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Diffusion of Water and Carbon Dioxide and Mixtures Thereof in Mg-MOF-74 Stephan Bendt, Ying Dong, and Frerich J. Keil J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08457 • Publication Date (Web): 04 Dec 2018 Downloaded from http://pubs.acs.org on December 8, 2018

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The Journal of Physical Chemistry

Diusion of Water and Carbon Dioxide and Mixtures Thereof in Mg-MOF-74 S. Bendt, Y. Dong, and F. J. Keil

∗

Hamburg University of Technology, Institute of Chemical Reaction Engineering, Eissendorfer Strasse 38, D-21073 Hamburg, Germany

E-mail: [email protected]

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Abstract Self-diusion coecients for CO2 , H2 O and mixtures thereof in Mg-MOF-74 have been determined using molecular simulations. The crystal structure was modeled in a rigid and exible manner with the intent to identify the impact of the exibility of the framework on the diusivity. The results show that especially at low loadings the mobility of the molecules is enhanced in exible lattices due to a small dierence in adsorption energy and the enlarged equilibrium distance to the main adsorption sites. In mixtures the exibility has the same inuence, however, due to the presence of the secondary species, water is predomiantly located in the close proximity of the magnesium ion which eectively leads to a segregation eect from the more freely moving CO2 .

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Introduction Carbon dioxide has been identied as one of the reasons for the present climate change. 1 As a consequence, reducing the amount of its emissions into the atmosphere is an urging task 13 with coal-based power plants being one of of the main CO2 sources. 4 The current state of the art technology to reduce the CO2 fraction in the emitted ue gas is amine scrubbing. Unfortunately, it has the detrimental side eect that high amounts of energy are required during the regeneration step. 5,6 Consequently, there is room for improvement regarding the separation of the greenhouse gas CO2 from the ue gas of (coal-based) power plants before release into the atmosphere. 7 In order to substitute the current state-of-theart technology 'amine scrubbing' with more eective ones, adsorption processes were found to have the potential to do so, whether they are based on amine-functionalized silica, 813 carbon-based materials, 1418 zeolites, 14,1925 and metal-organic frameworks (MOFs). 2637 Liu et al. 38 and Yu et al. 39 wrote excellent reviews regarding the latter materials with respect to CO2 separation. Out of all aforementioned materials, MOFs, which consist of metal ions and organic linkers within a single crystal structure, 40 are the most promising ones because of the huge variety of suitable metals and organic linkers readily available. This oers the potential to design materials for the separation problem at hand. 41,42 Due to the sheer number of possible crystal structures, screening processes based on adsorption capacity and selectivity, 35,4347 or parasitic energy 48 are necessary to identify the best ones. Mg-MOF-74, also known as CPO-27-Mg, 49 emerged as one of the front runners due to its high capacity and selectivity towards CO2 which is attributed to its so-called "open metal sites" (OMS) or coordinately unsaturated metal sites (CUS). 29,34,47,5055 According to Park et al., 56 the reason for the high interaction strength between the CO2 guest molecules and the OMS is due to a strong local electrical eld by the electronic density of the Mg2+ -ion which results in interaction of the CO2 electrons with the empty orbitals of the magnesium as in a coordination bond. In the beginning most of the studies regarding Mg-MOF-74 have been focused on the 3



separation of CO2 from binary mixtures with methane (natural gas) or nitrogen (ue gas). However, in reality ue gas consists of N2 (70-75%), CO2 (15-16%), H2 O (5-7%), and O2 (3-4%), whereas impurities, such as SO2 , NOx , and CO, are in the ppm-range. 3,5759 As a result, the adsorption of each species in Mg-MOF-74 has been investigated. 6062 It was found that CO2 is more favorably adsorbed than the likes of NOx , 60,61 SO2 , 60,61 CO, 34,63 and O2 60,61 because the former adsorbs quite strongly to the OMS. 34,47,53,63,64 The last compound in the ue gas, water, presents more problems when one is considering Mg-MOF-74 for real life applications. This environment induces problems when it comes to molecular modeling of interactions between any OMS containing frameworks and guest molecules, such as CO2 , SO2 , water, and propene, which have the potential to be inuenced by that eld. In essence, classical force elds, like UFF, 65 DREIDING 66 for example, cannot describe the potential energy surface around the OMS, which leads to false predictions of the experimental adsorption isotherms compared the the ones obtained from GCMC. 53,60,6770 Therefore, DFT and ab initio quantum chemical calculations have been employed as a mean to overcome this problem. Kundu et al. 64 calculated

