Molecular Mechanisms of Water-Mediated Proton Transport in MIL-53

Article pubs.acs.org/JPCC

Molecular Mechanisms of Water-Mediated Proton Transport in MIL53 Metal−Organic Frameworks Francesco Paesani* Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States S Supporting Information *

ABSTRACT: Metal−organic frameworks have recently been proposed as promising proton conducting materials for application in fuel cell technologies. Here, molecular dynamics simulations are used to reveal the microscopic mechanisms associated with water-mediated proton transport in the MIL-53 materials as a function of temperature, water loading, and pore size. The structure of the hydrated proton is found to resemble that of a distorted Zundel complex when the framework closes into a narrow-pore configuration. A transition to Eigen-like structures is then observed at higher water loading when the pores open as a result of the breathing effect. Although the free-energy barriers to proton transfer at room temperature are lower than in bulk water, proton transport in MIL-53 is largely suppressed, which is attributed to the low water mobility inside the pores. Faster proton diffusion is found at higher temperature, in agreement with conductivity measurements.

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INTRODUCTION Proton transport plays a central role in a variety of fundamental chemical processes, from acid−base reactions in solution1,2 to energy transfer and conversion in molecular systems.3−6 Despite recent experimental and theoretical progress, the microscopic understanding of the elementary steps associated with the mobility of protons in condensed phases remains particularly challenging. In this regard, only recently some consensus on the mechanism of proton transport in bulk water has begun to emerge.7−10 The current view combines the Grotthuss mechanism11 with the concept of presolvation derived from Marcus theory of electron transfer reactions.12 Within this picture the excess proton is predicted to hop between two water molecules only after the proton-accepting molecule has assumed a hydration structure compatible with the final stage of the transfer process. Proton transport over nanoscopic distances can thus be described as a charge transport phenomenon that involves dynamically changing bonding topologies of numerous molecular structures. Over the past decade metal−organic frameworks (MOFs) have emerged as an important class of porous materials with great potential for a wide range of applications, including gas storage, catalysis, and separation.13−31 More recently, MOFs have been proposed as promising separator materials that can transport protons at high temperatures and in relatively lowhumidity environments for application in fuel cell technologies.32−38 Compared to other porous materials like activated carbon and zeolites, MOFs are highly designable, which allows not only the size and shape but also the physicochemical properties of the framework to be tuned for specific applications. The possibility to modify the pore surface with respect to hydrophilicity/hydrophobicity and acidity via suitable organic ligands can enable the control of proton © 2013 American Chemical Society

conduction at the molecular level. In addition, because of their crystalline nature, MOFs can provide fundamental insights into the conduction mechanisms that are often difficult to characterize in polymer-based electrolytes because of the lack of long-range order.37 Proton conduction in MOFs has been demonstrated to occur through either intervening carrier molecules or ionizable groups that are part of the framework. In the latter case, carrier molecules adsorbed in the pores can still be involved in the overall shuttling process.37 A significant variation in proton conduction was observed upon water adsorption in a series of isostructural frameworks belonging to the MIL-53 family [M(OH)(bdc-R), with M = Al or Fe, bdc =1,4-benzenedicarboxylate, and R = H, NH2, OH, (COOH)2].39 The differences in the measured conductivities were correlated with the acidity of the functional groups. Similarly, the proton conductivity measured in HKUST-1 under methanol vapor was ascribed to the enhanced acidity of H2O molecules coordinated to the Cu(II) ions of the framework promoting proton donation to methanol molecules adsorbed in the pores.40 A family of four homochiral MOFs with general formulas Zn(γL)(X) [γ = l or d, X = Cl or Br, L = 3-methyl-2-(pyridin-4ylmethylamino)butanoic acid] was also investigated for proton conduction.32 Although all four MOFs were found to adsorb water, high proton conductivity was only observed in the two Zn(γ-L)(Cl) enantiomeric structures. Recently, high proton conductivity via H2O molecules adsorbed in the pores has been measured at ambient temperature and low relative humidity in NR3(CH2COOH)[MCr(ox)3] with R = methyl and M = Fe, Received: June 21, 2013 Revised: August 25, 2013 Published: August 27, 2013 19508

