Confinement Effects and Acid Strength in Zeolites

Confinement Effects and Acid Strength in Zeolites | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Confinement Effects and Acid Strength in Zeolites Emanuele Grifoni, GiovanniMaria Piccini, Johannes Lercher, Vassiliki-Alexandra Glezakou, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-79664/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 May, 2021 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Chemical reactivity and sorption in zeolites is coupled to confinement and - to a lesser extent- to the acid strength of Brønsted acid sites (BAS). In presence of water the zeolite Brønsted acid sites eventually convert into hydronium ions. The gradual transition from zeolite Brønsted acid sites to hydronium ions conversion in zeolites of varying pore size is examined by ab initio molecular dynamics combined with enhanced sampling based on well-tempered metadynamics and a recently developed set of collective variables. While at low water content (1-2 water/BAS) the acidic protons prefer to be shared between zeolites and water, higher water contents (n>2) invariably lead to solvation of the protons within a localized water cluster adjacent to the BAS. At low water loadings the standard free energy of the formed complexes is dominated by enthalpy and is associated with the acid strength of the BAS and the space around the site. Conversely, the entropy increases linearly with the concentration of waters in the pores, favors proton solvation and is independent of the pore size/shape. Catalysis Physical Chemistry Thermodynamics and statistical mechanics confinement effects acid strength zeolites Brønsted acid sites (BAS) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Background Brønsted acid catalysis is one of the most important classes of chemical conversion 1–11 and is critical for the reactions in petroleum refining and petrochemical industry, including for example hydrocarbon cracking 12–16 , alkylation 17 and oligomerization, dehydration of alcohols 18–22 , aldol condensation 23–25 , ketonization 26 , and esterification 27,28 . A wide variety of solid acids are used for such reactions with zeolites being one of the dominating groups 5,29,30 . Zeolites are tectosilicates with an impressive number of potential ways to link the corner shared SiO 4 tetrahedra forming a wide variety of pores and cavities 31–33 . Some of these framework tetrahedra are synthetically exchanged for other elements than Si 4+ , typically Al 3+ , but also Ga 3+ , B 3+ , Ge 4+ , and Ti 4+ . A charge imbalance is created, if the metal cation has a 3+ oxidation state. The resulting negative charge of -1 in the tetrahedron with oxygens is balanced by metal cations or H + . The proton is stabilized as an OH group on one of the four oxygen atoms linking the tetrahedron to a neighboring one. It may fluctuate its position among the four oxygen atoms. This results in a “bridging” OH group with the potential to act as a Brønsted acid site (BAS) ( Figure 1 ). In its water free state, the ability of a BAS to protonate a base has been studied experimentally and theoretically to an impressive extent 6,34,35 . While early studies had suggested that zeolites would act as super acids 36 and show widely varying acid strength, it was found that the pK A was lower than that of super acids and depended moderately on the crystal structure. Modern experiment and theory have shown conclusively that zeolites possess a high acid strength, but are relatively insensitive to structural effects and are mildly sensitive to the chemical composition 8,37 . It has been shown, however, that the constraints of the pores stabilize transition states of reacting molecules in a way that these materials show higher catalytic rates compared to counterparts of equal chemical composition on flat or mesoporous surfaces 7,38,39 . Aluminum containing zeolites have been shown to be hydrophilic. Purely siliceous materials are highly hydrophobic, i.e., they do not stabilize the continuous sorption of water molecules in a density equivalent or approaching liquid H 2 O, even if engulfed in water 40–42 . The fact that it takes substantial external pressures to force water into zeolite pores of siliceous materials demonstrates that the loss of entropy from bulk to confined water prevents the full utilization of the whole pore volume 43 . Recently, it was shown that sorbed water molecules form clusters around the BAS, forming eventually hydrated hydronium ions, whose size is limited by the difference between the standard free energy of the water cluster in the pores compared to the aqueous phase 44,45 . For MFI zeolites with pores ~ 0.6 nm, this balancing act leads to hydrated hydronium clusters containing approximately eight water molecules. The catalytic activity of such hydronium ions also benefits from the constrained environment, with rates approximately 1-2 orders of magnitude higher than those in an open aqueous environment 46–48 . Organic molecules appeared to adsorb in such environments only in the void left by hydrated hydronium ion clusters. This leads to marked discontinuities in the arrangements of molecules that have been shown to be equivalent to the impact of liquids of high ionic strength 44 . Understanding and controlling the impact of water ordering in zeolite pores leads to a better understanding of the hydrophobicity and allows us to predict and model the elementary steps of acid catalyzed reactions in confined spaces. This understanding requires addressing questions related to: (i) the nature and thermodynamics of solvation of the BAS in the presence of increasing chemical potentials of water and (ii) the size of hydrated hydronium ion clusters. In this work, we examine these questions by a combination of ab initio molecular dynamics (AIMD) and enhanced sampling based on the metadynamics formalisms for studying the rare events dynamics and evaluating the associated free energy landscapes. There have been several prior studies of water in zeolites at the classical molecule dynamics 49–52 (CMD) and AIMD 53–57 levels of theory. The latter studies, which account for both reactivity and diffusion, reveal a complex behavior of the protonation state as a function of the number of waters and the nature of the BAS ranging from sharing of the proton equally between water and a BAS, to complete solvation of the proton within water clusters. Recently, AIMD combined with IR and high-resolution solid-state NMR on H-ZSM5 zeolites, showed that the interaction between the proton and the water cluster formed becomes weaker with increasing water loading, but plateaus out at a maximum solvation of 7-8 water molecules per BAS 44,45 . A preliminary computational study performed with AIMD simulations and static DFT calculations supported these conclusions 58 , and showed that the bond distance between the acid proton and the releasing framework oxygen is proportional to the water concentration. Here, we ask if this formation of water clusters for proton solvation is an attribute of the MFI structure or if it is a generic property of all zeolites and their cavities? We focus on the role of confinement on the specific population of water clusters and assess the enthalpic and entropic contributions to the zeolite acid-base equilibrium. Due to the presence of energy barriers separating different protonation states, a standard simulation cannot fully address these questions. In order to overcome these limitations, we performed metadynamics simulations 59–61 to assess the relative free energies of potential protonation sites. We adapted a set of generalized collective variables, which enabled us to assess the relative acid-base properties of multiple sites and allowed to compute relative pKa values 58 . We use this method to investigate the protonation state of several zeolites as a function of water content to probe changes in acid strength and to determine if general behaviors exist to guide our understanding of the surface chemistry of protons in zeolites. The protonation state of the BAS was studied for four different zeolites 62 (MFI, CHA, FAU, and GIS) with pore diameters ranging from 0.5-1.5 nm 63 ( Figure 2 ). In all cases the BAS-proton pair correlation function changed with increasing water content showing at low loadings the formation of a complex in which the proton is shared between the BAS and the solvating water molecules. At high loadings complete protolysis occurred. It was observed that full protolysis is reached with four water molecules and further addition of water does not alter the equilibrium. Moreover, we find that for zeolites with a low concentration of BAS, the water clusters occupy only a small portion of the cavity independent of the cavity shape or size. This makes the entropic component in the acid-base equilibrium insensitive to the type of framework, while the enthalpic contribution, after an initial sharp decay, remains constant at all hydration levels. Thus, the zeolite structure plays only a minor role and the protonation free energy exhibits an approximately universal behavior. Results And Discussion Structure of water clusters within the zeolite framework In order to understand, how water molecules are arranged in pores, we calculated the water density around a BAS. The radii of the spheres centered on the aluminum atom holding 90% of these densities were taken as a rough estimate of the portion of volume explored by the clusters, shown in Figure 3 . It is noted that water molecules never reach some regions of the cavities and the fractions of occupied volume was not affected by the framework type. The radii of these spheres are nearly the same in every tested zeolite and the volume increases with the number of water molecules at the same rate for every system. This is caused by the first water molecule remaining close to the zeolite framework (avoiding excessive charge separation) and to the hydrogen bond network that keeps the water clusters compact and prevents waters to diffuse inside the entire cavity. An indication that the framework does not affect the cluster behavior comes from the analysis of their shapes. We know that these small clusters in the gas phase tend to organize in structures with defined geometrical arrangements 64–66 . Among these geometries, more interesting are the structures whose vertices are defined by 4 or more water molecules. A volume and a surface can be computed for these polyhedra and from these we can get an estimation of their sphericity according to the Wadell definition 67 : This formula defines the sphericity, Ψ p , of a generic polyhedron as the ratio between its volume V p and its surface A p. Ψ p can assume values between 0 and 1, where, by definition, the sphericity of the cluster is unity for a sphere, and decreases in solids with lower symmetry. We know from literature that 4, 6 and 8 water molecules in gas phase are arranged in a tetragonal, prismoid and cubic shape, respectively 65 . We also know the Ψ values for all these structures in their regular shape. The sphericities of these clusters inside the zeolites were calculated and compared with the values extracted from the relevant MD simulations in gas phase, as well from the respective regular three-dimensional geometries (see Table 1 ). Results show that clusters confined into the zeolite frameworks have values comparable with the gas-phase ones. Table 1 . Water clusters sphericity, ψ, into four different zeolite cavities, in gas phase (GP) and the regular (R) three-dimensional geometries. The analysis shows that water clusters confined in zeolite frameworks are not significantly impacted by a changing confinement. Previously, we reported a difference in shape and dynamic properties between a protonated octameric cluster and one confined within the channels of H-ZSMS5 44 , which is in apparent contradiction to the current analysis. However, using a similar analysis to the current approach, we find that the previous trajectory, which is not as well sampled as the current one, can also be classified as