Feasibility of Pure Silica Zeolites - ACS Publications - American

Oct 22, 2010 - For an investigation of thermodynamic synthesis feasibility of pure silica zeolites, we applied computer simulations with two force fie...
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J. Phys. Chem. C 2010, 114, 19157–19168

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Feasibility of Pure Silica Zeolites Yuriy G. Bushuev*,† and German Sastre Instituto de Tecnologia Quimica, UPV - CSIC, AVda. de los Naranjos s/n, 46022 Valencia, Spain ReceiVed: January 18, 2010; ReVised Manuscript ReceiVed: October 6, 2010

For an investigation of thermodynamic synthesis feasibility of pure silica zeolites, we applied computer simulations with two force fields BS and SLC. The recently developed BS force field excellently fits experimental enthalpies of pure silica zeolites with respect to quartz. On the basis of calculations with the BS force field, two empirical criteria may be adopted to assess thermodynamic feasibility. First, it was found that the upper energetic limit for synthesized pure silica zeolites is ca. 16 kJ/mol SiO2 above R-quartz and, second, the density of excess energy of pure silica zeolites lies in the region where ∆E/V < 0.5 kJ/cm3. We show how total energies and van der Waals, electrostatic, and three-body interactions correlate with the molar volume and topology of frameworks. The thermodynamic feasibility was not only studied from the structural viewpoint, but also the presence of organic templates and water was considered. We select a case study and propose a possible route for the synthesis of an MSO as-made material. An organic template that provides a large energetic stabilization is proposed. It is also determined that the influence of water on the material stability depends on the positions of molecules in the MSO framework. An effect of maximum stabilization is reached when d6r and mso cages are filled by water molecules. A comparison between solid water and crystalline silica structures stimulated us to put forward a hypothesis about stabilization of zeolite frameworks by high pressure applied during the zeolite synthesis. 1. Introduction Zeolites are a wide family of crystalline materials mainly characterized by their topology and chemical composition. Topologically, they are microporous three-dimensional (3-D) four connected nets, and chemically they are mostly based on aluminosilicates with a formula of the type Mn+x/n[AlO2]-x[SiO2]y[H2O]z, where the tetrahedrally coordinated atoms (T ) Al, Si) can be substituted by elements such as, for instance, B, Ge, Ti, Fe, and many others. Cations (Mn+) can be also of many types, and they are localized inside the micropore voids. Zeolites are used in the petrochemical industry and in catalysis,1 separation, absorption, and ion exchange due to their high pore volume, thermal stability, and well-defined pore structure. Expanding the diversity of zeolite structures would be helpful to improve performance in existing applications, to explore novel functions, and to answer basic scientific questions about zeolite synthetic chemistry. Millions of hypothetical topologies of four-coordinated frameworks were proposed, but only a fraction of the mathematically generated networks would be chemically feasible.2-7 There are roughly 190 zeolite structures recognized by the International Zeolite Association (IZA).8 The problem is important as the results will assist in the design of synthetic routes that lead to novel materials. Computational methods can play a stimulatory role in the discovery of new zeolite materials. Using computational methods, it is possible to investigate and to classify3,6,7,9 the known and hypothetical materials. One of the main properties of a zeolite is the energetic stability. Experimentally, the entropy differences between different crystalline siliceous polymorphs and R-quartz are known to be small and span a narrow range.10 This means that the enthalpy term of the Gibbs free energy * E-mail: [email protected]. † Permanent address: Ivanovo State University of Chemistry and Technology, Engelsa, 7, Ivanovo, Russia.

determines the thermodynamic feasibility of the zeolite synthesis. Zeolites are thermodynamically metastable states of silica material with respect to R-quartz, and the kinetic factor plays a significant role in the conditions of a real experiment. Computations11 predict that the MFI framework structure has a regime of thermodynamic stability at low pressures and above ca. 1400 K, relative to dense phases such as quartz, but SOD, LTA, and FAU zeolites exhibit no regime of thermodynamic stability. One of the methods to synthesize zeolites is based on using structure-directing agents (SDAs).12-14 Certain bulky organic molecules or cations, occluded in channels and cavities of the frameworks, stabilize the zeolite materials and make them thermodynamically feasible at hydrothermal conditions. The SDA particles are removed during the calcination of as-made materials. We have attempted a systematic investigation of the thermodynamic properties (under SiO2 composition) of all the fourcoordinated zeolite topologies currently included in the IZA database.8 From those (hereby labeled as “all topologies”), we will pay particular attention to topologies which have been synthesized as pure silica (throughout we use “synthesized” in a general sense to include also “naturally synthesized” zeolites) which will be referred to as “pure silica zeolites” (PSZs). Most zeolites across the IZA database were synthesized as nonpure silica materials. PSZs are interesting materials because they may represent reference systems for further investigation of real zeolite materials. They are highly thermally stable, structurally diverse, chemically simple, and closely related to catalytically interesting materials.15 Four-coordinated frameworks with a tetrahedral ordering of Si atoms have internal curvature. Any distortion of the four-coordinated tetrahedral framework increases the energy and creates mechanical stress in the material, but the stressed sites of the framework have a nonrandom distribution. The knowledge of topological properties of frameworks, the building units and their combination, helps to identify

10.1021/jp107296e  2010 American Chemical Society Published on Web 10/22/2010

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stressed sites and shows the ways for stress release through substitution of Si by other elements or for additional stabilization of the structure by SDA molecules and extra chemical compounds. Hence, we will focus the present work in two parts regarding the stability of zeolite structures in relation to (i) their structure and topology, and (ii) the presence of organic SDA and water molecules occluded in the microporous cavities. We calculated the energies of all four-coordinated zeolite frameworks included in the IZA database up to date using a new BS force field recently proposed for silica materials.16-18 The BS force field showed excellent accuracy in the reproduction of experimental enthalpies of pure silica zeolites at 298 K and gave good estimations of structural parameters of the frameworks. It was shown19,20 that some topologic properties of frameworks correlate with their densities. The frameworks of lowest density are those with a maximum number of 3-rings and 4-rings. The minimum framework density increases with the size of the smallest rings in the framework. However, Zwijnenburg and Bell established that there is theoretically no lower constraint on the framework density and pore size in siliceous zeolites.21 They found many very low density and/or very large pore hypothetical materials of comparable thermodynamic stability to currently synthesized materials. One of the goals of the present investigation is to establish correlations between the thermodynamic and topological properties of frameworks for pure silica zeolites included in the IZA database. Apart from energetics of PSZ, we have also considered particular case studies of feasible structures where we try to suggest a synthesis route in fluoride media with an organic SDA, and taking into account the role of water, which was shown to be important in previous studies.18 We propose appropriate strategies to suggest SDAs and experimental conditions for the synthesis of the MSO pure silica zeolite. 2. Methodology Section The classical method of molecular mechanics (MM) was selected for the simulations of zeolite systems. Pure silica zeolites are crystals built from SiO2 units with preferably tetrahedral ordered positions of Si atoms. Several force fields have been proposed for the simulations of the silica-based materials. In the present work, we used the force field proposed in our previous studies.16-18 Our unpolarizable BS force field has three terms: electrostatic, van der Waals, and three-body interactions.

