Computational Exploration of the Water Concentration Dependence of

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Computational exploration of the water concentration-dependence of the proton transport in the porous UiO-66(Zr)-(CO2H)2 Metal-Organic Framework Daiane Damasceno Borges, Rocio Semino, Sabine DevautourVinot, Herve Jobic, Francesco Paesani, and Guillaume Maurin Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b04257 • Publication Date (Web): 07 Feb 2017 Downloaded from http://pubs.acs.org on February 8, 2017

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Chemistry of Materials

Computational exploration of the water concentration-dependence of the proton transport in the porous UiO-66(Zr)-(CO2H)2 Metal-Organic Framework Daiane Damasceno Borgesa,b, Rocio Seminoa, Sabine Devautour-Vinota, Hervé Jobicc, Francesco Paesanid*, Guillaume Maurina* a

Institut Charles Gerhardt Montpellier, UMR-5253, Université de Montpellier, CNRS, ENSCM, Place E. Bataillon, 34095, Montpellier cedex 05 (France). b

Institute of Physics “Gleb Wataghin”, University of Campinas, Campinas - SP, 13083-970, Brazil

c

Institut de Recherches sur la Catalyse et l’Environnement de Lyon CNRS, Université de Lyon, 2 Av. A. Einstein, 69626, Villeurbanne (France).

d

Department of Chemistry and Biochemistry, University of California, San Diego La Jolla, CA 92093 (USA).

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Abstract The UiO-66(Zr)-(CO2H)2 MOF has been recently revealed as a promising proton conducting material under humidification. Here, aMS-EVB3 molecular dynamics simulations are performed to reveal at the molecular level the structure, thermodynamics and dynamics of the hydrated proton in this 3D-cages MOF as a function of the water loading. It is found that the most stable proton solvation structure corresponds to a H7O3+ cation and that a transition between this complex and a Zundel cation likely governs the proton transport in this MOF occurring via a Grotthuss-type mechanism. It is further shown that the formation of a H2O hydrogen-bonded bridge that connects the cages only occurs at high water concentration and this creates a path allowing the excess proton to jump from one cage to another. This leads to a faster selfdiffusivity of proton at high water concentration, thereby supporting the increase of the proton conductivity with the water loading as experimentally evidenced.


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I. INTRODUCTION Over the past decades, the metal-organic frameworks (MOFs), one of the latest classes of ordered porous solids1-4, have attracted significant interest due to the wide spectrum of materials that can be prepared as well as their promises for diverse applications5,6,, including, but not limited to, gas capture/storage7-9, biomedicine10, and energy storage and conversion11,12. In particular, this family of porous materials has recently received great attention as solid-state proton conductors13-21. Their designable architecture, the relatively easy grafting of functional groups at the organic linker and the capability to incorporate diverse species inside their pores, offer a broad range of options to design materials with high proton conduction performances. Therefore, there are nowadays a few water-mediated proton-conducting MOFs that largely compete with Nafion under humidification, sometimes surpassing the 10-2 S.cm-1 benchmark for fuel cells applications. As an example, the decoration of the pore walls of MOFs with channelaccessible acidic groups including sulfonic16, phosphonic22 or carboxylic23 acidic groups has been revealed highly efficient to create proton-conducting materials with promising performances. In this context, we recently evidenced that the Zr-based MOF grafted with carboxylic functions, namely the UiO-66(Zr)-(CO2H)2 exhibits a super-protonic conductivity under high relative humidity combined with an excellent water stability and an environmental friendly synthesis route21. A preliminary exploration highlighted that the interplay between the dynamics of protons and water in this 3D-cage like MOF is the key to explain the high proton conduction performance of the fully hydrated material. This calls for an in-depth exploration of the proton structure and the local proton transfer and dynamics inside the MOF cages at the molecular level.