dx.doi.org/10.1021/jp406163q | J. Phys. Chem. C 2013, 117, 19508−19516

The Journal of Physical Chemistry C

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but not in the two isostructural MOFs with M = Mn and R = ethyl or n-butyl.33 Besides water, other carrier molecules have been considered for proton conduction in MOFs. In this regard, particularly interesting are two isoreticular MOFs with general formula Al(OH)(L), with L = bdc or ndc (1,4naphthalenedicarboxylate).34 Despite their structural similarity, proton conductivity was only observed for Al(OH)(ndc) upon imidazole adsorption. Interestingly, the conductivity of Al(OH)(ndc) was found to increase by approximately 2 orders of magnitude upon histamine adsorption at 150 °C in a completely anhydrous environment.35 The presence of functional groups on the framework can also facilitate proton conductivity by either directly participating in the conduction pathways or providing an effective scaffold for adsorption of carrier molecules. It was demonstrated that proton conduction in β-PCMOF2, whose framework contains sulfonate groups, can be modulated by the controlled loading of triazole molecules.36 Importantly, β-PCMOF2 was successfully tested as a separator material by incorporating the partially loaded MOF into a H2/air membrane electrode assembly.36 Proton conductivity under H2 vapor was also measured at 25 °C and 98% relative humidity in PCMOF-3, a framework containing a polar interlayer lined with Zn-ligated H2O molecules and phosphonate oxygen atoms.37 Recently, a new family of MOFs has been synthesized with general formula M-SBBA, where M = Ca(II), Sr(II), and Ba(II), and SBBA = 4,4′-sulfobisbenzoic acid. SBBA possesses a sulfone functionality similar to that found in the polysulfone backbone of polymers currently used in proton conductivity applications.38 Although these three MSBBA MOFs share similar chemical formulas, they exhibit noticeably different proton conductivity, which is likely related to their different three-dimensional structures. To provide molecular-level insights into the mechanisms associated with water-mediated proton conduction in MOFs, the present study reports on molecular dynamics simulations of proton mobility in MIL-53(Cr) performed using the anharmonic multistate empirical valence bond (aMS-EVB3) model.41 MIL-53(Cr) is a three-dimensional MOF with chemical formula Cr(OH)[O2C−C6H4−CO2] built up from infinite chains of corner-sharing CrO4(OH)2 clusters interconnected by terephthalate linkers (Figure 1).42 The choice of MIL-53(Cr) for molecular-level studies of proton conduction in MOFs is 3-fold. First, MIL-53(Cr) belongs to the same family of MOFs for which proton conduction upon water adsorption was extensively investigated in ref 39, which implies that the molecular mechanisms that determine proton conduction through the pores would be similar. Second, since water adsorption in MIL-53(Cr) has been characterized through both experimental measurements and computer modeling,43−45 aMS-EVB3 molecular dynamics simulations can enable a direct connection between proton mobility and water behavior inside the MOF pores. Third, MIL-53(Cr) is a prototypical MOFs that undergoes reversible structural transitions from large- to narrow-pore configurations (the socalled breathing effect) in response to the amount of water adsorbed,43 which therefore allows for fundamental studies of proton mobility as a function of pore size and water loading.

Figure 1. Three-dimensional snapshots extracted from aMS-EVB3 simulations as a function of the number of water molecules (N) adsorbed per unit cell representing the instantaneous distributions of H2O molecules viewed along the MIL-53(Cr) channels. N = 0 corresponds to the empty framework. Color scheme: Cr(III) atoms are shown in blue, carbon atoms in cyan, oxygen atoms in red, and hydrogen atoms in white.

represented by a linear combination of empirical valence bond (EVB) states, |φ⟩, that describe all possible molecular configurations of the hydronium ion (H3O+) NEVB

|Ψ⟩ =

∑ ci|φi⟩ i

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(1)

where NEVB is the number and ci are the coefficients of the EVB states. By construction, the aMS-EVB3 model is thus capable of describing both the hydration structure and the corresponding charge defect associated with the presence of an excess proton in the water hydrogen-bond network. Specifically, the position of the center of excess charge (CEC) corresponding to the

