Computational Study of Water Adsorption in the Hydrophobic Metal

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Computational Study of Water Adsorption in the Hydrophobic Metal-Organic Framework ZIF-8: Adsorption Mechanism and Acceleration of the Simulations Hongda Zhang, and Randall Q. Snurr J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06405 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 15, 2017

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The Journal of Physical Chemistry

Computational Study of Water Adsorption in the Hydrophobic Metal-Organic Framework ZIF-8: Adsorption Mechanism and Acceleration of the Simulations Hongda Zhang and Randall Q. Snurr* Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States *Corresponding author: E-mail: [email protected]; tel. 1-847-467-2977

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2 ABSTRACT

Adsorption of water can have an important effect on chemical and physical processes in porous materials, such as zeolites and metal-organic frameworks (MOFs). However, the molecular simulation of water adsorption brings many challenges, especially the slow simulation speed. In this study, we examined the hydrophobic MOF ZIF-8 as a representative adsorbent to discover the adsorption mechanism of water in hydrophobic MOFs. Based on the mechanistic insights obtained, we proposed and investigated several advanced Monte Carlo algorithms including energy-bias moves and continuous fractional component Monte Carlo (CFC MC) and were able to accelerate the simulation speed by a factor of 6.7 over the conventional grand canonical Monte Carlo algorithm. The insights obtained from this work may also help improve the molecular simulation efficiency for studies of water adsorption in other hydrophobic materials.


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3 INTRODUCTION Water is one of the most common components in gas or liquid mixtures in nature. In addition, it is almost always a non-negligible factor when studying adsorption or separation processes in porous materials because the co-adsorption of water may significantly influence the ability of the materials to selectively adsorb a target species. Water adsorption in porous materials has been widely studied in industrial applications including carbon capture,1-3 biofuel recovery,4 and toxic industrial chemicals (TICs) capture.5 Metal-organic frameworks (MOFs),6-10 a class of nanoporous crystalline materials self-assembled from inorganic nodes and organic linkers, possess many advantages over the conventional adsorbent materials such as zeolites and activated carbons, including higher surface areas and pore volumes.11-14 More importantly, MOFs are highly tunable by appropriate selection of building blocks and topology and further functionalization of the linkers, which makes it possible to tailor MOFs for different purposes. In the past decade, MOFs have already shown promise for some important applications such as natural gas storage15-17 and carbon capture.18-20 However, when it comes to potential applications involving water, there has been less progress – perhaps because of a belief that MOFs are not stable in liquid water or even under humid conditions. Indeed, some well-known early MOFs, such as IRMOF-1, HKUST-1, and DUT-4, have been shown to be unstable in the presence of water vapor.21 Nevertheless, there are now quite a few MOFs that are stable even after being soaked in liquid water for days,22-25 and strategies to improve the stability of MOFs with respect



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4 to water have been investigated in the literature.26-27 Given these new materials, it is worthwhile to explore the potential of MOFs for applications where water is present. However, very little data, either experimental or theoretical, is available in the literature on water adsorption in MOFs4,

26, 28-33

compared with the data for other types of adsorbent materials, especially

zeolites.34-40 Simulated adsorption isotherms in porous materials are typically obtained from a series of grand canonical Monte Carlo (GCMC) simulations. In the grand canonical ensemble, the chemical potential, volume, and temperature of the system are fixed, and the number of adsorbate molecules is allowed to fluctuate, which mimics the experimental setup of an adsorption process. The loading of the adsorbed species at each chemical potential (corresponding to a given pressure of the external fluid phase) can be directly calculated from the simulation once the system reaches equilibrium. While GCMC simulations have become routine for other small molecules such as H2, CO2, and CH4, there are special challenges in applying this technique to simulation of water adsorption. These challenges include the following. First, despite the simple structure of the water molecule, to date, there is still no optimal force field that can capture all of the unusual physical properties of water, which arise from the hydrogen-bond networks formed within water clusters. In addition, the H-O-H bond angle and the dipole moment of water can change continuously during the adsorption process, which further complicates the problem, but most models of water treat these properties as constant. Second,