ab initio

Langmuir isotherm equilibrium constants from

Gibbs free energies to successfully reproduce CO and N2 adsorption isotherms. This method evolved into GCMC simulations on a lattice independent of a pre-determined isotherm and applied to predict the adsorption isotherms for CH4 /CO2 -mixtures. 71 Another successful approach was to generate small clusters out of the environment around the OMS 53,67,72 or use plane-wave DFT to sample the entire unit cell. 68,69,73 Subsequently, the DFT-based potential energy surface is t to common force eld functions, e.g. Lennard-Jones and Buckingham potential, and then to use them in GCMC-simulations. If the adsorption sites obtained from classical force elds coincide with the ones obtained from DFT, Kim et al. 74 adjusted the adsorption energies during GCMC simulations based on the UFF single point energy values from DFT. As a result, the simulated adsorption isotherms agreed very well with the experimental data. Furthermore, changing the guest molecule model by adding interaction sites, 67 by multiplying force eld interaction parameters with constants, 60,70 or developing 4


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polarizable force elds have proven to be a viable method to calculate adsorption isotherms in Mg-MOF-74 as well. 75 While Yazadin et al. 76 showed an benecial inuence of water on CO2 adsorption, the majority of publications on the adsorption of water showed that in fact the opposite is true: Canepa et al. 47 calculated higher adsorption energies for H2 O (73.3 kJ ). mol

kJ ) mol

than for CO2 (48.2

When pure component isotherms for each species were compared, it was observed that

the uptake for H2 O was higher, and saturation was reached at very low pressures. 54,69,7779 Yu et al. 80 calculated adsorption isotherms for humid and dry N2 /CO2 mixtures in order to see the negative inuence of water on the adsorption capacity using grand-canonical Monte Carlo (GCMC) simulations. Lin et al. 68 also determined adsorption isotherms for CO2 /H2 O mixtures with GCMC, showing in the process that very small fractions of water in the gas phase can drastically decrease the CO2 uptake in Mg-MOF-74. Recently, Daglar and Keskin 81 screened over 3800 MOFs for membrane applications regarding CO2 /N2 /H2 O separation. Zuluaga et al. 82 were able to explain the reason for the loss in capacity using DFT. OH− ions which come to existence in the proximity of the OMS due to the water dissociation reaction, occupy the adsorption spot. Furthermore, the complex elongates the metal-oxygen bond and, thus, weakens the structural integrity. Since the focus of research lies mainly with the adsorption of guest molecules in MgMOF-74, the number of studies regarding the diusion of guest molecules is very small. Canepa et al. 47 investigated the diusion of CO2 , H2 O and H2 barriers along the z-axis of the framework. Marti et al. 83 studied the orientation of CO2 molecules as a function of loading with NMR and DFT while Xu et al. 84 used 2 H SSNMR spectroscopy to look at orientations of D2 O and other molecules in Mg-MOF-74. Lin et al. 85 calculated free energy maps along the channel axis to identify orientations of the CO2 molecules and diusion barriers along the path using Monte Carlo simulations. To the best of our knowledge, only Krishna and van Baten 86 reported values for self-diusivity of CO2 in Mg-MOF-74 with the restriction that the aforementioned special nature of the OMS were not taken into consideration in 5



their paper. Another important factor for modeling diusion is the exibility of the MOFs. Compared to zeolites, MOFs are considered highly exible which, for instance can lead to breathing eects or linker rotation among other things. 87 The inuence of exibility in MOFs on diusion has received some attention recently. For example, ZIF-8 was investigated for its exibility, 88,89 and why it is capable to adsorb molecules with a considerably larger kinetic diameter than the (rigid) pore diameter. 90,91 Amirjalayer et al. 92 reported that due to the framework exibility benzene molecules diuse slower through MOF-5 than in the rigid case. Recently, Braun et al. 93 investigated multiple thermostats frequently used in molecular dynamics simulations. They were able to show that velocity rescaling algorithms, e.g. thermostats, can cause artifacts violating the equipartition theorem. As an example for such artifacts, they showed that the inuence of the framework exibility in the study by Amirjalayer et al. 92 was mainly the result of the chosen Berendsen thermostat. Consequently, one needs to be aware whether the deviation between a rigid and a exible lattice is caused by the the exibility and not by thermostat artifacts. Also, it was shown that for zeolites the introduction of exibility can cause the free energy to be less negative allowing molecules to diuse faster. 94 To date, the understanding of the MOF-lattice exibility modeling process is still in its infancy and experiments are essential to verify simulation results. 94,95 In this work, we calculate self diusion coecients for pure CO2 and H2 O systems as well as mixtures thereof in Mg-MOF-74. We compare results based on the UFF and the QM-based force eld derived in a previous study. 69 Furthermore, the inuence of exibility of the framework on the self- diusion coecients is investigated.