METHODOLOGY All simulations were performed with the anharmonic version of the third generation of the multistate empirical valence bond (aMS-EVB3) model.41 Within the MS-EVB formalism,46−51 the electronic wave function of a protonated system, |ψ⟩, is 19509



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The same expression was also used to calculate the water selfdiffusion coefficient (DWAT) by considering the displacement of the center of mass of each H2O molecule along the z-direction. The water orientational relaxation time (τ2) was extracted from the exponential fit to the long-time decay of the orientational time autocorrelation function C2(t) = ⟨P2[e(0)·e(t)]⟩ where P2[e(0)·e(t)] is the second Legendre polynomial of the angle spanned in time by the unit vector e(t) lying on one OH bond of each H2O molecule, and the brackets indicate an ensemble average over both OH bonds and water molecules.

location of the charge defect can be monitored explicitly during an aMS-EVB3 simulation by calculating the vector rCEC = ∑ici2r(COC) , where ci2 is the probability and r(COC) is the center i i of charge of the hydronium (H3O+) ion in the ith EVB state, respectively.47−49 A periodic system consisting of 32 MIL53(Cr) unit cells was used in all aMS-EVB3 simulations that were carried out at three different temperatures (T = 300, 350, and 400 K) for selected water loadings, ranging from N = 3 to N = 20 H2O molecules per unit cell. The force field parameters for MIL-53(Cr) were taken from ref 43 and were shown to accurately reproduce the breathing behavior of MIL-53(Cr) upon adsorption of CO2, H2S, and H2O.43,52,53 The parameters associated with the nonbonded framework−water and framework−hydronium interactions were obtained using the Lorentz−Berthelot mixing rule.54 The initial distributions of the water molecules inside the pores at T = 300 K were taken from ref 45, while additional simulations in the constant stress− constant temperature (NσT) ensemble55 were performed to determine the water equilibrium distributions at T = 350 and 400 K. One excess proton was then randomly added to one H2O molecule to form the initial H3O+ ion. Each protonated system was equilibrated for 1 ns in the canonical (NVT) ensemble using a Nosé−Hoover thermostat with a relaxation time of 1 ps. All structural, thermodynamic, and dynamical properties were then calculated from 1 ns long simulations carried out in the microcanonical (NVE) ensemble. In all cases, the equations of motion were propagated according to the velocity-Verlet algorithm with a time step Δt = 0.5 fs.56 A modified version of DL_POLY2 was used for all simulations.57 The permeation free energy associated with proton transport was investigated by calculating the potentials of mean force (PMFs) along the MIL-53(Cr) channels (parallel to the direction of the c unit-cell vector) as a function of the CEC distance, r(CEC) , from the oxygen atom (Oh) of a selected c hydroxyl group (μ2-OH) of the framework chosen as origin. Specifically, the PMF profiles were calculated by employing the weighted histogram analysis method (WHAM)58 to connect free energy segments obtained from umbrella sampling simulations56 in which the CEC position along the channel was restrained in each window by the harmonic potential Vumb 2 2 = 1/2Kumb(r(CEC) − r(0) c c ) with Kumb = 10.0 kcal/(mol Å ). In total, 15 windows with anchor positions, r(0) , separated by 1.0 Å c were used to recover each PMF. For each window, 1 ns long simulations were performed in the NVT ensemble, and each PMF was obtained by averaging the WHAM results over a single unit cell. Molecular information on the dynamics and mechanisms of proton shuttling through the MIL-53(Cr) pores was obtained from the analysis of the following continuous, Cc(t) = ⟨hi(0) Hi(t)⟩/⟨hi(0)hi(0)⟩, and pseudocontinuous, Cpc(t) = ⟨hi(0) hi(t)⟩/⟨hi(0)hi(0)⟩, correlation functions.8,10 Here, Hi(t) = 1 if the ith oxygen atom is the hydronium oxygen over the entire time interval [0, t] and Hi(t) = 0 otherwise, while hi(t) = 1 if the ith oxygen atom is the hydronium oxygen at time t and hi(t) = 0 otherwise. The proton self-diffusion coefficient along the MIL-53(Cr) channel was calculated from the mean-square displacement of CEC using the Einstein relation DCEC = lim

t →∞

⟨|rc(CEC)(t ) − rc(CEC)(0)|2 ⟩ 2t

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RESULTS AND DISCUSSION Figure 2 shows the radial distribution functions (RDFs) describing the spatial correlation between the CEC position