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5 simulations of water adsorption in porous materials including MOFs and zeolites converge extremely slowly, as pointed out in many publications.41-43 Only a few studies, mainly from Fuchs and co-workers, have attempted to accelerate the simulation speed by using different Monte Carlo algorithms, including the pre-tabulated energy grid method,43 pre-insertion of water molecules,40 orientational-bias moves,44 energy-bias moves,41 biased translational “jump moves,”40 and canonical replica-exchange Monte Carlo or parallel tempering methods.45 These works, in general, simply stated that the methods applied could improve the convergence efficiency of the simulations without providing any discussion of the performance of the various algorithms compared with regular GCMC or against one another. Accordingly it is still unclear which advanced Monte Carlo algorithms produce the biggest improvement of the simulation speed for these difficult systems. Hydrophobic MOFs are particularly attractive for some applications because they can selectively adsorb the target chemical species without interference by water vapor or liquid water. In addition, hydrophobic MOFs may be especially stable against hydrolytic degradation due to their limited uptake of water molecules. A number of studies in the literature have focused on searching for hydrophobic MOFs and increasing MOF hydrophobicity by introducing hydrophobic moieties, for example, fluorinated functional groups.46-51 ZIF-8,24, 52 one of the most famous hydrophobic or “hyperhydrophobic”27 MOFs, was revealed to be ultra stable and resistant to water by Kusgens et al.31 and later investigated in several water-involved applications,



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6 especially for biofuel recovery.53 ZIF-8 is a member of the zeolitic imidazolate framework (ZIF) family and consists of zinc atoms connected by methyl imidazolate linkers. These building blocks form a sodalite topology with spherical cavities of 11 Å diameter. The hydrophobicity and water stability of this MOF are mainly due to the methyl-functionalized imidazolate linkers and the coordinative saturation of the metal sites.54 The super hydrophobic surface of the cavities along with the narrow windows (3.4 Å) connecting them lead to an extremely low water uptake in ZIF-8 below the vapor pressure of water.31 Computational studies of water adsorption in ZIF-8 have been conducted by several research groups including ours.29, 42, 48, 55 Water isotherms in ZIF-8 from both simulation48 and experiment56 display a type V (“S”) shape57-58 along with a pronounced hysteresis loop between the adsorption and desorption branches. This phenomenon is quite similar to capillary condensation, which is commonly observed in mesoporous silica.27, 35 However, the pore diameter (11 Å) in ZIF-8 is less than the 2 nm critical diameter reported by Coasne et al. for capillary condensation to occur in porous materials at 298 K, and in this pore size range water adsorption is expected to follow a reversible pore-filling mechanism similar to that observed for microporous zeolites.35 This uncommon adsorption mechanism of water in microporous materials has been reported by Fuchs and co-workers for hydrophobic zeolites59 and one hydrophobic MOF with 1-D channels.43 In this work, we conducted GCMC simulations to reproduce both the adsorption and desorption branches of water isotherms in ZIF-8 at room temperature. We found that the pressure


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7 where the type V isotherm rises can shift if the simulations are not properly converged. By analyzing the siting of water molecules in the framework during the progression of the simulation, we obtained new insights about the water adsorption mechanism in ZIF-8 and the cause of the hysteresis loop, along with the main reason for the extremely slow convergence of the simulations. Based on these results, we investigated two advanced Monte Carlo algorithms, energy-bias insertion moves60 and continuous fractional component (CFC) Monte Carlo,61 and successfully accelerated the simulation speed. We then further tested the performance of these algorithms in another hydrophobic MOF and showed that these methods are transferable to other hydrophobic MOFs. COMPUTATIONAL DETAILS Model and Force Fields The ZIF-8 crystal structure and the force field to describe the interactions in the system are identical to those in our previously published paper on water and ammonia adsorption in ZIF-8.42 The ZIF-8 crystal structure was taken from the work of Park et al.24 and the framework was kept rigid during the simulations. Although ZIF-8 is known to be flexible upon gas adsorption,54, 62 this effect is most common in the presence of large hydrocarbon molecules with kinetic diameters (4.3-5.85 Å) significantly larger than ZIF-8’s nominal crystallographic aperture size (3.4 Å).63-65 We did not expect framework flexibility to be important for small molecules like water. The intermolecular interactions between MOF atoms and water molecules and also



