Molecular Dynamics Simulations for Loading-Dependent Diffusion of

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Molecular Dynamics Simulations for Loading-Dependent Diffusion of CO2, SO2, CH4, and Their Binary Mixtures in ZIF-10: The Role of Hydrogen Bond Zhen Yang, Xiangshu Chen, and Liangliang Huang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01537 • Publication Date (Web): 21 Jul 2017 Downloaded from http://pubs.acs.org on July 25, 2017

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Molecular Dynamics Simulations for Loading-Dependent Diffusion of CO2, SO2, CH4, and Their Binary Mixtures in ZIF-10: The Role of Hydrogen Bond Li Li,1 Deshuai Yang,1 Trevor R. Fisher,2 Qi Qiao,2 Zhen Yang,*,1 Na Hu,1 Xiangshu Chen,*,1 Liangliang Huang*,2

1

Institute of Advanced Materials (IAM), State-Province Joint Engineering Laboratory of Zeolite

Membrane Materials, College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang 330022, People’s Republic of China 2

School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman,

Oklahoma 73019, United States

ACS Paragon Plus Environment

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ABSTRACT The loading-dependent diffusion behavior of CH4, CO2, SO2, and their binary mixtures in ZIF-10 has been investigated in detail by using classical molecular dynamics simulations. Our simulation results demonstrate that the self-diffusion coefficient Di of CH4 molecules decreases sharply and monotonically with the loading while those of both CO2 and SO2 molecules initially display a slight increase at low uptakes and follow a slow decrease at high uptakes. Accordingly, the interaction energies between CH4 molecules and ZIF-10 remain nearly constant regardless of the loading due to the absence of hydrogen bonds (HBs), while the interaction energies between CO2 (or SO2) and ZIF-10 decease rapidly with the loading, especially at small amounts of gas molecules. Such different loading-dependent diffusion and interaction mechanism can be attributed to the relevant HB behavior between gas molecules and ZIF-10. At low loadings, both the number and strength of HBs between CO2 (or SO2) molecules and ZIF-10 decrease obviously as the loading increases, which is responsible for the slight increase of their diffusion coefficients. However, at high

loadings,

their

HB

strength

increases

with

the

loading.

Similar

loading-dependent phenomena of diffusion, interaction, and HB behavior can be observed for CH4, CO2, and SO2 binary mixtures in ZIF-10, only associated with some HB competition between CO2 and SO2 molecules in the case of CO2/SO2 mixture.


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1．INTRODUCTION In the past decades, metal-organic frameworks (MOFs), a novel class of crystalline nanoporous materials composed of metal centers and organic links, have been widely used in gas separation and storage, catalysis, drug delivery and other applications due to their ultrahigh porosity, various pore geometries, and chemical functionalities.1–6 Zeolitic imidazolate frameworks (ZIFs), a new subclass of MOFs, possess tetrahedral networks which resemble those of zeolites with tetrahedrally coordinated atoms (Si, Al, etc.) replaced by transition metal atoms (Zn, Co, Cu, etc.) and oxygen bridges replaced by imidazolate ligands, respectively.7–10 Recently, enormous experiments have confirmed that ZIFs possess exceptional chemical and thermal stabilities in both aqueous and organic media due to their tetrahedral networks, so ZIFs are better suited for practical gas storage and separation compared to other MOFs.7–14 Therefore, a deep understanding of adsorption and diffusion mechanisms for gas molecules in ZIFs is necessary for experimental scientists to exploit more new ZIFs with our desired properties. As a powerful analysis tool, molecular simulations can provide molecular-level insights into the fundamental adsorption and diffusion properties of various gases (including H2, N2, O2, CO, CO2, NO, NOx, SO2, CH4, C2H4, C2H6, C3H6, etc.) and their mixtures in ZIFs.15–30 Generally, grand canonical Monte Carlo (GCMC) simulations are commonly used to study the corresponding adsorption behavior while molecular dynamics (MD) simulations are employed to explore the diffusion behavior.


