavior and calculates entropies solely based on harmonic vibrational contributions. This way we can still keep the ab initio description of the chemical interactions between Cu and water and they are computationally more efficient, which allows for studying a larger variety of different Al configurations. Comparing the phase diagrams obtained in this work (Figure 4) to those obtained by Paolucci et al.20 at a water pressure of 0.02 atm reveals qualitative differences in occupation of Cu− water coordinations at low temperatures. We do not find CuOH(H2O)6 or CuOHH2O for 1Al-F and also Cu(H2O)6 is 6165


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Figure 6. Phase diagrams for 2Al-C using three different methods. We compare a hybrid functional with van der Waals corrections (HSE-TS, the method used for the majority of this work) to a GGA functional with van der Waals corrections (PBE-TS) and hybrid functional calculations without van der Waals corrections (HSE). While HSE-TS and PBE-TS show qualitatively rather similar results, HSE leads to large differences.

experiment. Furthermore, Kwak et al. performed DRIFTS studies of Cu-exchanged SSZ-13 when heating it from room temperature to 400 °C and found two spectral features at around 940 and 900 cm−1 that appeared and disappeared in the given temperature range.21,25 An adapted version of this data is displayed on top of Figure 7. To match this behavior, we calculated the temperature dependent IR spectrum of our sites using the occupational probabilities and the corresponding results are displayed in Figure 7. Indeed, we find the appearance and disappearance of signals in the given range. Due to the complexity of the experimental spectra and the different Al configurations present, it is difficult to arrive at an unambiguous assignment, but it seems as if our calculated wavenumbers underestimate the experimental values by about 15 cm−1, leading to signals around 890 and 925 cm−1. The two features correspond to Cu in the eight-ring (890 and 925 cm−1) with one H2O adsorbed, and the vibrations are a complex superposition of framework and water vibrations. Especially 1Al-F shows the appearance and disappearance of a spectral feature at 925 cm−1 around 400 K, which shows an excellent fit with the appearance and disappearance of a peak at 945 cm−1 at 375 K in the experiment. The appearance of a peak around 890 cm−1 for 2Al-B around 450 K can furthermore be associated with the appearance of a similar peak around 423 K in experiment. A clear assignment of different features in experimental measurements is difficult, because at higher temperatures more Al configurations start to contribute to the different signals. However, assuming the given assignments are correct, we find a slight overestimation of the transition temperatures compared to the experiment. Keeping the fundamental limitations of our approach in mind, this indicates that HSE-TS is a reasonable approach for studying the interactions between water and Cu cations in SSZ-13. Another point of interest are the implications of this work on our understanding of the Cu distribution in the materials and also how this can influence our understanding of the zeolite substrate. In the past, some of us have advocated that, similar to defects in other solids, Al atoms have a certain distribution in the material.16−18,20,23,36,37 This distribution most likely has a random element to it and it might not be possible to describe it in a fully periodic model of any size. To simplify the problem, it was furthermore assumed that the local Al distribution could be imitated by taking a set of primitive unit cells with a different local Al distribution.16−18 Although this work is still built on this assumption, it starts to reach its limitations, because

entropy contributions for the fully hydrated species, which is a reasonable assumption due to the high mobility of the solvated complexes. In a certain way the situation is reminiscent of short alkanes in zeolites, which are also highly mobile,27,28 and significant effort has to be made to adapt entropy calculations on the basis of vibrational frequencies to arrive at accurate values.29 All the studies discussed above are based on a fairly similar level of electronic structure theory. However, discussion in the literature indicates that the bonding between small molecules and Cu shows a large dependence on the used functional.30 Two aspects have been highlighted in the literature: (i) the bond strength of CO and NO is vastly overestimated by using density functionals in the generalized gradient approximation30 and (ii) van der Waals interactions are key contributions to the total adsorption strengths for alkanes in protonated zeolites.31 To test for the impact of these two aspects, we compared our calculations at van der Waals corrected hybrid functional level (HSE-TS)32−34 to van der Waals corrected PBE calculations (PBE-TS)32,35 and hybrid functional calculations without the inclusion of van der Waals interactions and the results are displayed in Figure 6. Though phase boundaries are slightly shifted between PBE-TS and HSE-TS, they are qualitatively very similar. The major difference is that for PBE-TS the eightring site for one adsorbed water molecule is preferred over the six-ring-site, whereas this is reversed for HSE-TS. When vdW interactions are omitted, the phase diagrams remain qualitatively similar. However, the transitions between Cu species with different hydration shells are shifted to about 100 K lower temperatures, which is a clear indication of an expected weaker binding of water in the zeolite using this method. These differences between the applied methods are quite concerning, and although the theoretical approaches with included van der Waals interactions capture the physics of the problem more accurately, it is not clear how well the obtained results compare with experiment. In agreement with HSE-TS, several studies confirm the presence of hydrated Cu species in zeolites under ambient conditions using XAS,13,22,23 UV− vis,19,23 vibrational spectroscopy,13,19,21,22,25 or EPR spectroscopy.13,19,24 In the following we will focus on the EPR and DRIFTS data. EPR measurements by Godiksen et al. revealed a loss of the hydration sphere of CuII at 523 K.24 We assume that, in a realistic zeolite, a distribution of Cu occupying different 2Al configurations is present, and for them we find good agreement between the solvation temperature in our model and 6166