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8 between different water molecules were described using a standard Lennard-Jones plus Coulomb model. The Lennard-Jones parameters for the MOF atoms were adopted from the DREIDING66 force field. The framework atomic charges were taken from our previous work,42 where REPEAT,67 a method to obtain partial charges from periodic DFT calculations, was used to obtain the charges. We also simulated water isotherms in another hydrophobic MOF, Zn(pyrazole),68 to test the transferability of the MC algorithms that we investigated. This MOF is topologically similar to IRMOF-1, with pores of 6.5 Å connected through windows of 4 Å. The DREIDING force field and REPEAT charges were also used for this MOF.42 We adopted the TIP4P69 model for water in this work since it is one of the most popular and widely tested water models and it can predict the saturation vapor pressure of water at 298 K (4.1 kPa70) relatively well compared with the experimental value (3.2 kPa71). This is a four-point rigid water model with a pseudo-atom site containing only negative charge to make the whole molecule neutral. All Lennard-Jones potentials were truncated at a cutoff of 12.8 Å with analytical tail correction terms. Lorentz-Berthelot mixing rules were applied for the MOF/water cross terms. Ewald summations72 were applied for all Coulomb interactions. The fugacity coefficient of water was specified to be 1 since the deviation of water vapor from an ideal gas in the pressure range we investigated (up to 4500 Pa) can be neglected.73 All Lennard-Jones parameters and partial charges used in this work can be found in the Supporting Information. GCMC Simulation Details


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9 GCMC simulations were carried out to calculate both the adsorption and desorption branches of the water isotherm in ZIF-8 at 298 K using our in-house simulation package RASPA.74 A 2×2×2 supercell (of dimensions 34×34×34 Å3) was used in the simulations to satisfy the minimum image criteria and to minimize the influence of periodic boundary conditions. Regular GCMC simulations containing 50% insertion/deletion, 25% translation, and 25% rotation moves were first attempted to produce the adsorption and desorption water isotherms. As a basic method to improve the energy calculation efficiency and accelerate the overall simulation speed, the grid method75 was applied by default. In this method, both the electrostatic field generated by the framework and the van der Waals interaction energies between the MOF and a water oxygen atom were pre-tabulated at grid points with a 0.1 Å spacing throughout the system. During the simulation, the energies at any point were then interpolated from the values at the grid points. Since one of the goals of this work was to investigate how long it takes the simulations to reach convergence, we initially used 10 million equilibration MC cycles for all runs. A cycle contains N MC steps, where N is the number of adsorbate molecules in the system at the beginning of the cycle (or 20 if there are fewer than 20 molecules present). If the system was not equilibrated after 10 million cycles, the simulation was extended for another 10 million cycles based on the restart file saved by the previous run, and this was repeated until the system finally reached equilibrium. The simulation time, MC move statistics, the siting of water molecules, and



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10 other useful information were extracted from the simulations for further analysis. For the adsorption branch, all points on the isotherm were run separately starting from an empty framework. For the desorption branch, all points used a fully saturated and equilibrated system as the initial configuration. Advanced Monte Carlo Algorithms to Accelerate Simulation Speed In order to accelerate the simulation speed of water adsorption in ZIF-8, we first tested the most straightforward method, which is pre-insertion of water molecules into the system at the beginning of the simulation.40, 43 However, we found that if we just randomly inserted a certain number of water molecules into the MOF, they were quickly removed during the first several steps because ZIF-8 is a superhydrophobic MOF and the randomly distributed water molecules cannot form favorable interactions with the framework. On the other hand, if we started with an already saturated and equilibrated system or even 2/3 of the saturation loading, the simulation fell onto the desorption branch of the isotherm for the few cases we tested. Using this method would make it difficult to predict the pressure at which the isotherm rises, and we did not pursue it further. In addition, we considered the parallel tempering method, which has been widely used to speed up MC simulations in many systems.76-78 However, due to the type V shape of the water isotherm, for the pressure points close to the rise of the isotherm, even a slight increase in temperature could lead to the water uptake dropping to zero, so the exchange moves between the adjacent systems with different temperatures would be ineffective in equilibrating the loading at


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11 the temperature of interest. Thus, neither of these previously reported methods seemed promising for our particular system. Based on the insights we obtained from studying the water adsorption mechanism in ZIF-8 (see the discussion in Results and Discussion), we investigated two other advanced MC algorithms, namely energy-bias insertion moves and continuous fractional component (CFC) MC. Energy-Bias Insertion Moves This method of biasing grand canonical insertion moves was developed by Snurr et al.60 to accelerate simulations of aromatic adsorption in the zeolite silicalite based on the general discussion by Allen and Tildesley72 of canonical ensemble Monte Carlo translation moves with preferential sampling. In energy-bias GCMC, the regular translation and rotation moves are not affected. For insertion moves, the simulation box is discretized into small cubelets, and each cubelet is assigned a weight , which can be calculated by inserting a probe at the center of the cubelet and measuring the potential energy that the probe would feel before the simulation starts:

= / ∑

(1)

Here , are the indexes of the cubelets, is 1/ , is the potential energy the probe feels in cubelet . In this work, the probe was selected to be the oxygen atom in the water molecule, and only the Lennard-Jones potential was used to bias the insertion moves. The discretization of the system and the pre-calculation of the weight were tightly incorporated with the grid method introduced above. During the GCMC simulations, when conducting an



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12 energy-bias insertion move, we choose a cubelet according to its weight and randomly insert a molecule into the cubelet. This move is accepted with probability

= 1,

! " # ∆ +[− ]0 (%&)() * () *

(2)

where 12345657 is the volume of the cubelet, 1 is the volume of the simulation box, 8 is the gas-phase fugacity, 9 is the number of adsorbate molecules in the system before applying the insertion, and ∆ is the change in the potential energy of the system due to the insertion move. In order to satisfy microscopic reversibility, an unbiased deletion move is performed with a modified acceptance probability as follows:

= 1,

%() *

! " #

+[−

∆

() *

]0

(3)

In this work, when using energy-bias moves, we kept the same probabilities for attempting rotation and translation moves as introduced in the GCMC Simulation Details, and all insertions were biased based on the weighting factors calculated on an empty framework before the simulations. Continuous Fractional Component (CFC) Monte Carlo CFC MC is a method developed by Shi and Maginn61 to improve the efficiency of insertion and deletion of molecules in simulations of dense systems in the grand canonical or Gibbs ensembles. Recently this method has been applied to simulate adsorption in MOFs but not for water.79 In the CFC MC scheme, there is always one “fractional” molecule in the system, whose interactions with the “real” molecules are scaled using a pseudo-continuous coupling parameter


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13 :. The modified Lennard-Jones potential and electrostatic interaction are then as follows:

;< (=# , :) = 4?: @ A IJ36 (=# , :) = :K

D E

[ (C)B &( B

LMNO

P PE

F

− G B

) ]

D E A [ (C)B &( )G ] B F

Q

H

(4) (5)

where ;< and IJ36 are the LJ and Coulombic interaction energies, respectively, between real atom and fractional atom 8, =# is the distance between the centers of these two atoms, ? and R are the LJ parameters, ?S is the dielectric constant in vacuum, and T is the partial charge of each atom. The core idea of CFC MC is to gradually insert or delete a molecule by increasing or decreasing the interaction strength of the fractional molecule with the real molecules. This is done via Monte Carlo moves that change the value of the coupling parameter :. During these moves, if : becomes greater than 1, this move is considered a CFC trial insertion, and if this insertion is accepted the fractional molecule is converted to a real molecule and a new fractional molecule is randomly inserted into the system with a new : value equal to : − 1. If : becomes less than 0, this move is considered a CFC trial deletion. If this trial is accepted, the fractional molecule is deleted and one of the real molecules is randomly chosen as the new fractional molecule with a new : value equal to : + 1. Because the Monte Carlo moves that change : are interspersed with normal translation and rotation moves, the system can gradually relax to accommodate the fractional molecule as its interactions with the real molecules increase or decrease. This procedure is schematized in Figure 1, and the derivation of



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14 the acceptance probabilities of the CFC moves can be found in the original paper.61

Figure 1. Summary of the CFC MC algorithm.

In our simulations, the method of Wang and Landau80 was applied to prevent : from being stuck in a small range of : values. To take advantage of the grid method, : is considered as unity for the interactions between the fractional molecule and the framework atoms and only affects guest/guest interactions. In this work, when using CFC MC moves, we kept the same types of moves and attempt probabilities as described in the GCMC Simulation Details and only substituted half of the insertion/deletion moves with CFC MC moves. We hypothesized that the normal insertion and deletion moves would help to quickly change the number of molecules in some simple cases, especially at low loading. In addition, when we combined CFC MC with energy-bias insertions, we treated half of the insertion/deletion moves with CFC MC moves and the other half with