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For example, a series of GCMC simulations proposed by Liu and Smit27 have shown that ZIF-69 is more beneficial for separating CO2 from CO2/N2 and CO2/CH4 mixtures than ZIF-68 due to the presence of Cl atoms in the ligands of ZIF-69, indicating the electrostatic interactions produced by the frameworks are essential for determining the adsorption separation performances in ZIFs. Xi and co-workers28 have compared the adsorption separation of C2H4/C2H6 mixture in ZIF-3, -6, -8, and -10 by using GCMC simulations and ideal adsorbed solution theory, demonstrating the C2H6 selectivity is affected more strongly by the ZIF topology than the pressure and gas composition. On the other hand, Zhang et al.29 used GCMC and MD simulations to examine the adsorption and diffusion of CH4, CO2, and their mixtures in ZIF-8 by incorporating structural flexibility. Their studies suggest that the structural flexibility of ZIF-8 has a negligible effect on adsorption compared to its significant effect on diffusion. More recently, Sholl and co-workers30 also showed that incorporating the effects of framework flexibility is critical to accurately predict self diffusion and transport diffusion coefficients of various light hydrocarbons in ZIF-8. Although previous simulations have provided plenty of detailed information on the adsorption and diffusion behavior of various gas molecules in ZIFs, the relevant adsorption and diffusion mechanisms are still obscure up to now, which are important for understanding adsorption, separation, and membrane processes of ZIFs. It is well-known that the interactions between gas molecules and MOFs, which are primarily attributed to the electrostatic, van der Waals, and hydrogen bond (HB) interactions, determine the adsorption and diffusion behavior of gas molecules in


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MOFs.31,32 Compared to the other two kinds of interactions, experimental observations of the relevant HB interactions are often fraught with enormous difficulties owing to its localized and directional characters.33,34 Recently, several experiments have shown that the strong HBs between CO2 molecules and amine groups can lead to higher adsorption selectivity of CO2 from CO2-related mixtures in amine-functionalized MOFs,35–37 which suggests that the HB interaction plays an essential role in determining the adsorption behavior of gas molecules in MOFs.32,38 Furthermore, Gee et al.39 reported that the adsorption uptakes of both methanol and ethanol at low pressures are considerably higher in ZIF-90 than those in ZIF-8 due to the HBs between the alcohols and the carbonyl group of ZIF-90. Recent MD simulations of Jiang and co-workers40,41 also confirmed that the water molecules can form stronger HBs with ZIF-25, -71, -93, -96, and -100 than that in bulk water. In addition, Liu et al.42 employed density functional theory calculations to reveal that the ligands of ZIF-69 and -78 can form HB interactions with the O atoms of CO2, which favors to enhance the bind capacity of CO2. The above studies demonstrate that the HBs have an important influence on the adsorption separation of gas and liquid molecules in MOFs (including ZIFs).32 To the best of our knowledge, however, few reported experiments and simulations focus on the relationship between the HB interaction and the diffusion behavior of gas molecules in MOFs, especially in ZIFs. To shed light on this issue, a series of classical MD simulations have been performed for the loading-dependent diffusion behavior of three typical gas molecules and their binary mixtures in ZIF-10. The structure of ZIF-10 is composed of twelve


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four-membered rings and six eight-membered rings, combing with the window size of ~ 8.2 Å, which has presented a high membrane-based separation selectivity for the gas mixtures.26 Herein, three typical gas molecules of CH4, CO2, and SO2 are considered, where nonpolar CH4 molecules can’t form HBs with ZIF-10 while nonpolar CO2 and polar SO2 molecules are able to form HBs with ZIF-10. In this work, we mainly explore how the HBs affect the relevant loading-dependent diffusion behavior of CH4, CO2, SO2, and their binary mixtures in ZIF-10 at a molecular level. This work is organized as follows. The simulation details are outlined in section 2. We present the simulations results for pure CO2, SO2 and CH4, as well as their binary equimolar mixtures in section 3. Finally, several brief conclusions are summarized in section 4.

2．SIMULATION DETAILS In this work, we have performed a series of NVT MD simulations to investigate the diffusion behavior of CH4, CO2, SO2, and their binary mixtures in ZIF-10 with a variety of loadings, i.e., 4, 16, 32, 48, 64, and 80 gas molecules per unit cell (UC). The crystal structure of ZIF-10 for MD simulations was constructed from the experimental X-ray diffraction data of the Cambridge Structural Database (CSD)43 and our simulation boxes were typically composed of 2 × 2 × 2 UCs for most loadings. However, it is necessary to construct two bigger simulation boxes composed of 4 × 4 × 4 and 3 × 3 × 3 UCs for the low loadings of 4 and 16 molecules/UC, respectively, to accommodate enough gas molecules to obtain reliable statistical results. Therefore,