Figure 2. CEC-Oh radial distribution functions, gCEC‑Oh, calculated as a function of temperature and water loading.

and the positions of the Oh atoms of the μ2-OH groups coordinated with the Cr(III) atoms of the framework. At any given loading, the CEC-Oh RDFs display a very weak dependence on the temperature. For N ≤ 10, they are particularly structured and characterized by two pronounced and relatively broad peaks located at R ∼ 3.0 Å and R ∼ 5.5 Å. These features are indicative of strong interactions between the excess proton and the μ2-OH groups of the framework. At higher loadings, when the pores open as a result of the breathing effect, the RDFs become less structured. This suggests that, as N increases, the excess proton is preferentially solvated by the water molecules, which effectively screen its interactions with the framework. Direct information on the energetics associated with proton transport along the MIL-53(Cr) channels can be obtained from the analysis of the PMF profiles shown in Figure 3 for T = 300 K and selected loadings (N = 3, 10, and 20). These results clearly demonstrate that, at low loading, the μ2-OH groups are the strongest binding sites for the hydronium ion, although the free energy barriers to proton transport are relatively low and comparable to the thermal energy. As the pores open for N ≥ 10, proton transport through the channels becomes effectively barrierless as illustrated by the PMF obtained for N = 20.

(2)

where |r(CEC) (t) − r(CEC) (0)| corresponds to the component of c c the CEC displacement vector along the channel (c-direction). 19510



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Figure 4. Schematic representation of the hydration structure of the excess proton in water. O0 and O1 correspond to the oxygen atoms of the water molecules that form the hydronium ion with the largest and second largest EVB probabilities, respectively. O2 and O3 correspond to the oxygen atoms of the two closest water molecules in the first solvation shell of O0. The green diamond corresponds to the location of the center of the excess charge (CEC). See main text for details.

Figure 3. Potentials of mean force (PMFs) along the MIL-53(Cr) channels calculated at T = 300 K as a function of the CEC distance , defining the origin from the oxygen atoms of the μ2-OH group, r(CEC) c of the unit cell along the direction of the c unit-cell vector.

Similar results were also obtained at T = 350 and 400 K, with the corresponding PMF profiles (not shown) lying within the statistical uncertainty of the curves calculated at T = 300 K. The dependence of the PMF profiles on water loading and pore size is directly related to the CEC-Oh RDFs of Figure 2, indicating that proton transport in MIL-53(Cr) is a thermally accessible process that is mediated by water and becomes less affected by the specific physicochemical properties of the framework as water loading increases. After having determined the proton structural properties and energetics, the proton dynamics associated with the actual transport process through the MIL-53(Cr) channels was also investigated. It is generally accepted that proton diffusion in aqueous media involves the interconversion of two limiting ionic structures, the so-called Eigen and Zundel cations,59,60 via the Grotthuss mechanism.9 To characterize the molecular mechanism of proton conduction in MIL-53 materials upon water adsorption, the average structure of the hydrated proton in the pores was first determined from the analysis of the twodimensional probability distribution P(δ,RO0O1) calculated from the aMS-EVB3 simulations. Here, δ = RO0‑CEC − RO1−CEC is the difference between the distances of the center of the excess charge (CEC) from the oxygen atoms (O0 and O1) of the “special pair” of H2O molecules61 forming hydronium (H3O+) ions with the two largest EVB probabilities, which effectively correspond to the two closest water molecules to the excess proton, while RO0O1 is the O0−O1 distance (Figure 4).62 As a reference, P(δ,RO0O1) peaks at (|δ| = 0.0 Å, RO0O1 ≈ 2.4 Å) and at (|δ| ≈ 1.5 Å, RO0O1 ≈ 2.5 Å) for isolated Zundel and Eigen cations, respectively.41 P(δ,RO0O1) calculated at T = 300 K is shown in Figure 5a for selected water loadings, from N = 3 to N = 20 water molecules adsorbed per unit cell. Qualitatively similar results were also obtained from aMS-EVB3 simulations carried out at T = 350 K and T = 400 K (see Supporting Information). For N ≤ 5, P(δ,RO0O1) is only slightly dependent on δ in the range 1.5 Å ≤ δ ≤ 1.5 Å. This shape of P(δ,RO0O1) along with the large probability at δ = 0.0 Å is largely consistent with the hydration structure of a (distorted) Zundel cation. As N increases, P(δ,RO0O1) splits into two distinct peaks, indicating that the structure of the hydrated proton at higher loading more closely resembles that of a distorted Eigen cation. The