Eijel.st. )

qiqj 4πε0Rij

(1)

EijvdW ) D0,ij[(R0,ij /Rij)12 - 2(R0,ij /Rij)6]

(2)

1 3-body Eijk ) kijk(θijk - θ0,ijk)2 2

(3)

where qi are partial atomic charges, D0,ij, R0,ij, and kijk are parameters of the potentials, e0 is the dielectric permittivity of vacuum, θijk is the bond angle, and θ0,ijk is the equilibrium bond angle between i,j,k atoms (O-Si-O and Si-O-Si). For a comparison of the results, we used the Sanders-Leslie-Catlow (SLC) interatomic potential22 for the calculations of synthesized PSZs.

Flexible modification of the single point charge (SPC) model23 was used for water. For the organic SDA cation, we have used the force field by Oie et al.24 for the intramolecular SDA interactions and the Kiselev force field25 for the intermolecular SDA-zeolite interactions. All of the components of the simulated materials were flexible. The total energy in the simulations is determined from the evaluation of the appropriate energy term for every atom-atom interaction in the system. We have chosen a force field with nonbonding contributions coming from electrostatic and van der Waals interactions, employing the Ewald method for summation of the long-range Coulombic interactions, and direct summation of the short-range interactions with a cutoff distance of 12 Å. The simulations were carried out with the General Utility Lattice Program (GULP).26 The simulation cells were converted to the P1 triclinic space group symmetry, allowing all crystallographic cell parameters and atomic positions to vary during the MM optimization. A combination of the use of NewtonRaphson and a rational function optimizer (RFO) as energy minimization routines, and a final phonon calculation, to check for the absence of soft modes at special positions in the Brillioun zone, was employed to guarantee that only true minima were found. After two types of independent minimization (NR and RFO), the structure with minimal energy was selected. We have investigated energetic and structural properties of PSZs. This task requires special demands from the force fields to be used. It was shown that calculated zeolite enthalpies, with respect to quartz, are very sensitive to the force field employed.6,17 For a test of our force field, we selected quartz and 11 pure silica zeolites whose IZA8 codes are AST, BEA, CFI, CHA, IFR, ISV, ITE, MEL, MFI, MWW, and STT. We compared calculated energies and the measured enthalpies27 of PSZ formation with respect to quartz at T ) 298 K, and an excellent correlation has been found,16-18 which means that it can be used successfully in MM for the prediction of the zeolite stability. Additional tests of the BS force field show that it reproduces the structure of PSZ with high accuracy.16-18 The potentials and interaction parameters used for zeolites, fluoride, and water can also be obtained from the Supporting Information, which contains also GULP input files with the used keywords. 3. Results and Discussion 3.1. Energetics and Structure of Pure Silica Zeolites. An idea to investigate thermodynamic properties of zeolites by computer simulations6,7 or by experimental methods10,27,28 and to search their correlations is not new. Such calculations were done for different force fields, and a correlation between energies and framework density or volume was established. Recently,6 it was shown that widely used force fields predict energies of PSZ with low accuracy. The BS force field was especially optimized16,17 to fit the known experimental enthalpies of PSZ, and we expanded the set of zeolites on all topologies from the “database of zeolite structures”.8 We calculated energetic and structural parameters for four-coordinated zeolite frameworks. The stability of the PSZ frameworks is determined by the small internal energy with respect to R-quartz, the most stable form of silica at normal conditions. According to the experiments, pure silica zeolitic frameworks are metastable with respect to dense phases by less than 15 kJ/(mol SiO2).10 The experimental data are available only for a limitted set of pure silica zeolites. The calculations with the BS force field for all synthesized PSZs show an upper limit of energy with respect to quartz of 16 kJ/(mol SiO2), in excellent agreement with the above experiments.

Feasibility of Pure Silica Zeolites There are several reasons for expecting a relation between energies and volumes of zeolite frameworks. First of all, the mean interparticle distances are increased with the molar volume of zeolite and we may expect weakening the long-range interactions. The second reason is a distortion of the tetrahedral framework, a fact which affects its internal curvature. By increasing the molar volume the porosity of the material increases, but it is impossible to create low curvature large cavities or channels without breaking bonds or largely distorting the tetrahedral framework. These effects were intensively studied29-33 for an explanation of hydrophobic effects. We now explain the case of water solutions and how this can be related to zeolites. In the liquid state, water molecules form random networks of distorted tetrahedral H-bonds. It was shown there are two regimes of hydration of the hydrophobic spheres. In the case of small solute radius, hydrogen bonding simply goes around the hydrophobic species. The overall amount of hydrogen bonding remains relatively unchanged with respect to pure water. The number of water molecules that are affected by the solute is proportional to the solute volume, and hence, the free energy of hydration is also proportional to this volume. Contrarily, not all hydrogen bonds can persist near the surface in the case of large solute radius. The nature of hydrophobicity changes when the size of solute surfaces depletes the number of hydrogen bonds and the free energy of hydration becomes proportional to the surface area of the solute. The case of water solutions (with large solute radius) is similar to zeolite+SDA systems, where the organic SDA resembles the hydrophobic part and the zeolite (tetrahedral network) resembles the liquid water-water tetrahedral H-bonded network. In several cases, water and silica crystals have the same framework topologies;34 for example, hexagonal ice Ih is isostructural with β-tridimite, and ices III and IX are isostructural with keatite.35 Ices VI and VII are high pressure water polymorphs, whose frameworks consist of two separate interpenetrating frameworks with no connecting hydrogen bond.36 Each framework of ice VI has the EDI topology, and ice VII frameworks have the topology of β-crystobalite: they are selfclathrate systems where water molecules which belong to one framework stabilize the other framework and vice versa. Framework topologies of clathrate hydrates are also present as zeolite forms. For example, clathrate hydrate type I has MEP topology, type II has MTN topology, and type H has DOH topology.8,37-39 Same topologies of some ice polymorphs and zeolites do not mean that these crystals have the same geometrical parameters. There is a difference between water and silica bonding. Water molecules form hydrogen bonds which are weaker than covalent “Si-O-Si” linkages. The minimum energy of water dimer configuration is observed for linear H-bonds.40 On the other hand, the Si-O-Si angle in zeolites can adopt a wide range of values from ca. 130° to 180°, with the most common value being 148°.15 The corresponding Si-O-Si and O-H · · · O angles in zeolite and ice crystals of the same topology are different. Crystals with minimal deviation from ideal tetrahedral T-T-T angle of 109.5° have the topology of diamond framework (βcrystobalite for silica or cubic ice Ic for water). Herein, T is designated a tetrahedral atom in a framework. All hexagons in a T-framework of diamond topology (the framework where the only T-atoms connected by “bonds” are taken into consideration) have “chair” conformation. β-crystobalite and cubic ice are metastable at low temperature with respect to R-quartz and hexagonal ice Ih (tridymite topology), respectively. Silica and ice polymorphs have different “zero level” reference systems.