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the dimensions of the simulation boxes with the periodic boundary conditions in three directions are 54.12 × 54.12 × 38.81 Å3 for 2 × 2 × 2 UCs, 81.18 × 81.18 × 58.22 Å3 for 3 × 3 × 3 UCs, and 108.24 × 108.24 × 77.62 Å3 for 4 × 4 × 4 UCs. It should be noted that the corresponding number of gas molecules were initially arranged into single unit cell of ZIF-10 by using the configuration-biased insertion technique44 for each loading. Then, each initial configuration was obtained by making a big block from the corresponding unit cell (containing gas molecules) at three directions. Herein, an uncharged single-point model was used for the CH4 molecule due to its tetrahedral geometry and nonpolar nature, while two sophisticated three-site models were employed for the CO2 and the SO2 molecules in order to accurately reproduce the corresponding experimental results.21,25 The recent force field proposed by Zheng et al.45 was used for the ZIF-10, which is compatible with the models of CH4, CO2, and SO2 molecules. It should be noted that the ZIF-10 structure was rigid in the following MD simulations partly due to the limitations imposed by the available force fields. Besides, the four-membered window openings connecting the merlinoite (MER) cages is up to 8.2 Å in diameter, which is much larger than the kinetic diameters of CH4 (3.8 Å),46 CO2 (3.3 Å),21 and SO2 (4.11 Å)21 molecules. Therefore, the flexibility of ZIF-10 maybe have a slight influence on the diffusion results since the large window openings promotes the passage of gas molecules from one cage to another cage. Based on above force fields, the nonbonded interactions were described by the combination of electrostatic and Lennard-Jones (L-J) interactions in this work. All L-J parameters and partial atomic charges used in this work were summarized and listed


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in Tables S1 and S2 of the Supporting Information. Then, the crossing L-J parameters were derived for self-parameters using Lorenz-Berthelot mixing rules. For each loading, at least three MD simulations with independent initial configurations were carried out in the canonical (NVT) ensemble, where temperature was fixed at 303.0 K and controlled by the Nosé-Hoover algorithm. Newton’s equation of motion was integrated by the velocity-Verlet algorithm with a time step of 1.0 fs. A cutoff of 1.0 nm was applied for the nonbonded interactions, while the long-range electrostatic interactions were treated by the particle-particle particle-mesh (PPPM) method.

47

In each MD simulation, we ran the first 10 ns for equilibration, and

then the next simulation from 20 to 50 ns was performed for trajectory analyses with the trajectories stored every 100 fs. Afterwards, an additional NVT MD simulation of 500 ps (following the corresponding final configuration attained from the above calculation was performed for each simulation system, but their trajectories and velocities were saved every time step (i.e., 1 fs) to better calculate the HB lifetimes and the velocity autocorrelation functions. In this work, all NVT MD simulations were performed by using the Lammps package.48

3．RESULTS AND DISCUSSION 3.1. Pure gas molecules in ZIF-10 The diffusion behavior of gas molecules in ZIF-10 can be directly investigated through the relevant mean square displacement (MSD). Then, their isotropic self-diffusion coefficients Di can be specified by the Einstein’s formulation49,50


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Di = lim t ®¥

where

[ri (t ) - ri (0)]2

[ri (t ) - ri (0)]2 6t

(1)

is the MSD of the ith kind of gas molecules at a certain time

of t. The angular bracket means that the ensemble average is taken over all tagged gas molecules at different reference initial times. The calculated MSD curves of CH4, CO2, and SO2 molecules in ZIF-10 are shown in Figure S1 of the Supporting Information. It should be emphasized that although there exists a sub-diffusive behavior for CO2 and SO2 molecules in ZIF-10 at high loadings, the diffusion coefficients in this work are calculated through the MSD curves in the time interval of 5000 ps, which far exceeds the corresponding bend points of sub-diffusive behavior, as shown in Figure S2 of the Supporting Information. Accordingly, we present the variation of their self-diffusion coefficients Di with the loading in Figure 1. We can see clearly from this figure that the Di values of CH4 molecules in ZIF-10 are expectedly much higher than those of CO2 and SO2 molecules at all loadings. Meanwhile, the Di value of CH4 molecules is found to decrease sharply and monotonically with the loading. Similar loading-dependent diffusion behavior of CH4 molecules was also observed in other MOFs51–53,59 and some diamond-like frameworks54 due to the enhanced steric hindrance between diffusing molecules at higher loadings. On the contrary, the Di value of CH4 molecules and other hydrocarbons in ZIF-8 was found to increase with the loading owing to a large decrease in the free energy barrier primarily arising from the narrow window (dw = 3.8 Å) of ZIF-8.29,30 This different loading-dependent diffusion behavior of CH4 molecules in ZIFs should arise from the difference in the window (or pore) sizes of various nanoporous materials compared to the kinetic


