Proton Conduction in a MIL-53(Al) MetalâOrganic Framework

Article pubs.acs.org/JPCC

Proton Conduction in a MIL-53(Al) Metal−Organic Framework: Confinement versus Host/Guest Interaction Emanuel Eisbein, Jan-Ole Joswig,* and Gotthard Seifert Theoretical Chemistry, TU Dresden, 01062 Dresden, Germany S Supporting Information *

ABSTRACT: In this contribution, we present and discuss results from a computational study of proton transfers between imidazole molecules confined in a MIL-53(Al) metal−organic framework. We combined molecular-dynamics simulations and a density-functional tight-binding method. The extensive analysis of trajectories resulted in two main competing effects: on the one hand, the one-dimensional channel structure of MIL-53(Al) arranges the imidazole molecules to allow proton exchange by hopping transport; on the other hand, the interactions between the MIL-53(Al) host system and the imidazole molecules influence the free movement retaining the molecules. We find that the retaining leads to an increase in proton transfers, when both vehicle mechanisms and hopping events are considered. Thus, a well-balanced relationship between these two effects is necessary for efficient proton transport in metal−organic frameworks. Furthermore, the lifetime of the transition state could be estimated to be on the order of 100 fs.

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53(Al) metal−organic framework, [Al(μ2−OH)(1,4-bdc)]n, the Al3+ ions are bridged by OH− ions in 1D and by 1,4benzenedicarboxylate (1,4-bdc) in the two other dimensions. From this specific combination of building blocks, a threedimensional network with one-dimensional channel pores results.32 In the experiment of Bureekaew and co-workers,24 the channels were filled with imidazole molecules, and the proton conductivity within this host/guest system was found to be much higher than in liquid imidazole. These findings have been the motivation for the present computational study, for which we employed molecular-dynamics simulations. The focus of this contribution is laid on the proton-transfer events and the influence of the spatial confinement by the metal−organic framework on these events. In order to study the special influence of the interactions between the framework and the guest molecules, three sets of independent molecular-dynamics simulations were performed as described in Section Computational Details. In each set, we chose a different description of the interatomic interactions. The results were obtained from Born−Oppenheimer molecular-dynamics (MD) simulations in combination with a full quantum-mechanical treatment by the density-functional tightbinding (DFTB) method. In order to differentiate between sole confinement effects and effects arising from interactions between channel wall and guest molecule, a quantummechanical/molecular-mechanics (QM/MM) treatment was

INTRODUCTION Proton transport phenomena are essential processes in many different areas ranging from biological environments1 to modern technology (e.g., in sensors2,3 and fuel cells4). As the proton transport usually is water-based and described by the Grotthuss mechanism,5,6 operating temperatures for technological applications are limited to the boiling point of water. This drawback produced interest in water-free proton-transport phenomena and the search for materials that exhibit it.4,7−14 The imidazole molecule is a protogenic group that has been investigated to large extent. Its proton-transport properties have been studied in the liquid15,16 and solid phase17 as well as anchored to surfaces.18−21 An alternative to anchoring the protogenic groups is confining them as molecules in channels or pores in meso-porous systems or tubular nanostructures.22 If the channel structure itself has protogenic groups implemented23,24 or a molecular crystal is able to pass on charge carriers,25,26 these might have a large influence on the conductance properties. Metal−organic frameworks (MOFs) are a special class of such meso-porous systems with well-defined pore and channel sizes. As they are built by self-assembly of building blocks, socalled connectors and linkers, their properties can be tailored by choice of these units.27−31 The resulting three-dimensional networks show a defined structure with pores of uniform shape and size exhibiting one-, two-, or three-dimensional (1D, 2D, and 3D, respectively) channels. Bureekaew and co-workers24 experimentally investigated the proton conductivity in filled metal−organic frameworks, especially in the MIL-53(Al)/imidazole system. In the MIL© 2014 American Chemical Society