J. Phys. Chem. C, Vol. 114, No. 45, 2010 19159 The large deviation from linearity of Si-O-Si angles makes it possible to form a large set of zeolite frameworks. The presence of smaller (3 or 4) rings will cause a greater distribution of T-T-T angles, and therefore, the framework will be less “tetrahedral”. We will treat these rings as non-tetrahedral motifs of a framework because T-T-T angles in 3- and 4-rings are not close to tetrahedral value. They are not typical for liquid and crystalline water.35,41 However, in terms of SiO4 tetrahedra, it is possible to have 4-rings and double 4-rings (d4r) in which the SiO4 tetrahedra are not significantly distorted, due to the flexibility of Si-O-Si linkage. According to Lum-Chandler-Weeks theory,29 the tetrahedral or close to it zeolite frameworks cannot enclose large template particles without breaking T-O-T bonds due to the limit of framework stability. The Gibbs free energy of solvation increases linearly with the solute volume until the stability limit is reached. At large radius (low surface curvature), the tetrahedral order must be broken either by breaking bonds or by forming non-tetrahedral motifs. The presence of non-tetrahedral motifs of frameworks locally decreases the internal curvature. Brunner and Meier19 predicted that the frameworks of lowest density are those with a maximum number of 4-rings. The silicogermanate ITQ-33 contains 3-rings and 4-rings in the structure.42 This gives a framework density for ITQ-33 of 12.3 T-atoms per 1000 Å3, which is quite low. ITQ-37 has the lowest framework density of 10.3 T atoms per 1000 Å3, and in this case this is achieved due to the fact that some T-O-T bonds are broken and terminated by hydroxyl groups.43 In both cases, low density is clearly related to a deviation of the perfect tetrahedral network. In the first case, the large cavities are formed due to non-tetrahedral motifs, and in the case of ITQ37 the framework achieves mesoporosity through breaking of bonds. The relation between the energy of the PSZ frameworks with respect to quartz and the molar volume is presented in Figure 1. Excess energies have a tendency to increase with the increasing of the molar volume, but the topology of the frameworks has an influence on the energy too. Most of the points in Figure 1a are located below 40 kJ/(mol SiO2), but some structures (codes BSV, CZP, OBW, SOS, OSO, AFY, and RWY) have large energies and quite surely cannot be synthesized as PSZs. Energies of known synthesized PSZs are presented in Figure 1b. Most of the points in the plot are inside a narrow band which represents the region of synthetic feasibility. The two points corresponding to the highest energetic structures are RRO44 (∆E ) 15.4 kJ/mol SiO2) and FAU45,46 (∆E ) 15.0 kJ/mol SiO2). Special experimental methods were used for the synthesis of these PSZs. RRO zeolite has been obtained by a calcination of precursors: the layered silicate materials. The high energy FAU zeolite has the largest molar volume, and it was obtained using a dealumination process of Na-Y material. Na-Y zeolite was treated with silicon tetrachloride vapor and subsequently washed and heated to create a zero defect faujasite structure. These PSZs show the upper limit of energy of ∼16 kJ/(mol SiO2), which was reached up to the present time. Taking into account the correlation of excess energy with molar volume, the upper line in Figure 1b may be treated as a weak upper estimation of energy for PSZs, which are possible to synthesize with SDA. RWR,47 CDO, and RRO48 zeolites were obtained by topotactic condensation of the corresponding intercalated layer silicates, and they form a separate group in Figure 1b. Several force fields were proposed for simulation of silica materials. The SLC force field22,49 was extensively used for

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Figure 1. Framework energy with respect to R-quartz versus molar volume.

Figure 2. Energies of pure silica zeolites calculated with BS and SLC force fields: (a) excess energies with respect quarts versus molar volume of zeolites and (b) difference between calculated and experimental excess energy.

simulations of zeolites.6,7 The SLC force field significantly overestimates6,17 experimental enthalpies10 of investigated PSZs. A comparison of enthalpies calculated with SLC and BS potential is made in Figure 2. The SLC potential gives higher excess energy than the BS force field. RWR, CDO, and RRO zeolites, which formed a separate group in the case of BS, were grouped with AST and ITW zeolites when the SLC force field was used. These two last topologies have d4r composite building units, and were obtained with template molecules not through topotactic condensation of precursors. Figure 2b shows the differences between calculated and experimental enthalpies. Calculations with the SLC force field give large systematically shifted up enthalpies, except for MTW. Meanwhile, BS enthalpies deviate up and down with respect to experimental values. It was shown18 that enthalpies calculated by molecular mechanics and molecular dynamics methods with the BS force field fit experimental data well. Experimental enthalpies at 298 K were calculated from the heat of zeolite dissolution in lead borate at 973 K with the use of a complex procedure, and the final results depend on the quality of the crystals. Another source for comparison of calculated data is the results of density functional theory (DFT) calculations. Unfortunately, the accuracy of the calculated energy is low. Periodic DFT B3LYP gives energies which noticeably underestimate experimental enthalpies.6 Recent DFT calculations50 with TZPB3LYP+D* basis overestimate energies of TON and ITW zeolites with respect to BS and SLC force fields. According to these calculations, TON has lower excess energy (9.94 kJ/mol