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Theory Force elds & computational details Adjustments and dierences of the force elds In order to calculate intermolecular energies and forces, two force elds are used in this work. The rst one is based on the UFF 65 (from here on called "UFF-FF") and the second is based on our previous work (from here on called "DFT-FF"). 69 In each case CO2 is described by the TraPPE, 96 and for the UFF-FF the framework atoms are modeled based on the UFF. 65 The dierences between the force elds are that in the UFF-FF Lorentz-Berthelot mixing rules are used to calculate cross-term parameters and H2 O is modeled according to the TIP5P-Ew water model. 97,98 In the DFT-FF the mixing rules involving framework atoms are replaced by specically derived interaction parameters, which reproduce the potential energy surface obtained from DFT calculations using the TIP3P 99,100 model, as described in a previous study. 69 Since the energy and force calculations in GROMACS are the most ecient using Lennard-Jones functions, the parameters have been retted from a function with four parameters to one with two and, furthermore, only one set of point charges for the guest molecules were used instead of two. Obviously, that leads to a loss in accuracy. Yet, comparing adsorption isotherms for CO2 and H2 O in Mg-MOF-74 show that the experimental isotherms are still predicted well, see Figures S7 and S8. For all interaction parameters in each force eld describing framework atoms and guest molecules and a more detailed discussion on the accuracy of the force elds, the reader is referred to the SI.

Simulation details All MD simulations were carried out using the GROMACS package version 5.1.1. 101 The setup was as follows: For each loading (one molecule per unit cell and so on) two constraints 7



have to be met: Firstly, the number of molecules was chosen so that at least 64 molecules are put into each simulation box in order to get good statistics each run. Secondly, the size of the simulation box must be twice the cut-o radius in every direction. As a result, the numbers of unit cells per direction vary from 3x3x7 to 1x1x5 in x-, y-, and z-direction, respectively, whereas the smallest box possible is the 1x1x5 unit cell conguration. A schematic unit cell of Mg-MOF-74 is given in Figure S2. To ensure that the system is sampled in an equilibrated state, a minimum of 5·105 Monte Carlo steps in the NVT ensemble is carried out using only the regrow move with the pre-dened number of molecules ranging from 1 molecule per unit cell to 36 molecules per unit cell or 66 molecules per unit cell for CO2 or H2 O, respectively. As for mixtures, the swap identity move is added, whereas both moves have a probability of 0.5 to occur. The loading represents the maximum uptake of the structure for the respective guest molecule according to GCMC generated adsorption isotherms. 53,68,69 In the next step, Maxwell-Boltzmann distributed velocities are assigned to each molecules individually. The production phase was run with a timestep of 1 fs for at least 50 ns, see SI for further information. The equations of motion were integrated using the Velocity-Verlet algorithm. The desired temperature of 300 K was controlled by means of the Nosé-Hoover-thermostat (τt = 1 ps) as implemented in GROMACS 5.1.1. 101 The framework was either kept rigid or exible depending on the simulation. Flexibility was modeled as described in the UFF. 65 Please note that the DFT-FF is not specically designed for the exible lattice but for the rigid one. As a result, the force eld might not reproduce vibrational frequencies or experimientally determined lattice parameters which are essential for exible force elds. 102 Additionally, the interaction parameters between host atoms and guest molecules have not been rened for that case. However, we believe that the parameters determined for the rigid case are a reasonable approximation since the average position of the framework atoms in the exible lattice agrees well with the ones in the rigid case, as is evident by the calculated adsorption energies and isotherms (see SI). Periodic boundary conditions were applied in all directions in all cases. A cut-o radius of 12.8 Å for the van 8