Received: May 5, 2014 Revised: May 28, 2014 Published: May 28, 2014 13035

dx.doi.org/10.1021/jp5043969 | J. Phys. Chem. C 2014, 118, 13035−13041

The Journal of Physical Chemistry C

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used additionally. Thereby, the charges on the MOF atoms were artificially set to zero so that the MOF channel in fact acted as a confining structure only. Additionally, QM/MM MD simulations with correct (nonzero) MOF charges were performed as an intermediate between the two extreme cases. The three set-ups are listed below in the order of increasing accuracy: Set 1, a QM/MM treatment in which the MOF was treated classically by the universal force field (UFF)33 with atomic charges set to zero, and the imidazole molecules were treated quantum-mechanically (DFTB), as described in Computational Details; set 2, a QM/MM treatment in which the MOF was treated classically by the UFF with charges sampled from DFTB MD simulations and the imidazole molecules were treated quantum-mechanically (DFTB) as described above; set 3, a fully quantum-mechanical treatment (DFTB) of both the host and the guest systems. The choice of set 1 and set 3 made it possible to either consider or not consider the host/guest interactions. The results from these simulations were used to draw conclusions about the influences of confinement and interaction.

Article

RESULTS AND DISCUSSION

In the host/guest system MIL-53(Al)/imidazole, structural properties and dynamic characteristics have different origins: the structural stability of the system results from the metal− organic framework, whereas the proton conductivity is rooted in the filling material. However, the interactions between both parts have an influence on the transport properties, as we will see below. In this contribution, we will focus on the analysis of the dynamic behavior of the guest molecules but as well consider and discuss their interactions with the host system. Spatial distributions and relative orientations of the guest molecules are two quantities that may elucidate the behavior of the imidazole molecules in the channel. They can be obtained easily from the trajectories: for the spatial distribution of the imidazole molecules, histograms of the molecular center-ofmass positions were compiled, which are described using the Heaviside step function according to p( r )⃗ =

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COMPUTATIONAL DETAILS For the present study, we employed Born−Oppenheimer molecular-dynamics simulations based on a density-functional tight-binding method,34−36 with a self-consistent charge (SCC) extension37 as implemented in the deMonNano computer code.38 This method is particularly suited for the calculation of large systems due to its computational robustness. The simulation box contained a super cell of MIL-53(Al) with three elementary units along the pore direction and two parallel channels in total. One channel was filled with four randomly oriented imidazole molecules (labeled “Im”), of which one (labeled “H-Im+”) carried initially an excess proton. In total, the supercell contained 265 atoms. In a first step, the system was equilibrated in such a way that the kinetic-energy distribution of all atoms resembled a Maxwell distribution at 400 K. Thereby, the MD time step was set to 0.25 fs. Afterward, the system was propagated over 4 ps within a microcanonical (NVE) ensemble; only the last picosecond was used for analysis. A good statistical distribution was guaranteed by performing 4000 individual MD runs with randomly generated starting configurations. The last picosecond of each run delivered 100 frames shot every 10 fs, so that the total number of frames used for statistics was 400000. Thus, all properties discussed below were the result of sampling over the trajectories as well as over time and in most cases over the participating molecules. In order to study the influence of the interactions between the framework and the guest molecules, three sets of each 4000 MD simulations were performed that differ in the description of the interatomic interactions as described above. The three sets have been defined in the introduction and use a QM/MM approach with zero charges on the MOF atoms (set 1), a QM/ MM approach with nonzero charges (set 2), and a fully quantum-mechanical treatment with the DFTB method as described above (set 3). For comparison, full density-functional calculations have been performed to obtain proton-transfer barriers: the generalized gradient approximation with the exchange functional of Perdew, Burke, and Ernzerhof (PBE)39 was used as implemented in the computer code deMon 2k.40

1 N

N

⎛ 1 ⎞ ⎛ 1 ⎞ Θ⎜ri , l − rl + Δrl ⎟Θ⎜− ri , l + rl + Δrl ⎟ ⎝ ⎠ ⎝ 2 2 ⎠ l=x ,y ,z

∑ ∏ i=1

⎧1, a ≥ 0, with Θ(a) = ⎨ ⎩ 0, a < 0

(1)