SiO2) than ITW zeolite (15.43 kJ/mol SiO2). The corresponding energies are 4.04 and 10.08 kJ/mol SiO2 for BS, and 7.77 and 14.78 kJ/mol SiO2 for SLC force field, respectively. The energy gap between structures (ca. 6 kJ/mol SiO2 for BS and ca. 7 kJ/mol SiO2 for SLC) is ca. 1 kJ/mol SiO2 higher for SLC than for the BS force field. Concerning the relative stability of TON and ITW zeolites, the BS result of 6.04 kJ/mol SiO2 is similar to the DFT calculation which gives 5.49 kJ/mol SiO2. Zeolite frameworks consist of a set of building units, and these units have different relative energies depending on the force field used for calculations. This is one of the reasons that explain the different relative stabilities of zeolites. It is interesting to remark that both BS and SLC force fields give close energies for zeolites with three-member rings: 16.1 versus 18.8 (MEI), 62.5 versus 55.5 (OSO), and 106.6 versus 103.8 kJ/mol SiO2 (RWY). The average interparticle distances in low dense zeolites are longer than those in dense zeolites, and this is the reason why both force fields give close energies because they are driven by electrostatic interactions. Summarizing, we may expect that the BS force field predicts enthalpies of PSZs more accurately than SLC. Excess energy tends to increase with volume (Figure 1), and the parameter p ) ∆E/V depends mostly on the framework topology. The values of p for different zeolite topologies and their statistical distributions are presented in Figure 3. We have calculated two statistical properties of the distributions: the frequency count is the number of times the values of p are encountered that fall within each bin with the width of 0.05 kJ/cm3, and the cumulative count is the total number of points

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Figure 3. Distributions of excess energy per molar volume from number of zeolite in the database (a), and histograms for number of points in the bins and the curves for cumulative number of points versus excess energy per molar volume (b). The lines were drawn as an eye guide.

Figure 4. Different contributions to the excess energy of synthesized pure silica zeolites.

falling with values less than the threshold. Synthesized PSZs have the values of the parameter distributed in a narrow range of p < 0.5 kJ/cm3, and we suggest that structures within such a range are feasible PSZs. This is an empirical criterion based only on calculated energies and volumes of synthesized PSZs. The corresponding distributions of p, calculated for all topologies, are wider. The parameter p is very large for some frameworks such as WEI, OBW, BSV, OSO, RWY, SOS, and CZP which should then be unfeasible as PSZs; however, many frameworks unrealized yet as PSZs have small values of p and are even smaller than synthesized PSZs as is the case for BIK (0.095 kJ/cm3) or CAS (0.12 kJ/cm3). We suggest that BIK and CAS can be synthesized as PSZs. Recently,51 the pure silica disordered material EU-20b was synthesized by the topotactic condensation of the silica layers of the precursor EU-19. The authors have proposed that it consists of 88% CAS-type stacking and 12% NSI-type stacking of layerlike building units. Our calculations show that CAS and NSI zeolites should have close molar volumes (28.67 and 28.63 cm3/mol SiO2, respectively) and excess energies of 3.4 and 3.6 kJ/(mol SiO2) with respect to quartz. These calculations explain the experimental result: the component with lower energy prevails in the EU-20b material.

More than 100 zeolite topologies satisfy both criteria ∆E < 16 kJ/(mol SiO2) and p < 0.5 kJ/cm3, and according to our results these structures can be synthesized as PSZs. The list is included as Supporting Information. The most promising cases are those with small values of ∆E and p. 3.2. Interatomic Interactions in Pure Silica Zeolites. We have decomposed the excess energy with respect to quartz on four terms (eqs 1-3): electrostatic, van der Waals, and threebody Si-O-Si and O-Si-O interactions. The results of such decompositions for synthesized PSZ are presented in Figure 4. van der Waals and O-Si-O energies are positive with respect to quartz for all synthesized PSZs, and the variations of these energies are rather small. This means that they are not the dominant contribution to total excess energies and do not influence significantly the relative stability of zeolites. Meanwhile, three-body Si-O-Si and electrostatic interactions with respect to quartz are very different among different zeolites. Three-body Si-O-Si interactions are positive except in the FAU case. Excess energies of electrostatic interactions are positive and negative with respect to quartz, and sometimes (DOH, MTN, NSI, TON) they compensate positive Si-O-Si three-body interactions. The high excess energy of FAU zeolite is due to unfavorable electrostatic interactions. The less stressed

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Figure 5. van der Waals, electrostatic, and O-Si-O and Si-O-Si three-body interactions with respect to quartz versus molar volume.

Si-O-Si angles are found in FAU, IFR, and CHA. For FAU, these three-body interactions are even more favorable than those for quartz. Zeolites from the outstanding group in Figure 1b (RWR, CDO, and RRO) have largely positive both electrostatic and three-body energies. Excess van der Waals, electrostatic, and three-body interactions for all zeolites are presented in Figure 5. Most of the structures have positive values of energies, but for some of them the energies are negative with respect to quartz. The three-body Si-O-Si interaction range of variation is several times larger than the range of variation of van der Waals and O-Si-O interactions, which means that three-body Si-O-Si interactions, in addition to electrostatic, play a more significant role in the stability of zeolites. We can observe significant stress of O-Si-O interactions only for KFI and RWY frameworks, which have a large number of 4-rings and 3-rings. Three terms of interactions, namely, vdW, Si-O-Si, and O-Si-O, seem independent of molar volume, which is easy to understand taking into account the short-range nature of these interactions. All zeolite topologies, with the exception of BCT, lie in accessible regions of energy if we take into account only these types of interactions. Excess electrostatic energies with respect to quartz calculated for all topologies show a wide energetic range (ca. 100 kJ/mol SiO2), and the corresponding plot in Figure 5 looks similar to Figure 1a. In both cases, energies tend to increase with molar

volumes. The reason for such a behavior is the long-range nature of electrostatic interactions. Many topologies have high electrostatic energy, and this energetic term plays an important role in the total energy, and its contribution is crucial for the feasibility of PSZ, especially for low dense zeolites. Perhaps it is possible to select templates for the zeolite synthesis taking into account the electrostatic energy of the framework, trying to compensate this high energy through electrostatic interactions with template ions. It is difficult to expect that neutral SDAs may stabilize low dense zeolites. The total excess energy for each topology is a sum of terms. This is a specific combination of mutually enhanced or compensated interactions. This is the reason why the different force fields predict different relative stabilities of zeolites. Every term gives a specific contribution to the total energy. Electrostatic interactions play a crucial role in the thermodynamic stability of RWY, OSO, and OBW low dense topologies. For similar structures, the total energy does not depend significantly on short-range interactions. The correlation between excess energies and molar volumes observed in Figure 2a for two force fields cannot be extrapolated to framework topologies with low density. Both BS and SLC force fields give very close excess energies for RWY and OSO topologies. However, the coefficients of the linear scaling equation ∆E(V) for synthesized PSZs are very different for BS (0.99)17 and SLC (0.674)6 force fields, showing a much better result for BS than for SLC.