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der Waals and Coulomb interactions was employed. The long-range electrostatic interactions were calculated using the Particle-Mesh-Ewald method. 103,104 Unless interaction parameters between guest molecules and or framework atoms were specied in the force eld, they are determined using the Lorentz-Berthelot mixing rules. The (self-)diusion coecient for one simulation can be calculated using the velocity auto-correlation function or the meansquared displacement (MSD). In this work the latter is used. The Einstein equation relates the diusion coecients to the average MSD of molecule i (for all i in the system): self Dxyz =

∂h∆r2i (t)i 1 ∂h| ri (t) − ri (0) |2 i 1 · lim = · lim 2 · 3 t→∞ ∂t 6 t→∞ ∂t

(1)

self describes all three space directions. It is possible to calculate each direction individuDxyz

ally, for example in z direction:

Dzself =

1 ∂h| rz,i (t) − rz,i (0) |2 i · lim 2 t→∞ ∂t

(2)

self is obtained by: Then, the dimensionally averaged Dxyz

self Dxyz =

Dzself + Dyself + Dzself 3

(3)

Mg-MOF-74 and its derivatives consist of honeycomb-like channels in z-direction without intersections. Because of that, only diusion coecients in that direction are of interest and, self hence, Dself . Pair distribution functions were generated from the trajectories xyz equals Dz

of the guest molecules. For the evaluation for both the diusion coecients and the pair distribution functions the trajectories of each molecule are taken within the simulation time of 5 to 45 ns in order to avoid artifacts at the beginning of the simulation and insucient sampling at the end.

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Results Comparison of the force eld in the rigid crystal It has already been established that classical force elds fail to describe the interactions between the open metal sites (OMS) and certain guest molecules which interact strongly with them. The improvement of DFT derived force elds with respect to adsorption isotherms has been well documented in the literature. 53,6769 As for dynamic properties, to the best of our knowledge, this has not been the case yet. In Figure 1, the self-diusion coecients for CO2 at 300 K obtained from simulations as a function of loading are compared to results published by Krishna et al., 86 which are calculated using UFF 65 and DREIDING. 66 Our results, based only on the UFF, reproduce the trend of the reference data well. With increasing number of molecules inside the simulation box the diusion becomes slower. This loading dependency is commonly observed in nanoporous materials. 105 With increasing loading collisions between molecules occur more frequently and, thus, the diusion resistance is increased for each molecule, eectively slowing all of them down. 106 The deviation between Krishna et al. 86 and this work can be explained by the fact that slightly dierent point charges were assigned to the framework atoms. Self-diusivities calculated using the DFT derived force eld yield a reduced mobility, lowering the diusion by a factor of almost ten at low loadings to twice at higher ones. This is expected since the estimated adsorption energy is lower for the UFF than for the DFT based force eld, see SI. Furthermore, the behavior of the diusivity as a function of loading became more complex: At low loadings the diusivity decreases with an increase of loading until a minimum is reached at 15 to 18 molecules per unit cell. Then, a maximum is found at 30 molecules per unit cell. The reason for this behavior may be explained in the following way: It is unlikely that the decrease in diusivity is caused by molecule-molecule collisions since the channel is quite large and saturation is far from being reached. 18 molecules per unit cell is an important level since there are 18 OMS or 18 Mg-ions per unit cell, respectively. At this or close to this loading, statistically, the OMS 10


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the main adsorption sites in this crystal 53 are saturated. Thus, leading up to that limit, due to the strong interactions with the OMS, a higher fraction of molecules is adsorbed and found in (close) proximity of the adsorption site, e. g. the Mg-ion, where the molecules are trapped and their movement is slowed down. The fraction of non-adsorbed molecules which move faster decreases. When the loading is increased above 18 molecules per unit cell, the diusivity increases because all the OMS are occupied and due to more and more CO2 -CO2 interactions the attraction strength of the OMS is somewhat diminished and the weaker adsorption sites close to the linkers are occupied. In other words: due to the adsorbed CO2 molecules the channel wall becomes less attractive and the channel itself smaller resulting in faster movement of the guest molecules in the middle of the channel until there is less and less free space. At loadings higher than 30 molecules per unit cell the molecule-molecule collisions are much more frequent and there is less and less free pore volume available. As a result, the self-diusivity decreases similar to the UFF-based results. It is interesting to note that for the highest loadings, for which the interaction energies are dominated by moleculemolecule interactions, the diusion coecients predicted by either force eld are very close to each other. The loading dependency of the self-diusion coecient for H2 O is shown in Figure 2. To the best of our knowledge, there is no data available in the literature. The results based on the UFF increase monotonically with loading to a plateau value as the maximum. The diusivity ranges from approximately 1·10−11 m2 s