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15 energy-bias moves. We implemented both of these two algorithms in our in-house code RASPA74 and tested their performance for accelerating the convergence speed of water adsorption simulations in hydrophobic MOFs. RESULTS AND DISCUSSION Water Adsorption Mechanism in ZIF-8 We first simulated the water adsorption isotherm in ZIF-8 at 298 K; see Figure 2. We started simulations at different pressures separately and simultaneously by using the regular Monte Carlo moves introduced in the GCMC Simulation Details plus the grid method to improve the simulation speed. To monitor the equilibration of the system, we kept track of the intermediate water loading for each pressure as a function of simulation time. In Figure 2, red, green, and blue curves represent the adsorption isotherms we obtained after 10 days, 35 days, and 70 days of simulation per pressure point, respectively. The brown curve is the equilibrated isotherm. Our criterion for convergence was that the increase or decrease of the instantaneous value of water uptake was within 2 molecules/unit cell after more than two weeks of simulation time. The reason for the long equilibration times is discussed later in this section. As a comparison, the simulated water adsorption isotherm from our previous paper42 is also included as the solid black line in the figure. After 10 days of simulation per pressure (red line), we started to observe some water uptake for the pressure points ranging from 2500 Pa to 3500 Pa, which had shown no



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16 water adsorption in the previously published work.42 As we kept the simulations running for 35 days and 70 days, the water uptake in this pressure range continued to change, and the inflection point of the isotherm kept shifting toward lower pressure. In addition, the intermediate isotherms (red, green, and blue lines) are not smooth, which is another indication that they are not equilibrated. The water uptake increased faster in some systems and slower in others, and there is no clear trend that can be observed. This random and unpredictable growth of water loadings in different simulation runs seriously limited the overall speed of generating a complete water isotherm. In general, these simulations were all extremely slow, and the worst case among these runs took 115 days to converge.

Figure 2. Adsorption and desorption isotherms for water in ZIF-8 at 298 K from GCMC simulations. All water loadings reported in this work are absolute uptakes. Solid black: simulated adsorption isotherm from Ghosh et al.42; dash black: desorption isotherm from this work; red, green, and blue: new adsorption isotherms from this work after 10, 35, and 70 days of simulation per point, respectively; brown: fully converged isotherm.


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17 Eventually, after the simulations converged (brown line), the rise of the isotherm occurs around 2800 Pa, which differs from the value of 3600 Pa predicted previously. This deviation can be attributed to incomplete convergence for the points in the intermediate pressure range in the previous simulations, where the simulations were “stuck” at zero loading. A comparison between the simulated (this work) and experimental31 water isotherms is shown as Figure S2 in the Supporting Information. The new capillary condensation pressure of 2800 Pa is much lower than the vapor pressure of bulk water predicted by the TIP4P model (4100 Pa), and our model is, thus, not consistent with the experimental observation31 that there is no water adsorbed below the saturation pressure. Note that this is a limitation of the force field, and only with this “correct” simulation result we can make this evaluation of the accuracy of our model. Further discussion about the force field used in the simulations can be found in the Supporting Information; however, improvement of the force field is beyond the focus of this work. The desorption branch of the water isotherm (black dash line) is also shown in Figure 2, indicating the existence of a significant hysteresis loop for this system. We did not run very long simulations for the desorption branch, and within the simulation time we used (around one month per point) the desorption branch did not show any unusual isotherm shape or irregularity as was observed for the adsorption branch. We cannot be sure that the desorption isotherm does not also suffer from convergence issues, but we did not investigate this further due to the already-long simulation times.



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18 In our previous work,42 we also plotted the isosteric heats of adsorption for water in ZIF-8 at different loadings and showed that in the low coverage region the theoretical heat of adsorption is consistent with the experiment. In general, at low loadings, the heats of adsorption are quite low due to the weak framework-water interactions. As the loading increases, water-water interactions start to dominate, leading to heats of adsorption slightly above the heat of vaporization for bulk water. In order to understand what leads to the unpredictable and extremely slow progress of the simulations, we examined more closely how the simulated systems approached equilibrium at different pressures. Here, we show results at 3400 Pa as an example. Figure 3 shows the progress of the water uptake in ZIF-8 at 298 K and 3400 Pa with respect to simulation time. In Figure 3a, it can be seen that the system tends to be stuck at certain loadings, for example around 55 molecules/unit cell and 68 molecules/unit cell, until finally it reaches the saturation loading, which is 75 molecules/unit cell. The stepped behavior in this profile significantly slows down the overall simulation. When we zoomed into the low-uptake region of the same profile, which is shown in Figure 3b, we discovered that the system can be stuck at a series of highly-ordered loadings with an almost fixed interval: 4, 8, 12, 16, 20 molecules/unit cell etc. This raises an interesting question: do these loadings correspond to special states or configurations of the system? After looking into these steps and analyzing the siting of the adsorbed water molecules we found that the answer is yes.