The spatial distribution was sampled over all frames, trajectories, and molecules (all summarized in the normalization factor N) and is, thus, normalized with respect to a single molecule. The Heaviside step function Θ employed in eq 1 considers the position of the center of mass of the respective molecules in 3D space. The index l refers to the three Cartesian coordinates (the individual molecular orientation will be considered in eq 2, see below). Two different distributions distinguishing the molecules protonation state (Im or H-Im+) were calculated. The resulting spatial distributions of the imidazole molecules in the MOF channel are depicted in Figure 1. The framework confines the molecules to the very center of the pore. In both QM/MM simulation approaches (set 1/set 2), the distributions of the neutral and the protonated species are almost identical. However, the distributions of the neutral and the protonated species differ significantly in the QM simulations (set 3, Figure 1d): here, the protonated H-Im+ species has a higher probability of being located at the inner edges of the pore, whereas the neutral imidazole molecules show a similar distribution as before. The H-Im+ location in the inner edges results from the interactions of the protonated H-Im+ molecular ion with the carboxylate groups of the MOF, which are partly negatively charged. Although set 2 (QM/MM) takes electrostatic interactions into account, a full quantummechanical treatment seems to be necessary to comprehensively describe the system. To obtain further insight into the influence of the MOF channel on the behavior of the guest molecules, the orientation of the molecules within the pore was analyzed. It is described by two polar coordinates as shown in Figure 2a. For the characterization of the molecular orientation, a vector defined by the molecular structure has been used, and its orientation relative to the direction of the channel and to an arbitrarily defined axis perpendicular to the channel has been calculated. The angle distribution 13036



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Figure 1. (a) Alignment of the guest molecules in the MOF channel (color code: H/white, C/turquoise, N/blue, O/red, and Al/green); (b−d): spatial probability of the imidazole molecules in a MIL-53(Al) channel resulting from (b) set 1: MD simulations without host/guest interactions, (c) set 2: QM/MM simulations, and (d) set 3: QM simulations. The probabilities of neutral (Im) and protonated (H-Im+) imidazole molecules are depicted in red and blue, respectively.

p(Ω⃗) =

1 N sin θ

N

Figure 2. (a) Schematic representation of an imidazole molecule in a MOF channel. The polar coordinates θ and φ defining the molecule’s orientation relative to the channel are indicated. The vector connecting the two nitrogen atoms (highlighted in blue) has been used to calculate the angles. (b−g) Resulting orientation profiles according to eq 3 of the protonated (left column) and neutral (right column) imidazole molecules in a MIL-53(Al) channel resulting from (a and b) set 1, MD simulations without host/guest interactions; (c and d) set 2, QM/MM simulations; and (e and f) set 3, QM simulations. The color code shows high and low probabilities as red and blue, respectively. Note that low probabilities are not necessarily zero.

⎛ ⎞ 1 Θ⎜Ωi , l − Ωl + ΔΩl⎟ ⎝ ⎠ 2 l=θ ,ϕ

∑∏ i=1

⎛ ⎞ 1 × Θ⎜ −Ωi , l + Ωl + ΔΩl⎟ ⎝ ⎠ 2

(2)

was sampled over all frames, trajectories, and molecules (normalization factor N), and Ω⃗ = (θ,ϕ), with θ being defined as the angle between the molecular vector and the pore axis (0 ≤ θ < 180°), and ϕ describing the rotational angle of this vector around the central pore axis (0 ≤ ϕ < 360°). For better visibility, the original probability distribution in eq 2 was renormalized according to p′(Ω⃗) =

p(Ω⃗) − min[p(Ω⃗)] max[p(Ω⃗)] − min[p(Ω⃗)]