m2 s

at 1 molecules per unit cell up to 1.8·10−9

at high loadings exceeding 40 molecules per unit cell. This loading dependency follows

the type III self-diusion process described by Kärger et al. 105 At low loadings due to the very strong interaction with the Mg-sites the movement of the water molecules is slow and limited. With increasing number of molecules in the framework, the relative number of strong interaction sites are reduced which leads to an increase of the overall mobility. This mechanism was experimentally veried and reported by Kärger et al. 105 Another inuence could be the strong attraction between water molecules, e.g. hydrogen bridges: One water 11



molecule passes by and is able to free a trapped molecule and drags the freed one with it. That ultimately leads to cluster formation which then have a lower occupancy within the channel. 107 When approaching the aforementioned plateau at around 40 molecules per unit cell,the increased number of molecules reduces the available pore volume and more and more water-water collisions take place. This results in a transport resistance which balances out the cluster movement of the water molecules. The results obtained using the DFT-based force eld are basically identical for loadings higher than 20 molecules per unit cell, which corresponds to the saturation of the OMS of the framework. The inuence of the dierent force elds is seen at low loadings at which interactions are still dominated by frameworkwater interactions. Two ndings stand out at loadings below the threshold of 20 molecules per unit cell: Firstly, the diusivity is lower by roughly a magnitude. In fact, the deviation increases with loading up to a factor of 15 at 15 molecules per unit cell. This was to be expected as the UFF cannot predict the adsorption capacity at low pressures accurately compared to the DFT-FF because the former underestimates the interaction energy between the framework atoms, the Mg in particular, and water molecule(s). 68,69 Since the interaction is stronger between those in the DFT-FF, the guest molecules diuse more slowly. Secondly, while the trend of the DFT-FF based results are the same as the UFF ones, one can see a "step" at around 18 molecules per unit cell. At levels where almost all of the OMS are occupied, the self-diusion coecients increases greatly because the adsorbed water molecules form a layer around the pore wall and, thus, "shield" the passing water molecules from the Mg-ions resulting in enhanced mobility. At loadings beyond that threshold, the reason for the course of diusivities is the same as for the UFF.

Inuence of framework exibility on diusion CO2 In order to investigate the inuence of the exibility of the framework, simulations were carried out in which the framework was modeled as being exible using the UFF to describe 12


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intramolecular interactions (bond, angle, and torsion) while the intermolecular forces were described by the DFT-FF. The limitations of the force eld as described above, should be kept in mind. This allows us to have an indication on whether exibility reduces or enhances the diusivity of CO2 and water in Mg-MOF-74. The self-diusivity of CO2 in the exible framework, see Figure 1, decreases monotonically with increasing loading to a minimum at around 20 molecules per unit cell. A maximum is then reached at 25 molecules per unit cell after which the self-diusion coecients decrease again. This behavior of the exible case resembles closely the one obtained for the rigid framework. Consequently, since the behavior is the same such that there is a similar reasoning for it, as explained above. It is remarkable, however, that the exibility causes the molecules to move much faster through the nanoporous structure: For 1 molecule per unit cell the self-diusion coecient for the exible framework is almost tenfold the value for the rigid one. The adsorption energy of the rigid and exible system is less negative thancalculated by DFT (dierence of around 6

kJ ), mol

see Table S6, meaning that the interaction is not as strong and, consequently, the

transport resistance is lower and the mobility is higher. At the highest loading (36 molecules per unit cell) all force elds predict similar diusivity at around 1·10−9

m2 . s

It shows that

the movement at high loadings is dominated by interactions between the CO2 molecules themselves, and exibility of the crystal becomes less and less important. Yet, the fact that for the exible case the framework could expand, and in this way reduce the impact of the high loading on the mobility does seemingly not play a role, because the volume gained by the exibility seems to be quite insignicant compared to the total volume. This hypothesis is supported by comparing the pair distribution functions for CO2 in the rigid and exible case, respectively, see Figure S1 and Figure S3a. At low loadings, e.g. 1 molecule per unit cell, it is obvious that the CO2 molecules are much closer to the Mg-ions in the rigid case compared to the exible one (Figure S3a), which indicates a stronger interaction and lower diusivity consistent with the free energy proles. As the loading increases the dierence does not vanish but becomes less ecacious. This coincides with the ndings on framework 13