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The proton structure in aqueous environments has been intensively treated using both experimental and modelling techniques24-29. It is generally accepted that the structure of the aqueous proton can be described as several possible complexes from which two limiting structures can be identified: the Zundel cation H5O2+ 30, and the Eigen cation H9O4+ 31. The first complex corresponds to a proton shared by two water molecules, while the second one is depicted as a hydronium strongly solvated by three water molecules. The formation of an Eigen complex is favorable in pure water owing to the large number of hydrogen bonded water neighbors per water molecule (3.6)32. The proton dynamics in aqueous solutions is generally described as the diffusion of a “defect” in the hydrogen bonded network connecting the water molecules. This mechanism is usually termed as “Grotthuss mechanism”33. Thus, the proton transport occurs in the picosecond timescale, same as for the hydrogen bonds formation/breaking processes34,35. However, the Zundel-Eigen interconversion occurs in shorter times, within 100 fs36-38. In fact, Zundel-Eigen interconversions can occur many times before an actual proton transport event is completed, a phenomenon which is usually referred to as “special pair dance”38. This suggests that the mechanism of proton transport is a complex process that involves not only a Zundel-Eigen interconversion, but also the rearrangement of the water molecules at distances beyond the first solvation shell of the excess proton, which is the currently accepted hypothesis for the rate determining step of aqueous proton transport.26,39 Different scenarios for the proton structure/dynamics are expected to take place in highly confined environments, where the number of water neighbors is generally reduced resulting in the formation of “distorted Zundel” or intermediate species H7O3.+40-42 In this context, following our preliminary study on UiO-66(Zr)-(CO2H)2

21

, the present work reports an in-depth


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fundamental analysis of the structure, thermodynamics and dynamics of the hydrated proton in this 3D-cages MOF as a function of the water loading. This study is achieved with molecular dynamics simulations (MD) using the anharmonic multistate empirical valence bond (aMSEVB3)43,44 that has been successfully employed in the past to model proton transport in aqueous environments45,46 and more recently in MOFs42.

II. METHODS The calculations were performed using the anharmonic version of the third generation Multistate Empirical Valence Bond (aMS-EVB3)43 method, initially developed by the Voth group27,28 and implemented into a modified version of the MD simulation package DL_POLY247. Compared to previous MS-EVB models27,28,44, this model leads to structural and dynamics properties of the aqueous proton that are in better agreement with experimental findings. Importantly, the description of the reorientation dynamics is substantially improved and the proton diffusion, which is underestimated in the previous models, matches better the experimental findings. Subsequent MS-EVB models with further improvements can be found in the literature.48 Briefly, the MS-EVB is an extension of the EVB formalism introduced by Warshel and Weiss49,50. The assumption is that an excess proton in an aqueous environment is delocalized over several water molecules and can thus be represented in terms of diabatic (or valence bond) states |𝜑𝑖 ⟩. According to this formalism, the electronic wave function of the system, |Ψ⟩, is represented by a linear combination of valence bond states |𝜑𝑖 ⟩, that describe all possible molecular configurations of the hydronium ion. 𝑁

|Ψ⟩ = ∑𝑖 𝐸𝑉𝐵 𝑐𝑖 |φi ⟩

Equation 1 5

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where NEVB is the total number of EVB states and 𝑐𝑖 is the expansion coefficient associated to the i-th EVB state. In practice, at each step of the simulation the valence bond configurations are generated by identifying first the “pivot hydronium”, which corresponds to the valence bond state with the largest value of 𝑐𝑖 . All water molecules located in the first three solvation shells of the pivot hydronium are also allowed to form hydronium ions, resulting in additional valence bond states 𝜑𝑖 with different topologies for both the hydronium ion and the surrounding hydrogen bond network. Specific details on the parametrization of the aMS-EVB3 are reported in the original reference43. The present aMS-EVB3 simulations were performed considering one conventional unit cell of UiO-66(Zr)-(CO2H)2 loaded with a variable number of water molecules, from 20 to 80 molecules per unit cell. The latter loading correspond to the simulated saturation capacity of the MOF as previously obtained by Grand Canonical Monte Carlo (GCMC) simulations21. The MOF was treated as a fully flexible framework with the potential parameters taken from our previous study7,51. The non-bonded Lennard-Jones framework-water and framework-hydronium interactions were obtained using Lorentz-Berthelot mixing rules52,53. The initial distributions of the water molecules were obtained from Monte Carlo simulations performed in the canonical ensemble at 400 K. The excess proton was randomly added to the vicinity of one H2O molecule to form the initial H3O+ ion. In order to improve the statistics, at least 5 simulations were performed with different initial configurations. Each initial configuration includes a proton located inside different cages of the framework. All MD simulations were thermalized at 400 K and after 1 ns of equilibration, the systems were simulated in the microcanonical (NVE) ensemble for a period of 5-10 ns. In all cases, the equations of motion were integrated using the velocity-Verlet algorithm with a time step of 0.5 6 ACS Paragon Plus Environment

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fs. From the mean-square displacement (MSD) curves averaged over multiple time origins and the five different MD trajectories simulated for each water loading, it was possible to extract the self-diffusion coefficient Ds for both water and the center of excess charge (CEC) using the Einstein relation. Similarly, further analyses of other structural properties were carried out by averaging over all five MD simulations.