variation of the local proton hydration structure as a function of N can be directly monitored by analyzing the evolution of the oxygen−oxygen RDFs centered on the oxygen atoms (O0, O1, O2, and O3 in Figure 4) of the water molecules located within the first hydration shell of the hydronium cation.9 The four RDFs (g0, g1, g2, and g3) calculated at 300 K are shown in Figure 5b. As a reference, g0 = g1 and g2 ≈ g3 for the Zundel cation, while g1 ≈ g2 ≈ g3 for the Eigen cation. For an hydrated proton in MIL-53(Cr), the shapes of the four RDFs are strongly dependent on the amount of water present in the pores. For N ≤ 7, g0 is characterized by a broad peak with a maximum at RO0O ≈ 2.4 Å and a slight shoulder at relatively larger distances (RO0O ≈ 2.5 Å). At the same low loadings, the first peak of g1 approximately coincides in both position and height with the maximum of g0, the first peak of g2 overlaps with the shoulder of g0, and the broad peak of g3 overlaps with both the second peak of g1 and the shoulder of g2. These specific features provide support for the presence of Zundel-like structures of the hydrated proton in the narrow pores of MIL-53 materials as inferred by the analysis of P(δ,RO0O1). As N increases, the peak position of g0 shifts to larger distances and the shoulder, which was barely visible at low loading, becomes the actual maximum. At the same time, the height difference between the first and second peak of g1 decreases, which is particularly noticeable for N ≥ 14. Overall, the evolution of the four RDFs with N is compatible with the formation of Eigen-like complexes. However, the differences between g1, g2, and g3, which still persist at higher loading, suggest that the average structure of the hydrated proton in the large pores of MIL-53 materials may be more precisely described as that of a (H7O3)+ cation. The transition from Zundel-like to Eigen-like structures as a function of loading directly correlates with the breathing behavior of MIL-53(Cr).43−45 At low water loading MIL53(Cr) closes into a narrow-pore configuration with the water molecules forming one-dimensional hydrogen-bonded chains along the channels (Figure 1). This spatial distribution favors the formation of (more linear) Zundel-like structures for the hydrated proton. As the pores open in response to the increased loading, the water molecules fill the available volume and arrange in three-dimensional hydrogen-bonded assemblies 19511



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Figure 5. (a) Two-dimensional distribution, P(δ,RO0O1), calculated as a function of the number of water molecules (N) adsorbed per unit cell at T = 300 K. Here, δ = RO0‑CEC − RO1−CEC and RO0O1 is the distance between O0 and O1 (see Figure 2). (b) Oxygen−oxygen radial distribution functions gi (g0: black; g1: red; g2: blue; g3: green) centered respectively on the O0, O1, O2, and O3 oxygen atoms depicted in Figure 2. ROiO is the distance between Oi and the oxygen atom (O) of any other water molecule. All RDFs are normalized to the height of the corresponding g0 for each value of N.