having a similar volume as the gas phase counterpart. From a statistical mechanics’ point of view, entropy, and more precisely the translational contribution, is proportional to the accessible volume of the system. We also know that the positive charge can move only inside the water network hopping from water to water through the hydrogen bond network. As a consequence, translational entropy grows proportionally to the volume of the water cluster and not necessarily with the zeolite cavity size. This implies that the entropic contribution to proton solvation is independent of the zeolite framework type and does not stem from the mobility of the overall cluster in the available pore. Free energy surfaces for proton transfer. In order to further probe this hypothesis, reaction free energies have been computed and decomposed to their enthalpic and entropic components. For this purpose, we adopted two recently developed descriptors 58 , known as Collective Variables (CVs), as are a measure of the protonation state of our systems (s p ) and the distance between the charge carrier and the BAS site (s d ), see section S1 in SI for details. As can be seen from Figure 5 , free energy surfaces (FESs) projected along the two CVs have roughly the same shape for all these systems with a deep and narrow minimum for and equal to zero and an elongated branch for equal to one. These states represent the undissociated and dissociated BAS, respectively. In all four cases, we observe the same trends as a function of the number of waters. At low water loading (n = 1, 2) there is a preference for the proton to remain in the vicinity of the BAS site (s p =0, s d =0). However already at n=2 there is finite probability for the proton to move away from that wall by as much as 4 Å (s p = 1, s d = 4). This tendency increases with the number of water molecules, such that by n=8 the proton is completely solvated by water molecule (s p = 1, s d > 4). This is in agreement with previous AIMD studies which show that the proton becomes “solvated” at higher water concentrations, but remains close to the BAS site at low hydration levels 45 . From these FESs it is possible to distinguish three well defined thermodynamic states ( Figure 6 ), i.e., an undissociated state with the proton covalently bonded to the zeolite (A), a state where the proton transfers to the closest water molecule forming a Zundel-like structure (B), and finally an end state where the hydronium ion is fully solvated and free to diffuse (C). The FESs, thus, obtained were divided in these three different areas and integrated in order to get their relative population. From these populations, we can observe that the same trend of transferring the proton from the wall as a function of hydration level occurs in all four zeolites see Figure 7 . In all cases, minimum A with the proton at the BAS becomes negligible once the water concentration exceeds 2 per BAS. It is minimum B, with the Zundel-like structure, where the most distinction between the zeolite frameworks occurs. Although the population of B is maximum at n=3 and drops off with increasing n, the rate at which it does so is not the same amongst the different zeolites. Its population decreases more rapidly the smaller the cage. Hence a more careful analysis of the energetics is required to quantitatively understand these trends. The role of enthalpy and entropy in determining protonation state. In order to understand the thermodynamic parameters determining the protonation state of water in zeolites, we use the relative trend in free energy between the undissociated (A) and the hydrolyzed states (B+C) as a function of the water loading. This function shows a universal behavior among different zeolites, see Figure 8 . Most importantly, except for small differences, all systems present the same decay trend with increasing n, but are offset at n=1 due to the differing acid strength of the BAS as imposed by the zeolite framework. Indeed, shifting vertically all these curves by a constant value that compensate these small differences shows that all these curves can be collapsed in one. This implies that although the free energetics at low hydration level may depend on local structural features (small differences in enthalpy), the behavior at increasing n is being determined by a structurally insensitive free energy term. To further probe this observation, we separate the free energy into contributions by the internal energy () and entropy () 68 to determine the driving force for proton solvation. The trends in as a function of the number of waters are given in Figure 9 , and shows that in all zeolites varies significantly between n=1-3, but tapers off to about 20 kJ mol -1 for n=3. This initial fast drop as well as the identical behavior of the four zeolites is attributed to the fact that the hydronium needs a certain number of water molecules to be stabilized, while the framework of the zeolites plays only a minor role. Once the cluster is sufficiently large, further addition of water molecules does not impact the solvation energy of the proton. The result clearly show that for more than 3 water molecules further association does not lead to a better enthalpic stabilization. This is further substantiated when one considers the entropy computed ( Figure 9 ), showing a nearly linear contribution to the free energy with increasing number of water molecules. All zeolites show a similar decrease with a slope of approximately -4.0 kJ mol -1 /H 2 O molecule regardless of the cavity size, i.e., the entropy increases solely as a function of the number of waters, and is not influenced by the cavity size. Thus, we conclude that the main factor for this increase is related with the larger environment in which the proton can be mobile, i.e., the entropy of the proton depends on the size of the hydrogen bond network it is part of and that scales with the volume of the cluster. As the zeolite framework perturbs this property of the clusters very little this entropic stabilization of the proton is, to first order independent of the zeolite lattice. Conclusions The universal behavior of BAS solvation in a select group of zeolite frameworks was examined by means of ab initio metadynamics methods. Independent of cavity shape or size, water molecules cluster at BAS to fully solvate the proton at n ≥ 3. The volume of the water cluster and entropy of solvation are independent of the zeolite cage structure. As a result, the free energetics of proton solvation follows a universal behavior in which the enthalpy contributes only very little to the stabilization of the cluster n≥3 and the entropic contribution grow linearly with the number of water molecules. This provides a straightforward extrapolation to predict the acid strength ( pk a ) of a BAS in any Zeolite framework as a function of water content. The results show that water is not evenly distributed within the zeolite, but is primarily located close to the negative charge in the zeolite lattice in order to minimize charge separation. Thus, overall the result set the computational framework necessary to model adsorption of organics and their reactivity in zeolites exposed to high chemical potentials of water. Methods Metadynamics Simulations: Breaking and forming covalent bonds, such of those involved in these reactions, implies high activation energies. Transitions between different protonation states occur on a time scale that can be reached with difficulty in a standard simulation. In order to accelerate the barrier crossings, metadynamics, an enhanced sampling method, is used to study chemical reactions. This method belongs to a class of enhanced sampling techniques based on the identification of the slow degrees of freedom involved in the reaction of interest 59,69,70 . These degrees of freedom, known in chemistry as Collective Variables, are functions of the atomic coordinates and must be chosen in order to extract the collective behavior connected to the reaction mechanism. Sampling is then accelerated by adding an external bias potential, a function of the chosen CVs, to the system potential energy. It is easy to understand how the choice of the CVs is crucial to obtain correct sampling. In order to accelerate the exploration of every possible protonation state, as well as the diffusion of the hydronium ion inside the cavities, we adopted a recently developed set of CVs 58 extremely versatile for the study of reactions involving proton transfer. A first CV, , was used to enhance the exploration of new protonation states and push the zeolite to release a proton to the water cluster and vice versa. A second one, , was used to explore the distance between the BAS and the hydronium accelerating the diffusion of the charge carrier inside the cavity, see section S1 of SI for additional details. Born-Oppenheimer MD simulations were performed combined with Well-Tempered Metadynamics 59,60 using PLUMED2 71 driving the CP2K package 72 . The exchange-correlation energy, , was computed using PBE 73 functional, see below. The four zeolites, with varying cavity shape and size shown in Figure 2, were studied loading each with an increasing number of water molecules per Brønsted acid site in a range from 1 to 8. The smallest zeolite tested, GIS-NaP1 could only accommodate up to 4 water molecules in its small cavity. The ratio Al:Si was kept constant at 1:95 which is comparable to typical experimental loadings. AIMD Simulations : Periodic density functional theory (DFT) based AIMD were performed within the generalized gradient approximation (GGA) with the exchange correlation functional of Perdew, Burke and Ernzerhoff (PBE) 73 and Grimme’s second-generation dispersion corrections (DFT-D2) as implemented in the CP2K package. Starting with the optimized zeolite unit cell with 95 SiO 2 units and a single Al atom for each system, AIMD simulations were performed with 1, 2, 3, 4 and 8 water molecule(s) at T=300K within the canonical NVT ensemble using a 0.5 fs time step and the CSVR 74 thermostat to determine the local structural properties. For each simulation, well-equilibrated trajectories of ~350 ps were collected to obtain reliable statistical properties. For further details of the simulations and system models see section S2 of the SI. Declarations Acknowledgements E.G. GM. P. and M.P. thankfully acknowledge the financial support provided by the European Union Grant No. ERC-2014-AdG-670227/VARMET. V.-A.G., R.R. and J.A.L. were supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division at Pacific Northwest National Laboratory (PNNL). 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-79664","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":2498303,"identity":"f9d08fb7-b51c-4243-9a30-acf2c6936ad9","order_by":0,"name":"Emanuele Grifoni","email":"","orcid":"https://orcid.org/0000-0002-3638-4929","institution":"ETH Zurich","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Emanuele","middleName":"","lastName":"Grifoni","suffix":""},{"id":2498304,"identity":"26539075-c3b8-44f4-ac75-d59419c6c163","order_by":1,"name":"GiovanniMaria 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2","display":"","copyAsset":false,"role":"figure","size":240002,"visible":true,"origin":"","legend":"Structures of zeolites employed in this work. (a) GIS, which consists of 8 and 4 ring size cages with diameter 4.97 Å, (b) CHA which consists of 8, 6 and 4 ring size cages with diameter 7.37 Å, (c) MFI which consists of 10, 6, 5 and 4 ring size cages.","description":"","filename":"F2.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F2.png"},{"id":2563197,"identity":"aefa6906-2efe-445a-a71f-135eaa8dd323","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":169087,"visible":true,"origin":"","legend":"Al-Ow radial distribution function overlaid on a faujasite cavity and its water molecules","description":"","filename":"F3.