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19

a)

b)

Figure 3. Progress of the absolute water uptake in ZIF-8 at 298 K and 3400 Pa from GCMC with respect to simulation time. a) Whole uptake range; b) zooming into the low-uptake range.

For instance, the first step occurs at 4 molecules/unit cell and a snapshot of the system at this loading is shown in Figure 4a. There is a big cluster of 32 water molecules (equivalent to 4 molecules/unit cell since a 2×2×2 supercell was used) in the cavity at the center of the simulation box. In this snapshot, there are no other water molecules adsorbed in other cavities. These clustering water molecules build up hydrogen bonds and form an energetically stable complex network as in the bulk liquid phase. This configuration corresponds to a meta-stable state of the system or a local minimum on the potential energy surface. It is very difficult to add or remove water molecules in this already stabilized cluster. Furthermore, due to the highly hydrophobic nature of the cavities, it is also energetically unfavorable to insert new water molecules in other empty pores to start forming new clusters. As a consequence, the simulation



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20 was stuck at this loading for a long time. Similarly, the second step (8 molecules/unit cell) corresponds to two of the cavities being occupied by water clusters, as shown in Figure 4b. In this configuration, two water clusters are present in two adjacent cavities and are connected through the narrow window. In the configurations we investigated, including systems at different pressures and loadings, the water clusters are always in adjacent cavities and connected through the MOF windows, although in our simulation box, there do exist cavities which are not next to each other. It seems that formation of a new water cluster in a neighboring cage is facilitated by interactions through the window with water molecules in the already formed cluster. Thus, water clusters fill the cavities in the MOF one after another, and each step in the profile in Figure 3 corresponds to a certain number of cavities being occupied, each representing a meta-stable state of the system.


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21 a)

b)

Figure 4. Snapshots of water clusters filling the cavities of ZIF-8 at 298 K and 3400 Pa from GCMC simulations at loadings of a) 4 molecules/unit cell and b) 8 molecules/unit cell. Carbon: green; nitrogen: blue; oxygen: red; hydrogen: white.

To support this conclusion, we plotted in Figure 5 the histogram of cavity filling in ZIF-8 at different water loadings corresponding to steps in Figure 3a. In our simulation box there are 16 cavities. The two top graphs show the situation when one or two cavities are occupied, respectively, as in Figure 4. The histograms show the number of water molecules in each cavity from snapshots while the system was stuck at the given loading. In agreement with the discussion above, at a loading of 8 molecules per unit cell, two cavities contain around 32 water molecules each, while the other cavities have a loading of zero. As the total water uptake increases, additional cavities are filled, and eventually at the saturation loading all of the cavities are occupied as shown in the last graph. In addition, as the total loading increases, the number of



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22 water molecules per cavity also increases slightly. For example, in cavity 3, the initial cluster contains 32 water molecules, and when the system reaches equilibrium, this cluster grows to 39 water molecules. Thus both the number and the size of the water clusters gradually increase during the adsorption.

Figure 5. Histogram of cavity filling in ZIF-8 at different water loadings during equilibration at 298 K and 3400 Pa. The cavities in the 2×2×2 supercell are numbered 1 through 16.

Based on these results, we can summarize the adsorption mechanism of water in ZIF-8 as a pore filling process, where one cavity after another is filled, often with the assistance of existing water clusters through the windows. Different numbers of occupied cavities correspond to


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23 different meta-stable states of the system. This adsorption mechanism is consistent with the results of Paranthaman et al.43 for water adsorption in hydrophobic 1-D MOF channels, where the channels are either completely full or empty, again corresponding to meta-stable states of the system. Due to the hydrophobic nature of ZIF-8, it is difficult to either grow a new water cluster or increase the size of an already existing cluster. Thus, the energy barriers between these meta-stable states are large, and unusually long simulation times are required for the density fluctuations of the system to overcome these barriers and for the system to reach equilibrium. For these types of systems, special attention should be paid to checking that the simulations are converged. One may need to run extremely long simulations in order to obtain the correct results. Even for the low-pressure region, where one might think that insertions are easy, we found that it is difficult to initiate the first cluster in an empty framework, and it may take a long time for the water uptake to change to a non-zero value. One can easily under-predict the water loading in this region and incorrectly estimate the rise of the isotherm, as demonstrated above. The large energy barriers between meta-stable states is also the cause of the hysteresis loop. If the system starts with an empty framework or a fully saturated MOF, the system can be easily trapped with different loadings at the same pressure. Acceleration of the Simulation Speed for Water Adsorption in ZIF-8 Based on the insights we obtained about the water adsorption mechanism in ZIF-8, we proposed the use of two advanced Monte Carlo algorithms to accelerate the simulation speed.