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Figure 6. Molar volume and excess energy with respect to quartz versus ring concentrations in the PSZ frameworks.

3.3. Influence of Rings on Energy and Volume. Part of the aim of this work is to find topological descriptors related to the energetic stability of pure silica zeolites, and we analyze a possible relation between excess energy and ring concentrations, energy and concentrations of composite building units of the zeolite frameworks. Recently Zwijnenburg and co-workers52,53 showed the link between framework topology and energetics. For frameworks corresponding to simple tilings, the polyhedral tiles become more stable with increasing average face size and with decreasing variance of face sizes. In the present work, we investigate the correlations between energetics of the framework and concentration of specific rings, instead of average ring size and variance. We have calculated the rings using zeoTsites software9,54 and have plotted volume and energy versus ring concentrations in zeolites. The results are presented in Figure 6. There is the tendency of increasing volume with the increase of 3-ring and 4-ring concentrations. Tetrahedral coordination creates the curvature of space, but triangle and square motifs are mostly flat and the angles between T-atoms (T-T-T angles) are substantially deviated from tetrahedral. These structural elements are valuable for the synthesis of zeolites containing large pores, which have a small local curvature. The diversity of structural motifs leads to the diversity of the framework topologies and creates the conditions to form zeolites with low density. Due to the increase of interparticle distances, the electrostatic interactions become weaker and the excess energy increases

(Figure 6). Quite the contrary, the 5-rings and 6-rings are the typical motifs of the tetrahedral frameworks, and in that case we do not see any tendency of energy and volume changing with the increased concentration of these rings in the frameworks. Flat rings may form convex polyhedrons such as d4r, d6r, d8r, mtn, sod, clo, and lta composite building units.8 The size of convex polyhedrons in the frameworks with tetrahedral geometry is limited, but they can be stacked together through flat faces, so that frameworks of a wide range of density can be built.55 Examples of LTA framework expansion with d4r units and FAU with d6r units were proposed by Zwijnenburg and Bell.21 The square and hexagonal tubes in section may be built from d4r and d6r units by addition of 4-rings and 6-rings in consecutive order. If a synthetic route to stabilize the tubes is proposed, this will make zeolites with very low densities feasible. This will require that the correspondingly high electrostatic energy be compensated by appropriate templates. The d4r and d6r rings contain 4-rings, and they often occur in zeolite frameworks. The corresponding excess energy versus molar volume plots are presented in Figure 7. Both types of zeolites have 4-rings, and the excess energy has the tendency to increase with increasing molar volume. Our plot shows that PSZs lie within the feasibility condition that makes small the parameter p ) ∆E/V. It is possible to synthesize pure silica zeolites with d4r using the fluoride route.56 It was established that fluoride resides within double 4-ring cages and stabilizes them.57 Among the zeolites containing d4r (Figure 7a), we

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Figure 7. Excess energy with respect to quartz versus molar volume of PSZs for zeolites containing d4r (a) and d6r (b) composite building units. The lines were drawn as an eye guide.

suggest that topologies ITR, IWV, and UFI should be feasible as pure silica. A previous work also suggested that ITR should be feasible as pure silica material.58 Some low energy zeolites were produced with the substitution of Si into Ge: ITQ-34 (ITR), ITQ-26 (IWS), IM-12 (UTL), IM-10 (UOZ), SU-15 (SOF); or into Al: ITQ-27 (IWV), UZM-5 (UFI). There are only four pure silica zeolites with d6r units: CHA, FAU, MWW, and SAS. It was shown that fluoride resides within d6r cages.59,60 All the zeolites presented in Figure 7b locate in the thermodynamically accessible region and formally could be synthesized as pure silica zeolites. This includes, among others, MSO, SSF, and TSC. The proposed criteria of feasibility of zeolites are based on statistical distributions of their thermodynamic parameters, which are nonlocal properties. In a specific system, the feasibility depends on the details of the framework structure. A low excess energy of the framework does not mean that the structure has not stressed motifs. In the case of specific systems, a detailed energetic and structural analysis should be done. This includes taking into account not only the structural and topologic aspects but also additional factors that, during the synthesis, stabilize the zeolite. 3.4. Structure and Composition of Hypothetical AsSynthesized Pure Silica MSO Zeolite. It is not possible to simulate the real process of nucleation and crystallization of zeolite systems, sometimes lasting several weeks, which is governed not only by thermodynamic but also by kinetic factors. Free energy calculations should be performed in order to solve the problem of the thermodynamic stability of the systems. It is a very complicated task especially if we have close packed multicomponent systems, and this cannot be solved at the present time using direct simulation techniques. For the investigation of the relative stability of the systems, we have compared the energies of their local minima obtained with the energy minimization method. This method was usually applied for investigation of the as-made zeolite materials’ stability. In the previous part of this study, we have shown that many zeolites could be feasible under SiO2 composition, and we have tried to rationalize the properties contributing to the energetic stability. Now we would like to suggest appropriate structural-directing agents (SDAs) to make the synthesis viable. It would be a daunting task to do this for all the feasible structures, and we only want to suggest a general procedure that can be applied to any desired structure. To illustrate this, we select the case of MSO zeolite.

Figure 8. Hypothetical structure-directing agent for pure silica MSO zeolite synthesis (a) and its possible precursor (b).