continuous, Cpc(t), correlation functions first introduced in ref 10 are analyzed in Figures 6b and 6c, respectively.8,10 By construction, the time decay of Cc(t) depends on the lifetime, τc, of the hydronium cation that remains centered on the ith oxygen atom for the entire time interval [0, t]. The time scales associated with Cc(t) are thus directly related to the free energy profiles shown in Figure 6a. The values of τc determined from the fit to the long-time decay of Cc(t) at 300 K range from ∼200 fs (for N = 3) to ∼1 ps (for N = 14). Identity changes that are undone when the sequence of two consecutive proton transfer events restores the same hydronium cation (proton rattling) are excluded in Cpc(t) that, consequently, displays a significantly slower decay. The lifetimes, τpc, obtained from fits to the long-time decay of Cpc(t) are for all loadings on the order of tens of picoseconds, with τpc > 100 ps for N = 3, 5, and 10. As a reference, τpc ∼ 1.7 ps for an excess proton in bulk water.10 The slow decay of Cpc(t) thus indicates that long-distance proton transport mediated by H2O molecules adsorbed in MIL53 materials is largely suppressed compared to bulk water. This is confirmed by the analysis of the proton self-diffusion coefficient, DCEC, shown in Figure 7a. Independently of loading, proton mobility in MIL-53(Cr) at 300 K is significantly slower than in bulk water. In agreement with the experimental conductivity measurements of ref 39, DCEC calculated from the aMS-EVB3 simulations increases at higher temperature, although its value still remains relatively low for N ≤ 10 when the framework is in the narrow-pore configuration. Importantly, DCEC is predicted to vary with the number of H2O molecules adsorbed per unit cell, with higher mobility being found at N = 7, 14, and 20. Since the amount of water adsorbed by the material correlates with the breathing effect of the framework, the variation of DCEC with N indicates that proton

that thus favor the formation of (more space-filling) Eigen-like structures. Besides structural information, the aMS-EVB3 simulations can also provide molecular-level insights into the energetics and mechanisms of proton transport through the MIL-53(Cr) pores. In particular, within the MS-EVB formalism, the transition free energy describing proton transfer between two neighbor water molecules can be expressed as ΔF = −kT ln(qreac), where qreac = c12 − c22 with c12 and c22 being the probabilities of the two EVB states that contribute the most to the total MS-EVB wave function.46−49 Since the central point (qreac = 0.0) corresponds to a transient configuration in which the excess proton is equally shared by the donating and the accepting water molecule, it effectively captures the transfer event. As shown in Figure 6a, the free energy barriers to proton transfer calculated in the MIL-53(Cr) pores at T = 300 K for different loadings are appreciably lower than in bulk water except for N = 10 when the MOF material is undergoing the narrow- to large-pore transition.43,45 As expected, a further reduction of the barrier heights is found at higher temperatures with some variation of the overall free energy profiles depending on both pore size and water loading (see Supporting Information). The existence of relatively low free energy barriers to proton transfer between neighbor H2O molecules indicates that the pores of MIL-53 materials provide a confining environment that can effectively facilitate proton conduction. However, although the free energy profiles shown in Figure 6a are directly related to the kinetics of local proton transfer events, the actual proton long-distance transport also depends on the collective rearrangement of the underlying water hydrogen-bond network.8−10 To determine the relevant time scales associated with the actual proton mobility through the MIL-53(Cr) pores, both the continuous, Cc(t), and pseudo19512



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Figure 7. (a) Proton diffusion coefficient, DCEC, (b) water diffusion coefficient, DWAT, and (c) water orientational relaxation time, τ2, calculated MIL-53(Cr) as a function of both temperature and number of water molecules (N) adsorbed per unit cell. The dashed lines indicate the corresponding values calculated for bulk water at 300 K.41

Figure 6. (a) Free energy profiles of proton transfer in MIL-53(Cr) calculated as a function of the MS-EVB reaction coordinate qreac = c12 − c22. The results for bulk water are taken from ref 41. (b) Continuous time correlation function, Cc(t). (c) Pseudocontinuous time correlation function, Cpc(t). All results for MIL-53(Cr) were obtained at T = 300 K as a function of the number of water molecules (N) adsorbed per unit cell.

faster at higher temperature although it is important to mention that at T = 400 K the adsorbed H2O molecules may likely escape the pores.42 Overall, relatively higher water mobility is found at N = 14 and 20 when the MIL-53(Cr) framework assumes a large-pore configuration. This directly correlates with the relatively larger values of DCEC calculated at these loadings, indicating that the transport of the excess proton through the large MIL-53(Cr) pores involves a significant vehicular component (i.e., the excess proton is mainly transported as a hydronium ion). By contrast, although water mobility inside the pores is limited at all three temperatures for N = 7, the corresponding DCEC is relatively larger. This indicates that proton hopping between H2O molecules via the Grotthuss mechanism is largely responsible for the transport of the excess proton at this loading. The aMS-EVB3 results thus suggest that both pore size and water loading can significantly impact proton conduction in MIL-53 materials. Within the current picture of proton transport in aqueous media, the overall low proton mobility inside the MIL-53(Cr) pores can thus be explained by considering that, due to the slow rearrangement of the hydrogen-bond network, potential proton-accepting water molecules rarely assume hydration structures compatible with the final stage of the transfer process.