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F3.png"},{"id":2563198,"identity":"7648a0b6-c651-468f-a4bd-7b8519c9df1c","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":43728,"visible":true,"origin":"","legend":"Radius of a sphere around the aluminum atom enclosing the 90% of the water density. Dashed lines report the maximum Al-Si distances in the respective cavities. The dashed lines indicate the diameters of the main channel or cavity.","description":"","filename":"F4.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F4.png"},{"id":2563199,"identity":"1794084f-aa22-432e-a4b5-d5da9819b2c6","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":223933,"visible":true,"origin":"","legend":"GIS, CHA, MFI and FAU free energy surfaces along sp and sd at different hydration levels. Differences in free energies are expressed in kJ mol-1.","description":"","filename":"F5.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F5.png"},{"id":2563200,"identity":"32d876ff-9cdd-4350-8172-4007dad429fa","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":87949,"visible":true,"origin":"","legend":"The three thermodynamic states visible in the free energy surface and the relative structures.","description":"","filename":"F6.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F6.png"},{"id":2563201,"identity":"7e0fb7e1-075e-49c7-b34a-1c7a8064f5ec","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":114537,"visible":true,"origin":"","legend":"Relative population in each thermodynamic state for every zeolite at different level of water loading.","description":"","filename":"F7.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F7.png"},{"id":2563202,"identity":"59ab30a0-1c91-493e-9b1b-4042c0bdd3b1","added_by":"auto","created_at":"2020-09-23 18:17:29","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":81277,"visible":true,"origin":"","legend":"Differences in free energy between states A and B+C as a function of the water loading (top panel) and same curves rescaled by a factor δ that minimize the offsets among them. δc = 0, δm = 4.56, δF = 0.79, δG = 9.75. ","description":"","filename":"F8.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F8.png"},{"id":2563203,"identity":"9e63e102-8667-43dc-a632-3fa5f7ac216b","added_by":"auto","created_at":"2020-09-23 18:17:30","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":56074,"visible":true,"origin":"","legend":"Exponential and linear decay of the enthalpic and entropic contribution to the generation of the hydrated hydronium ion.","description":"","filename":"F9.png","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/F9.png"},{"id":13596129,"identity":"d86574fe-d288-4299-819b-834cdb5af887","added_by":"auto","created_at":"2021-09-17 05:27:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1190606,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/41a755b6-3a26-4f82-891e-1957d8ae92f2.pdf"},{"id":2563205,"identity":"a15a6e42-eeeb-4c3f-89ed-7ef0371c8094","added_by":"auto","created_at":"2020-09-23 18:17:30","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":943203,"visible":true,"origin":"","legend":"Supporting Information","description":"","filename":"SI.docx","url":"https://assets-eu.researchsquare.com/files/rs-79664/v1/SI.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Confinement Effects and Acid Strength in Zeolites","fulltext":[{"header":"Background","content":"\u003cp\u003eBr\u0026oslash;nsted acid catalysis is one of the most important classes of chemical conversion\u003csup\u003e1\u0026ndash;11\u003c/sup\u003e and is critical for the reactions in petroleum refining and petrochemical industry, including for example hydrocarbon cracking\u003csup\u003e12\u0026ndash;16\u003c/sup\u003e, alkylation\u003csup\u003e17\u003c/sup\u003e and oligomerization, dehydration of alcohols \u003csup\u003e18\u0026ndash;22\u003c/sup\u003e, aldol condensation\u003csup\u003e23\u0026ndash;25\u003c/sup\u003e, ketonization\u003csup\u003e26\u003c/sup\u003e, and esterification\u003csup\u003e27,28\u003c/sup\u003e. A wide variety of solid acids are used for such reactions with zeolites being one of the dominating groups \u003csup\u003e5,29,30\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eZeolites are tectosilicates with an impressive number of potential ways to link the corner shared SiO\u003csub\u003e4\u003c/sub\u003e tetrahedra forming a wide variety of pores and cavities\u003csup\u003e31\u0026ndash;33\u003c/sup\u003e.\u0026nbsp; Some of these framework tetrahedra are synthetically exchanged for other elements than Si\u003csup\u003e4+\u003c/sup\u003e, typically Al\u003csup\u003e3+\u003c/sup\u003e, but also Ga\u003csup\u003e3+\u003c/sup\u003e, B\u003csup\u003e3+\u003c/sup\u003e, Ge\u003csup\u003e4+\u003c/sup\u003e, and Ti\u003csup\u003e4+\u003c/sup\u003e.\u0026nbsp; A charge imbalance is created, if the metal cation has a 3+ oxidation state. The resulting negative charge of -1 in the tetrahedron with oxygens is balanced by metal cations or H\u003csup\u003e+\u003c/sup\u003e. The proton is stabilized as an OH group on one of the four oxygen atoms linking the tetrahedron to a neighboring one. It may fluctuate its position among the four oxygen atoms. This results in a \u0026ldquo;bridging\u0026rdquo; OH group with the potential to act as a Br\u0026oslash;nsted acid site (BAS) (\u003cstrong\u003eFigure 1\u003c/strong\u003e).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;In its water free state, the ability of a BAS to protonate a base has been studied experimentally and theoretically to an impressive extent\u003csup\u003e6,34,35\u003c/sup\u003e. While early studies had suggested that zeolites would act as super acids\u003csup\u003e36\u003c/sup\u003e and show widely varying acid strength, it was found that the pK\u003csub\u003eA\u003c/sub\u003e \u0026nbsp;was lower than that of super acids and depended moderately on the crystal structure. Modern experiment and theory have shown conclusively that zeolites possess a high acid strength, but are relatively insensitive to structural effects and are mildly sensitive to the chemical composition\u003csup\u003e8,37\u003c/sup\u003e. It has been shown, however, that the constraints of the pores stabilize transition states of reacting molecules in a way that these materials show higher catalytic rates compared to counterparts of equal chemical composition on flat or mesoporous surfaces\u003csup\u003e7,38,39\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAluminum containing zeolites have been shown to be hydrophilic. Purely siliceous materials are highly hydrophobic, i.e., they do not stabilize the continuous sorption of water molecules in a density equivalent or approaching liquid H\u003csub\u003e2\u003c/sub\u003eO, even if engulfed in water\u003csup\u003e40\u0026ndash;42\u003c/sup\u003e. The fact that it takes substantial external pressures to force water into zeolite pores of siliceous materials demonstrates that the loss of entropy from bulk to confined water prevents the full utilization of the whole pore volume\u003csup\u003e43\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eRecently, it was shown that sorbed water molecules form clusters around the BAS, forming eventually hydrated hydronium ions, whose size is limited by the difference between the standard free energy of the water cluster in the pores compared to the aqueous phase\u003csup\u003e44,45\u003c/sup\u003e. For MFI zeolites with pores ~ 0.6 nm, this balancing act leads to hydrated hydronium clusters containing approximately eight water molecules.\u003c/p\u003e\n\u003cp\u003eThe catalytic activity of such hydronium ions also benefits from the constrained environment, with rates approximately 1-2 orders of magnitude higher than those in an open aqueous environment \u003csup\u003e46\u0026ndash;48\u003c/sup\u003e. Organic molecules appeared to adsorb in such environments only in the void left by hydrated hydronium ion clusters. This leads to marked discontinuities in the arrangements of molecules that have been shown to be equivalent to the impact of liquids of high ionic strength\u003csup\u003e44\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eUnderstanding and controlling the impact of water ordering in zeolite pores leads to a better understanding of the hydrophobicity and allows us to predict and model the elementary steps of acid catalyzed reactions in confined spaces. This understanding requires addressing questions related to: (i) the nature and thermodynamics of solvation of the BAS in the presence of increasing chemical potentials of water and (ii) the size of hydrated hydronium ion clusters.\u003c/p\u003e\n\u003cp\u003eIn this work, we examine these questions by a combination of ab initio molecular dynamics (AIMD) and enhanced sampling based on the metadynamics formalisms for studying the rare events dynamics and evaluating the associated free energy landscapes.\u0026nbsp; There have been several prior studies of water in zeolites at the classical molecule dynamics\u003csup\u003e49\u0026ndash;52\u003c/sup\u003e (CMD) and AIMD\u003csup\u003e53\u0026ndash;57\u003c/sup\u003e levels of theory.\u0026nbsp; The latter studies, which account for both reactivity and diffusion, reveal a complex behavior of the protonation state as a function of the number of waters and the nature of the BAS ranging from sharing of the proton equally between water and a BAS, to complete solvation of the proton within water clusters.\u0026nbsp; Recently, AIMD combined with IR and high-resolution solid-state NMR on H-ZSM5 zeolites, showed that the interaction between the proton and the water cluster formed becomes weaker with increasing water loading, but plateaus out at a maximum solvation of 7-8 water molecules per BAS\u003csup\u003e44,45\u003c/sup\u003e. A preliminary computational study performed with AIMD simulations and static DFT calculations supported these conclusions\u003csup\u003e58\u003c/sup\u003e, and showed that the bond distance between the acid proton and the releasing framework oxygen is proportional to the water concentration. Here, we ask if this formation of water clusters for proton solvation is an attribute of the MFI structure or if it is a generic property of all zeolites and their cavities?\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe focus on the role of confinement on the specific population of water clusters and assess the enthalpic and entropic contributions to the zeolite acid-base equilibrium. Due to the presence of energy barriers separating different protonation states, a standard simulation cannot fully address these questions. In order to overcome these limitations, we performed metadynamics simulations\u003csup\u003e59\u0026ndash;61\u003c/sup\u003e to assess the relative free energies of potential protonation sites.\u0026nbsp; We adapted a set of generalized collective variables, which enabled us to assess the relative acid-base properties of multiple sites and allowed to compute relative pKa values\u003csup\u003e58\u003c/sup\u003e. We use this method to investigate the protonation state of several zeolites as a function of water content to probe changes in acid strength and to determine if general behaviors exist to guide our understanding of the surface chemistry of protons in zeolites.\u003c/p\u003e\n\u003cp\u003eThe protonation state of the BAS was studied for four different zeolites\u003csup\u003e62\u003c/sup\u003e (MFI, CHA, FAU, and GIS) with pore diameters ranging from 0.5-1.5 nm\u003csup\u003e63\u003c/sup\u003e (\u003cstrong\u003eFigure \u003cem\u003e2\u003c/em\u003e\u003c/strong\u003e). In all cases the BAS-proton pair correlation function changed with increasing water content showing at low loadings the formation of a complex in which the proton is shared between the BAS and the solvating water molecules. At high loadings complete protolysis occurred. It was observed that full protolysis is reached with four water molecules and further addition of water does not alter the equilibrium. Moreover, we find that for zeolites with a low concentration of BAS, the water clusters occupy only a small portion of the cavity independent of the cavity shape or size. This makes the entropic component in the acid-base equilibrium insensitive to the type of framework, while the enthalpic contribution, after an initial sharp decay, remains constant at all hydration levels. Thus, the zeolite structure plays only a minor role and the protonation free energy exhibits an approximately universal behavior.