According to our calculations, MSO pure silica zeolite should have an energy of ca. 6.56 kJ/mol SiO2 with respect to quartz (van der Waals energy is 3.70, electrostatic energy is 0.16, and three-body energy is 2.70 kJ/mol SiO2). The parameter p is low (p ) 0.21 kJ/cm3), suggesting that the synthesis is feasible. All these values are within the accessible ranges (Figures 1-5). The unit cell of the MSO framework contains three mso, six d6r, and nine lau composite building units, which form three large [46620] cavities. This framework has the minimum energy among topologies with d6r cages (Figure 7b). The aluminum containing material MCM-61 was synthesized61 with the 18crown-6 ether, whose molecules are occluded in the large cavities. The negative excess charge of the framework due to incorporation of aluminums is compensated by extraframework potassium cations. We consider that for pure silica zeolite synthesis neutral SDA molecules in the cavities should be substituted by charged molecules such as, for instance, quaternary ammonium cations. In this case, fluoride ions can stabilize d6r cages. The cation must be bulky and have a high degree of symmetry to fit the ellipsoidal shape of the MSO large cavity. The proposed hypothetical cation with its possible precursor62 is presented in Figure 8. Our goal is a test of the capabilities of our computational methodology. Feasibility of synthesis depends not only on the framework energy but also on the chemical accessibility of SDA cations. Several cations may fit the large cavity of MSO, but it is important to assess the corresponding energetic stabilization. The templating effect is based on filling the voids in the framework. The shape of the template should correspond to the shape of the cavity for minimizing of van der Waals and electrostatic SDA-framework energy of interactions. In the specific case of clathrasil MSO zeolite, the distances between the centers of [46620] cavities are large, and the occluded SDA

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Figure 9. Quaternary ammonium cation, fluorides, and water occluded in the cavities of pure silica zeolite with MSO topology (fragments of structure): (a) Configuration with minimal energy; water molecules are in mso and d6r cages. (b) Configuration with high energy, water molecules are in lau cages (highlighted).

TABLE 1: Calculated Stabilization Energy, Estab, Energies of Intra- And Inter-Component Interactions, Eij, and These Energies with Respect to the Anhydrous Material, ∆Eij (i ) 1 for SDA+-F-; i ) 2 for MSO; i ) 3 for H2O), for [(SDA+-F-)3(SiO2)90]nH2O As-Made Materials n

E11a

E22

E33

E12

E13

E23

∆E11

∆E22

∆E12

Ewtot

Estab

0 3b 3c 6d 1e 9f

325.5 325.6 327.5 335.6 330.0 351.8

-357505.8 -357574.3 -357510.9 -357578.8 -357508.9 -357382.1

4.2 10.3 -33.4 1.8 13.3

-2484.4 -2395.4 -2455.4 -2371.0 -2452.5 -2374.2

-130.3 -53.0 -186.6 -47.3 -137.5

-7.8 -83.0 -90.9 19.9 -40.5

0.2 1.9 10.0 4.4 26.2

-68.5 -5.1 -73.0 -3.1 123.7

89.1 29.1 113.4 32.0 110.2

-44.6 -41.9 -51.8 -25.7 -18.3

-38.7 -34.2 -43.4 4.7 10.6

a Eij (eV/(unit cell)), Ewtot, and Estab (kJ/(mol H2O)) are calculated according to eqs 4-6. b Molecules are located only in mso cavities. Molecules are located in d6r cavities. d Three molecules are located in mso and three are located in d6r cavities. e Molecule is located in lau cavity. f Molecules are located in lau cavity. c

cations are far from each other. This means that van der Waals SDA-SDA interactions are weak and electrostatic SDA-SDA interactions will be weakly dependent on the SDA structure (distant SDA charge molecules will behave as point charges). Therefore, we may expect that only SDA+-F- interactions will be sensitive to the charge distribution among SDA cations (see Figure 9). Our goal, mainly, is to test the role of water on the stabilization of the (SDA+-F-)/zeolite system, and we expect that the result will not depend on the SDA structure. There are two d6r cages per each large cavity, which may contain bulky cations in the MSO framework. There are two possible anion positions in the framework: close or far from the methyl group of the cation. Our calculations of the anhydrous (SDA+-F-)3(SiO2)90 material showed that energies of both configurations are close and differ only by 0.13 eV (12.8 kJ/ mol unit cells). The configuration where fluoride is farther from the methyl group of the cation is more stable (see Figure 9). The as-made zeolite may be considered as a three component system. The first component is (SDA+-F-), whose molecules are in an ionic dissociated state in the zeolite. We treat the SDA cation and the fluoride anions units as one component because the charge compensation is needed for the calculation of electrostatic interactions in the unlimited periodic cell system. The second component of the as-made material is the all-silica zeolite, and the third is water. As it was shown previously,17 water is not the only media for synthesis, but it may stabilize the zeolite materials. Theoretically, for each MSO framework unit cell, water molecules may be occluded in three mso, three

empty d6r, and nine lau cages, but the real occupation numbers depend on thermodynamic and kinetic factors. From the energetic point of view, the occupation number will be larger if the water molecule decreases the energy of the system. The molecules in different sites have different energies. We made an analysis of interactions for each possible water molecule position inside the MSO framework. The total energy (Etot) of the unit cell may be presented as the sum of intra- and intercomponent energy of interactions as follows:

Etot ) E11 + E22 + E33 + E12 + E13 + E23

(4)

where Eij is energy of interactions between of i and j components (1 ) SDA+-F-; 2 ) zeolite; 3 ) water). We calculated absolute energies, the energies that give the used force fields. The E11 term consists of strong electrostatic interactions between SDA cations and fluoride anions and contains intramolecular interactions of SDA and rather weak van der Waals SDA-SDA interactions. The calculated energies are summarized in Table 1. The main contribution to the total energy is the energy of zeolite (E22), corresponding to 90 SiO2 units. The next valuable term is the interaction between SDA+-F- and zeolite, E12, and this strong interaction contributes significantly to stabilize the system. Water gives a relatively small contribution to the total energy.

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We investigated five possible cases of water molecule positions in the unit cell of the MSO framework, namely, three molecules are inside mso (3b, Table 1); three molecules are inside d6r (3c); six molecules simultaneously fill the both mso and d6r cages (6d); one (1e) and nine (9f) water molecules are inside lau cages. The sign of water-water interactions is determined mostly by electrostatic interactions because the molecules are separated in the framework cages that prevent their close contact. Energy of water-water interactions (E33) is negative only when six molecules per unit cell occupy positions in mso and d6r cages as is depicted in Figure 9a. The molecular dipoles are oriented by the strong electrostatic field of ions. Additional stabilization is achieved due to the formation of weak H-bonds between water molecules occluded in the neighbor cages (rOO ) 3.2 Å, rOH ) 2.4 Å). The absolute values of the interaction energies are not very informative. In the case when there is no information about interactions of components in the initial mixture, it is possible to take the anhydrous as-made material as the reference system and investigate the influence of water on the system stability. The values of ∆Eij,