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24 First, we recognized that, due to the hydrophobic nature of the MOF, it is difficult to insert the first several water molecules into an empty cavity and start forming a new cluster. Thus, we proposed that energy-bias insertion moves, which insert water molecules more frequently into favorable framework locations, may assist the system in overcoming the energy barriers between different meta-stable loadings. Second, we saw in Figure 5 that the size of the water clusters grows as the simulation progresses. However, since these clusters are energetically stable through their hydrogen-bond networks, it is difficult to change the number of molecules or configuration of the clusters. To overcome this problem, we proposed CFC MC moves, which gradually insert or remove water molecules and should be especially effective in the high-uptake region when most of the cavities have already been occupied. We selected one simulation point at 298 K and 4500 Pa as a test case to evaluate how long it takes the system to reach equilibrium using these different algorithms. The methods that we tested were regular GCMC simulations, the grid method, energy-bias insertion moves, CFC MC, and energy-bias insertions plus CFC MC. For all simulations involving energy-bias or CFC MC moves, we also used the grid method by default. To test the reproducibility of the algorithms, we ran two separate simulations with exactly the same simulation settings for each method. The results can be found in the Supporting Information. The equilibration times for the two separate runs of each algorithm are not identical but are quite close, and the difference does not affect the ranking of the algorithms for


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25 accelerating the simulation speed. To make a simple and direct comparison across all of the methods investigated, we only focus on the better performer from every pair of runs. The results are summarized in Figure 6, which shows the progress of water uptake with respect to simulation time for the different methods. It is clear that all of the algorithms that we investigated, including the basic grid method, greatly improve the efficiency of the simulations and shorten the time for the system to reach equilibrium compared to regular GCMC. The ranking of the methods based on their acceleration performance is: energy-bias plus CFC > energy-bias > CFC > grid > regular GCMC. The simulation time that is required for the system to reach the saturation loading using the different methods is summarized in Table 1. The grid method cut the simulation time by half (from 30.1 days to 15.7 days), and the CFC and energy-bias methods performed even better, with 12.7 and 10.6 days, respectively. When we combined the two advanced methods together, we further shortened the simulation to only 4.5 days, equivalent to an acceleration factor of 6.7, which is a significant speed-up.



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26

Figure 6. Progress of water uptake with respect to simulation time in ZIF-8 at 298 K and 4500 Pa using regular GCMC, the grid method, and different advanced MC algorithms.

Table 1. The simulation time in days required for the equilibration of the system in Figure 6 using different methods. Method Regular Grid CFC Energy-bias Energy-bias GCMC + CFC Simulation time 30.1 15.7 12.7 10.6 4.5

To validate if these algorithms indeed improve the efficiency of the insertion moves, we analyzed the statistics of these MC moves. See Table 2. The grid method improves the number of insertion trials per second by roughly a factor of 2, but obviously it does not affect the acceptance probability of the insertions, since it only makes the energy calculations more efficient but does not change the basic Monte Carlo algorithm. On the other hand, the energy-bias insertion moves enhance the probability of successful insertions. For example, looking at the overall simulation (water uptake ranging from 0 to 75 molecules/unit cell), the


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27 acceptance probability of insertions increases from 0.23% with regular GCMC to 0.32% with energy-bias insertions. Because the weighting factors used in the energy-bias moves were calculated based on an empty framework, this algorithm is expected to be most effective when the system is still relatively empty. So when we zoom into the lower water uptake range (0 to 30 molecules/unit cell), we find that the effect of the energy-bias moves is more obvious, and the acceptance probability is almost doubled from 0.53% to 0.98%.

Table 2. Statistics of Monte Carlo moves for different water uptake ranges. Method

Insertion trials/s

Accepted insertions/s Water uptake range: 0 to 75 molecules/unit cell Regular GCMC 18.8 0.044 Grid method 41.7 0.092 Energy-bias 48.5 0.154 Water uptake range: 0 to 30 molecules/unit cell Regular GCMC 28.6 0.151 Grid method 69.4 0.367 Energy-bias 78.4 0.768 Water uptake range: 50 to 75 molecules/unit cell Regular GCMC 14.4 0.0052 CFC: CFC insertion 4.7 0.285 CFC: total insertion 26.0 0.288