III. RESULTS AND DISCUSSION Figures S1 and S2 report that the proton conductivity measured by Complex Impedance Spectroscopy for UiO-66(Zr)-(CO2H)2 at 298 K increases by two orders of magnitude (from 7.4 × 10-6 S.cm-1 to 8.5 × 10-4 S.cm-1) when the relative humidity goes from 40% to 90%. This trend coincides with faster proton dynamics at high water loading as evidenced by Quasi-Elastic Neutron Scattering (QENS) experiments performed at 373 K (Figure S4). This experimental observation emphasizes the key role of water in assisting the proton transfer in this MOF. aMSEVB3 MD simulations were thus performed to provide molecular-level insights into the dependence of the UiO-66(Zr)-(CO2H)2 proton conductivity on the water loading. Figure 1 reports the simulated self-diffusion coefficient Ds for both water (Ds(H2O)) and proton (Ds(CEC)) at 400 K in the whole range of water loading. The self-diffusivities of both species are slower than those reported in bulk water. Ds (CEC) and Ds (H2O), which span from 0.03 to 0.06 Å/ps and 0.005-0.025 Å/ps, respectively, when the water loading increases, are one order of magnitude lower than the values obtained in protonated bulk water using the same aMS-EVB3 model43. Ds (CEC) and Ds (H2O) show different trends, with the former increasing substantially with water loading. This behavior is consistent with the increase in proton diffusivity and conductivity observed experimentally (Figures S1-S3). In contrast, the self-diffusivity of water 7 ACS Paragon Plus Environment


shows a maximum at intermediate loading. Similar loading-dependent behavior of molecular self-diffusivity has already been observed for diverse guest molecules in this family of 3D-cages type MOFs53-56. This is attributed to an increase of the guest hopping rate between cages until an intermediate loading is reached after which effects associated with steric hindrance become predominant and lead to a decrease of the self-diffusivity. This prediction deviates from the QENS data that indicate an acceleration of the dynamics of both species (i.e., larger Ds (CEC) and Ds (H2O)) when the water loading increases (Figure S4). Figure 1 further shows that Ds (CEC) remains higher than Ds (H2O) in the whole range of water loading. The aMS-EVB3 results thus suggest that the dynamics of the excess proton in UiO-66(Zr)-(CO2H)2 is not driven by a vehicular mechanism24 in which the excess proton would be transported along with the water molecules that solvate it, but it mainly involves proton hops between hydrogen-bonded water molecules according to the Grotthuss mechanism.

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nH2O /uc Figure 1: Self-diffusivities of water (empty symbols and dashed lines) and the center of excess charge (full symbols and solid lines) simulated at 400 K in UiO-66(Zr)-(CO2H)2 as a function of water loading defined as the number of water molecules (𝑛𝐻2 𝑂 ) per unit cell (uc). 8 ACS Paragon Plus Environment

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Proton hopping events between water molecules can be characterized from the analysis of the MD trajectories by following the motion of the CEC as it moves from the ith oxygen atom (“pivot hydronium”) to the jth oxygen atom (new “pivot hydronium”) along the cages of the UiO66(Zr)-(CO2H)2. To this purpose, we calculated the pseudo-continuous time correlation function 𝐶𝑝𝑐 (𝑡) = 〈ℎ𝑖 (0)ℎ𝑖 (𝑡)〉/〈ℎ𝑖 (0)ℎ𝑖 (0)〉, where ℎ𝑖 (𝑡)=1 if the ith oxygen atom is the pivot hydronium oxygen, and zero otherwise28. 𝐶𝑝𝑐 (𝑡) is defined as the pivot-hydronium decay and can be used to determine the mean lifetime (𝜏𝑝𝑐 ) of the hydronium species according to the 𝑡

threshold method where 𝐶𝑝𝑐 (𝜏𝑝𝑐 ) = 𝑒 −1 ≈ exp (− 𝜏 ). Figure 2 shows the decay of 𝐶𝑝𝑐 (𝑡) for 𝑝𝑐

each water loading, The associated relaxation time 𝜏𝑝𝑐 decreases from 130 ps to 17 ps as the water loading increases from 20 𝑛𝐻2 𝑂 /𝑢𝑐 to 80 𝑛𝐻2 𝑂 /𝑢𝑐, indicating that proton hopping is much faster at higher water loading. The water-loading dependence of the proton transfer rate was also calculated as 𝑘𝑃𝑇 = lim𝑡→∞ −𝑑𝑙𝑛𝐶𝑝𝑐 (𝑡)/𝑑𝑡27,42,46. The inset of Figure 2 shows that the transfer rate increases linearly with water loading. It is important to note that 𝐶𝑝𝑐 (𝑡) excludes protonrattling events, i.e. when the excess proton rapidly rattles between the oxygen atoms of two neighboring water molecules. 𝐶𝑝𝑐 (𝑡) is thus associated with effective proton transfer events. This analysis is thus consistent with the aMS-EVB3 prediction of faster proton self-diffusivity at higher water loading.