results in a more flexible guest system in which all orientations are present. A similar alignment of proton-conducting media in spatial confinement was found by Wang and co-workers,41 who attributed high proton conductivity to highly ordered helical water chains in the pores of a one-dimensional crystal structure. In accordance with the MD simulations of Voth et al.,15 highly ordered domains in liquid imidazole result in an efficient proton conduction mechanism. Besides the optimal alignment, the interactions with the channel structure have influence on the proton conductivity as well, as the confinement results in stronger interactions between the guest molecules and, consequently, in a more distinct hydrogen-bond network. An experimental indication that corroborates our findings is the enhanced proton conductivity in [Al(μ2−OH)(1,4-ndc)]n (1,4ndc: 1,4-naphthalenedicarboxylate) found by Bureekaew and co-workers24 in hydrophobic pores. For imidazole, these hydrophobic pores act similarly as the solely spatial confinement used in set 1. The alignment of molecules has a direct influence on the formation of hydrogen bonds, and the resulting hydrogen bond network. We therefore analyze the residual probability of the proton in Figure 3, which was sampled from the MD trajectories, considering all XH distances between acidic hydrogen atoms (H) and nitrogen/oxygen atoms (X = N and O) in neighboring molecules or the MOF.

(3)

The resulting distributions are shown in Figure 2, from which we get the following picture: If the MOF acts as a solely confining channel (set 1, Figure 2, panels b and c), both the neutral and protonated imidazole molecules align along the pore axis. In this case, hydrogen bonds form between the guest molecules only, and orientation angles θ ≈ 0° and 180° show the highest probabilities. On the other hand, if the system is described quantum-mechanically (set 3), the protonated species is interacting with the MOF carboxylate groups (Figure 2f), which are located at the Ω⃗ orientations for which Figure 2f shows four maxima. As a consequence, the alignment of the neutral molecules is developed to a less extent (θ ≈ 0° and 180° ± 20°). In summary, a solely spatial confinement leads to enhanced interactions between the molecules, and the periodicity causes a chainlike alignment (see the Supporting Information). In contrast, a quantum-mechanical description 13037



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Figure 3. Distribution of hydrogen-bond (XHX) angle θ as a function of HX distance (X = N and O) between neighboring imidazole molecules (i.e., both HX distance are below 2.2 Å): (a) set 1, MD simulations without host/guest interactions; (b) set 2, QM/MM simulations; and (c) set 3, QM simulations. (d) NHO angle distribution between the protonated H-Im+ and the MOF carboxylate groups obtained from set 3 (QM).

Figure 4. Comparison of the proton-transfer energy barrier for the proton exchange between two imidazole molecules. For each curve, the NN distance was fixed, and single-point calculations were performed whereby the proton was moved successively from one molecule to the other. DFTB energies (solid lines) are compared to full DFT (PBE, dashed lines) for different fixed NN distances. The minima have been shifted to zero.

The probability plots in Figure 3 (panels b and c) result from set 2 (QM/MM) and 3 (QM) and consider only interactions between imidazole molecules. Besides a maximum at approximately 1 Å resulting from covalent NH bonds, the less distinct maximum at 1.9 Å describes the hydrogen bond. The nonzero probability in between visualizes proton transfers. The diagrams do not resolve, if the transfers were successful or not (i.e., they explicitly include the so-called proton rattling).14,42 Proton exchange occurs in sets 2 and 3, whereby the probability in set 3 is slightly higher. In the transfer state, the arrangement is almost linear, which is essential for a successful transfer.14 In contrast, we find in Figure 3a, resulting from set 1 (QM/MM), the two probability maxima merged to one maximum at 1.3 Å. As no interactions with the MOF influence the molecular system, the proton is shared by two imidazole molecules. This transition state has a Zundel-ion-like character (i.e., the excess proton is stabilized by two adjacent imidazole rings), and a comparison with Figure 4 shows that the elongated hydrogen bond matches the minimum in the energy−distance plot. Finally, Figure 3d shows that no proton transfer occurs between the imidazole and the MOF carboxylate groups. The carboxylate groups act as proton attractors rather than acceptors and trap the protonated imidazole species but do not contribute to the hopping. The mobility of the guest molecules was monitored by calculating mean-square displacements of their centers of mass. Thereby, we distinguished between the different QM/MM descriptions and between protonated and neutral molecules; the latter distinction made it possible to calculate mean-square displacements for exclusive vehicle transport (as the meansquare displacement of the protonated species) and for combined hopping and vehicle transport (by including the proton jump). The resulting curves are displayed in Figure 5. Generally, the protonated imidazole molecule is less mobile than the neutral molecules due to the fact that it is either hydrogen-bonded to other imidazole molecules or to the MOF carboxylate groups. The comparison of the three setups reveals the effects of the confinement on the mobility: set 1 (green curves in Figure 5) shows nearly no dependence on the monitored property, that is the neutral and protonated molecules show essentially the same