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exibility reported by Zimmermann et al. 94 It is noticeable that the increase of diusivities at loadings (slightly) above the OMS saturation occurs at a lower number of molecules and is higher compared to the rigid case due to the inuence of the framework.

H2 O As for water (Figure 2), the inuence of exibility on the diusivity is quite obvious and can be broken down into two loading regimes: At loadings above 24 molecules per unit cell, the diusion in the exible framework is only slightly higher (less than 10%) than in the rigid one due to the assumed absolute higher free energy. 94 At loadings below this threshold, however, the impact of the framework exibility is much more pronounced, ranging up to a factor of 100 for 1 molecule per unit cell. In order to understand this one compares the adsorption energy at innite dilution for both cases, see Table S7. It can be observed that the interaction energy for the guest molecules in the rigid crystal is 71.2 3

kJ mol

kJ mol

which is around

higher compared to the exible case. Hence, this results in a reduced diusivity. While

it explains the dierences at loadings higher than 24 molecules per unit cell, it cannot solely be the reason for the deviation in the low loading regime. When taking a look at the pair distribution functions, see Figure S2 and Figure S3b, the impact of the exibility is more obvious: For example, at 1 molecule per unit cell the rst water molecules are found at a distance with respectto the Mg-atoms of about 2-3 nm in the rigid and at around 4 nm in the exible case. Furthermore, the likelihood to nd water molecules at those distances is much higher for the exible lattice. In other words, not only is the interaction not as strong in the exible case as in the rigid one, the moving framework atoms cause the water molecules to be further away from the adsorption sites which ultimately leads to the much higher movement and diusion coecients. Additionally, the dierence in the pair distribution functions at higher loadings for both cases (Figure S3b) becomes less and less prominent. The function of the diusivity in the exible case itself has a rather complex behavior. It can be divided into three regimes due to the present minima and maxima: The rst one is from 14


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0 to 18 molecules per unit cell (low loading), the second from 18 to 36 molecules per unit cell (medium loading), and higher than 36 molecules per unit cell (high loading), respectively. The rst boundary (18 molecules per unit cell) corresponds to the loading at which all open metal sites are occupied and the second one (36 molecules per unit cell) to where the water molecules occupy the organic linker as adsorption sites, eectively covering the channel wall completely. 69 In the low loading regime, a maximum is found at around 12 molecules per unit cell. While in the rigid case the self-diusion coecient monotonically increases with loading, the movement of the framework atoms cause a reduction in the mobility of the water molecules. Since the increase in diusivity with loading in the rigid framework was attributed to the formation of (small) water clusters, it seems reasonable to assume that the introduction of exibility inhibits the formation of them to a certain degree probably due to the lattice vibration which eventually leads to more isolated molecules adsorbing at the main adsorption sites (the Mg-ions). Due to the break-up caused by the lattice vibration even at higher loadings, more and more small water clusters are present in the system which leads to the reduction of mobility caused by adsorption at loadings above 12 molecules per unit cell. In the medium range, a maximum is found at 30 molecules per unit cell. While the dispersion eects of the framework still hinder the cluster formation and the fact that the OMS are not available anymore together with the fact that the secondary adsorption sites are not as strong, lead to a general increase of the self-diusion coecient. Above 36 molecules per unit cell, all sites, e.g. the pore walls, are saturated and the cluster formation is not hindered. This results in an increase in mobility until the structure is fully packed, at which point the diusivity goes down due to steric hindrance. Please note that we have not been able to prove this theory of the inuence of coalescence and break-up in our simulations but based on our results and experience there seems to be a valid argument for it.