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t /ps Figure 2: Pseudo-continuous time correlation functions for the pivot-hydronium calculated from the aMS-EVB3 simulations performed at 400 K as a function of water loading. The error bars are calculated from the average over the 5 different trajectories. The hydronium lifetime is approximately 17, 32 and 130 ps for high (70 and 80 H2O/u.c.), intermediate (40 and 50 H2O/u.c.) and low water (20 H2O/u.c.) loadings, respectively.

Within the aMS-EVB3 formalism, the energy barrier for the Eigen-Zundel interconversion is computed from the free energy profile Δ𝐹 = −𝑘𝑇𝑙𝑛(𝑞𝑟𝑒𝑎𝑐 ), where 𝑞𝑟𝑒𝑎𝑐 = 𝑐12 − 𝑐22 with 𝑐1 and 𝑐2 being the coefficients associated to the two EVB states that contribute the most to the total aMS-EVB3 wave function. The free energy profiles associated to bulk water and water confined in UiO-66(Zr)-(CO2H)2 are reported in Figure S5. Independently of water loading, the freeenergy profiles in UiO-66(Zr)-(CO2H)2 are very similar, with energy barriers of ~0.6 kcal/mol slightly higher than in bulk water (0.4 kcal/mol, as obtained by the aMSEVB3 model). This difference may be associated with the limiting cation structures formed in UiO-66(Zr)-(CO2H)2 which differs from the bulk water. In order to clarify this point, a close inspection of the MD trajectories was further carried out. Figure 3 reports the radial distribution function 𝑔𝑂𝑤𝑂∗ (𝑟), 10 ACS Paragon Plus Environment

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between the oxygen atoms of water (Ow) and the oxygen atoms of pivot-hydronium ion (O*). The first peak centered at 2.5-2.6 Å suggests the formation of Zundel cations, since this distance falls into the range of values generally attributed to the Zundel O-O* pairs (2.5 Å)30. The analysis of the coordination number function, 𝑛𝑂𝑂∗ (𝑟) shown in the inset of Figure 3 indicates that 𝑛𝑂𝑂∗ < 3 in the first coordination sphere (defined as a sphere of radius 𝑟 = 3 Å centered on on O*). This confirms that the pivot-hydronium ion does not have sufficient H2O molecules in the first solvation shell to form Eigen cations. The most stable proton solvation structure thus corresponds to an intermediate state of H7O3+ (𝑛𝑂𝑂∗ = 2). In other words, the reorganization of the water molecules around excess protons is limited to the formation of H7O3+ cations and Zundel cations where the proton transfer takes place. The proton transport in UiO66(Zr)(CO2H)2 is thus predominantly governed by the interconversion of H7O3+-Zundel cation complexes similarly to the scenario already reported in other confined solids like carbon nanotubes40,41.



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Figure 3: Radial distribution function 𝑔𝑂𝑤 𝑂∗ (𝑟), calculated from aMS-EVB3 simulations at 400 K between the oxygen atoms of water (Ow) and the oxygen atoms of the pivot-hydronium ion (O*) in UiO-66(Zr)-(CO2H)2 for different water loadings. To complement the structural analysis in the vicinities of the excess charge, the organization of water confined in the 3D cages of UiO-66(Zr)-(CO2H)2 was further investigated. To this purpose, we carefully quantified the number of hydrogen bonds (HB) formed between two water molecules using the following geometric criteria: d(O-O) < 3.5 Å and the angle formed between the intramolecular O-H vector and the intermolecular O-O vector is shorter than 30°57. The average numbers of HB per water molecule were found to be 1.1, 1.5, 1.7, 2.0 and 2.15 for 20, 40, 50, 70 and 80 H2O/u.c., respectively. These values are significantly lower than 3.6 obtained for bulk water32 and can be explained in terms of the high confinement existing in the MOF cages and the involvement of water molecules in hydrogen bonds with the –CO2H 12 ACS Paragon Plus Environment