Figure 5. Mean-square displacement of the imidazole molecules as a function of simulation time: (a) only neutral imidazole molecules are considered; (b) only vehicle transport by protonated imidazole molecules is considered; and (c) vehicle and hopping transport by protonated imidazole molecules is considered. The color code refers to the three sets defined above.

displacements in a solely spatial confinement. The QM/MM simulations of set 2 give an increase in the mean-square displacements, when hopping is considered (vehicle + hopping) that even exceeds the mobility of the neutral molecules. The quantum-chemical simulations of set 3 show again that the mobility is in fact hindered by interactions between the protonated imidazole molecule and the MOF channel structure. The local proton-exchange mechanism can be studied by monitoring the interatomic distances and the changes in the partial charges during the proton transfer. During the proton transfer period, the proton is oscillating (“rattling”42) between its two neighboring acceptor atoms. In order not to count these oscillations as multiple events, we include them into the transfer event and define the beginning and the end of a proton transfer event by a certain time criterion, during which no rattling occurs. Here, we arbitrarily chose a time of 100 fs. 13038



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Figure 6. Sampled NN and NH distances (upper panels) and partial charges (lower panels) during the proton transfer process for the system of interest for set 2 (QM/MM, left column) and set 3 (QM, right column). The statistical errors are highlighted as shaded areas.

simulations were performed for this purpose, employing a density-functional tight-binding approach. We considered three different theoretical descriptions: (i) a QM/MM description with the charges of the MOF atoms set to zero, (ii) a QM/MM treatment, and (iii) a QM treatment (DFTB) of the whole system. Sampling over 4000 short trajectories in each case gave access to sufficient statistics. The calculation of a spatial distribution of the imidazole molecules within the channel pores of the MOF showed that the framework confines the molecules to the very center of the pore. The charged H-Im+ species are located at the inner edges of the pore interacting with the carboxylate groups of the MOF structure. The orientation confirms these interactions because the imidazole molecules have a preferred orientation with respect to the attractive carboxylate groups. Moreover, the molecules are rather aligned along the pore axis, and the molecules carrying the excess proton interact more pronounced with the carboxylate groups and are, thus, limited in their movement. The hydrogen-bond network was analyzed with respect to angle and distance criteria. In the QM description, proton transfer events can be observed via a nonzero residual probability between the covalent and hydrogen-bonded states. No proton exchanges occurs between the imidazole molecules and the MOF carboxylate groups, so that these do not contribute to the hopping. The analysis of the proton-carrier mobility in terms of meansquare displacements showed that the neutral imidazole molecules are more mobile than the protonated species, which are attracted and trapped by the carboxylate groups. We find the vehicle transport to contribute considerably in this special system, but hopping events increase the overall transport in excess of the system in a solely spatial confinement. Finally, the statistical monitoring of the geometries and charges show that during the hopping events, the geometry is affected in the vicinity of the transferred proton only, but the charges vary in the whole Zundel-like system. Thus, the proton