∆Eij ) [Eij(n) - Eij(0)] /n

(5)

are characterized by the change of intra- and intercomponent energies due to the presence of water, where n is the number of water molecules in the unit cell. Ewtot is the total energy of the water molecules in the asmade zeolite,

Ewtot ) (E33 + E13 + E23) /n

(6)

These energies are negative (Table 1). The comparison with water condensation energy (-41.5 kJ/mol)63 shows that the water molecules in the mso and d6r cavities have lower energy than the molecules in pure liquid water. The reason is the strong electric field created by the SDA+-F- ion pairs (see Figure 9), which make E13 < 0 in all the cases. This result is expectable because it is an ionic hydration. During the nucleation and crystallization periods, the ions have solvation shells in the gel that consist of water and polymerized SiO2 units. Some water molecules may be entrapped by forming framework at these stages of zeolite synthesis. Energies of zeolite-water interactions (E23) are negative in all cases except when the water molecule in the lau cage is close to the fluoride anion in the nearest d6r (Table 1, 1e), but the average value of energy is negative when all lau cages are filled by water (Table 1, 9f). Water in the d6r cavities (Table 1, 3c) strongly interacts with the framework (E23 ) -27.7 kJ/mol H2O). Both E13 and E23 terms give the main contribution to the total energy of water in MSO zeolite Ewtot which reaches the highest value (-18.3 kJ/mol H2O) where all the lau cages are filled by water. This means that interaction with water occluded in lau cages is hydrophobic, whereas the interactions of water molecules in mso and d6r cages are rather hydrophilic, and they become more hydrophilic when both cages are filled by water. The hydrophilicity of as-made zeolite is determined by strong water interaction with ions rather than water-zeolite or water-water interactions. However, some “loosely held” water molecules may be occluded in the framework cavities after the calcination.

Stabilization energy with respect to the anhydrous material (Estab, Table 1) contains Ewtot and the terms of excess energy of SDA+-F- and zeolite subsystems due to the presence of n water molecules in the unit cell.

Estab ) Ewtot + ∆E11 + ∆E22 + ∆E12 )

[Etot(n) - Etot(0)] /n (7) This energy is negative (effect of stabilization) for all the investigated cases except the water molecules occluded in lau cages. The last configurations are energetically unfavorable and we expect only trace amounts of such “loosely held” molecules in MSO framework. The largest stabilization of the as-made material is observed when both types of cages, mso and d6r, are filled by water (Table 1, 6d). Stabilization effects of the water molecules have a different nature. Water stabilizes the silica framework, and ∆E22 are negative, except in the case where all lau cages are filled (Table 1, 9f). Molecules occluded in mso cavities (3b) decrease the energy of framework more largely than when they are located in d6r cavities (3c). There is an additive framework stabilization effect in the case of n ) 6 (6d), for which ∆E22 is only slightly higher than the sum of terms observed for the cases of the three molecules occluded in mso and d6r cavities (3b, 3c). Water molecules destabilize the SDA+-F- subsystem in all the investigated cases. The energies of interactions, ∆E11, are positive and the largest destabilization effect is observed when all the lau cages are filled by water molecules (9f). Water molecules destabilize the interactions of (SDA+-F-) with zeolite, and ∆E12, too. And this effect is several times larger than the first one (∆E12 > ∆E11). Water modifies the interactions in the (SDA+-F-)3(SiO2)90 material. The final energetic effect depends on the water molecule positions inside the MSO framework. We found that water stabilized the material if molecules are occluded in mso or d6r cages. This effect reaches the maximum value when both types of cages are filled by water. The electrostatic field created by ions and the framework stabilization make the positions in mso and d6r cages more hydrophilic. However, the lau cages are not preferable for water, because the strong destabilization effect makes these cages hydrophobic. We expect that pure silica MSO zeolite may be synthesized using the fluoride route in not very concentrated aqueous media and the most stable as-made material composition should be (SDA+-F-)3(SiO2)906(H2O). We believe that problems of pure silica zeolite synthesis concern the selection of appropriated SDAs and the stabilization of stressed sites of frameworks. MSO zeolite was selected as an example of low energy framework with d6r cages. Our computation shows that theoretically it is possible to obtain the as-made material with the stabilization of the framework aided by water molecules. Pure silica zeolites are hydrophobic materials, but the electrostatic field of the SDA+-F- subsystem decreases the hydrophobicity and makes hydrophilic some positions inside framework cages and channels. A usual way of tetrahedral framework stabilization is the substitution of Si by other chemical elements: Al, Ge, B, for example, but there are other routes of stabilization. 3.5. Hypothetical High Pressure Route of Structure Stabilization. Water is a system with tetrahedral ordering of molecules, and in that sense solid water and silica materials are similar as it was discussed above, and in fact there are several ices and high-pressure gas hydrate polymorphs.34,39 The interpenetrating frameworks of ice VI and ice VII form self-clathrate

Feasibility of Pure Silica Zeolites systems. Water molecules which belong to one framework stabilize the other framework and vice versa. Ice VI is formed from liquid water at 1.1 GPa. The EDI topology of each ice VI framework consists of four-membered rings joined as tricyclohexamers (nat composite building unit). Ice VII is formed from liquid water above 3 GPa and consists of two interpenetrating cubic ice lattices. The example of ice VI shows that the stabilization of nontetrahedral units may be achieved by using the pressure of ca. 1 GPa. A range of clathrate hydrates stabilities is ca. 0-90 GPa.39 These hydrates are stabilized by hydrophobic molecules, the molecules with weak interaction with water. In the case of synthesis of pure silica materials, we have solvophobic solvation of water by SiO2 polymerized units, when the water molecules interact weakly with the solvent. The water molecule is small and can stabilize cages of zeolite frameworks. It was shown64-67 that water can penetrate in hydrophobic pure silica zeolites at high pressure (ca. 0.1 GPa), and the water-zeolite system plays the role of a molecular spring (MFI, DDR) or bumper (Beta zeolite) because they may accumulate, restore, or dissipate mechanical energy. Our calculations show that the stabilization effect increases with increasing the water content in MSO asmade material. Achieving a relatively high water content in the synthesis of a hydrophobic pure silica material may require high pressure, and hence, high pressure may equally be a promising research field for the synthesis of pure silica zeolites. It is possible to expect feasibility of low density pure silica zeolite syntheses at high pressure and low concentration of Si atoms in the initial gel. 4. Conclusions The number of synthesized pure silica zeolites is only ca. 25% of the currently known and included in the IZA database zeolite topologies. Computer simulations using a new force field, which excellently fits experimental enthalpies of pure silica zeolites with respect to quartz, show that many zeolite topologies are thermodynamically feasible as pure silica. Based on statistical distributions of thermodynamic properties, two empirical parameters may be adopted as criteria of thermodynamic feasibility. It was found that the upper energetic limit for synthesized pure silica zeolites is ca. 16 kJ/mol SiO2 above R-quartz, and the densities of excess energy of pure silica zeolites lie in the region where ∆E/V < 0.5 kJ/cm3. We have shown how total energies and van der Waals, electrostatic, and three-body interactions correlate with the molar volume and topology of frameworks. Electrostatic and threebody interactions are the main terms that determine thermodynamic feasibility of the zeolites. Energies of electrostatic interactions correlate with molar volume of zeolites, while energies of three-body interactions are mostly determined by framework topologies. Total zeolite energies and molar volumes increase with increasing concentration of 3-rings and 4-rings, while there is no relation of these parameters with the amount of 5-rings and 6-rings in the frameworks. Most of the 3-ring containing frameworks from the IZA database are thermodynamically unfeasible as pure silicates, but most topologies with 4-rings, namely, the frameworks containing d4r and d6r composite building units, are thermodynamically feasible. From them, we select MSO zeolite as a case study to consider more in-depth a synthesis route. Calculations show that it is possible to choose an organic cation, which matches the MSO large cavity shape. Further stabilization of the framework comes from the fluoride as the anion, which stabilizes the d6r cage, and water molecules as empty cage fillers. The influence