\u003c/p\u003e"},{"header":"Results And Discussion","content":"\u003cp\u003e\u003cem\u003eStructure of water clusters within the zeolite framework\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn order to understand, how water molecules are arranged in pores, we calculated the water density around a BAS. The radii of the spheres centered on the aluminum atom holding 90% of these densities were taken as a rough estimate of the portion of volume explored by the clusters, shown in \u003cstrong\u003eFigure 3\u003c/strong\u003e. It is noted that water molecules never reach some regions of the cavities and the fractions of occupied volume was not affected by the framework type.\u003c/p\u003e\n\u003cp\u003eThe radii of these spheres are nearly the same in every tested zeolite and the volume increases with the number of water molecules at the same rate for every system. This is caused by the first water molecule remaining close to the zeolite framework (avoiding excessive charge separation) and to the hydrogen bond network that keeps the water clusters compact and prevents waters to diffuse inside the entire cavity. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAn indication that the framework does not affect the cluster behavior comes from the analysis of their shapes. We know that these small clusters in the gas phase tend to organize in structures with defined geometrical arrangements\u003csup\u003e64\u0026ndash;66\u003c/sup\u003e. Among these geometries, more interesting are the structures whose vertices are defined by 4 or more water molecules. A volume and a surface can be computed for these polyhedra and from these we can get an estimation of their sphericity according to the Wadell definition\u003csup\u003e67\u003c/sup\u003e:\u003c/p\u003e\n\u003cp\u003e\u003cimg style=\"width: 435px;\" src=\"data:image/png;base64,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\" alt=\"\" /\u003e\u003c/p\u003e\n\u003cp\u003eThis formula defines the sphericity, \u0026Psi;\u003csub\u003ep\u003c/sub\u003e, of a generic polyhedron as the ratio between its volume\u0026nbsp;\u003csub\u003e\u003cspan style=\"font-size: 11px;\"\u003eV\u003c/span\u003ep\u0026nbsp;\u003c/sub\u003eand its surface A\u003csub\u003ep.\u003c/sub\u003e\u0026nbsp;\u0026Psi;\u003csub\u003ep\u003c/sub\u003e can assume values between 0 and 1, where, by definition, the sphericity of the cluster is unity for a sphere, and decreases in solids with lower symmetry. We know from literature that 4, 6 and 8 water molecules in gas phase are arranged in a tetragonal, prismoid and cubic shape, respectively\u003csup\u003e65\u003c/sup\u003e. We also know the \u0026Psi;\u0026nbsp;values for all these structures in their regular shape. The sphericities of these clusters inside the zeolites were calculated and compared with the values extracted from the relevant MD simulations in gas phase, as well from the respective regular three-dimensional geometries (see \u003cstrong\u003eTable 1\u003c/strong\u003e). Results show that clusters confined into the zeolite frameworks have values comparable with the gas-phase ones.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable \u003c/strong\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e Water clusters sphericity, \u0026psi;, into four different zeolite cavities, in gas phase (GP) and the regular (R) three-dimensional geometries.\u003c/p\u003e\n\u003cp\u003e\u003cimg style=\"width: 559px;\" 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0fFLlw9/ajkpMNh0ySWXmDxic2dXmak9LgWtxiZqLVgedpF7J76MuI1dqS2Zxo0bZ8575JFHmtOSgRU6Z8yYYdaJzZjpmmIXMbuhfCWaCrD8YmtZa7P9Ahd7qFrrW2IhGHWzWnB2+Tc02bZDgcEmCgnsNmMXn1sbaLcHcxqMetu2KjZzDSqarXNT7xfytR9e1O6zLXkL9A0qSBMyBYMXT0sGbP/UCrH8Ym9pSsMeE4nYYHo+dt99d7NNnAx3KallyOcTk8ScdSis+spr77devXqZvM39J5iMyKYhdbR1kvBp5kOHJgMSPs3wu+CCC+xmz1QGzTDbaNbhncSBsUWfrcHgFcizx9tsh+8tatX5bH/55Ze98eiyHwIqYPqB01Y3vfvuu+Zhw4fZ8uXLa2GgNoDr+TvhhBNM1wHt5NzdBOzS5XZxynDYbW1/YiBu1otjR61j1rdA7QPtEXlMcaLZJfunn35qtrV0VzLtdGzXLW1LL730UlMOlpPdUPZlz25Lf5o3y5s2hnyY8YuZgjS1YNSIcl1Lp0Drxi5O1ruua1ZXfWzbsfa0ixcv9pgXXHfddXXtFrT1gdab3WnUXLLe1Lo3JNk6N+V+ofZeHOicBx980JyK9yTPzfUtkQLlZctIBtSe2ecLtW5MFNJpUsDeEr7k+Rxgl693sgwpSNFGjvaoFAjcH752H3u/8bnVEimYjHhtG1JHWy+2B37QU1Cnto37i2Ol3eyZWtt4cbDxrOOMOMiYfWSQjVrrm3MhUF6BPnv4zPFO4iBlOJDfmWee6Wzbts07iy77IKACpg8obX0Vu1B4I4nH6y4oqE2inRO3015HwhfVstnhdr7w2C3K47h/1uDelw3QLidyrbDd8jyfr2RtM88991xfm5t1HbWn1JRYoYJc7I9detQMsCvFX6Izgt3HTum4RE7s/mytFEjd6ITBuohnf63i8+VBhwv7E89Vz3bbdrgfu3zJgPPUTNNYX0JAefI250wg9abmmmX2de/4KrOtc1PuF/Kgwx1NKKzQxe5Tnp8fXS2VAuHFMloGvMbW3IUOhNYxhZpdGezB1OvAAw/cpVp2f7YXCukHHXSQaTve9ph2R3u/WaHcrm/OabAYNbSOrAu1wGwLdDBkojaTy3QkdCe2HR6XH7T8QHInauy4jy/NpjtfsOcD4RXIs4c9JXUlao6tooOOdK3x4V9X2UJ1vQqYoXplQrhc7BrnV56vF751TKEGwTvRc5wPK9t9zO28SXnj0mNYRg4ymhi3Aw/zWA9sGmv7SsOHDzfHbW6DfV/ntuvIZO+99zblYD3qEyrtfpzSM5Fc+BKlDZKETDHL3l2m7n1acr4pdZNx600d+MJ3J76w+AHC+lITQM2KTbbtsJ2QBbv0+FL01c7sPs05bUq9aRLBunnba9VVTlvnht4v7uNYmzpGUJCQT+ZntcYvvviiO2uLzDeFFwtmGVB7xvZAzSP58YPUth+aiZArP2i9k92fH3o2sdfEV1cwt9v7zdsT3e7bnNNAGTW0jjQRYMQKMrNtw9qHy1C/tapobb35seKdKOjzGN999533phZZbgqvQJ49vu5Dd0XZs0LhkkwktJZ7k877IKBxMKWlaGocAXkBwD1yjXvv6dOnm0UREtyrId0WEMES8qUM0bh4tjGOmAgQJqYd45UxHp50J5uxvm0m6SI3s9zXO3311Vdg7EkOxcix0lsryb1lysHzS9c4pFuvQUUhF3nRgWOVM24m440yBqB045nhOsWWqEHHac5MTakb48QxifBTq2jSLQlx/jIxDzk0HIfPtMm2HREqIE49dnWrTZtSbw4FyiQa7QaV29a5ofeLPah8mEG04yaWrNgf2tWQl6uJu+mOaejZ2MwzTeHFIpGB2HSb2IycctACPgN4v9u4l5aTe3QsWx27TT7w7CqIdtIM5+pZsXPG3m88tnSre29u9uVAGLFwDakj84ljoRnYQT40aj2LxGGnVrxL5hUBkxMTT9jMuP589tlnEPteiF2ka23LzTaFVyDPHl/ty11bjsbG0e5ES+4ZiMS9Xee9CMgF1KQEgkbA2h0yPIg7UTshTc+hdsqd6GHt9qoVwdV0j7rzWC8+byceajrt16S3M5J7/5aYt/ZNrCM9hRuarOH9Pvvs49lFXoKmK4ZOLb5syDwZW2imKXWz3VS8nu40a9Ys0w4YNsU72bYjLzXvTa2y3JR6W3MOOka4E22U2WXr7cFr69zQ+8Uek/aDdLSjhtednnnmGcOX3cAtnZrCi2UkAzp22MRucN5HNr4stVg2BqYE6bfZPFPLsCHtxt5vjErQGikQRmTSkDryHIze4B0BhPWlIxWP4+4lYmg0rvMO82bNEugw01qpKbwCefbIYCC1qkptt/e9JB8/hldrmGTVKlwYLGgXeRhcpHApIg2fbSBp2tC4E+P/8SHmz7Ce3p20cfHOwy5S61lIWyAKXexmt16l3g8A93lbav6pp54y9fMWLOo7v7V3ZXexO9m4ma3hQe4uB+ebUjcKBdbxgvvzhcY4fow4wHbg3b1E73Dbdrwdy7zL01LLTak37dloE8k60oaW9oF0lDj66KPNOnah29TU+4UfUzy+aP/toTxTBoDmNu8POU+GZpxpCi/LgGYhNtE+l/eDtSu1L3TaObNduVNj242933zF0nQft7nmm8KoMXWkzbZtf9YT39alrKzMExxcRjOyqx12kVu7eX7o0KmSgji70q2DlSdzC880hVdjnz22DfK+cb+3yJJc+HFDLvzwJyu+i2iv6h1btYXRhMXpVMAMi8sUHoW0sTN5ozLOnH0Z8CFh7e74Zf3000/vUiHaDNHGkhpJt+OHzciXtPVC5/Gp3eNoPu4Xts3bGlPaXbJc9NpsaGI4DMuFDyx6v9ok3TDmeLRH89Z62TwtNW1K3Vg2PqztqE+8XqwL7VRZZ297WXfboe0YBbPWTk2tN19CtCFke2CdbXulwE0bW5vcdW7o/cJ7iSx5TP7cgfupiWI7stv4UdeSqbG8+HygEMPy0kNchrfcpbgyVKEnGgHzed9fbob1tRv3/VbXc2iXAgR5RWMZ8fQNrSN5Wg0lWdEe190DYj/4uI3CujuUFT9aqK3jvWnbLJ/H7D1qzdQUXixvU589bI/2vcVj0A7YPqPZRsmOAnxdIedak1UonjuKhRJompRAqxGgzYyE6MGGDRsgNy46depUZ1nECQDyYATHIvZlk1nnjs28QbRzoF0cyyXCQjOfrWUPH2jdZCQeYw9GO1napvI6i7lDy1aiCWcLtN6iAYF8GEFioBobYdrZRnIKlFcks7F1C3VGIpBCzBDMcywU2mugvILx7BHPevNs57tHBHhIxAd7OXVaDwEVMOsBpJublwAdfGh4TkcdsdOEhHcBH3INdZJp3tLp0ZWAElACSkAJKIGmEIhuyk66jxIIFgEZsxkyjjIkoLLxMn/++efRtWtXWE/AYJ1Hj6MElIASUAJKQAm0HAHVYLYcaz2TFwGxs0PHjh13ESYZuobdEZqUgBJQAkpACSiB8CSgAmZ4XjcttRJQAkpACSgBJaAEQpaAdpGH7KXRgikBJaAElIASUAJKIDwJqIAZntdNS60ElIASUAJKQAkogZAl0OpDRUrMrZCFowVTAkpACSgBJaAElECwCLSlyJCtLmC2JdjBaqB6HCWgBJSAElACSkAJhDIB7SIP5aujZVMCSkAJKAEloASUQBgSUAEzDC+aFlkJKAEloASUgBJQAqFMQAXMUL46WjYloASUgBJQAkpACYQhARUww/CiaZGVgBJQAkpACSgBJRDKBFTADOWro2VTAkpACSgBJaAElEAYElABMwwvmhZZCSgBJaAElIASUAKhTEAFzFC+Olo2JaAElIASUAJKQAmEIQEVMMPwommRlYASUAJKQAkoASUQygRUwAzlq6NlUwJKQAkoASWgBJRAGBJQATMML5oWWQkoASWgBJSAElACoUxABcxQvjpaNiWgBJSAElACSkAJhCEBFTDD8KJpkZWAElACSkAJKAElEMoEYkO5cK1RtrKyMkydOhU5OTkYPHgwJk6ciJiYmNYoip5TCSgBJaAElIASUAJhSUAFTNdlq6mpwRNPPIFPPvkEKSkp+Prrr0GB86ijjnLl0lkloASUgBJQAkpACSgBfwS0i9xFJz8/H9988w2ys7MxcuRI9O3bF9OnTzdCpiubzioBJaAElIASUAJKQAn4IaACpgtOQkKCES6zsrJwyMEHY+jQoUhNTUV0tGJyYdJZJaAElIASUAJKQAn4JaCSkwsPhckTTzwRNZWVmDLlUyxetAgdOnRAfHy8K5fOKgEloASUgBJQAkpACfgjoDaYXnQOPfRQ9O/fHz/++CM++OADFJaWYsPGjejSubNXTl1UAkpACSgBJaAElIAS8EVANZg+qPTr1w9/+MMfMGzYMOTOno1XHn7YRy5dpQSUgBJQAkpACSgBJeCLgGowfVGRdbS7PFq0mV8+8gg+X7Ec5cVFSEhMwui998aEww5DXFxcHXvqaiWgBJSAElACSkAJtG0CUY6kto2g7toXbt+Oiw87FMXLl6OkvAQxThSc6BhMOutsXHnXXYhT28y64ekWJaAElIASUAJKoM0S0C5yP5f+/ZdewgZx9CkpKkByVTUyUI0spwo/Pv8cvv/wf3721E1KQAkoASWgBJSAEmi7BFTArOPaV1RUYLoEXI+vrEBqTDQ6Spd4j9h4tIuKQSpq8ON774CB2TUpASWgBJSAElACSkAJ1CagAmZtHp4lR4RHp6Ic8VFAsthj7p6ShFP6dEC/pHgkIRrVhUWoqa725NcZJaAElIASUAJKQAkogR0EVMCsoyUkJCZi3IEHyTjkceBI5PHRUchIikVmbIyZr85MR6w6+tRBT1crASWgBJSAElACbZmACph1XP2qqirkb9qIzgnxyEhIwqyiMjy7cBPmlVWjpOcwTF27Ff/4xz/ArnRNSkAJKAEloASUgBJQAr8TUAHzdxaeOdpWPvnoI1jzxsvolJyF4uEHoaBLX+Rk90X+mKPQ78ZbcfyNt2H6knU48+xzsGHDBs++OtMwAhz3ff369Q3LHKK5Nm/eHLSS8UNl7dq1QTtecxyorKwMRUVFTTo07yneJ421Ww7ldhIID0LcLlEqtm3b1iCejcnboAO2QqZA7pfG1J+BUXJzc1uhhsE5ZSCcbAl4n+Xk5KCkpMSuiphpIHwa044iBlgrVkQFTBf8Uhm1Z+uWLXhJvMdXrFmLzEOPxpZJl2HUWXdi1GVPYdCFj6Bm9IlI7dYBseL4c9yl18HpPABnnHsR5syZ4zqSzvojsHXrVowYMQKjR4/2ly1ktz311FMYM2YMunbtim7duuHuu+9uUlnXrVuHq6++GrvtthsGDRqEG2+80XOcLdIOuX7kyJF1/lpKIF21ahXOPvtsdJbRrDp27IiJEyeC6xqS2BNw1VVXISUlxfDicKznnHMOiouL6909VNtJIDxY6WnTpplrmpGRgaysLDNy2NSpU33yaExenwcIgZWB3C+NqT8/Rk499VTTTnv27GmmN910U6M/aloLWSCcvMt8zz33oHfv3nj++ee9N5llCp577bXXLs+WO++802f+UFgZCJ+GtqNQeu6GAvOAy8A4mG09ydee87///c+54IILnLPOOMO54rLLnT9fd40z+bQbnQeeX+k88OwSmS5x7n9miXP6le87d30003ngi9+cB76c7Tw6bYlzxf3POeMOONh55ZVX2jrKBtX/5JNPZuxVR4SVBuUPpUz//Oc/TdnFPMKRDxLn8ccfN8s33HBDo4r52muvOcnJyU6PHj2cr7/+epd95QVhjktOvn4dOnRwRHjbZb9gr1izZo0jL2tnwIABzuzZsx15iTuDBw92unTp4qxYsaLe08kL3klKSnIOOuggh2W2dRGhs959Q7GdBMpj48aNhsPAgQOdffbZx4mKijJMZOAGR7RutZg0Jm+tHUNoIZD7pTH1JzsZec2Rj1aH+8nHiXPJJZcYtjIqWwgR8V2UQDh5H/HXX3914uPjTd0fffRR781mua7nC/cNxRQIn8a0o7q42OdWSz13Q/EaNKVMaMpOkbbPwoULnSOOOMI5SQSfKy+8yPn7VVc44/Y5yrnj4VnO/c8ude777yKZLnIefGGJc+GfP3X+/uJ3zoNfzXbu/1x+X8x2Hpu22Ln59c+dvQ6d7Nx6622OdHfugki+GJ3q6upd1re1FS+88IJHyAg3AXPu3LlOTEyMeYnxo4SJ0z333NOsX7x4cYMu57PPPmsYjB071rwIvXfiMSmAsE1SEJ05c6bz22+/mZ98iZt9L774Yu/dmmX5lFNOMed79913Pcf/+OOPzbrTTz/ds87XzE8//eQMHz7cIziVl5c7or00+2ZnZ/u8T+xxQrWdBMKDdTv66KOdhx56yFbTmT9/vkPhki+w//znP571jc1ba8cQWQj0fmkMq8suu8ww/P777z215wcgP+DIVjTEnvWhNhMoJ3d9WGcK2lYg8iVg8l3UqVMnR7SVzhdffOH5udm5j9na84HyaWg7CqXnbmszD9b5VcAUkp999pkzefJk5/rrr3c+Fk3mLbf/y7noby85Dz23wrlPBEv+KGA+9MJS57pbpjlX3PuZ89DXcz0C5gNfznEe/maeaDTnOEeceZnzxzPPMV/RvEhiY+U89OCDzhVXXOHcfPPNzpIlS4J17cLuONK16KSnpzv/+te/zAOQD7lwSuedd54pN7WX7vTwww+b9fUJXNyH11+6ix3pHq1TA0jBjMKlrw+VN954w5zryy+/dBehWeZXr15tzpWQkGC0te6T8EuewrY/oXrBggWOmAG4d3PElMRzTL7ofKVQbSeB8mBdP//8812qfNxxxxkm//d//1drW2Py1toxRBYCvV8aWn+xhTUaO7ZHb60+hSgKW9QWh2oKlJO7XldeeaX5qKPWlvV+7LHH3JvN/H333eeISU7YKDwC5dPQdhQqz91dLlgYr1AbTLkLpfsPGWlpSJbQRNFiW4n4FGS16yR9k7UDqTtRNcjITMH2zWUimNfeVl1dI+OXA0dfdAXQZQDOuehSyJcXXnv+BXz/5ZfYInaHtJkTzUyTHSWkqGGb5OsQZ555Jo488kiIIBaW9RAtoim3aB5rld8uv/nmm37tvSorK3HaaacZ+8N///vf6NOnT63j2IVx48bho48+8jnePc8hgjn2228/m73ZptIlbo4tWkgkyr3hTrRBFY08WJ660pAhQ4zdpXt7mtxnTPIChHSduzeZ+VBuJ4HyYAXFVGCXOpNJtDw8aOfqTo3J694vVOYDvV8aWv/lMpQvneRiY2MlrByDyv2eaMPMxLLIe/r3DSE0FygnWxXa8T7xxBN4+eWXd7lfbR46pt0lwxzLhy4OPPBAMx+I04w9bnNOA+XT0HYUKs/d5mTZ0sdWAVOI0xhauhyxYeMmvPrxDyiq6YP2md1R4yVE1lQ7SE1NRHWJg8oKCbIexcslf3Y+t5i9SoKz7z/5JAw5+ET86dq/4/1vpiMjOxt7iFBCxxYaoq9ds6alr3Orn4+OMHSOkC6bVi9LUwpAwUc0cmZX0d7VOkT37t3NsnQB+/WMf/rppyHd3cbh5bDDDsMHH3wA0X7iq6++MsJarYP6WKBhPgXPE044YZcXqY/sAa/iBxKTd325ztZ55cqVXGxwEptVSBce6ITgK4VyO2kOHqIVxZQpU/DII4+gb9++vpB41jUmr2enVpoJxv3iXfS66l9QUGCy8v7z9h7v1auX2UanMrGf9T5kqy8HixMd4ug8d/vttxvHnboq9swzz5hoDhS2v/nmG4jtuHkvfSKj1oViChYfd93qakfuPO75ln7uus8d7vMqYO68gj1FyJy/ZC06dzkA3TuNQIwMCVlLg2mESSAuIQZxMfEozC9DjARfx04hNMpImzuEzQr5Shw8ZiyOuvwGpPcdhkTxoB0+bCh2lxdrlswjaufBwr31NLD8/AIV8wCjvc3MzGzgXqGVbdmyZWCUAaZ27drVKpx0+3uWKUTXlb777juziS+78ePHG69xMZ0wmgR+ZdOD0V8S20cTdkScX/xlC9o2K1B515cnsHX2V193QRii6JprrgG9VEeNGiUfaqnuzWY+1NtJMHnwxUmN0/7772+uKSMG1JUak7euY7T0+mDcL7bM9dWfPVA28R5xJ4alsYkRDUItBYsTFSTsMWDEBn+JXvb8yKWW86STTjJZxQkGYpIDcXT1t2urbAsWHxa+vnZUVwVb+rlbVznCcb0KmHLV2L3y5xv+hu59JqJnz/6oqikHu8M9HSpWHtw5zcxIQ0FuCaLYJy7DRlKLGcXc3IEypnwdVpSXIVMEkd32nYjK5M6Y8vk0fDvtZwwaMhiffvqp6TKX3BGf2CXzxz/+0Tz4+DIN18RuOJu8BS52b9rkrUGx6zn9+eefzeJZZ51ltKHUiP7yyy9gFym1CRTA/CV2RzNU0IQJE/xlC9o2W2dfHwW2zv7qawsyb948I0iJ7ZdZJdEWsPfeexttvs0TDu0kWDxYZ4anEttLo9VnbFFeU2q4faXG5PW1f2uss6x47qbeL7bc9dW/ffv2HpMRavDYS2STRGgws2yv4vBjV4fMNBicXnzxRYizjglJJFEJ/NaN14LmLTTVEXtu87MfixdeeGGDwof5PUGQNwaDjy1Sfe3I5vOetvRz1/v84bz8+5sxnGsRYNlpF7l6AzD+gONRXlHiOZr3zRoVFW26zTPSk1GcX+Gy6XFkfueNLUKm3a+qqlqEzCwMmXQk4vqOxttTvsSSFTnoKDZ0L7/6KorqiQW4dOlSvP3220Ygtd1AnsKFyQy7YGhrd8stt4RJiX0X09sG0Z3LHdOxX79+7k2eeXZh2Yfl+eef73npMhaoeMCafHxR1BV4m9pT2z1uhTvPwZtpxtbZ1/lsneuqr7tItOGkzRe1mGKwbzbNmjUL77//vidbOLSTYPFgpR944AHwnn7vvffko7YnqF277bbbPDzcM43J696vNectK19lsG2H2xrSfhpSf5re8OOLz8zdd9/d2LNSU25jy1LLKd76vorTqusC5cRg6nx+MEYk4/I2NlGLSY0mY7Ly/uQHbyilQPm469KQduTOz/nWeO56lyGcl2PDufDBKDu1K08++x6OPvlmOZx0oXg+ACk0UljccRbKjw6qEe3EIDU9CWVrq8XeUpapvdqpuWRO5jf7md1qRC0fjfj4OPQZORxHXHAlvn3rZSQlJqHbsrl4ce5sHHTF1Vi+YL7YdFZgkDwQB0k3OtO3otF6RB6a1IbSeP3HH380WkA+CMIlSUw1PPjgg6Y7WGKMeopdWFho5qlpoGMDXwx0egnlxIDqNrHcEmbHLnq++ulgIDEiPevdM27B0b0v84iHq8nKa71o0SLDy70v59lNwxdzS3WP85y2zm6NENczWSGB9pQNTbzO1NLRVo6DGbBLjtc/XNpJsHmwvRx77LGQkFQmqD6FBT6PKJB7p8bk9d63NZYtK567KfeLd5nrqz/bIU0snnzyScOQWs1bb70VZ5xxhhkxie0sFFOgnMRr3AhBtOfmzyZrjiMh0cy7g13oNMvxlSh801SHvCRslkcb7CtvS68LlI93eetrR975W+O5612GcF5u0wImjXf/7x93YLc9T0G77A4or9phY7dDppS/O2Z2TM0iO8JrEJ8UK4JmNIq3lyGjXZIRItkITHYKm5604wASMRGOOP/0HjoE7a68HjNeeQE1X3wFp7IcN3z4kbysi8TmMwrxIjwefcWVOOX8C/DxR58hNSVVvNYzjAaQD2l2sR588MGeo4f6zKZNm0wRKRzz551omsCRJujcEOoCJrvXJFyPEY7YLdy/f39PdSgYMFEbwzy+Up8+fYzdIbtD8/LyjL2UzcfuYmq9KWBa7bfdZqdvvfWW0VDsu+++dlWzT20dfXWD2zo3RsC0BebLngImtbpM4dJOmosHbefowSpxCD1MLCvvaWPyeu/bksuB3i91ldVf/RldQUI9eXaVuKJGuJQBDXDuued61ofSTKCcaD/J6BR1jdjDdwZ/tPGuS8AkD7utPkezlmYXKJ+6yuuvHbn3aY3nrvv84T7fprvI7733fhRVdMDw0ft5hEvPBfVIiy6JkevkFy3OPWny0CrYWIqomhixHhatpYQpoibTk9vOeI6zw8M8LS0F+59xIeYN3QtbRUjtJoJnhlOJdjWVQF4uXhJv0lv+eSty165HSloqJk2ahEMPPRS0g3MbrHvKGcIztLmkRs77J3HJTKk5TB630X4o1BO7+altYpo+fXqt4vKrn8mX5slmpODIKAJM1FK5E7+qqQlnHl8aUHbTUNtH73Ff3dXuYwVznqGEmCQ+3C5e7g2pc11lsd2iVjgNl3bSXDzIyZtJXewam9ffcZpzW6D3i7+yNYQVteTsEmWihz6HOA3FFCgnCkDez1cuS1xnU10K3Fymva+/xI9IPltk0Ah/2Vp8W6B8/BW4vnbUWs9df2UOt21tVsDk2KQffjYLk466UDSQ5bWvm0solLHcjB+P6CCNhkk8gFAlX4ztstOwLa9UXHxEMGDPelU0HDmMQyUoD1cujj8Vsi/nRXaU3nXzY6ijys2FIixuxTo5Tr5oMTPEtrNzdCwGxMVieHZ7sceqRGcZ6Stezl0sWlY+LHnz86srnBIfDhxj2/tnvT5lODOzrXfv3mFRLdvN7z1utI0FSSN5m9avXw92U9Fz0SZ2UzGx28q9nsdjTEnaQ/kygWAYG2o+W7J7nOVke2P3PT9srIMS19NxgrHzOJaxFZpZH9aXdlz1JTq5Uai2PMOlnTSGBxn4agO+2NDB6dtvvzXX39t8wjt/Y/J679vSy/b6NvV+8VXehtafds4MS8R7khrzUE6BcGK4MO/nK5f58c5Eu0wu26gNFCS9eyT4fmHYMDoZ+nLoa212jeHT0OdQQ9pRaz13W5t3MM/fJgVMhoP55233Y99J5yMpJV4cdyj9/Z6M8lGEOxN0nd3b1E7yVyNbYqQrUzSY6VnJKC+rRqVoH8FeUflFJcqP8/Hy4+hvQpeCYbSEPJLgRvIvAXE1CSKoRqE6f5toP6uRIkMRj0pJxjG9sjFWpu1zViJq4Tz8QWxixonNzJLFi80X6OGHHx52AubvRCNjjtpk2irJyE8mxAxrRScseoDLEIJG08x1dNigpyaDobvjfjLQPLWQNKqnUb7NS4GT9on0gPWVKMDSFsnaavrK01zrnnvuOWNvSmcJPrz5VS8jXplYnrSvtYn1ZH3pYGHDwdCxi+UmM8bLZFce68Jj3XHHHX7j9dnjhtq0oTx8tQEK37S3ZHckPXjJg0Io2w6dGayXPevcmLyhxsiWJ5D7pan154cY7S4ZhkdGDDOBx215QnUaCKfG1IlCVR8x1WG385/+9CewJ4nxL/lcoYaXvEIxNZQPy+79HGpqO+KxWvO5y/NHQop4G8wyeSHSISFF4u5Zj7Q77rwXqe3Hone/wfKQ32F36bmYVFjSW1yEPxk6XARE6QKXdYgVaZHTnb+4RIqMMSgtqkB6O4ltKc4/7DqnHR0FVo70UyMvkLLyMpTJ+cuKt6OocDvKSopQIWVKy05GfG4M4iV/n7REjBvWBe9NX4ntorHMEO/zoeLwM0Je1rQTpV0fNT6Rkmw3r52GU73uvfdec01OPPFEE2ycXqv04uR6m9jVTccsJm/PVQqWFNSozaRgyetLGzHaqNqg0PY4nPKlwO5x2pDVZZ/pzh/sedodyjjkuOiii4y3M8tDBwp+3dsRjHhOW0/W25aTmkkKUDL2tvmxHVMLSGeEhoRasu3DToNdt6Ycr6E8fLUBMqKzF9sMhUrWi5omhoyRMedrjWzUmLxNqUdL7dPU+6Wx9WeAfpra0HyFAhO16a3xQdZUrk3lVNf57D1jp8zH95+My43XX38dMoQkOOgB70dqeK+99lrTHus6XmuvbwgfltH7OdTYdmTr2drPXVuOcJ9GiUBkrQXDvS61yk/B8i3Rvnz11pvYvHYduvbsgTOuvQ7b5OV++z1v4Lgz/iqCpAiDIkhGMWA6E1GQBhdlHddHi2Bntsu6HXEva+QFGo0YkR8WzFmFhOwqtOsQhxIRHsvLilFeWiYxMIulJ73CCBJGiyld33HJiUgVO8pkeaHUxCZimby0E957BfHSRd5Xuop7JMZhbVkl1omW9Ojb/42DXV7XLJqm0CJAwZBDB1Ij5atbk1pyBgmuy6aJX9bU6vEBb7uzfNWQDzpqGqgZbEoYEl/HbOo6GXfcxIwdOnSozw8e2mpSAHPzYDclf+yio30pzSIiJdXHw1cboAaYAibNDsiKmuu6UmPy1nWMUFnflPulMfXnBw9jPNL8xt/9FCo86ipHUzjVday61rP90TmINtDeMUrr2idU1tfHh+X0fg41ph3ZeobSc9eWKRynESNgUivEGF4rVqzAYHlpT339NXwow/Al11QZW8ZkERRLE5KwsecoHHLqP5Etw/1Vi62jkSbZm01jAen+jhJbSAqUjhyvqqrcaDjLykpEaBTNY3mJaCSLUVFZIrJolXh8FqK4qhB9hnZFXHwCEiRgdrxobZLkZRolQmWpaDCpOU0VZ50oOX9hQTEWTJuJwhXLcMTeuyErPxdfStdi1LZ8yqFIat8B46V7Z/INN4oAG/HK5XC8X7TMSkAJKAEloASUQAMIRIwU88477xhvwVLR+MSKcBglgmZyVQWSpLsyW7q3k0WCLBFtYVxMJrLbd5Xu6xJx1qlAVXUFKkWQrJCu8vLSQrExE0Gysli6xyvFObwGMXExSEhMQKx0L8SnJCJdugcTxFaSwz/WiC3lwmUrMGzfAaY7nUKpqDdRVFqM72bOwjaxs0ySfLsPHYaty1ejcNkSTBq/G44/7waPV+Mehx6Glb/9KpqdBPSWbvFuohHTpASUgBJQAkpACSiBcCYQERpMqs0vv/xyMzIGux7LJb5e2vo1SBPP3M5i9zQxK81oJOcWlWF5UntEHXwBUjLTIMpKGVtcLCnjYxArAl6s2IjFJyUjQbSQCTKNiYtHXKxsi91heCmWlTsVnvQpFyE22sGsmfMxamxPJCUnSLc410Xj+5m/Yu3qtRLnshK5K9ciZdsW/OnMk3DSCZPDrksinBu3ll0JKAEloASUgBJoHQIRocGkYwHDK9CAnl3lUWLnFRMrXtvVVUgVe8kRndNQKvaN80XATIkuR1HlWhSWZSMuMQ2JSfFISc5CSla20TbGU1spAqUoIsUUU5x8RJCkiaZDxx05do3Ybe5w9JEwQtINnpgUjTlzFqJd+xRxfuiAROkOL9uUj95yvt2GDMIGCTdUXpyKM/54ijhziDOQJiWgBJSAElACSkAJRDiBiBAw6ThAT0yGWUgSLeQoic9XJsMvbvphmjh/R+GLlVtRKg4820Vc3O+UU3HcX/6CAjGy35JfgA2bcrFm3UZszFuNvOVlKCqvkgEjxbEnIVkEznRkSZd4ogiGiansFk9ErAiV0dHUVNZg+frlmCuOHlXripDQUaRQCV0UK57niauWolenDMSUt0e3zh3QqfMI8eBLivCmpNVTAkpACSgBJaAElMAOAhHRRW4vJj3jOKRiHxl6MG/detx07DHotCYHheLyXS7ONmNk+YxbbjPe3HYf7ynjqDGIdG7eZixfmYOHH3scyb1GILNzNzglhUhhl7p4hMdnp2DWtBlInLceWSX5SI+tFs1oAdJ7dcXAAydibwmVsVGGBOTwZQxIzZAtmpSAElACSkAJKAEl0BYIRIQG014ohvywYT/S2mUhRkITlUoX99GXX4FB++yL3hKWgdaU/hLDqfDXu3dvrF+7Bh3aZWBAr3YSWDoKeeJAVFm2DevXbEXVzB/QVQTRRNF3do2RUXZEi1pUWYVF8zdj1NlnYqIE5dakBJSAElACSkAJKIG2SCCiBEz3BZwzZw6qO3dBn0mH4BCJKcng6Y1NW8RZqJ2EHho/Yog48STip3WrEd+xPfr16YnydctQvHkTCmWUnkHSdX5gjyx8tHIzKksrUVlU3NhTaX4loASUgBJQAkpACUQMgYgUMCsqKvDtV18hIyUVAwcNbpJwySt8wAEHYNasWZg9Z7YZ5aDXqJFmOECOjlAwcSLukBEQKnKWS4D0CkxbX4DcSnEEElvLIXuNj5gGohVRAkpACSgBJaAElEBjCUSUDSYrv2DBAjPO81oZraBbdiecedXl2H30bo3l4snPwO3UhnaQwOx77LFHrZFIfpw6FU9cfhkqxVFIYrQjJj0dx1xzLY6VkEl2uDzPgXRGCSgBJaAElIASUAJthEBECZiMh3ndddciTxx0KBAmJmeKBnMQLjj3jzK0XfMoa5fNnYsZMkxZjHir73bARAwcM6aNNB2tphJQAkpACSgBJaAEfBNoHqnL97mafe1WsZlcs2at8dyePHkyCrYVYMHCRSgqLEZGZkaznL//iBHgT5MSUAJKQAkoASWgBJTADgKN93wJYXLZ2dkYIuOQJ0gszO0S57K4pEiCn7cTr3ANcB7Cl02LpgSUgBJQAkpACUQYgYjqIue1WbZsGV5++WUzbORAGdf7uOOOMxrNCLtuWh0loASUgBJQAkpACYQsgYgTMEmaXuSlpaVIF6cbdbYJ2banBVMCSkAJKAEloAQilEBECpgReq20WkpACSgBJaAElIASCAsCEWWDGRbEtZBKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwAipgRvgF1uopASWgBJSAElACSqClCaiA2dLE9XxKQAkoASWgBJSAEohwArGRXL/8/Hy8//774HTcnntin733juTqat2UgBJQAkpACSgBJRASBCJWg1ldXY2nnnoKP/zwA6qqqvCBCJozZ84MCehaCCWgBJSAElACSkAJRDKBiBUwqbWcMWMG4uPjsccee6BLl674YfoPkXwttW5KQAkoASWgBJSAEggJAhErYKalpaFTp07YujUf7733AVYuzUHXrl1DAroWQgkoASWgBJSAElACkUwgYgXMhIQEXHLJJcjKysT6pcsQXZCPAQMHBHQta2pqsGbNGqxevdp0uwdysPLy8kB2132VgBJQAkpACSgBJRCyBKIcSSFbuiAUjILcSy++iF9m/orx++yFM844HVFNOG5paSneeOMNzJ8/H0lJSejTpw+OP/54pKenN+poBQUFeO2115CTk4NBgwZh8uTJyMjIaNQxNLMSUAJKQAkoASWgBEKZQMRqMC10ajKPOfZYVNVUY+7307F22TK7qc4pNZWVlZW1tn/22Wf46aef0K9fPxwrx4uOjsaUKVNQl3xeWVGBVQsXYsW8eSgX4dSmN0VIXbhgAcaNG2e0oe+9957dpFMloASUgBJQAkpACUQEgYgOU2SvUIcOHTC2fz/MvO8ePDJ7JtIGDMTeRx6F/U46ETExtREsFQH0jddfR3FxMSZNmoSJEyciKioKv/7yixEmKVhSgxkTE4NVq1ahSgTROHEkcqdVixbhub//HWt+/RWOeLP3HDYMJ/3tb6iQ/ebMnYuOWVlIEsGXx9qwYYN7V51XAkpACSgBJaAElEDYE6gtXYV9dXxXgNrIvGVLUV1aDEcEyGWLF2HhRx8hd+0aHH/l1WJPWQl2gefl5uLZp59GdHwcRo0ahU8+/tg4Cg0TATE9IxOLli7FAhEeKRSWl5ehc8dOiI2tjXDbli24/9JLsXnWTLSLjkJGTDTyfpiGB6VrvoZd4aN3x8rt27F67VoUlZTinHPP8V1oXasElIASUAJKQAkogTAlUFs6CtNK1Ffs2T/+iO/efgtZkjErNgbjs1Mwa1sJvnrgfmwTzWRply4o6dQVxdsKULp2ExJ79UJGVnskxCVh/dp1oIB5hGg8p3/6GYqkq317/jakipf6IWcehijRQrrTL199jXW/zkKKU4X9xMFon37t8db8DXK+fGSIF/tBRx+NvK1bsWHdOozcbTcceOCB7t11XgkoASWgBJSAElACYU+gTQiY8xhgXbSUDmrEwcdBv9QErC+uQIloLX/+6AOUDhqGigEjkJ6UgA3bSxC/ogBbtn+HrVvW4KCDY7B+/Xrk5m5EUVkJoldvR7ex43HiySca7WauaD3Zhc4uc2ozF86dLY3CQYz821ZehYVrC1BS5aBa7DpHH3oYjhanHk1KQAkoASWgBJSAEohkAm1CwOzQrSsqRAgsE0FvQVkpflhehQrRQBZ274qsMROQkZ2NZOnKjk1MRHanbqhw4lDsxCApqz9e+3kBomYsQu68n5Gc3Q7liEZ8chymfjYFT7/zIRKzO4ttZhVKi4tEs7kFq36bhWgnGr1qqjCjqAy/FZWgxIlCSVSMscWM5MakdVMCSkAJKAEloASUAAm0CQFzn0mH4NWRuyHvt19QI0Lm+ugkVJQ6iKpJRfe4VGS374JOPfsgLbsD4qLjUVNagljp+i4tKcT66V9g44rFiMpZhpQundB1+AicfsYZmDt3DrbOmIOycgfbcvMRJU7naQk9MH7CaMyr+gT5yz5HrFNtWhn/9jtgP+x5yCFmWf8oASWgBJSAElACSiCSCUR8HEx78ZYtXIT//PlazPvhZ5QkdkaHnv0xZtIpSExOQu6mlcjLX4+q6GpkdmyPHp0GIrG6EotevgdRq5eJoChd3jKeeaVoIbP23gtjzz0Pq3NWYeGi1cjosi+ysrshMSkNseKRHiM2nlu3rMdXr92KxFXz0F6WBx99DC66+WZ06tbNFkenSkAJKAEloASUgBKIWAJtRsDkFcyRsEJXXf0P9B96oAiFXREXFwdHnHaio2VaXYWiwnzxJM/Bps1rgPnfInHNUmSK1WafhHiMTEvE4sIyLKqqRvX4vVHZuRMyu+yJnv0ORGVFMRg7M1rsMFHjICExGVOnPIm8Dx/GqHbZuOnr79C1b5+IbURaMSWgBJSAElACSkAJuAnUdoF2b4nA+aTkZKS2a49OXXqKtjEaNSJUMlB6tWgra8QxJzW9HQYM3RtD++2G8o1rRPisQqrkG52RhHHDOqFPRiKSJK5l2YocJLYbjY7dxqKivNiQMsKlzEUJ0RqnBjHRiegwck+k7LY7nDgRPDUpASWgBJSAElACSqCNEGgTNpj2WtLbO0oGxqyqrBDPb8rWdtBIWSmCJoXMqqoKFG7LRVllOVIlR6loJBeK5rJs/iasL61AZbSD+IQ09O47AVEifHI/78RV0cw3cDicTmlc8M6iy0pACSgBJaAElIASiFgCbUrA5Mg5URL8PIpSJpNIgqK/lEmp0Vaa1TWipRRNZmV8MspKt2FbTSUWllZjVVmFeJADRaKdTOrYE9FxCdKtXns4SYZAoswqcqzpKo+LqkKNDBlZWFjEs2lSAkpACSgBJaAElECbINCmVGsUMJkcsZekLMjwQk7NdpmRbm75OTX54mUuAdHbdUTmwBHYLlrOIslbIL9cETS3yq8wJhFpI8UbXATVWmmnJpOro0VojUlORXJqMnqLreYbMv74xo0ba2XXBSWgBJSAElACSkAJRCqBNiVgMhi6eOKIYMnOcPkZoXKH9tKpFv0kNZoOp0UYdeARiBFP863RCaiOSUBVTDyK5fMP+QAAQABJREFUpGu84yHnocOQfVAj3eyScWe7sNMdne5FEt6oRjzSe/fqjQkHTZRu9ypMnzY9UttQQPVioPrCwsKAjtFaO2/evLlFTk0+27Zta5Fz+TtJWVkZioqCp433d+1Z31Coc0vyqJDejrUyhKy/RGfCnJwclJSU+MsWktuCeb/4Y0W7eratcE3B5OSPQag8V/yVUbeFN4E2JWCaLnKreHRkZJ8adnqLcCjOPKZbm/3b8nCqkfXJaZkyYs8EdJs0GVVjJiJu72Mw6Kzb0ffAc8yoQDuEUWb/XbjkPBerxW6zqLQcK1avxjvvvme0lympKeHdUoJUejJ66623cPjhh6NHjx447rjj8N133wXp6C1zmKeeegpjxoxBVxn6s5uEnrr77rsbdOItMk79bjI86MiRI+v8uQWMTz75BEOHDkWGjGGflZWFXjKE6dNPP12rzTXoxAFmWiXRF84++2x07twZHTt2xMSJE8F1jU31XXsKT4888gi6d+9u2kbPnj0N4wcffLDF6+yvbsHiwXOskyFjr776atMuBg0ahBtvvNHfqXHPPfegd+/eeP755/3mC6WNTb1fvOtQH6v8/Hyceuqppp2y7bC93nTTTSbCh/exQnE5UE786Nhrr712ebbceeedtaobKs+VWoXShYgk0PZsMOUy0vIS0j0ukqX8Zxh0/kS4NInbxLayRiwqRXM5cPeRiItNQGxcR0Sn9tzpeV4tAqnYckr+HQKmmTN7U7hMFPtNp6JU4mFuRvnmMgwYNhR77733jsO34b9bZQx2vgCmTp2KSy65xAiaKSnhJXjfcsst+Mc//mF+06ZNMy/6iy++GBQe//3vf/u9us899xxmz+ZQor5Thw4d0KVLF7Px66+/xpFHHmnaF1+WGzZswGr5YLnggguwadMm/O1vf/N9kCCvpcC7//77IyEhAd9++y1YFr7E2J5Z/z59+jTojA259rfffjv+7//+zwjsl156qTnuf/7zH1x55ZVGy91SdfZXoWDx4Dlef/11nHvuuciWkcRefPFFw9nfuX/77TfDx1+eUNsWyP3irkt9rPLy8syHT3x8PObMmQNO2V5uvfVWLFu2DK+88or7cCE3HwxOjz32GH788cdd6nbooYd61oXKc8VTIJ2JaAJtKg5mqYw9funV/0S//vvI2OGiqaySbseaUnOBKShGifWkTdEiXC5bvga9Bu6LePEWj4oTb/DYOMlDLaXVWv4+3SGecjlKNJjA3Jmv469XnSZORdFyvv7mBW2P3Ran/LreY489sGDBAiOUnXnmmWGHYd68eR4N5C+//GI+MtgWKHDNlPHuWbeBAwf6rBfzDR48GP2lLbDunHLseqbi4mLss88+oKDKlwTTqFGjzLEotPbr189ouo4//nj8/PPPZj/a9FIwae7EDwK+3N99911MnjzZnI4akCOOOAKnn366EYzqK0NDrj3NSNq1awcK2RQI+AHHxHu2U6dOSJRhXEOh2zMYPFgvfmycc845GDt2LD777DOjoeb6uhLNE5h3/vz5Jsujjz5qPtLqyh8K6wO5X9zlbwiryy+/HA8//DC+//57cy9xfzLj/bhmzRrzUTtp0iT3YUNmPhiceJ/wY++aa64x7cRWjh+GfLbYFCrPFVsenUY2gd8lqsiup6ldUlKSCJa0wRQxkTaX4rRjhUUTtsh6l8twkdFx8vKOSkR0fDqik9sDMQzKTrvNHULlzvefhxrXesRNyRMjgmV/ebgNHTaszQuXhMRuQApgfBGEo3DJOtx///0SM7UaxxxzjEcAoiB0hgwdyvXUltSVZsyYYYTK9957D6eccorpYufDnj92/TGdfPLJZrp+/Xps374dzzzzjBEuuZJd8a+++qppvxTGZs2aZfI25x++mClc8iV12GGHeU5F8wYKgizPkiVLPOvrmmnItadWljZhFEbJ0ibeszQPYJ3d6+32lpwGi8fSpUtx2WWXGdMHOgCyfvUldp2zrf3hD38wWa0AXt9+rbk9kPvFlrshrMrLy/Hkk0+ae2P8+PF2V/NRQs5MN998s5mG4p9gcHriiSeQmZmJ6667DgceeKDn5xYuQ+W5EorXQMvUPATahIBJoXC2dC999umnKC8plrCU9B6nYwm7ur0QyKg+0bF84CdRGck+cMnLF55oOHcoVcy8FTS53pFucZd4KTY/kl8yt/YLUQoVEonaL74A2L1KG7JwTeyiZKImyZ3s8ptvvlmnvde4cePw0UcfmdGj3PtynvtRS7fffvuZTXxRsCsrLU205q7Ut29f8MfUEtpL250/fPhw87J2FcUIyGzfLLu/1NBrTwGa7YOa2euvv95zSJaBpgEnnHCCESA8G1phJhg8KisrcdpppxmtNbXT1DrVl2hSQgHi5Zdf3uU61Ldva24P5H5huRvKavny5aDTD3sEjCOnq9K0d2ZiWX5/ZrsyhMBsoJyoqb3rrrvMxx6FS877chQKledKCCDXIrQQAS/pqoXO2oKn4UPl7bffxr333Yc333gd8+b8isqyzaJhpBAoBTFC407JMSpelmONJnIXwdOqJ3/XU8rO7FaXXTwUJRP/i6aTMdjDQcvQ3JeC/GlvyXTWWWcZG8T//ve/eOmll0zXVXOfP1jHpwMKNbBM1N65E51SmKhJoZagMYkaOwqebgEqWUacokOPr8QXR2pqqtF8+toezHVz5841h/OuL1faOq9cubLOUzb22p9//vnmWPfJvXrRRRcZb+mTTjoJFHBvu+22Os/TUhsC5cFy0kmL5hS0PaZW+IMPPjBdu1999ZXPD1LarrIrnfapVlhqqfoGcp5g3C8NZVVQUGCKyvvP24zC3kc0Q6EGOtRSMDixp4M22rzfvvnmG9xwww0YMWIEaMriTqHyXHGXSecjm4BHNIrUarKrkTcav972O2AiSkqLsHb1UtFiuqsuYqJoLmVoHsFACZFDSNIJiIlCpPyTLDvFULPObDJzkl9sLj0/yU8NZkwM9/l9D5u/rU3ZxcXuTyZqYdjFxwcgu5XpNUvnhnBItAuknRMTbQXdKT093bNID+PGpI8//th0C9vucX/7UsClpyy72L01Nf72a+o2K1B515fHs3X2V9/GXvu///3vRrvH41Pj3adPH/Oi/OGHH4yGl+tbMwXKg2W3ERMo8LA7l13fV1xxhenSPOigg4yzmLuOtMsdMmQIrrrqKvfqkJ8Pxv3SUFYDBgzw8OD95E58/ttEM4tQS8HgRLtgfrRQw80PMib2BNBO+n//+1+9VW7p50q9BdIMEUPALWVFTKXcFaE3IbUF9DL84qvPUVZRLOaUtKfcmcuhqjFWFihc7poYM5PJeJ67NlPoNMKobK5hN/rOHDt0mnJIibiuAiaMUwqxtW/fHi+88IJx4KCWgdpMCmzUWi1evNhFNjRn2Q1nk7fA5f5Y8dag2H3qmrKLmeFUJkyYUFcWz3raeFKw+9e//uVZ15wzts78OPNOts7+6kuHJKaGXnveL3To6N27t9mPGhnamrKLPBRSoDxYB8uE7Z8vdv7oMEZzCGqf6KRhEz++vvjiC+MUF27PEsuKdWnq/dJQVmxf1ryEml5+hNlEUxMmtleGRQu1FAxO5MuwaTS9oE0vf/YD8MILLzTmGP7q3dLPFX9l0W2RRSDiBUw6CZx33nlIEUeFgpzVyExLR3ex96p2pIvcCJciWJo+btFEmiSCo9Fk7hAg+dcIkma6c16ESmN3uVNIra2o3KnBlJXh9lLwVDGIM/YlQWcWGy6DD3vGO6TNFG2nHn/88SCesXkORS/muhK1UTbR47uhiQK27R63Altd+1KLxxcHzQtor9kSydbZV9lsnf3Vt7HXnjZ31MDQpozaTGppqSGlXdnChQtbosp+zxEoD3Z3W4GCH1ZW8Bo9erRx+uHJKVQywDyDqdNBhbERGW813JJl5avctu1wW13tpzGseBx61fNDjVrz3Xff3cRt5TPHxhWlljNOFAuhlgLl5Ks+vIeo0WT8XHad8wOmrtQaz5W6yqLrI49AxAuYvGR80FwpmoHSWPEOF2/waBnNx2gsOf3dgFLWUciMEd0khQl2lct/M+H6nc48RqjcsSwruZaTnYmOQDsEzNjYGK9ueJunbU3taCzeTinUKjPoOFMoCA/1XRU6odjk1pBwnX1hUiBiKKKGJnbncd/6usf5kmCev/zlLzjxxBMbeviA89k6e9eXB7Z1HiZREupKjb321157Ld5//31jM02tCu0TaTdGEwt2A9JerTVTsHiwDt73g/X2pdZ20aJFJvYnP0DI4Oyzz/b8qOVkevbZZ806X3EPTYZW/mNZsRje7ce2HX/3i2073L8+VszDdkhnGcaTpEMdtZpWM8ftZBiKKVBOddWJAjVNL5hsaCvvvK31XPEuR3MuH3LIIUbRQ2WP++fdJpuzDG352OwbbhOpj3jfZkpXwpr1W1AptjgJSQkSqsi76tIIo5NEZNyht+RWaidlrUxFFmfsTAa53ClUWuGS3ehGW0lh1HiUS8jMWImdWVu16X2yNrFMY3Mmmih4J75U+aUdDpzYvcZwPdaRgHEsbaK2iYnaGOZpaOKIRtRO7bvvvnXuQiGDYZFon8cXZksmW0df3eC2zv4EzMZce2ot2T3Oc9pBCWhDxgDZjP/J4Nk//fSTiTnakgzc5wqUR58+fYyDFofb5P1A20qbWGfeBxQwOaUNHTW6dY3YQ+0wf2wX7tA89nitPQ30fmkMK1tXavYZqN8mBumnDSY/Us4991y7OqSmgXLyVxnbLmzkCXfe1nyuuMvR3PPUavfu3XuX07SEDfsuJ22DK9qEBpPXlV3l/TLTUbIpVxx9qhAj3bO1E4XIZCNg8gFPgZIyZZR0lxdu34qN6xYif0uOiJYS2kjsK2l3yeQRLmWeCtFo2VZaXGa2aSPeoT0mDF9f0bSPZeJwiKGe2H6OPfZYU8zp06fXKq6tG72dG5r4gKcBPr3HfXVB8zgUZtndRS0Hu8bdgji3URhpzmRjLlKw8w651ZA6s+eAyeZ1l9X72rOrjnEwrRBn85I5BWwmK9TabS09DZQHr58Vuhlc2534rGA7YB5qwfnxQU2m988Gu6cgxW0cajUUU6D3S2NY+ao/748HHnjAbKI5Doc4DcUUKCd/deKHIdvUnnvuWStbaz9XahWmmRdo989IF94/a6PazKdv84dvMwImb7R2EjsoqrgcM7+bh1VL14hAKBKh0U7KCD3RqebHZSbj3CPCZe76eVi78B2kVM5HSvVsbF0/3XTVUZBkMtpNec8zsHpBXj6+f/tT/PLKM1j11ot45Y7bUSZhaNpyovE9BUg+7D788MNaKOjdz+sSqtqFWoWVBQ7TyMS4hO5kY0HSoN4mhiuiF2xd3bpTpkwBNVl1dY9TAKVwRS0Wg527P1boFEXzAuudb88Z7Ck1bNQyUwtk7Sl5DjpOMFwSRzCyAhPryfqy282mxlx7G06GI7Gw7u5kh89s7TA9jeHB8vtqA/QKZ2IXt7ttsE1RiOcHBW3nGAaKURa8fzYoOzXf3MaQVaGaAr1fGsrKV/1p48qwRLwnQ7V73JY7UE58tnr3MlCIZMxhOo25nfRC4bli663TNkBAtCBtIr379FPOCV07Owent3P2aj/KGdVlb+fcc+5w7nnoE+eu++T3wFTnzvv5+8z87nnwC+e8i253Tjz5LOeSi8933nn7LWfGjJ+ca6+9xvm/Oz9w7n1qrnPX47Ocux79xblHpv+6f5ozadx1zkG9TnfOad/TuaZdunNmVqbz9F//6lRXVbUJxnVVUozMHTGwd6SrxhH7K5NNtIBUvzl//vOf69otJNeLXZMptwzvZ8onmiazLKGDPOUVodCRrhmz/qGHHvKsd8+INswRzaSETBVduFcSwdMRxxazv2heHBG+zE+60xwRMBzR7pjtXrs1y6I4TThiA+eIsOiIAORI3E5Hhvx0xIZW7ocZnnOynryerDfrb1Njrr0I2+YYonGyuzviQe6IwOWIsO1Z15ozDeXhrw2I1trUU5zbTFWYV8adN+wkbI3f6klMTLOvDCnqN1+obAz0fmksK9GCOzKEqblHJNpCqGCotxxN5SQCoyMmAI70CDgSb9iRDxVHbLsd8Sp3Jk6c6Iig6Tl3KD1XPIXSmYgm4N1PHJEi9Qb5kn3+jjvgFG7DqPhEdEkuxbfl1Zj1zdeISk5Ackqy1FtGIheNJbtm+IuNjkX+1g0oLshDSlJ7/Dp7DpaLqr1YuvEWrZgBxG3CkKG9xBM002g7l85ZiO25W9C5Ig/HtXPQIbU9Xlu1BZ+/8DwOkpiPvRvh/BFpF4FenbSlY8B1ambYZcNRUTiSCWNihlO69957TdxKOtuwLvRapbcv19tk2s9OEwxfnqu0N2T3ODW3zOudOJLNl19+aVZ7ayZsXsYRbYnELmuOxsPA5xxph2WnAwU1sHYEI5bD1pORAdx1asy1p70h7eiuvPJK00VMDR/NEajhYVsJhdRQHv7aAD3DWTdq6KjJZLB92gnSYcdqcuuqKzX+THZaV75QWR/o/dJQVnfffbcJ6cT2Qq07tenWcSpUWPgrR1M50Qv96KOPNr0c8tFhInJQ006tLZ3m3O0klJ4r/ljotsghEEXxOXKq47sm3332KW6Srqe0snKMTUvGRvEm/619FgqzkjBMHkZde/ZAlXRF0j+HOGSIcnmCV2Lt4qWIlZXOxiIJgdEJJfJyLSivwkZ0R2pCBjYXFiBBXgzF22X85NwCpG+NRufiOTg4djniYmLwa2Gp5I3GrTJSy0gx4m/riSGJ6DHO7l52m7sffuHGhkIBheSBMt68t5cr67JlyxYT89Pb/onbKKR9/vnnJpxKOIWgYdc8ryGvnbvLnnVioq0mBTBfPBpz7cmH7YT3IruBGXEgFFN9PPy1AdaH5gS0DaNAYLu+Q7GewShTIPdLQ1jxg4dhn+g9Hc4sm8qJH7p0DKPTnQ1/FYzrpsdQAoEQaBMC5kIRBK448nAkJqcgOyML61fnYGm5jPDQqxtOEhudngN7orKGo/f8LmtHx1Ri0Yw56NSnG+a89iW6lNVgQ2omVsdnIiEtA+2T47GuoFAGAIpHclKi2F/mIn/WIvTbuAj7RZVjcVU5KkU5Fd+1F+4VYaLzzuEEA7lYuq8SUAJKQAkoASWgBMKBQJvoIu8tX7WDjjwaxVXV6CzdfBWLFqLs86no3Kkv1sxeLCNDVqPboJ5iZC9CprlqVTLyY7Us74i7FyPB2QsSHPTf/1CUrd+KvA3rsamoGh06dUZ/EVJzF87D6D6dsLl8M5y+Y7Bm+TIUrMlBdUIizv7TpSpchsOdoGVUAkpACSgBJaAEgkagTQiYW2QEjXXi9dqjW3fsJd63ldK92f3UU3DTbbcjV7oy75FwFr+sWoeRB+4h3bZAdan0kXMscScGZRJyKE6Gkkxul44MCXUxoXc/LJJxqTesWonoTTmIRREuOPIg5BdXYYbE0CzZsBJlYhczYMhQ7H/sZBxzxulBu1h6ICWgBJSAElACSkAJhAOBNiFgMtZYsgh9GzduwPsfvG+M6q+86iqkSjgQ/u676y48/cyzmPLqJxg2ajTaZ7YTI3yxxSwUgXFRPqLEvgW9+yJWbMHy8zahbPF8jMxMhniYm1Atb4kTxMeffYe9xo5EXnwVOuwxxjhFhEMD0DIqASWgBJSAElACSiDYBNqEgEmng7POOgsMuro1Px/7S2zG0TuHKSRQjr5y6SUXY+TwYXjwsSewuUMX9BfnjQrRVBasWIbUZQtRVViCOeIslC2xwa/84wlGsKSTCmPX/SSeizEVRchOT0HR9hQsWLDABMluzKguwb6wejwloASUgBJQAkpACbQWgTbh5GPhMjg0A9By+ChfXrDMxzFw7733fsz+8H2k5KxCgjj+DBGv580yrE/0mLG4+c03kZj2e3BjOgZxpIgvP/8CyakpJkQLPfkYEiKcvaQtM50qASWgBJSAElACSqCxBNrMSD4Ew/h9HHavLuGSeTjqwb6D+iNm1SoJUVSFHjKm+JDsFHSPj0LBjJ8w9Zn/MpsnMd7dmWeeiXHj9zTH7SVORBLoV4VLDyGdUQJKQAkoASWgBNoagTalwWzIxa2WAMjXyBB9Od9+hSwRHkeJ7ebh/dpj5eZi/C93OxIkZt2tUz+X4Oy7xuaj9pNDtzHYtCYloASUgBJQAkpACbRVAioJeV152lTmb9+GKqcGZRLHck1lFT5cvhklIngWS+ii7ZvzUCqj+fgSMN1jvnodVheVgBJQAkpACSgBJdBmCLSpLvKGXNX4uDgMElvLMrG5LK2oRjuxsdwuQuaiilIJSARk9+2LdBkxQpMSUAJKQAkoASWgBJSAbwIqYPrgcrKM7pPQtQcq2ndE4h5jsVkCphdVOSiJk3FfL/4T4uLFlVyTElACSkAJKAEloASUgE8CKmD6wDJg8BBccttt6DB2T1SOHY9ccdyJ6dYT5/zrdkycfKyPPXSVElACSkAJKAEloASUgCWgTj6WhGvKOJYvv/KK2FoWo50480THxeCs885DNxE0NSkBJaAElIASUAJKQAn4J6AaTC8+FRUVeP7557FVhpAcPWY09jlkEkrFDrOotNQrpy4qASWgBJSAElACSkAJ+CKgAqYXlXwZ6WeZjOBTVlaGDRs3Yt3atSguKsK8efO8cuqiElACSkAJKAEloASUgC8CGqbIi0pWVha6dOmCDRs2GKFy4cKFRtjs2rWrV05dVAJKQAkoASWgBJSAEvBFQDWYXlTixUP8/PPPN8HS8/LyQI3m+PHjMWbMGK+cuqgElIASUAJKQAkoASXgi4A6+fiiIutWr16N2bNnm+El99hjDx2dpw5OuloJKAEloASUgBJQAt4EVMD0JqLLSkAJKAEloASUgBJQAgER0C7ygPDpzkpACSgBJaAElIASUALeBFTA9Caiy0pACSgBJaAElIASUAIBEVABMyB8urMSUAJKQAkoASWgBJSANwEVML2J6LISUAJKQAkoASWgBJRAQARUwAwIn+6sBJSAElACSkAJKAEl4E1ABUxvIrqsBJSAElACSkAJKAElEBABFTADwqc7KwEloASUgBJQAkpACXgTUAHTm4guKwEloASUgBJQAkpACQREQAXMRuIrKyuD4ziN3EuzKwEloASUgBJQAkqg7RCIbTtVDaym69atwxdffIGSkhJkZGSYsckHDhwY2EF1byWgBJSAElACSkAJRCABFTAbcFGLiorw1FNPGc1lz549kZSUhKlTpyIhIQG9evVqwBE0ixJQAkpACSgBJaAE2g4B7SKv51rn5eXhs08/xdKlSxEVFYWRI0figAMOQEpKCubMmVPP3rpZCSgBJaAElIASUAJtj4BqMP1c8+nTp+PVV1/Fpo0bUVFZicLCQsyfPx+rV6/Gxk0bkZqa6mdv3aQElIASUAJKQAkogbZJQAVMP9f97XffRVRsLI46+li8+fobRtCsqqpCtKxDdQ0mHXSwn711kxJQAkpACSgBJaAE2iYBFTDruO7Tp0xB7rdfo7yoGDNXrUJ8fDxKq2OxPmcjuiYA/YaPwG67jfK5d3V1NX744Qej6ezevTvGjRuHxMREn3l1pRJQAkpACSgBJaAEIo2ACpg+ruinr7+Ox6+4HIllRUiodpC3agWyhgzBtc+/gheeewkbly5ARZygi4nxsTcwRYTTd0X7OWDAACxZsgTrN6zHEYcfgV9//RVl5eXo1aMHyjdtwobly5DZqRMGjhmLdl26+DyWrlQCSkAJKAEloASUQLgRiJKYjm0uqOO2bduQn5+PrKwsZGZm1rpmlSIAXjhhAormz0HX+DhMaJeGDWWVmL69CH/673Mobd8RLz33HDqnpWBEehoGjh6DwRMnIqNDhx3HEZw3/fUfyC/ejpNPPAH5m/Mw7ccfEJ+QiMrKCnTq1BlbCwqw7oP3ELtyBZzoGKT36oOTb7kVex51ZK2y6IISUAJKQAkoASWgBMKRQFhqMNkF/eWXXxrtYO/evbHffvshLS1tF/6rRXuYI0456e3aoa94f6eJQDl37lw8//zzYOihLqI1PPGEE9BfNI2Mb7lFhM5Zs37Br7kbgE7ZaC9CYec+HbB8awkWbK3EPa+/iSynBlsXzEfHinKsFKFzYfR/8UW/ftjjyquQLNN40WrmlVZjW2ECPpryE8pK85GbtwWx0VUYs/toHHf8Cfh62jRs7tUbvdatRbL48a9bvQrPX3cNegwbgq59+u5SD12hBJSAElACSkAJKIFwIhCWGswPP/wQr7zyCnpIVzPDBXXs2BHnnXeesZMk/BrRIr52772Y8ujDqM7fhlgR+jpLUPRjr78eU2fPwaYNG0yoofKKSvzy229I6NoehTWVWC/e4St/no0aEfpisxKRFZMkAmU0tkfHYlNCd8Qvn43sZXOQJY4+45KT0DcpEdtRgzVlVchJSUXlWRciLj0dFSJ8bsndBqesGmVlhYipBtKkq31wr2wMGNgXS1auxOa583DaqjnolRqHt5fkYm5FNU5/8AFMOv3McGo/WlYloASUgBJQAkpACexCIOw0mOzR/+6778T8MQYjRoxAZ+ma/kyCnj/00EPoLUHPu4ngt2LpMrz6r9uQXlOFzKhotBcjgLJFC/Hfiy5E5aRJiO3ZAznbC5BXsB1r4qMxdq/BSBFnnpKlOejbuQs2bNiIqvVFKE4RATElGRCtZXTuEqStW4FO0Q46iMNOp8R47DGsExIyEvHO9yuwrbgIGXHxyNrnYDjSFV5RUYzCbfmoytuOTYtzMG9hDuISqrAhdxqKy0qApYuRU1SCgjJxHKqsRpWUsUg0opqUgBJQAkpACSgBJRDuBMJOwGSwc8af5Jjgv/zyi9g2xmPz1i3YuHkzFv70E7Z/PhXiso14EURjRLvYT+aP7JeNB3JK8JvIb86CHJRtkq7wmXMRIzaW7XtkY7PYW25bvg7V24sxTITWYydPxsfvvYf1ebnITExC8sb1WDv7N8SkpqMS0Sh3qkXj6aBCrn5+XhG2V9WgqqYaW5YsQGHPvshfuxbFWwqAciAuJgVpSe2x127JyBWBc+WyLahauQhdclfiRwl3VLnNQYkThbKYOPQaPjzc25OWXwkoASWgBJSAElACCDsBk9fsxBNPRE5OjvxWIzE5BftP2Ad9xf5x1cLFWCTd1wtmzECsU4VE0QqKPIqisgqkoZfYQQ4Q08r26Dy5H/KW5yJFhnpM6xAljjirsT2/CFVFpdgqwmpuWqqxhSySvvIq+RVEp8Bp30W0kmUorSpHMaKwtLwC22atEc2jeJlLTMwyKVfRhmIkzMtHelJ3dO42Wrrv0xBtPc1L16FLu7Wo3rwBS0vyUBi93mhGq2X/anH02evEkzB8zz21SSoBJaAElIASUAJKIOwJhKUNJqlv2bIFCxYuRGZGhukqt1eC9pc3nHUm5rz3LlJFq5guWsJMETLXxQzFxqhR6HrYAOx18QRUs09aBMWa6lUihG5H8fYyzHzjR8SVViIlNQvVoqksSijBkhnr0bv7cIzZcyymv/044lb+hnTRjKaI5BobFSNHAKrgoDI+Gb0vfgTtB45DlQiiNVWlMna5GF/KNke62KM4Ld8mp4wR56TVWPHtU4jPX4MuYj869uBDcNYNNyDdy6Pd1kmnSkAJKAEloASUgBIIJwJhqcEk4OzsbEzYd99dWEeL4HfYKafgp0+mILqsGE5VhWgL47E1pj1qEmrQdWwPVBZWorpSBMzYEjhR+XKMGulVj8OYE/fA2oWbULSlBh3ETrNfl0TkLPpEtJRRSMvsiOH7H49fNq9FTdFmxIhtZ7L8SkWIdUSIzdrvD0jvMxLlEjvTqa6UY+4QLkWuNEnESzjx7Y3t6MixneW8JZgwOg0nnTAZaeIYpEkJKAEloASUgBJQApFCIOZmSZFSGVuPXv37I1FCEn3/08+iXYxFQVwfVGcPx7BTx6DXyN6ozhXhr1h0ik4pouJEwBSv8RqxqYxPiEWH7tno2n8AsjoPRcG2aqyYMQeo2NHX3rv/YGT2GoxCETgL5BD5UbGI6tAdHSaejt4Hno0o0VQabaVoUam5/P/2rgQ8qvJcv8kkkz1hhwSBBDUurAoCraKCKCIParV6rbXV+lRrW5eq1dvbRa329umjta3a3fbR6tVaV3BFRVkEQURAECSyLwmBACH7MpOZ+73/5J8cxkkgGaIzJ9+XZ3K2//xz/vds73xrSAIy4SdJzOXk88miMU3B3j27ceroAoweNSLUTP8rAoqAIqAIKAKKgCLgEgQSVoPZEf6e5GRccNlleHbBBxg8bAKSAhnoU9wHefk58It2MljfSgD9aZLoPBNJ2U1C+iQkKCC+lsF+SE7KBX0jP1q1UkzdTRg9ZghKNn5qgosGDzkBAwqOFU1lAz5evRAnjpiMfkPHoEX8MEOmcBrNSSeFYhqOGZR5qfgj/QeFmNJUTvIZEM1nqCVbqygCioAioAgoAoqAIuAeBFxJMHl6mM4oo1cuhp5dDI9oKMnx/NXiLVnbSuuSRKvo8yKpYRiQKWRPorgl5ltIX7Ihin4hjLU1fviTMhFI9aBFCCHTCAUkX2ZQtmVm9UdGTj68eYOFXNLP0prEpV8xnZNiiodn6IsZacTlQzSbEuVuA4Bkq4oioAgoAoqAIqAIKAJuQYBMyJWSmpoKjxA6X0ACboRMBgISaOMXoiem8DaR+RYxcwfThf+Ra9NTkppIMZeneDBkaCEamwdg2fJSNPlSMGBQgWg6s4Ss9kFyKjWdXkNGuZ/5kECSTIY/EgQkEeIkl6E2MuGctKO2M0V8N1UUAUVAEVAEFAFFQBFwGwKuZTiGYCYzSlxIXwoJoMzXU6MYwalJOLmZYqfSllxx5MnF8G3yIi8tBwMH95ba5b2kiQfJ0i9JotnB7CP9kjTKGuot29aTSMoit5gp50NCgukxqlW7RqeKgCKgCCgCioAioAi4A4EItuWOQXEU1A7SBB2QJOhMzm7FEMOkVrZnpkICmbKIUeVhEkhiSN/JIPIH98XoU4pN1LpZY0zhoT5Nt2ZZerffQUZp+pHW4XXhb2+dkf5Fo5pitJt2W8+YHjx4EPy4QfZJcv+uSktLi1SM2i3uFXStOLz4Jb/rl40bixvU1n4x1aYS4Tr5IvGwVwgtMcwBXF8v1cASTGK5X7oy1ETF6mji1NzcjF1S+ONIpDNtj6Q/baMIuJpgpoqGMCDlIkMihM/LOcsiQyRS8rEjKEV3AvtluVK2NVPL2SYM3vH7xO9SfDApSfSvlGZ8eDHnptFZthLJkPbSNDP/DJklUQ0x0dYNsg93k3/UhPYEIVZ/+tOfcMwxx5j68UOHDkVBQQEefvjhVk1wYqHw6KOPYty4cWYMgwcPxgMPPHDEA9i0aRNmzpwpSfizTB+ZmZlm+bPPPovah0+uvX/84x844YQTcMcdd0Rt090rt23bhmuuuQaDBg3CAMnbOmXKFHDdkcivf/1rjB49ut3Pz372s3A3iXKdxIIH8/eOHTu2XTyIVUeE4Le//S0KCwvxr3/9K4xbvM909X7paVh1FafI819aWopbb73VXGd8bvzkJz+JbBJe7kzb8E46owgcIQKuNZFz/ClGgyl5Kg0RFCqYJRSwWoik1Hgk5zPEj3yyIUQUg1JnXKJ6kJQnUykDZHihE8hWYkhyaKLBTSdtDbhov6ttLdeFSKvRikobihxFj/HBJMn4xS9+YYjYD3/4QzP+Bx98ELfccgtqamrgJBlmYxz/u/fee3H33Xebz5IlS8yL/oYbbjCJ/3/zm990eOR79+7FmWeeiT59+mDlypU4+eSTsX79elx00UWGtK1atcoQONvJG2+8gZtuugmbN282q6ZOnWo3fWFTkp2zzjoLaWlpWLRoEfjj4Ctf+Qq++tWvguMvKipq91iamprw+9//Hh1pZK677rrw/olwncSCBwf6+OOP4+OPPw6POXKmf//+yM/Pj1xtllevXm3uo6gb43RlLPdLT8IqFpycp/4///kPrr32WmNxe/LJJ82969zunO9MW+d+Oq8IHCkCrtVgEoAUyTvZ4m9NB0RymCbEsL8QyxxZyBGSZ3wzDWsM4xWUmo/BGlknCssk42sZSj8kfFCEZJUfmZVUSJLRUjSbof1JIg8ll7K+ldiGOo8grD3EB5Om3fvvvx/Dhw/H7bffjoyMDPPhfE5ODh566KEQPAnw/5NPPgFfBKeccoohmOlS5/7666/HRCnxSc1Se1pIOzS+MGkWpyaS5JLCKbWDZWVleO6552xTMx0/fjzWrFmD733ve4es/yIXfvzjH2PHjh3mHFK71kuqTf3ud78z47jrrrs6PJQXXngBDQ0Npv0777wDEiT7ufLKK+UWSjZlX9lJolwnseDB58Pf//53XHDBBXjmmWewYsWKMB4k65RLL700anYJmuOvuuoqKVcrv44TRGK5X3oSVrHg5LwU+Hy54oorzDOFP2L4w7A96Uzb9vrQ9YrA4RBwNcFM8wrBFBMjiaIhe8L5kjIlEdEA+UgN8mQhmSEhSZSPUTSKbpEk05rKxU+TPDFELEkSmSg91F/IJG42CtWkapL9tEp4Njxz6AbplPk63S579uwxWkr6jDn9DUk0e0syfBIL5/p4xuMPf/iDOdYLL7wwdA3IwfJa+Na3vmXW33fffR0e/saNG832SD9GugtQqPFzCrVZNKEXFxc7V39h8zt37gS1HNRenn/++eHvnTFjBnhs//73vzsk1c8//zzmzJljzHXUvo4ZMyb8IdE8QypxWW1dIlwnseLx4Ycf4jgpAjF79mz8l1Qbo5uFxYSmSsrll18extk5QzMnr7VvfOMbZrV5BjkbxOF8LPdLT8IqFpzsaeez5cYbb0SelE5+9tlnzbPVboucdqZt5L66rAh0BgFXM5w0b6pEkUcEUZAtkguKOdyYxMNoyXqiwW3USsq73pBGwy5DJu62hzpJJ4kjP9HEro+chtrafXtCFDl9FGlWLS8vx5133hkGi7+wqRlrT2MTbhhHMyRFFGoWnWKXqYGkH2F7QtMyhZq/rVu3hpu9/PLLhjxcJsUBogkzInwZYk25I0eOlFKqksrLISRH/GEQqXV1NMGLL76Ic845x7nKzNMtgB8nmUqE6yRWPCZMmIDXXnsN0c4ncRw4cKBxoYgE7O2338bf/vY3PPXUU587D