Figure 6 shows the distance curves that result from the sampling over the 4000 trajectories. As the proton transfer to all species is only observable in fully quantum-chemical simulations, we discuss only set 3 (QM) at this point: tracking the NH distances in the Figure, a clear distinction between covalent bond (∼1 Å) and hydrogen bond (∼1.8 Å) can be made. These two curves approach each other close to the transfer event, where their statistical deviations decrease as well. At the same time, the participating acceptor/donor atoms approach. Thus, thermal vibrations are sufficient for the proton transfer event to occur, whereas tunneling effects can be neglected at room temperature and above.16,43 At NN distances below 2.6 Å (minimum of rNN in Figure 6), the energy barrier vanishes; this value can be obtained from Figure 4, which also shows that the DFTB description results in energy barriers that are in good agreement with DFT calculations. Using the statistical error bars in Figure 6 (in the charge diagrams as well as in the distance diagrams), we can estimate the lifetime of the transition state, the so-called Zundel-like ion, to be on the order of 100 fs. Whereas set 2 (QM/MM) gives a symmetric crossing of the error bars and a lifetime of 140 fs, set 3 (QM) shows a lower lifetime (slightly below 100 fs) and, moreover, an asymmetric error bar crossing. This indicates that the initial formation of a Zundel-like complex occurs faster than its final breakup. Additionally, the progression of the partial charges in Figure 6 proves the transfer mechanism to be concerted, as they vary as well on atoms that are not directly involved in the transfer.

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CONCLUSIONS In the present computational study, we investigated a MIL53(Al) metal−organic framework filled with imidazole molecules in order to gain insight into the proton-transport that occur in these systems. The motivation for our study was an experiment by Bureekaew and co-workers,24 in which the proton transport was found to be higher in the host/guest system compared to liquid imidazole. Molecular-dynamics 13039



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Elementary Reactions, and Phenomenology. Chem. Rev. 2004, 104, 4637−4678. (5) Grotthuss, C. J. T. van. Sur La Décomposition de L’eau et Des Corps Qu’elle Tient En Dissolution À L’aide de L’électricité Galvanique. Ann. Chim. 1806, 58, 54−74. (6) Ludueña, G. A.; Kühne, T. D.; Sebastiani, D. Mixed Grotthuss and Vehicle Transport Mechanism in Proton Conducting Polymers from Ab Initio Molecular Dynamics Simulations. Chem. Mater. 2011, 23, 1424−1429. (7) Schuster, M.; Kreuer, K.-D.; Steininger, H.; Maier, J. Proton Conductivity and Diffusion Study of Molten Phosphonic Acid H3PO3. Solid State Ionics 2008, 179, 523−528. (8) Weber, J.; Kreuer, K.-D.; Maier, J.; Thomas, A. Proton Conductivity Enhancement by Nanostructural Control of Poly(benzimidazole)-Phosphoric Acid Adducts. Adv. Mater. 2008, 20, 2595−2598. (9) Kreuer, K.-D.; Schuster, M.; Obliers, B.; Diat, O.; Traub, U.; Fuchs, A.; Klock, U.; Paddison, S. J.; Maier, J. Short-Side-Chain Proton Conducting Perfluorosulfonic Acid Ionomers: Why They Perform Better in PEM Fuel Cells. J. Power Sources 2008, 178, 499−509. (10) Herz, H. G.; Kreuer, K.-D.; Maier, J.; Scharfenberger, G.; Schuster, M. F. H.; Meyer, W. H. New Fully Polymeric Proton Solvents with High Proton Mobility. Electrochim. Acta 2003, 48, 2165−2171. (11) Steininger, H.; Schuster, M.; Kreuer, K.-D.; Kaltbeitzel, A.; Bingöl, B.; Meyer, W. H.; Schauff, S.; Brunklaus, G.; Maier, J.; Spiess, H. W. Intermediate Temperature Proton Conductors for PEM Fuel Cells Based on Phosphonic Acid as Protogenic Group: A Progress Report. Phys. Chem. Chem. Phys. 2007, 9, 1764−1773. (12) Steininger, H.; Schuster, M.; Kreuer, K.-D.; Maier, J. Intermediate Temperature Proton Conductors Based on Phosphonic Acid Functionalized Oligosiloxanes. Solid State Ionics 2006, 177, 2457−2462. (13) Joswig, J.-O.; Hazebroucq, S.; Seifert, G. Properties of the Phosphonic-Acid Molecule and the Proton Transfer in the Phosphonic-Acid Dimer. J. Mol. Struct.: THEOCHEM 2007, 816, 119−123. (14) Joswig, J.-O.; Seifert, G. Aspects of the Proton Transfer in Liquid Phosphonic Acid. J. Phys. Chem. B 2009, 113, 8475−8480. (15) Chen, H.; Yan, T.; Voth, G. a. A Computer Simulation Model for Proton Transport in Liquid Imidazole. J. Phys. Chem. A 2009, 113, 4507−4517. (16) Münch, W.; Kreuer, K.-D.; Silvestri, W.; Maier, J.; Seifert, G. The Diffusion Mechanism of an Excess Proton in Imidazole Molecule Chains: First Results of an Ab Initio Molecular Dynamics Study. Solid State Ionics 2001, 437−443. (17) Kawada, A.; McGhie, A. R.; Labes, M. M. Protonic Conductivity in Imidazole Single Crystal. J. Chem. Phys. 1970, 52, 3121−3125. (18) Marschall, R.; Sharifi, M.; Wark, M. . Proton Conductivity of Imidazole Functionalized Ordered Mesoporous Silica: Influence of Type of Anchorage, Chain Length and Humidity. Microporous Mesoporous Mater. 2009, 123, 21−29. (19) Cavalcanti, W. L.; Portaluppi, D. F.; Joswig, J.-O. Preconditioning Immobilized Imidazole Arrays for Optimal Proton-Transfer Feasibility. J. Chem. Phys. 2010, 133, 104703-1−104703-6. (20) Tölle, P.; Cavalcanti, W. L.; Hoffmann, M.; Köhler, C.; Frauenheim, T. Modelling of Proton Diffusion in Immobilised Imidazole Systems for Application in Fuel Cells. Fuel Cells 2008, 8, 236−243. (21) Tölle, P.; Köhler, C. Water Free Proton Transport in Imidazole Functionalised Silicon Dioxide Material: Calculation of Free Energy Barrier Dependent on the mCEC Proton Coordinate. Phys. Status Solidi B 2012, 249, 376−383. (22) Mann, D. J.; Halls, M. D. Water Alignment and Proton Conduction inside Carbon Nanotubes. Phys. Rev. Lett. 2003, 90, 195503/1−4. (23) Hurd, J. A.; Vaidhyanathan, R.; Thangadurai, V.; Ratcliffe, C. I.; Moudrakovski, I. L.; Shimizu, G. K. H. Anhydrous Proton Conduction