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diameter of CH4 (3.8 Å). When the window sizes of nanoporous materials are comparable to the kinetic diameter of CH4, the free energy barrier from the windows dominates the diffusion of CH4, and the corresponding Di value increases with the loading. But when the window sizes are larger than the kinetic diameter of CH4, the diffusion of CH4 is determined by the steric hindrance between diffusing molecules, and the corresponding Di value decreases with the loading. Figure 1 illustrates that the Di values of both CO2 and SO2 molecules in ZIF-10 initially display a slight increase at low loadings from 4 to 16 molecules/UC, and follow a slow decrease as the loading increases from 16 to 80 molecules/UC. In previous MD simulations proposed by Zhang et al. and Zheng et al.,29,55 their simulation results showed that the loading has a slight influence on the Di value of CO2 molecules in ZIF-8 at low loadings, which can be also supported by recent experimental pulsed field gradient (PFG) NMR.56 And recently, Tovar et al.57 have also demonstrated experimentally that the diffusion coefficients of CO2 molecules in large Cu-BTC crystals have very little dependence on the loading at low pressures. More similarly, Zhong and co-workers58 performed a series of MD simulations to explore diffusion behavior of CO2 molecules in ZIF-68 and ZIF-69, where both corresponding Di values initially increase with the pressure when the pressure is lower than 1 atm and follow a decrease with the pressure. Meanwhile, Johnson and co-workers59 have used GCMC and equilibrium MD to study the adsorption and diffusion properties of CO2/CH4 mixtures in ZIF-68 and ZIF-70 at 298 K. Their results showed that the corresponding Di values of pure CH4 component


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monotonically decrease with loading, and the values of pure CO2 molecule increase and then decrease as a function of loading. Such loading-dependent diffusion behavior of CO2 and SO2 molecules in ZIF-10 is significantly different from that of CH4 molecules in ZIF-10, which can be attributed to different interaction mechanisms between gas molecules and ZIF-10. Figure 2a shows the average interaction energies between gas molecules and ZIF-10 at different loadings. All average interaction energies are found to be negative and their absolute values always show the order SO2 > CO2 > CH4, meaning the corresponding interaction order is SO2 > CO2 > CH4. As shown in Figure 2a, furthermore, the magnitude of interaction between CH4 molecules and ZIF-10 is found to remain nearly constant regardless of the loading, while those of both CO2 and SO2 molecules decease rapidly from 4 to 16 molecules/UC and follow a slow decrease with the loading. The weaker interaction between CO2 (or SO2) molecules and ZIF-10 imposes less restrictions on gas molecules, which is favorable to their diffusion in ZIF-10. However, increasing loading can generally lead to an increase in the interaction between gas molecules (shown in Figure S3 of the Supporting Information), which is unfavorable to their diffusion in ZIF-10. Therefore, a slight increase in the self-diffusion coefficients Di of both CO2 and SO2 molecules in ZIF-10 (see Figure 1) from 4 to 16 molecules/UC arises from the competition between the gas-gas and gas-ZIF interactions. Nevertheless, there is no such competition for the CH4 molecules in ZIF-10 as the loading increases, as the interaction between CH4 molecules and ZIF-10 is always constant. This behavior causes the Di value of CH4