Acceptance probability 0.23% 0.22% 0.32% 0.53% 0.53% 0.98% 0.036% 6.064% 1.108%

As noted above, the CFC method is expected to be most effective in the high loading region, where it can aid in inserting molecules more successfully into already formed water clusters. Accordingly, Table 2 shows the statistics for the CFC method in the uptake range between 50 and



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28 75 molecules/unit cell. We see that the acceptance probability of the CFC insertion moves (6.064%) is much higher than that for regular GCMC insertions (0.036%). However, we need to point out that in addition to 4.7 CFC insertion trials/s (CFC moves attempting to change the value of : to greater than 1), there are also many CFC MC moves (33.1 trials/s) carried out to change : between 0 and 1, which are not included when calculating the insertion acceptance probability. In order to make a fair comparison, in this case, we should look at the number of accepted insertions per second, which directly reflects the efficiency of the insertion moves. Considering the CFC MC insertions only, 0.285 accepted insertion moves can be carried out per second, and if we consider the normal insertions as well (we kept half of the insertion moves as normal insertions in our CFC implementation), 0.288 accepted insertions per second can be reached, which is a significant improvement compared with 0.0052 accepted insertions per second from regular GCMC. The results show that there is a strong benefit from the energy-bias moves and CFC moves in the low-uptake and high-uptake regions, respectively, and by combining both of these methods, we can significantly accelerate the simulations. Transferability of the Algorithms to Another Hydrophobic MOF We further tested if these algorithms could be transferred to accelerate the simulation speed of water adsorption in another hydrophobic MOF. Zn(pyrazole) was selected as the new test case because it had already been reported to be hydrophobic and stable under humid conditions in the literature.68 We conducted water adsorption simulations with the different methods in this MOF


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29 at 298 K and 4500 Pa and compare the performance of the different algorithms in Figure 7. The result is quite consistent with our conclusion for the ZIF-8 system that all of the methods tested can also accelerate the simulation speed in this MOF. The best performer is again the combination of energy-bias and CFC moves, which can shorten the simulation time required to equilibrate the system from 63.5 days to 21.9 days, giving an acceleration factor of 2.9. The results suggest that these algorithms are transferable to simulation of water adsorption in other hydrophobic MOFs, and these methods are recommended for future studies of related systems.

Figure 7. Progress of water uptake with respect to simulation time in Zn(pyrazole) at 298 K and 4500 Pa using regular GCMC, the grid method, and different advanced MC algorithms.

CONCLUSIONS In this work we simulated the adsorption and desorption branches of the water isotherms in a hydrophobic MOF, ZIF-8, and provided new insights into the water adsorption mechanism and



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30 the formation of the hysteresis loop in this MOF by analyzing the siting of water molecules during the progress of the simulations. Water molecules fill the MOF cavities one after another and form stable clusters through hydrogen bonds inside the cavities. Different numbers of cavities being occupied correspond to different meta-stable states of the system. The energy barriers between these meta-stable states are large due to the hydrophobic nature of the MOF, and it is difficult for the system to overcome these barriers and reach equilibrium, which leads to an unpredictable progress of the water uptake in different simulation runs and the overall slow simulation speed. The system can be stuck in different meta-stable states when one attempts to increase the loadings starting from an empty framework or desorb water from a fully saturated system, and this causes the hysteresis loop. Based on these observations, we tested two advanced Monte Carlo algorithms, energy-bias insertion moves and continuous fractional component Monte Carlo, to speed up the simulations and obtained an acceleration factor of 6.7. By analyzing the statistics of these MC moves, we explained why these algorithms are effective. Furthermore, we tested the transferability of these algorithms to another hydrophobic MOF, Zn(pyrazole), and obtained a consistent acceleration in the equilibration. Accordingly, these methods are recommended for speeding up water adsorption simulations in hydrophobic MOFs and other hydrophobic porous materials.


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31 SUPPORTING INFORMATION Lennard-Jones parameters and partial charges for ZIF-8 atoms and water, comparison between simulated and experimental isotherms, discussion about the force field, and the results of reproducibility tests of the algorithms investigated including CFC MC, energy-bias moves, and energy-bias + CFC MC.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy under Award DE-FG02-08ER15967. H. Zhang acknowledges support from a Ryan Fellowship from the Northwestern University International Institute for Nanotechnology. Thanks also go to Dr. Benjamin J. Sikora for his help with the implementation of the algorithms.



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41 TOC Graphic


Computational Study of Water Adsorption in the Hydrophobic Metal

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