hopping is a truly concerted mechanism involving not only the donor and acceptor atoms but also the whole donor and acceptor molecules through a synchronized charge balance. The proton transfers are nudged by the thermal vibrations of the system, so that tunneling plays no role at room temperature and above. During the transfer, proton rattling increases the lifetime of the transition state, a Zundel-like complex, to approximately 100 fs. This value corresponds to experimental findings for the lifetimes of the Zundel and Eigen species in water.44 From the presented analysis, we get the following overall picture: a quantum-chemical description of the system shows that the carboxylate groups of the metal−organic framework attract and trap the protonated imidazole molecules. Trapping decelerates their movement compared to neutral molecules but stimulates proton hopping events. In a solely spatial confinement without interactions to the guest molecules, this effect does not occur. As a result, the molecules align as Zundel-like complexes, which share the excess proton. Similarly to the motivating experiment by Bureekaew and co-workers,24 who compared the proton transport in hydrophilic and hydrophobic MOF channels, we as well found the proton-transport being dependent on the hosting system, as hydrogen-bond interactions with the MOF slow down the protonated molecules but activate hopping, whereas in a solely spatial confinement, the proton is shared and complexed, which decreases the overall proton transport.

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ASSOCIATED CONTENT

S Supporting Information *

Video showing a side view of the MIL-53(Al) metal−organic framework channel containing four imidazole molecules obtained from a long BOMD trajectory. An excess proton is present, and the protonated imidazole molecule is highlighted in pink. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Deutsche Forschungsgemeinschaft within the SPP 1362 “Porous metalorganic frameworks” (project no. SE 651/33-2). The authors acknowledge valuable computational support by Knut Vietze and the Center for Information Services and High Performance Computing (ZIH) at TU Dresden.

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REFERENCES

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