15



Self-diusivity in mixtures As the next step, self-diusion coecients for CO2 and H2 O mixtures in the rigid and the exible framework were determined, respectively. We chose the following mixture ratios: rich on water (10/90), rich on CO2 (90/10), and one equimolar (50/50). Please, note that those ratios depick the ratios of molecules of either species present inside the simulation box, e.g. the crystal, and not the bulk gas phase. These ratios allow to investigate the behavior of each species in dierent scenarios easily. In addition, the number of molecules for the "10%"-species is low. Consequently, the statistics lead to rather large error bars, in particular for water. The results for the self-diusion coecients for CO2 and for H2 O for the rigid crystal case are given in Figure 3 and for the exible one in Figure 4, respectively. Comparisons for each component individually can be found in Figure S4. The introduction of framework exibility does not have any dierent implications as in the pure components cases of CO2 and H2 O, respectively, see Figure S4. In the case of CO2 , the inuence of the exibility decreases with increasing loading up to a level where the results are basically indistinguishable. While the CO2 molecules diuse slower in the mixture water moves slightly faster. Overall, the molecules still have a larger equilibrium distance to the open metal sites compared to the rigid framework, which overall enhances the mobility for both species as alluded to in the previous chapter. In the rigid case, see Figure 3, it is obvious that the CO2 molecules move faster than the also present H2 O ones. The diusivity as a function of loading for CO2 is relatively independent on the fraction of water present in the mixture since all values are relatively similar to one another. Yet, the more water is in the system the faster is the movement of the CO2 molecules since the free and non-adsorbed water molecules seemingly do not slow them down. Additionally, minima and maxima can be found at around 15 -20 molecules per UC and around 30 molecules per UC, respectively. The reasoning herefore is a bit more complex. Despite of the occupation of the Mg-site by the water molecules the now water cluster around the ion is an attractive site. As a result, CO2 molecules adsorb on this complex which leads 16


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to a reduction of the mobility. Basically, up to the point where water is predominant in the system, CO2 is barely inuenced by the second species. Furthermore, compared to the pure CO2 results shown in Figure 1, the diusivity is only reduced by approximately 20% in general due to the slower movement of water. As for H2 O, water molecules barely move at all resulting in self-diusion coecients lower than 10−13

m2 , s

which is too low to be calculated

accurately with MD and, consequently, all values below that threshold are considered to be zero. The reason for water not to move is simple: Since water molecules interact much more strongly with the open metal sites as indicated by their respective adsorption energies (Table S6 and Table S7), they are only found in close proximity to the Mg-ions surrounded by CO2 molecules and nowhere else. In test runs at low molecule numbers, the starting conditions of the MD simulations were manipulated in such a way that more water molecules were put closer to the middle of the channel. Yet, those runs yielded the same results as the original ones due to the fact that the water almost immediately moves towards the OMS to adsorb. It proves that there is a strong segregation eect due to the OMS of Mg-MOF-74, rendering Maxwell-Stefan-Diusion predictions to be inaccurate. Even with an increase of water molecules due to the increase of water fraction, most of the water is adsorbed at the Mg-ions or located nearby. Since space is limited, more and more of them can move freely among the CO2 molecules which in turn leads to an increase in diusivity. At high loadings in the CO2 rich mixture, the self-diusion coecients of water follow the trend of the CO2 ones albeit at roughly 50% of their values. This indicates that the freely moving water molecules are dragged along by their CO2 counterparts. In Figure 4, the results for the self-diusivities in the exible case are presented. Similar to the results based on the rigid crystal, the diusivities of CO2 are higher than the ones for water, which is the expected result. With the exception of CO2 in the 90/10 mixture, the diusivity is monotonically decreasing with loading. In the latter case the behavior follows the trend of the pure CO2 results showing that the eect water has in this situation is a decrease of mobility by circa 25%. The absence of a maximum at higher loadings in the other 17



investigated mixtures is likely caused by the slowing eect the water molecules have on the CO2 . This eventually leads to the fact that at loadings above 35 molecules per UC CO2 and H2 O have the same diusivity. The self-diusion coecients for H2 O as a function of loading are very similar to the pure component results having a maximum at 10-15 molecules per UC and a maximum at 15-20 molecules per UC, for example. However, the CO2 molecules in the system accelerate the water ones so that the overall mobility is increased compared to the pure water diusion.