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groups of the framework as shown by the corresponding radial distribution function 𝑔𝑂𝑤𝑂𝑓 (𝑟) in Figure S6. The HB dynamics is further analyzed by computing the pseudo-continuous time 𝐻𝐵 (𝑡) correlation function for hydrogen bonds which is defined as 𝐶𝑝𝑐 = 〈ℎ𝑖𝑗 (0)ℎ𝑖𝑗 (𝑡)〉/

〈ℎ𝑖𝑗 (0)ℎ𝑖𝑗 (0)〉, where ℎ𝑖𝑗 (𝑡) = 1 when ith and jth water molecules are hydrogen bonded and 0 𝐻𝐵 (𝑡) otherwise. 𝐶𝑝𝑐 is shown in Figure 4 for different water loadings. The associated mean HB

lifetime 𝜏𝐻𝐵 is relatively long at low loading (93 ps), becomes faster at intermediate loading (23 ps) before increasing again at high concentration (52 ps). This trend can be explained as follows: at low water loading, the water molecules are strongly trapped in the cages forming hydrogenbonds with the grafted –CO2H functions that are difficult to break. This implies a slow translational and rotational dynamics of water as reported in Figure 1 and Figure S7. At intermediate loading, the additional water molecules are involved in less favorable interactions with the framework and have more “freedom” to rotate and to break/make hydrogen bonds leading to a low HB lifetime and fast water dynamics. At higher loadings, the effect of steric hindrance becomes evident, resulting in a more static HB network that is consistent with a slowing down of the water dynamics. Importantly, at high water loading 𝜏𝐻𝐵 is appreciably longer than 𝜏𝑝𝑐 , which reinforces the notion that the HB dynamics is not the limiting factor for proton transfer.



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Figure 4: Pseudo-continuous time correlation functions for hydrogen bonds calculated from aMS-EVB3 simulations performed at 400 K as a function of water loading. The averaged HB lifetime 𝜏𝐻𝐵 values are approximately 95, 52 and 23 ps for high (70 and 80 H2O/u.c.), intermediate (40 and 50 H2O/u.c.) and low water (20 H2O/u.c.) loadings, respectively. Further analysis of the water distribution in the MOF cages was carried out. The unit cell of UiO-66(Zr)-(CO2H)2 contains 8 tetrahedral cages and 4 octahedral cages labeled as [1 to 8] and [9 to 12] respectively, each octahedral cage is connected to 8 tetrahedral cages. The averaged distribution of water molecules in the two types of cages calculated from the MD trajectories is shown in Figure 5. At the initial stage of adsorption, the water molecules are preferentially located in the more confined tetrahedral cages. Some cages are found empty which diminishes the connectivity of the HB network. When the uptake progressively increases the water molecules are more homogenously distributed in the cages and effectively occupy all of them at the highest loading considered in this study (80 H2O/u.c.). The relatively similar occupancy of the octahedral and tetrahedral cages comes from the fact that the octahedral cage is not drastically much larger than the tetrahedral cage (7.0 Å vs 5.2 Å as shown in the pore size distribution plotted in Figure S8) and that the orientation of the –CO2H functional groups makes 14 ACS Paragon Plus Environment

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part of the octahedral cages inaccessible for water (Figure S8). This homogeneous distribution of water is an optimal scenario for the formation of a percolated HB network that connects the cages through the triangular windows via a HB bridge between water molecules.

Figure 5: Simulated distribution of water in the tetrahedral (from 1 to 8) and octahedral (from 9 to 12) cages of UiO-66(Zr)-(CO2H)2 averaged over aMS-EVB3 trajectories carried out at 400 K for three different water loadings.

The residence time for water 𝜏𝑂𝑤 in the cages as a function of water loading is shown in Figure 6. The residence time is shorter at intermediate loadings consistent with a relatively fast water dynamics resulting from cage to cage diffusion. At high loading, the water molecules only rarely migrate from their initial cages since the residence time is close to 1.5𝑛𝑠 consistent with both slow translational and rotational water dynamics and the formation of a more static and percolated water HB network as shown by the rather long HB lifetime (Figure 4). 15 ACS Paragon Plus Environment


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nH2O/uc Figure 6: Residence time of water molecules in the cages of UiO-66(Zr)-(CO2H)2 averaged over aMS-EVB3 trajectories carried out at 400 K as a function of water loading.