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molecules to decrease sharply and monotonically with the loading, as shown in Figure 1. Unlike the CH4 molecule, the O atoms of CO2 and SO2 molecules, which have partially negative charges, can form HBs with electron-deficient C–H groups of the imidazolate ligands in ZIF-10. Recent first-principles calculations proposed by Hochlaf and co-workers60 have revealed that there exist s-type C-H…O hydrogen-bonding interactions between CO2 and the Zn2+-imidazole complex, indicating that the interaction between CO2 and ZIF-1 or ZIF-6 is a s-type C-H…O HB. Furthermore, Holman and co-workers61 reported a reproducible synthesis of phase-pure ZIF-10 by employing the MeMeCH2 macrocycle as a kinetic template. The relevant X-ray single crystal structure revealed that templating the MER framework mainly results from the HBs between the C-H bonds of imidazolate rings (the HB donor) and the O atoms of MeMeCH2 macrocycles (the HB acceptor). On the other

hand,

recent

experimental

studies

showed

that

the

addition

of

imidazolium-based ionic liquids can enhance CO2 uptake considerably in monoethanolamine, since the 2-H, 4-H, and 5-H of the imidazolium ring in cations can form HBs with CO2 molecules.62 The quantum theory of atoms in molecules (QTAIM) by Lourenco et al.63 also showed that there are HBs between the 2-H protons of imidazolium rings and the O atoms of CO2 molecules in imidazolium-based ionic liquids. More recently, Lau et al.64 further reported that the 4-H and 5-H protons of imidazolium rings are vital for the electrochemical reduction of CO2 to CO, since the acidic H protons at the C4- and C5-positions serve to stabilize


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a CO2 anion radical intermediate via the hydrogen-bonding interactions. Compared to nonpolar CO2 molecules, the O atoms of polar molecules, such as SO2 and H2O molecules, should form strong HBs more easily with the imidazolate rings. For example, earlier IR and Raman spectra revealed that three H atoms of the imidazolium ring of [Bmim][BF4] ionic liquid can form strong HBs with H2O molecules.65 Therefore, there should be HBs between CO2 (or SO2) molecules and the imidazolate rings of ZIF-10. In addition, the average interaction energies between CO2 (or SO2) molecules and ZIF-10 are further decomposed into the van der Waals (i.e., the L-J part) and electrostatic (i.e., the charge-charge part) interactions, as shown in Figure S4 of the Supporting Information. Compared to the van der Waals interaction, the magnitude of electrostatic interaction energy is found to have a much larger decrease from 4 to 16 molecules/UC. Obviously, such large decrease in the electrostatic interaction can’t be attributed to the increasing distances between gas molecules and ZIF-10, since the electrostatic interaction should decay much more slowly with the distance than the corresponding van der Waals interaction.66 Strictly speaking, the HB interaction is a type of electrostatic interaction since a hydrogen bond can form when a hydrogen atom covalently bonded to a strongly electronegative atom, such as nitrogen, oxygen, and so on.67 Therefore, evaluating the effect of loading on the relevant HB behavior for both CO2 and SO2 molecules in ZIF-10 is necessary to understand different loading-dependent interaction mechanisms of CH4, CO2 and SO2 molecules in ZIF-10


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(see Figure 2a). As shown in Figure 2b, the HB formation in this work is defined in terms of the following distance and angular criteria68

R OH < R OH and q CHO < q CHO C C

(2)

where O is the oxygen atom of CO2 (or SO2) molecules, C and H are the carbon and OH hydrogen atoms of the imidazolate rings of ZIF-10, respectively. R is the distance CHO between the oxygen and hydrogen atoms, while q is the C-H…O angle. RCOH

and q CCHO are the upper limit distance and angle of HB formation, respectively. As shown in Figure S5 of the Supporting Information, the RCOH values for CO2 and SO2 molecules are 3.7 Å and 3.9 Å, which are obtained from the first minimum valley of the corresponding radial density profiles. Accordingly, the q CCHO value is fixed at 120°, which is obtained from the first maximum of the corresponding angle distribution. It should be noted that the radial density profiles and the angle distribution are calculated at the lowest loading of 4 molecules/UC, where both CO2 and SO2 molecules almost form the HBs with the imidazolate rings of ZIF-10. Figure 2c presents the average HB number per CO2 (or SO2) molecule in ZIF-10 as a function of the loading. It shows that average HB numbers of both CO2 and SO2 molecules are found to decrease monotonically with the loading, which is favorable to a decrease in the interaction between CO2 (or SO2) molecules and ZIF-10 (see Figure 2a). Furthermore, the SO2 molecules always have more HBs than the CO2 molecules at all loadings, which is well consistent with the stronger interaction between SO2 molecules and ZIF-10 compared to CO2 molecules (see Figure 2a). On the other hand, the corresponding HB strength (i.e., average lifetime) can be accurately characterized


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through the continuous time correlation function (TCF) S HB (t ) , which is defined as69,70