Conclusions In this work the diusion behavior of CO2 and H2 O in Mg-MOF-74 and the impact of framework exibility on said diusion were investigated. Molecular simulations were carried out to calculate self-diusion coecients at dierent loadings whereas the crystal was modeled as rigid and exible, respectively, for the pure components indivudially and in mixtures of them. Firstly, the force eld derived from DFT was compared to experiments and simulations available from literature in order to verify the adsorption and diusion results inside the rigid framework. Once the force eld was established self-diusion coecients for CO2 and H2 O in the exible crystal were determined. It was shown that the main consequence of the exibility was the enlarged equilibrium distance of the guest molecues to the open metal site, e.g. the Mg-ion, compared to the rigid crystal while the adsorption energy did not change dramatically. Consequently, the higher mobility results in higher self-diusion coecients. For both species the impact of the introduced exibility is the hightest at lower loadings, up to 20 molecules per unit cell for water and up to 30 molecules per unit cell for CO2 , respectively. Lastly, mixtures of both components were investigated. The results for the self-diusion coecients showed that there is a segregation between the stronger adsorbing water molecules and the CO2 . Thus,the former stayed closely to the open metal sites which in turn leads the latter to move more freely. In general, the presence of water

18


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had a slowing down eect on the CO2 molecules and an accelerating eect on water. The results indicate that due to these consequences of the segregation, diusion models, such as Stefan-Maxwell, are not able to predict diusivities for this system successfully.

Acknowledgement The authors acknowledge nancial support by the German Research Foundation [Deutsche Forschungsgemeinschaft (DFG)] in priority program SPP 1570 under Contract KE 464/12-3. S. B. thanks A. N. Rudenko for the calculations regarding the DFT-based force eld. S. B. and Y. D. thank S. Jakobtorweihen and N. E. R. Zimmermann for the very helpful and fruitful discussions on the topic of diusion.

Supporting Information Available Additional information and gures accompanying the article. The Supporting Information is available free of charge. Pair distribution functions of CO2 and H2 O at dierent loadings in the exible and rigid crystal; self-diusion coecients of CO2 and H2 O in mixtures; force eld parameters and validation of the applied force elds; CO2 adsorption isotherm at 298 K; inuence of cut-o radius and simulation length; mean-squared displasments as function of time.

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0.2

0.4

Loading (molecules per open metal site) 0.6 0.8 1 1.2 1.4 1.6

2.5

Self-diffusion coefficient (10-8 m2/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.8

2

Krishna et al. (UFF) This work (UFF,rigid) This work (DFT,rigid) This work (DFT,flex)

2

1.5

1

0.5

0 5

10

15 20 25 Loading (molecules per unit cell)

30

35

Figure 1: Self-diusion coecients based on dierent force elds for CO2 in Mg-MOF-74 at 300 K as a function of loading. The simulation data by Krishna et al. 86 is based on DREIDING and UFF.

33



0.5

Loading (molecules per open metal site) 1 1.5 2 2.5

3

3.5

25 Self-diffusion coefficient (10-10 m2/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 37

20

15

10

5 This work (UFF,rigid) This work (DFT,rigid) This work (DFT,flex)

0 10

20 30 40 50 Loading (molecules per unit cell)

60

Figure 2: Self-diusion coecients based on dierent force elds for H2 O in Mg-MOF-74 at 300 K as a function of loading.

34


Page 35 of 37

0.4

0.6

Loading (molecules per open metal site) 0.8 1 1.2 1.4 1.6 1.8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

2.2

35

40

10:90 50:50 90:10

20

15

10

5

0 0

5

10


Figure 3: Self-diusion coecients in the rigid framework for CO2 (closed symbol) and H2 O (open symbols) in three CO2 /H2 O-mixtures (90/10 (black dot), 50/50 (blue triangle), and 10/90 (red square)) at 300 K based on the DFT-FF.

35



0.4

0.6

Loading (molecules per open metal site) 0.8 1 1.2 1.4 1.6 1.8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2

2.2

35

40

10:90 10:90 50:50 50:50 90:10 90:10

140 120 100 80 60 40 20 0 0

5

10


Figure 4: Self-diusion coecients in the exible framework for CO2 (closed symbol) and H2 O (open symbols) in three CO2 /H2 O-mixtures (90/10 (black dot), 50/50 (blue triangle), and 10/90 (red square)) at 300 K based on the DFT-FF.

36


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Graphical TOC Entry

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Diffusion of Water and Carbon Dioxide and ... - ACS Publications

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