As a further step in characterizing both proton and water dynamics in UiO-66(Zr)-(CO2H)2, Figure 7 shows the water-loading dependence of the proton migration from one cage to another of the MOF, which was obtained by following the time evolution of index associated with the cage occupied by the excess proton. At low loading (20 H2O/u.c.), the excess charge only jumps through tetrahedral cage (index 6) to the octahedral cages (indexes 10 and 11) and then goes back to tetrahedral cage (index 6) over a period of 10 ns. This corresponds to a proton-rattling event between these cages. At intermediate loading (40 H2O/u.c.), the excess charge migrates from at least two tetrahedral cages (indexes 1 and 3) and constantly crosses the octahedral cages (index 9) over the same time period. Finally, at high loading, an effective transport of the excess


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charge can be observed with migration towards at least 3 tetrahedral cages (indexes 1, 6 and 7) involving the crossing of octahedral cages (indexes 9, 10, 11 and 12).

Figure 7: Time evolution of the cage indexes (tetrahedral cages from 1 to 8 and octahedral cages from 9 to 12) occupied by the excess proton calculated from 10 ns of a MS-EVB3 trajectory at 400 K. The connectivity of the different cages is illustrated. These scenarios are illustrated in Figure 8 which shows the position occupied by both water molecules and excess proton during 10 ns of aMS-EVB3 trajectories at 400 K for both low and



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high water loadings. Clearly, the absence of water HB bridges between cages at low water loading hampers the migration of the excess proton, which is consistent with the low conductivity measured experimentally. In contrast, at high water loadings, the excess charge can move from one cage to another through the water HB network, which is at the origin of the high conductivity measured for UiO-66(Zr)-(CO2H)2 at high relative humidity.

Figure 8: Illustration of the positions occupied by water (blue) and proton (white) in the 3D-cage UiO-66(Zr)-(CO2H)2 (grey atoms) over a 10 ns aMS-EVB3 trajectory at 400 K (top: 20 H2O/u.c., bottom : 80 H2O/u.c.)

IV. CONCLUSION We used aMS-EVB3 MD simulations to derive a microscopic picture of the structure and dynamics of excess protons in the super-protonic UiO-66(Zr)-(CO2H)2 MOF as a function of water loading. The self-diffusivity of proton was found to continuously increase with water 18 ACS Paragon Plus Environment

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loading, which is consistent with higher values of proton conductivity observed experimentally at high relative humidity. The aMS-EVB3 simulations indicate that the proton self-diffusivity remains higher than that of water over the entire range of water loadings considered in this study. This indicates that proton transport in UiO-66(Zr)-(CO2H)2 mainly consists of hopping events according to the Grotthuss mechanism, with transitions between H7O3+ and Zundel complexes. The percolated water hydrogen-bond network established at high loadings forms a pathway that connects the MOF cages and allows proton transfer over long distances. The molecular-level characterization of proton structure and dynamics in UiO-66(Zr)-(CO2H)2 presented here paves the way towards a better control of MOF porosity and the role of functional groups to optimize the proton conduction performance of this class of materials. Future simulation studies might focus on the refinement of the description of the MOF models with the development of EVB models for the functionalized linkers such as the –CO2H groups of UiO-66(Zr)-(CO2H)2 which may be involved in the proton conduction mechanism.

Acknowledgements We thank the Institut Laue-Langevin (Grenoble, France) for the neutron beam time on µIN5 and Dr. J. Ollivier for his help during experiment. G. M. thanks Institut Universitaire de France for its support. F.P. is supported by the National Science Foundation through Award No. DMR1305101. D.D.B acknowledges FAPESP for financial support through grant n.2015/14703-9. We also thank Farid Nouar and Christian Serre from the Institut des Matériaux Poreux de Paris, FRE 2000 CNRS, Ecole Normale Supérieure, Ecole Supérieure de Physique et de Chimie Industrielles de Paris, Paris Sciences Lettres for the the MOF samples.



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Author Contributions S.D.V. and H.J. performed the Complex Impedance Spectroscopy and the Quasi-Elastic Neutron Scattering experiments respectively while D.D.B., R.S., F.P. and G.M. were involved in the modelling part of the work. D.D.B. and G.M. wrote the manuscript and R.S. and F.P. contributed to the paper writing. All authors discussed the results and commented on the manuscript.

Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org. The Supporting Information contains the QENS and Complex Impedance Spectroscopy data as well as more details on the computations. Corresponding authors Email: [email protected] (Guillaume MAURIN) and [email protected] (Francesco PAESANI).

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H+ H2O


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Computational Exploration of the Water Concentration Dependence of

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