5Ft42k5lvulJ2EVC0483/TTpkWgrq4OdNMpKipq9zLoTNt2O9ENisARIuBqgumVF3OLzx8iipGACPcjYRSqaLaEyKPMhxblrpXVosW0JnBDPB19WLIZaPWv5I4h4mgb2Y5Cy+St9kPTYJBa0PCX2X3cOf3ud79rBkZ/PJp7GQVLMkXi8qtf/SohBk3iSFJEofbOKQxeolADSVN3ezJr1ixDIg4cOGB8GD/44APjl0otH4OghgwZEnVXe63ZadRG3bBy7dq1ptfI8XKlHbOTKB/pIZBM8R7gjwunxPt10l14ULtP4hntxxavle985zuwwVJOvOJ5/mjcL9HG5zasjgZODAKkuwUDB2lp4A/WP/7xj5g/f/7nrEOdaRsNf12nCHQGAVcTzLS0VPidPktG60h4hPyR33nE5G0QaCOHXG1EtJjJEoWekiq+lpLyqKOXuw3iCbVpI6khQinfIR2SytJSn+pJQn1jtXxvI1566WUwkIN+am6Wn//85+YXNsdIH7SioiKMGjUKS5cuNYQrEcbO6G97nhik45Tc3NzwYkfR1SRqJBLZ2dlGo0uN5j333ANqqL7//e+H+4iXGUuoIsfL47Nj7mi87Y2DBJPBToxKd0q8Xyfdhcfrr79u0g45NboWFwaQnXTSSfjRj35kVyXE9GjcL9EG6jasjgZO7733noGKGsxJkyaZqPGbb74ZdEuhBYHR+FY609buo1NFoKsIuJtgpqaJiVxyVkb4OoZM30L6UoXx2Th6IkF/y9bcmDShV1TuQ+mu3SjfscdoJ40vZ8hR0+BtCWUb+bTk0mov26ZUWEpxIKGZfmz4VHyx8jMx/tQxoK/RK6+80tXzlxD7ER86lRcWFprjpaaXUdQ0kSeK2EhuHm8k4aI2zgojxTsSmpb/8pe/mCbEgRqZt956q6NdvrRtdswM7IkUO+bDjTdyv08//RTr1q0zGuzIbfF+nXQHHsSAhJtke/LkyYdAwihgBkcxJVHbM+aQJnG7YLHiAcZyv0QO0G1YHQ2cli9fbmC6+uqrjZWFlpaPPvrIBFEuXLgQt912WxjGzrQN76QzikAXEWh7M3axg3jcjalvmKiZeTCDkmidg2TEd0hoFCcRlI+QyySJLDcNzDppIev5MF/50Wq8+9o8rF/xKeY/sxCL5ryPhrpGqVkuLJGqSLYP98me2WfrlBMRs2j/ywJdO2tqa7Bvj5AQScBZIP6JXq8XdLruyHcv1Fvi/qffD03ijISllooJ8Kn54i9sEo5EkEgfROcxU3Ng5dhjj7WzUackDD/4wQ9M9Pmpp55q2jDKnhqHeBM7Zksmncdnx3y48Tr34TwJAs9/pHmc2+L9OukOPKgVt+ZxJ850I2HQBnMj2iAwYpQoYrGKdrz22uG2zlw/bsQqVpzoQmFJKl1MLJlnpgtePxT+UOH7sDNtzY76TxGIEQGrv4uxm/jZ/f3335cozTkmenz/wUb0HjehlVyG6J45UpJLkkNqK7NlIlV8gs0hAuoRc/iunaVYv3YdvJkBjJM0Rx40S7RsGT7OWovRZxxrEq/n5OQLdbQ+nNKP6d78k77bpnaO60SZKrkvpUZ6dgo27dhuXh518oKZcvbZxictflA8ukfClET0M2QqFuZPpGmYhJORw0yrwfyPzpfr0f32o9Mbg1CsVFZWmjxzdtm+MEmcTjzxRLv6c1OS6q997WsGg7/+9a9hsyjNfo888ogxG3/961//3H5f1go7Zo43UuyYR4wYEbmpw2VrHmdAS6TE+3XSHXjw3BPLSPM4c8SSUNGfjh8r1sT52GOPYdmyZaAJnWbReBOLFY+rq/dL5JjciFWsODmre/Xt2/cQyE4//XSzTEvJhg0bDsmxe7i28XhNHTK4I1w477zzjAtSZHOSbWYxUeleBFxFMKm5fPL/njRm8alSbaS6JoC15TUI+ITZtTG9VkS5QozlXiGJuTIvFfBINJMEkYraCgTSW5Ai1djOkFrm6VnN2FjrQVNjCWordqF3VjbqKzehsWGvKDNJMtu6l0WjHOWXhCgr51q3y42e5k1Dft981G7YjFpvPcbJQ+Diiy8ONXLhf2otaR5nehaSSwrzAD799NO45JJLTJ5HBrvYCOt4hYABOEzXw0AemoU5HivUNlGojWGb9oRRwLxGmdaIWnI65TNX5LRp0wz5prYqngimHWM0M7gdc2cIJl9yzPlnXQScOCXCdXK08eD4mcqJGkqmbHIKsy5Qo9texR6aOvmhj108koGjcb848eC8G7GKFaeioiLj083UZxUVFcZf1+LG5y2fMySYnHamre0j0ad0PSksLPzcMKgMUOl+BFxlIqc/214xP5u6zVVV2Lu/DHVVB+CXG8xEbcs0zP6ILZmh/EtKF6LJ6j2SFzM5Jwnp/bxI8QYRaAxiaW0Ar+z3wZNbh/4FB9G/TxYuvuQCnDKyAL1yGpCRnhmymLcyWN7MITGGeNN/6IskIl38N4OBJKmP7kdOQQ4ukpx39I+J/DXZ2oErJgzkIamyL2c7KFavYT5JiiUrdls8Tpm3k8dMoZbcKfQppDAqviOxvpZOLGgiYwQ5Jd58Um3ORf4AiMxVeqRjduJBgtCeeTwRrpOjjQc1lK+++qpxF4jU4BMrEvLIj/0xyspY3EaNeDzK0bhfnONyK1ax4kTiyIBJCn+8OYX3Gq8rtqFlpTNtnf0k8vwTTzxhUsIx24XzY4MUE3lsiXDsriKYDEYYNmyY8TVZKCkaNqzbAE/fNBMpbiO9QyeljQRymZHkqZkpSM1LRX1LAyp270PggPhLiuJzQ2EQWwoDaO5TC19TA5qafdh3oBIV+w8gSVLXLF+6Fls3l4oZXiLOxeeTydOp1Qz9haglv428U7aioakRVVUVounymAowoeNx73+eD8rixYvDUdh2tDbJNivEJILYsoaM+nYKzb4UVvWxwnRFNGc6fWstFpZo2rYWB/uisOvt1PYRSfLs9u6aMnqZZrbq6mqjLbPfs2DBAlP+kVpne8w8Ro6XlYraE+J0triDREt7ZLGJ5+ukM3gQg2jXgBObuXPngpqnSPM42zANFOtIR36sWY9aT25jRoJ4lVjvF+e43IxVrDjRTYJCtwn7rOAyn1N8ZtAdiQnYKZ1pa3bQf4pADAi4imDSPEk/LgaPBMQ0G6yukVKRIQLZRvVa0RLGx190npRk1Inmc8O6TVi9ZD1ef/ZdbN1Shn7F+RhyivjdDUlDdrGYtY9PRfXBGvMr6HlJIL3iwxViktiL5qQDWLZ6OT6Qkn5bduxE2e69qDpYLeb0plAEe1C+w3xPCnz+ZpRt3A7/RyVolvrS6ZkZMZy6xNiVJSL5AuWLlA9AK6yKQjM5tYK2bKLdFq9TmrIZjEOCaEkmTdyM1GRllunTp5tDpwad0eJMxfPnP/85PByWGUwRH1/rdM8NfAE88MADJvk2t0cTS9rsNFqb7lpH9wZq2FlJhi8vapKYMJ/m/Ycffjj8tRwnx8vAJY4/UlhGk2Uvo5Eptk2U6+RI8WjvGnDiQsJNHzzrK+fc5ob5WO8XJwZuxipWnL797W8bLThzYdLNhsLrj89bmoiZQ9VKZ9rafXSqCHQVAVf5YBIEPrBvuukmDJCcg6+8+hp8QgpDLzx6RJJUknDKPyF+TbXNKN+1H8uWrJQI8XqkSRnJFNlWfPJQjJ843kR419bslZd/heTE9GP13OWo2FKKgb5mVDb5sOVAHYaNbEROrmg/j2nGgOOzcXCfRIlLpLivSmqW+ySoJ5iMNI8XdaV7sHtNCVoqa1BQewDVLaLpoWqzBwj9yBjUwcAFmv5IVGhm5i93Vp5IJGEdbrpi0FeSWiZbdo3rrfCHC4kkxVm1hZpaav+uueYaQ6qpASQO1EIxkpjVS5zCCh8ktAzmoDBnKtvcfffdmDlzprNpt83TnP/SSy+ZBPmsyERfyX79+oEaJVvBiF9ux8lxc/yRQoLAbfS7bU8S4To5Ujzauwbs2IkjzePXXnttVLxsu8ipNaXbaeT2eFuO5X6xY+kJWMWKE4kln6vUUJJY8hnFMrN8dljrgMWzM23tPjpVBLqCQJL4DLqS5lDb89P/+W9U7k9F8cwpGCgaSb72muqFHO6pQVVFnVnec2AvNm7/DKOGFUgATio27zuI6edOR1pKunBQaePZJTywmdTUvAiWP7sA2XuqUdVrAD6WfrIHDIUnKw9TzjwNQ44ZKO0k76a8YFsCfiG2LfCLCnXl7FXYP28DaKQ4JrkFg+oXYUugCpf88l5ceEP8JdjuyoV0JPvwRcG0RLzkaN6jFixRhQ9wlg5knfBoPrRMbswkyhMnTow6RNaepk8QSRsd/aORsqg7fokrS0pE8y6FC6hxjuYkT19NErBoeFB7SUymSPDd4SRRrpPD4dHRNcAxzps3z2h8EzEN0eHOYeT2WO6XnoRVLDgRc773+FyhO4d1p4g8F3a5M23tPjpVBDqDgGsJJkG45/Zb8crjy5A/+ER4h/dBTuFAJPfKQ3avDPQdlIdefXOxZftOLFywCNmpXkmBnoTc3r0kqvccSVrpk9RFO0Xb2SjqGaGmQhpZO3zDknUI7qhFhpgeNksaJOQOQvGIkzGkQMhlkHXPLV+Xyj2iDW1orMcbz8yVfeqQva8Wk4I7cF6GmIe37kdg+HG4X/Ii5kZJZN2Zk6htFQFFQBFQBBQBRUARiCcEXOWD6QS2TFLHlCxZjCz/fuSVVyLw/g6UPbcSTXvLUTh6MLIlGrxZ/FQK8gdh5OiRaElLQWZuFsaOHSNEUrSVHgniSRc/TiGdwWahjVT0Cs/MyBHNpswzGc2g/v0w4dSRKBo2WNoJuZS8msY6KFNqMpOldA8zJFU2VWJ71Ups3v0GciXVUWWD3+hE6w5W4oDkglRRBBQBRUARUAQUAUXATQi4zgfTnpw5jz+GOknjUSSksNJ3ENuCWQiIKXvbmj1IH5KJocXHwpuRZfwsTzttHEaNZMLooJDLVDFvC7H0V4e6SpUJ02g2i+k702vM6BVLl4h/SxYaJk1GUMzqLWzQKqSWnlSBVbSX+0t346N5b6Ju6TsYlOzHWRkpqKppwgvih8kI9ZzsLORFJMe1/ehUEVAEFAFFQBFQBBSBREXAtQSzZM1aIYoB+ESbeGZGAJNSajF39y7U7U6Gb1B/1DbUYU+VJGH3piAtJw95AwYib+AAZKR5kbRfomDrSBWl1KTsDyknmZyXgoObylH60kJ4y0rRNy0d1ZVzURVMQ6ZEQqdmSDokIbP8V7ZlKzYvex8lK5ZiQN88TDt3KjIlWn3/+k9RsupDlvNBUAJ/zrv0MvSWgAkVRUARUAQUAUVAEVAE3ISAawlmSkY6fGLKbpAC4Jsafegl/pPHiZ9leW4Opp57Jr557fUScLIepaVlEnHXiPWSNmhHyTpU1wu5bA4iMz2AvN59wNyamRKMUi/R4Z898SIydm5DgSTHLk73IrOxEmUvPI6y0s0YfOud2L1lG7YuX4rjB/bBhRNG4+WKcklBMgGTJk7Aa1ISbhek7nb/gWKKz8W0y6/A1e2kpXHTBaZjUQQUAUVAEVAEFIGeh4BrCebp08/HB5IGBL5G7PQ1YZf4UfpEI5lVfCLeWrYEO5ivUnJVepI9OL7wBNxx441IF1LK5MiMwtu0ZQtKPtuIzevXo1b6aNlVhrSd28XN0of0JC+G983EKbnpmF2yB9s+WIQPH/FgmNRlvuuGq00OREaIepLEeC6lBRkZyFRJ5155Jc6T0m5ZOTkSeCQ5NlUUAUVAEVAEFAFFQBFwIQKuJZjTJd/e+lWr8PbTT8Ev5nBW2vFI5PeIiZOwaeNGbFy/AcOOL5a0KWfjvcXL8O78BZJbcIbJo8lcmrY2MGtPk3Q+dNut2B70i7dlKEqcydO9XinFRbu4JMuefsJwXPe/vwxfIgX5+WgWYrv6k7VYV7LB5A9kIu7jpGSXiiKgCCgCioAioAgoAm5GwLUEk2btnz74IC765lVYs+JDU01n4tSpKJQ8fS/Pno1/SjLaxsYGMZGXor6uCuVCIqMJqwMVFRWhnxDGz4RcNorZvUJ8OxeXVyNpd5VoRv1oFI6ZJkltnXKS5Aq8WRK+z54zBySprHIy+YwznE10XhFQBBQBRUARUAQUAVci4FqCybPF5NUjx51qPs6zN0oqqnDbdkllRILp8/kwa9YsZ5PPzQ8dMRLzpGh5st+H3cEm+MW3c2xKKgKyXCPTIbLdKex/2rnn4ozJk432kr6cKoqAIqAIKAKKgCKgCPQEBFydaL2jE7h48WJTAo/+keeIXyRrYttyd9H22yv5Km+Rmtq7xeyeJtV5ksQsPlaquKQVHYcGiUS/+5//RJYE76goAoqAIqAIKAKKgCLQ0xHosQSTJ54J0xl80xGxdF4gu0Tj+ej992Op1GGuqqnB4PHjMen0s1A4rAjTLjgfffoowXTipfOKgCKgCCgCioAi0DMR6NEEs6unvHTnTlSUl+Otee9i3/Zd6D2gP/ypGRgxohjnn3+uJGE/1B+zq9+j+ykCioAioAgoAoqAIpCICLi2VGR3nozBQ4Zg7GmnISMzG7XJQQyQUpGzZk3Djp1b8eabb4bKSnbnAWjfioAioAgoAoqAIqAIxDECSjC7eHKqqqrwyfo1kqGoGQGJKk+VJO7MYLRu3Tqz3MVudTdFQBFQBBQBRUARUAQSHgFXR5F359nxer1GU0miuXr1apSUlAT3CmAAAAGNSURBVKCurs7k0ezO79W+FQFFQBFQBBQBRUARiHcEVIPZxTOUkZGBGTNmoLKy0qQ62rZtGyoqKjBhwgR4PJ4u9qq7KQKKgCKgCCgCioAikPgIaJBPDOeQUeiLFi3C/Pnz0dzcbNIdTZkyBcnJyttjgFV3VQQUAUVAEVAEFIEER0AJZoKfQD18RUARUAQUAUVAEVAE4g0BVbXF2xnR41EEFAFFQBFQBBQBRSDBEVCCmeAnUA9fEVAEFAFFQBFQBBSBeENACWa8nRE9HkVAEVAEFAFFQBFQBBIcASWYCX4C9fAVAUVAEVAEFAFFQBGINwSUYMbbGdHjUQQUAUVAEVAEFAFFIMERUIKZ4CdQD18RUAQUAUVAEVAEFIF4Q0AJZrydET0eRUARUAQUAUVAEVAEEhwBJZgJfgL18BUBRUARUAQUAUVAEYg3BJRgxtsZ0eNRBBQBRUARUAQUAUUgwRFQgpngJ1APXxFQBBQBRUARUAQUgXhDQAlmvJ0RPR5FQBFQBBQBRUARUAQSHIH/B/Dz25aIzsCaAAAAAElFTkSuQmCC\" alt=\"\" /\u003e\u003c/p\u003e\n\u003cp\u003eThe analysis shows that water clusters confined in zeolite frameworks are not significantly impacted by a changing confinement. Previously, we reported a difference in shape and dynamic properties between a protonated octameric cluster and one confined within the channels of H-ZSMS5\u003csup\u003e44\u003c/sup\u003e, which is in apparent contradiction to the current analysis. However, using a similar analysis to the current approach, we find that the previous trajectory, which is not as well sampled as the current one, can also be classified as having a similar volume as the gas phase counterpart.\u003c/p\u003e\n\u003cp\u003eFrom a statistical mechanics\u0026rsquo; point of view, entropy, and more precisely the translational contribution, is proportional to the accessible volume of the system. We also know that the positive charge can move only inside the water network hopping from water to water through the hydrogen bond network. As a consequence, translational entropy grows proportionally to the volume of the water cluster and not necessarily with the zeolite cavity size. This implies that the entropic contribution to proton solvation is independent of the zeolite framework type and does not stem from the mobility of the overall cluster in the available pore.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eFree energy surfaces for proton transfer.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn order to further probe this hypothesis, reaction free energies have been computed and decomposed to their enthalpic and entropic components. For this purpose, we adopted two recently developed descriptors\u003csup\u003e58\u003c/sup\u003e, known as Collective Variables (CVs), as are a measure of the protonation state of our systems (s\u003csub\u003ep\u003c/sub\u003e) and the distance between the charge carrier and the BAS site (s\u003csub\u003ed\u003c/sub\u003e), see section S1 in SI for details. As can be seen from \u003cstrong\u003eFigure 5\u003c/strong\u003e, free energy surfaces (FESs) projected along the two CVs have roughly the same shape for all these systems with a deep and narrow minimum for \u0026nbsp;and \u0026nbsp;equal to zero and an elongated branch for \u0026nbsp;equal to one. These states represent the undissociated and dissociated BAS, respectively.\u003c/p\u003e\n\u003cp\u003eIn all four cases, we observe the same trends as a function of the number of waters. At low water loading (n = 1, 2) there is a preference for the proton to remain in the vicinity of the BAS site (s\u003csub\u003ep\u003c/sub\u003e=0, s\u003csub\u003ed\u003c/sub\u003e=0).\u0026nbsp; However already at n=2 there is finite probability for the proton to move away from that wall by as much as 4 \u0026Aring; (s\u003csub\u003ep \u003c/sub\u003e= 1, s\u003csub\u003ed \u003c/sub\u003e= 4).\u0026nbsp;\u0026nbsp; This tendency increases with the number of water molecules, such that by n=8 the proton is completely solvated by water molecule (s\u003csub\u003ep \u003c/sub\u003e= 1, s\u003csub\u003ed \u003c/sub\u003e\u0026gt; 4).\u0026nbsp; This is in agreement with previous AIMD studies which show that the proton becomes \u0026ldquo;solvated\u0026rdquo; at higher water concentrations, but remains close to the BAS site at low hydration levels\u003csup\u003e45\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFrom these FESs it is possible to distinguish three well defined thermodynamic states (\u003cstrong\u003eFigure 6\u003c/strong\u003e), i.e., \u0026nbsp;an undissociated state with the proton covalently bonded to the zeolite (A), a state where the proton transfers to the closest water molecule forming a Zundel-like structure (B), and finally an end state where the hydronium ion is fully solvated and free to diffuse (C).\u003c/p\u003e\n\u003cp\u003eThe FESs, thus, obtained were divided in these three different areas and integrated in order to get their relative population. From these populations, we can observe that the same trend of transferring the proton from the wall as a function of hydration level occurs in all four zeolites see \u003cstrong\u003eFigure 7\u003c/strong\u003e. In all cases, minimum A with the proton at the BAS becomes negligible once the water concentration exceeds 2 per BAS. \u0026nbsp;It is minimum B, with the Zundel-like structure, where the most distinction between the zeolite frameworks occurs.\u0026nbsp; Although the population of B is maximum at n=3 and drops off with increasing n, the rate at which it does so is not the same amongst the different zeolites.\u0026nbsp; Its population decreases more rapidly the smaller the cage. Hence a more careful analysis of the energetics is required to quantitatively understand these trends.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe role of enthalpy and entropy in determining protonation state.