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Figure 7. Experimental (top) and modeled waterfall IR spectra between 300 and 800 K. For the theoretical plots the inset in the top right shows the studied Al configuration, whereas the inset in the top left gives the occupational statistics for the different sites. The changes in occupation lead to changes in the IR spectra with dependence of the temperature. All calculations were performed for a partial water pressure of 0.02 atm. Experimental measurements are adapted from data originally published by Kwak et al.21

energetics and structures of Cu in the eight-ring sites show large dependence on the Al distribution, a quantity that is determined by two neighboring unit cells. Therefore, the data

presented here in connection with the eight-rings carries information about the Al distribution on a larger scale than one unit cell. Our study furthermore shows that the adsorption of 6167



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water can lead to a stabilization of CuII in the eight-ring. This site is clearly in competition with a possible Cu−OH site and probably the distribution of Al in the eight-ring will determine which site is most stable. In this context it is quite interesting to see that we found water to be more stable than OH and H for the fully solvated species as long as another Al with H was present in the unit cell. This indicates that upon solvation CuOH and H recombine as long as two Al atoms are reasonably close.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b00254. Energetic data and the full structural data for all the studied configurations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*F. Göltl. E-mail: [email protected]. *I. Hermans. E-mail: [email protected].

CONCLUSION In this contribution we develop a thermodynamic model for the interactions between water and Cu in the zeolite SSZ-13. We first analyze the structural features, calculate occupational probabilities based on the energetics and construct phase diagrams for Cu in different local Al configurations. In agreement with the literature we find that at varying temperatures and pressures, different amounts of water are adsorbed to Cu. Though it is fully solvated at low temperatures and high water pressures, the bare cation is encountered at low water pressures and high temperatures. We furthermore find a strong dependence of the amount of adsorbed water on the Al configuration in the unit cell and develop a model that shows under which conditions different Cu locations are favored. Finally, we calculate temperature dependent IR spectra for these sites, which show excellent agreement with experimental measurements. The work presented here shows how it is possible to create a thermodynamic model based on static density functional theory calculations that can arrive at accurate results. It can be applied to understand various reactions and whether similar models can be developed to understand more complex systems.

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Article

ORCID

Florian Göltl: 0000-0002-7217-0450 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Janos Szanyi (PNNL) for providing the experimental data in Figure 7,. F. Göltl, A. M. Love, and I. Hermans acknowledge financial support from the University of Wisconsin Madison and the Wisconsin Alumni Research Foundation (WARF). The authors acknowledge computational time at Phoenix Supercomputer, which is in part supported by National Science Foundation Grant CHE-0840494 and the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Project No. m2070-Zeo-genome. This research was in part performed using the computer resources and assistance of the UW-Madison Center For High Throughput Computing (CHTC) in the Department of Computer Sciences. The CHTC is supported by UW-Madison, the Advanced Computing Initiative, the Wisconsin Alumni Research Foundation, the Wisconsin Institutes for Discovery, and the National Science Foundation and is an active member of the Open Science Grid, which is supported by the National Science Foundation and the U.S. Department of Energy’s Office of Science.

COMPUTATIONAL SETUP

All calculations were performed using the Vienna Ab-Initio Simulation Package (VASP),38,39 a plane wave code using PAW pseudopotentials,40 adapted by Joubert and Kresse.41 All calculations were performed using an energy cutoff for plane waves of 420 eV and were restricted to the Γ-point. The basic unit cell parameters for periodic calculations are given in the literature11 and the volume was set to 830 Å3. As described in the main text, all structures were optimized using density functional theory in the parametrization of Perdew, Burke, and Ernzerhof35 and van der Waals interactions were introduced using the Tkatchenko−Scheffler force field.32 In a subsequent step, harmonic vibrational frequencies using the frozen phonon approach were calculated. Vibrational and translational entropies as well as zero-point vibrational corrections for gas phase molecules and zeolite unit cells were calculated using the code thermo.pl,42 a code provided by the National Institute of Standards and Technology, and only vibrational frequencies above 50 cm−1 were considered in the analysis. Following the ideas of Anggara et al.,33 total energies were then corrected by calculating total energies for the PBE-optimized structures using the HSE06 hybrid functional with van der Waals corrections.32−34 As discussed in the main text, occupational probabilities are calculated using a Boltzmann distribution and finite temperature IR spectra were calculated by adding IR spectra for the different configurations multiplied by their respective weights.

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REFERENCES

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