J. Phys. Chem. C, Vol. 114, No. 45, 2010 19167 of water on the material stability depends on the positions of molecules in the MSO framework. Molecules in the lau cages destabilize the as-made material, but they stabilize when they fill d6r or mso cages. An effect of maximum stabilization is reached when cages of both types are filled. Comparison of solid water and silica crystalline structures stimulated us to put forward a hypothesis about stabilization of zeolite frameworks by high pressure applied during the zeolite synthesis, through an effect of water penetration in hydrophobic structures at high pressure. Acknowledgment. G.S. acknowledges Ministerio de Ciencia e Innovacion for funding through project MAT2007-64682. Y.G.B. acknowledges ITQ for a postdoctoral contract. Supporting Information Available: GULP files with the employed potential and a list of pure silica zeolite structures that satisfied both feasibility criteria. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Corma, A. J. Catal. 2003, 216, 298. (2) Treacy, M. M. J.; Randall, K. H.; Rao, S.; Perry, J. A.; Chadi, D. J. Z. Kristallogr. 1997, 212, 768. (3) Friedrichs, O. D.; Dress, A. W. M.; Huson, D. H.; Klinowski, J.; Mackay, A. L. Nature 1999, 400, 644. (4) Boisen, M. B.; Gibbs, G. V.; O’Keeffe, M.; Bartelmehs, K. L. Microporous Mesoporous Mater. 1999, 29, 219. (5) Foster, M. D.; Simperler, A.; Bell, R. G.; Friedrichs, O. D.; Paz, F. A. A.; Klinowski, J. Nat. Mater. 2004, 3, 234. (6) Zwijnenburg, M. A.; Cora, F.; Bell, R. G. J. Phys. Chem. B 2007, 111, 6156. (7) Deem, M. W.; Pophale, R.; Cheeseman, P. A.; Earl, D. J. J. Phys. Chem. C 2009, 113, 21353. (8) Baerlocher, Ch.; McCusker, L. B.; Olson, D. H. Atlas of Zeolite Framework Types, 6th rev. ed.; Elsevier: New York, 2007; http:// www.izastructure.org. Three letter codes from IZA will be used throughout. (9) Sastre, G.; Corma, A. J. Phys. Chem. C 2009, 113, 6398. (10) Navrotsky, A.; Trofymluk, O.; Levchenko, A. A. Chem. ReV. 2009, 109, 3885. (11) Ford, M. H.; Auerbach, S. M.; Monson, P. A. J. Chem. Phys. 2007, 126, 144701. (12) Barrer, R. M.; Denny, P. J. J. Chem. Soc. 1961, 971. (13) Zones, S. I. Zeolites 1989, 9, 458. (14) Burton, A. W.; Zones, S. I.; Elomari, S. Curr. Opin. Colloid Interface Sci. 2005, 10, 211. (15) Wragg, D. S.; Morris, R. E.; Burton, A. W. Chem. Mater. 2008, 20, 1561. (16) Bushuev, Y. G.; Sastre, G. J. Phys. Chem. C 2009, 113, 10877. (17) Bushuev, Y. G.; Sastre, G. Microporous Mesoporous Mater. 2010, 129, 42. (18) Bushuev, Y. G.; Sastre, G.; de Julian-Ortiz, J. V. J. Phys. Chem. C 2010, 114, 345. (19) Brunner, G. O.; Meier, W. M. Nature 1989, 337, 146. (20) Akporiaye, D. E.; Price, G. D. Zeolites 1989, 9, 321. (21) Zwijnenburg, M. A.; Bell, R. G. Chem. Mater. 2008, 20, 3008. (22) Schro¨der, K.-P.; Sauer, J.; Leslie, M.; Catlow, C. R. A.; Thomas, J. M. Chem. Phys. Lett. 1992, 188, 320. (23) Cygan, R. T.; Liang, J.-J.; Kalinichev, A. G. J. Phys. Chem. B 2004, 108, 1255. (24) Oie, T.; Maggiora, G. M.; Christoffersen, R. E.; Duchamp, D. J. Int. J. Quantum Chem. 1981, 20, 1. (25) Kiselev, A. V.; Lopatkin, A. A.; Shulga, A. A. Zeolites 1985, 5, 261. (26) Gale, J. D.; Rohl, A. L. Mol. Simul. 2003, 29, 291. (27) Piccione, P. M.; Laberty, C.; Yang, S.; Camblor, M. A.; Navrotsky, A.; Davis, M. E. J. Phys. Chem. B 2000, 104, 10001. (28) Petrovic, I.; Navrotsky, A.; Davis, M. E.; Zones, S. I. Chem. Mater. 1993, 5, 1805. (29) Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570. (30) Chandler, D. Nature 2002, 417, 491. (31) Chandler, D. Nature 2007, 445, 831. (32) Rajamani, S.; Truskett, T. M.; Garde, S. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9475. (33) Jedlovszky, P.; Predota, M.; Nezbeda, I. Mol. Phys. 2006, 104, 2465.

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