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eIn order to understand the thermodynamic parameters determining the protonation state of water in zeolites, we use the relative trend in free energy between the undissociated (A) and the hydrolyzed states (B+C)\u0026nbsp; as a function of the water loading. This function shows a universal behavior among different zeolites, see \u003cstrong\u003eFigure 8\u003c/strong\u003e. Most importantly, except for small differences, all systems present the same decay trend with increasing n, but are offset at n=1 due to the differing acid strength of the BAS as imposed by the zeolite framework. Indeed, shifting vertically all these curves by a constant value that compensate these small differences shows that all these curves can be collapsed in one. This implies that although the free energetics at low hydration level may depend on local structural features (small differences in enthalpy), the behavior at increasing n is being determined by a structurally insensitive free energy term.\u003c/p\u003e\n\u003cp\u003eTo further probe this observation, we separate the free energy into contributions by the internal energy () and entropy ()\u003csup\u003e68\u003c/sup\u003e to determine the driving force for proton solvation.\u0026nbsp; The trends in \u0026nbsp;as a function of the number of waters are given in \u003cstrong\u003eFigure 9\u003c/strong\u003e, \u0026nbsp;and shows that in all zeolites \u0026nbsp;varies significantly between n=1-3, but tapers off to about 20 kJ mol\u003csup\u003e-1\u003c/sup\u003e for n=3. This initial fast drop as well as the identical behavior of the four zeolites is attributed to the fact that the hydronium needs a certain number of water molecules to be stabilized, while the framework of the zeolites plays only a minor role. Once the cluster is sufficiently large, further addition of water molecules does not impact the solvation energy of the proton. The result clearly show that for more than 3 water molecules further association does not lead to a better enthalpic stabilization.\u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis is further substantiated when one considers the entropy computed (\u003cstrong\u003eFigure 9\u003c/strong\u003e), showing a nearly linear contribution to the free energy with increasing number of water molecules. \u0026nbsp;All zeolites show a similar decrease with a slope of approximately -4.0 kJ mol\u003csup\u003e-1\u003c/sup\u003e/H\u003csub\u003e2\u003c/sub\u003eO molecule regardless of the cavity size, i.e., the entropy increases solely as a function of the number of waters, and is not influenced by the cavity size. Thus, we conclude that the main factor for this increase is related with the larger environment in which the proton can be mobile, i.e., the entropy of the proton depends on the size of the hydrogen bond network it is part of and that scales with the volume of the cluster.\u0026nbsp; As the zeolite framework perturbs this property of the clusters very little this entropic stabilization of the proton is, to first order independent of the zeolite lattice.\u0026nbsp;\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe universal behavior of BAS solvation in a select group of zeolite frameworks was examined by means of ab initio metadynamics methods. Independent of cavity shape or size, water molecules cluster at BAS to fully solvate the proton at n \u0026ge; 3. The volume of the water cluster and entropy of solvation are independent of the zeolite cage structure. As a result, the free energetics of proton solvation follows a universal behavior in which the enthalpy contributes only very little to the stabilization of the cluster n\u0026ge;3 and the entropic contribution grow linearly with the number of water molecules. This provides a straightforward extrapolation to predict the acid strength (\u003cem\u003epk\u003csub\u003ea\u003c/sub\u003e\u003c/em\u003e) of a BAS in any Zeolite framework as a function of water content. The results show that water is not evenly distributed within the zeolite, but is primarily located close to the negative charge in the zeolite lattice in order to minimize charge separation. Thus, overall the result set the computational framework necessary to model adsorption of organics and their reactivity in zeolites exposed to high chemical potentials of water.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cem\u003eMetadynamics Simulations:\u003c/em\u003e Breaking and forming covalent bonds, such of those involved in these reactions, implies high activation energies. Transitions between different protonation states occur on a time scale that can be reached with difficulty in a standard simulation. In order to accelerate the barrier crossings, metadynamics, an enhanced sampling method, is used to study chemical reactions. This method belongs to a class of enhanced sampling techniques based on the identification of the slow degrees of freedom involved in the reaction of interest\u003csup\u003e59,69,70\u003c/sup\u003e. These degrees of freedom, known in chemistry as Collective Variables, are functions of the atomic coordinates and must be chosen in order to extract the collective behavior connected to the reaction mechanism. Sampling is then accelerated by adding an external bias potential, a function of the chosen CVs, to the system potential energy. It is easy to understand how the choice of the CVs is crucial to obtain correct sampling.\u003c/p\u003e\n\u003cp\u003eIn order to accelerate the exploration of every possible protonation state, as well as the diffusion of the hydronium ion inside the cavities, we adopted a recently developed set of CVs\u003csup\u003e58\u003c/sup\u003e extremely versatile for the study of reactions involving proton transfer. A first CV, , was used to enhance the exploration of new protonation states and push the zeolite to release a proton to the water cluster and vice versa. A second one, , was used to explore the distance between the BAS and the hydronium accelerating the diffusion of the charge carrier inside the cavity, see section S1 of SI for additional details. Born-Oppenheimer MD simulations were performed combined with Well-Tempered Metadynamics\u003csup\u003e59,60\u003c/sup\u003e using PLUMED2\u003csup\u003e71\u003c/sup\u003e driving the CP2K package\u003csup\u003e72\u003c/sup\u003e. The exchange-correlation energy, , was computed using PBE\u003csup\u003e73\u003c/sup\u003e functional, see below.\u003c/p\u003e\n\u003cp\u003eThe four zeolites, with varying cavity shape and size shown in Figure 2, were studied loading each with an increasing number of water molecules per Br\u0026oslash;nsted acid site in a range from 1 to 8. The smallest zeolite tested, GIS-NaP1 could only accommodate up to 4 water molecules in its small cavity. The ratio Al:Si was kept constant at 1:95 which is comparable to typical experimental loadings.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAIMD Simulations\u003c/em\u003e: Periodic density functional theory (DFT) based AIMD were performed within the generalized gradient approximation (GGA) with the exchange correlation functional of Perdew, Burke and Ernzerhoff (PBE)\u003csup\u003e73\u003c/sup\u003e and Grimme\u0026rsquo;s second-generation dispersion corrections (DFT-D2) as implemented in the CP2K package. Starting with the optimized zeolite unit cell with 95 SiO\u003csub\u003e2\u003c/sub\u003e units and a single Al atom for each system, AIMD simulations were performed with 1, 2, 3, 4 and 8 water molecule(s) at T=300K within the canonical \u003cem\u003eNVT\u003c/em\u003e ensemble using a 0.5 fs time step and the CSVR\u003csup\u003e74\u003c/sup\u003e thermostat to determine the local structural properties.\u003csup\u003e\u0026nbsp; \u003c/sup\u003eFor each simulation, well-equilibrated trajectories of ~350 \u003cem\u003eps\u003c/em\u003e were collected to obtain reliable statistical properties. For further details of the simulations and system models see section S2 of the SI.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eE.G. GM. P. and M.P. thankfully acknowledge the financial support provided by the European Union Grant No. ERC-2014-AdG-670227/VARMET.\u0026nbsp; V.-A.G., R.R. and J.A.L. were supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division at Pacific Northwest National Laboratory (PNNL). \u0026nbsp;E.G. was partially supported by the PNNL alternate sponsored fellowship program during a six month visit to the Richland campus. PNNL is operated by Battelle for the US Department of Energy under Contract DE-AC05-76RL01830. Computational resources were provided the Swiss National Supercomputing Centre (CSCS) under project IDs p503, s768 and s910 and the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility located at Lawrence Berkeley National Laboratory (LBNL) and operated under Contract No. DE-AC02-05CH11231.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003e(1) \u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Taarning, E.; Osmundsen, C. M.; Yang, X.; Voss, B.; Andersen, S. I.; Christensen, C. H. Zeolite-Catalyzed Biomass Conversion to Fuels and Chemicals. \u003cem\u003eEnergy and Environmental Science\u003c/em\u003e. The Royal Society of Chemistry March 1, 2011, pp 793\u0026ndash;804. https://doi.org/10.1039/c004518g.\u003c/p\u003e\n\u003cp\u003e(2) \u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Climent, M. J.; Corma, A.; Iborra, S. 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Phys.\u003c/em\u003e \u003cstrong\u003e2007\u003c/strong\u003e, \u003cem\u003e126\u003c/em\u003e (1). https://doi.org/10.1063/1.2408420.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"confinement effects, acid strength, zeolites, Brønsted acid sites (BAS)","lastPublishedDoi":"10.21203/rs.3.rs-79664/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-79664/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Chemical reactivity and sorption in zeolites is coupled to confinement and - to a lesser extent- to the acid strength of Brønsted acid sites (BAS). In presence of water the zeolite Brønsted acid sites eventually convert into hydronium ions. The gradual transition from zeolite Brønsted acid sites to hydronium ions conversion in zeolites of varying pore size is examined by ab initio molecular dynamics combined with enhanced sampling based on well-tempered metadynamics and a recently developed set of collective variables. While at low water content (1-2 water/BAS) the acidic protons prefer to be shared between zeolites and water, higher water contents (n\u003e2) invariably lead to solvation of the protons within a localized water cluster adjacent to the BAS. At low water loadings the standard free energy of the formed complexes is dominated by enthalpy and is associated with the acid strength of the BAS and the space around the site. Conversely, the entropy increases linearly with the concentration of waters in the pores, favors proton solvation and is independent of the pore size/shape.","manuscriptTitle":"Confinement Effects and Acid Strength in Zeolites","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-09-23 18:17:27","doi":"10.21203/rs.3.rs-79664/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d94f2a24-6c67-46df-a515-05f766b1e774","owner":[],"postedDate":"September 23rd, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":593943,"name":"Catalysis"},{"id":593944,"name":"Physical Chemistry"},{"id":593945,"name":"Thermodynamics and statistical mechanics"}],"tags":[],"updatedAt":"2021-07-27T20:57:14+00:00","versionOfRecord":{"articleIdentity":"rs-79664","link":"https://doi.org/10.1038/s41467-021-22936-0","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2021-05-11 20:57:14","publishedOnDateReadable":"May 11th, 2021"},"versionCreatedAt":"2020-09-23 18:17:27","video":"","vorDoi":"10.1038/s41467-021-22936-0","vorDoiUrl":"https://doi.org/10.1038/s41467-021-22936-0","workflowStages":[]},"version":"v1","identity":"rs-79664","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-79664","identity":"rs-79664","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}