mobility in MIL-53(Cr) is effectively dependent on the pore water density. Considering that the free energy barriers to proton transfer in MIL-53(Cr) are lower than in bulk water (Figure 6a), the slow proton diffusion predicted by the aMS-EVB3 simulations is suggestive of a slow rearrangement of the water hydrogenbond network in the pores. To verify this hypothesis, the selfdiffusion coefficient (DWAT, Figure 7b) and orientational relaxation time (τ2, Figure 7c) were calculated for H2O molecules adsorbed in the MIL-53(Cr) pores as a function of temperature. Independently of loading, DWAT and τ2 at T = 300 K are indeed respectively smaller and larger than the corresponding values calculated for bulk water, which is in agreement with previous molecular dynamics simulations carried out with different force fields.43,44 The slow water diffusion and reorientation inside the MIL-53(Cr) pores can be traced back to the relatively strong water−framework interactions. In particular, as discussed in ref 45, the adsorbed H2O molecules establish strong hydrogen bonds with the hydroxyl groups coordinated to the Cr(III) ions of the framework, which, in turn, drastically reduce their mobility inside the pores. Both water diffusion and reorientation become 19513



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CONCLUSIONS Elucidating the molecular mechanisms that govern proton transport in MOFs is key to the rational design of de novo frameworks that can efficiently conduct proton at high temperature and low relative humidity for future applications in fuel cell technologies. In this regard, despite water-mediated proton conduction has been observed in several MOFs, a fundamental understanding of proton mobility inside the pores has been missing. In this study, aMS-EVB3 molecular dynamics simulations were employed to characterize the structure, thermodynamics, and dynamics of the hydrated proton in MIL-53(Cr) as a function of both water loading and temperature. A direct correlation was found between the proton hydration structure and the breathing motion of the framework, with Zundel-like and Eigen-like complexes preferentially forming when the MOF material exists in the narrow-pore and large-pore configurations, respectively. Similar proton hydration structures have also been identified in carbon nanotubes and biological channels.6,62−65 The low free energy barriers to proton transfer predicted by the aMS-EVB3 simulations indicate that the MOF pores provide a suitable long-range ordered environment that can facilitate proton conduction. However, this is offset in MIL-53(Cr) by the strong interactions of water with the hydrophilic component of the framework which, slowing down the rearrangement of the water hydrogen-bond network inside the pores, effectively suppresses long-distance proton mobility at room temperature. Proton diffusion was found to increase at higher temperature for specific water loading, indicating that both pore size and amount of adsorbed water (which is proportional to the relative humidity) can significantly affect proton transport through the MOF pores. The present aMS-EVB3 results suggest that watermediated proton conduction in MOFs can be enhanced by tuning both the pore size and the physicochemical properties of the material (for example, through inclusion of hydrophobic subunits into the framework which can effectively mimic the environment found in biological proton channels).6,65 Future simulation studies will focus on determining the impact of different functionalized ligands,39 electronic polarization,45 and nuclear quantization44 on proton mobility in the MOF pores.

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Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

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ASSOCIATED CONTENT

S Supporting Information *

Additional figures illustrating the temperature dependence of both thermodynamic and dynamical properties associated with the molecular mechanisms governing proton transport in MIL53(Cr). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I thank Ms. Corinne Allen and Prof. Seth Cohen for valuable discussions in preparation of this manuscript. This research was partially supported by start-up funds from the University of California, San Diego, the Hellman Fellowship Program, and the National Science Foundation (award number DMR1305101). This research used resources of the National Energy 19514



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Molecular Mechanisms of Water-Mediated Proton Transport in MIL-53

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