S HB (t ) =

< h(0) H (t ) > < h(0)h(0) >

(3)

where the variable H (t ) is unity when the tagged HB pair is continuously kept from time 0 to time t, and zero otherwise. Hence, the continuous TCFs can provide an accurate average lifetime of HBs ( t SHB ), which is calculated by fitting the S HB (t ) curve through the three weighed exponentials (with a total weight of unity, i.e., A + B + C = 1)

R(t ) = A exp(-t / t a ) + B exp(-t / t b ) + C exp(-t / t c )

(4)

t R = At a + Bt b + Ct c

(5)

and then

where A, B, and C are tunable parameters, while t a , t b , and t c are the time constants. The calculated S HB (t ) curves of CO2 and SO2 molecules in ZIF-10 at different loadings are shown in Figures 2d and 2e, and the corresponding t SHB values are shown in the insets. Then, the values of t SHB for both CO2 and SO2 molecules are found to decrease considerably with the loading at low loadings, especially from 4 to 16 molecules/UC, and follow an increase with the loading at high loadings. Therefore, such a considerable decrease in the HB strength between CO2 (or SO2) molecules and ZIF-10 at low loadings, associated with the decreasing average HB number, should be mainly responsible for the rapid interaction decrease from 4 to 16 molecules/UC (see Figure 2a). However, the increase in the HB strength at high loadings will weaken the effect from the decrease in the average HB number, resulting in a slow interaction


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decrease at high loadings, as shown in Figure 2a. Next, Figures 3 and 4 present the two-dimensional density distribution of CH4, CO2, and SO2 molecules in ZIF-10 projected on the x-y plane at different loadings. Generally, different interaction mechanisms between gas molecules and ZIF-10 can lead to different density distributions of gas molecules in ZIF-10. As shown in Figure 3a, Site 1 refers to the four-membered window between the MER cages and Site 2 mainly corresponds to the MER cages in ZIF-10. Then we can see from Figure 3 that the main adsorption sites are found to be around Site 1 and the corners in Site 2 for all gas molecules. These sites correspond to areas, which are close to imidazolate ligands of ZIF-10. It should be emphasized that there are no open metal sites acting as the adsorption sites in ZIF-10, which is considerably different from the adsorption behavior in common MOFs. This is because the Zn atoms of ZIF-10 are not accessible by guest gas molecules due to the steric hindrance of imidazolate ligands so that the interaction between Zn atoms and gas molecules are negligible (see Figures S6 and S7 of the Supporting Information). As the loading gradually increases, the density distribution of gas molecules can also gradually cover the whole available space in ZIF-10, but the higher densities are still found to be close to the imidazolate ligands of ZIF-10. This holds especially true, especially for CO2 and SO2 molecules due to the presence of HBs, as shown in Figure 4. As shown in the enlarged Figures 5a-5c, further, we can find that there are almost no CO2 and SO2 molecules at the center of MER cages at the loading of 4 molecules/UC, which is very different from the density distribution of CH4 molecules in ZIF-10. Such a different density


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distribution can be attributed to the presence of HBs between CO2 (or SO2) molecules and ZIF-10. By comparison with CO2 molecules, there is a larger cavity in the density distribution of SO2 molecules at the loading of 4 molecules/UC. This indicates that the ability of SO2 molecules to form HBs is higher than that of CO2 molecules, which agrees well with a higher average HB number per SO2 molecule in ZIF-10 (see Figure 2c). As the loading increases from 4 to 16 molecules/UC, the density distribution of both CO2 and SO2 molecules gradually cover the center of MER cages, where more gas molecules are free without HBs in ZIF-10. For gas molecules in porous materials, a common phenomenon is that increasing loading can increase the collision frequency among gas molecules, which is unfavorable to the diffusion motions. On the other hand, the collision frequency between gas molecules and ZIF-10 do not always vary monotonically with the loading. In general, one insight into such microscopic collisions can be gained by the center-of-mass velocity autocorrelation functions (VACFs) of gas molecules since both kinds of collisions can change the magnitude and direction of their velocities. The normalized VACFs can be expressed as71

! ! vi (0)vi (t ) Cv (t ) = ! ! vi (0)vi (0)

(6)

! where vi (t ) is the velocity of gas molecule of type i at the time of t. As shown in Figure 6, all VACF curves cross the axis and then become negative. A negative correlation coefficient means that the gas molecule is moving in the direction opposite to that at t = 0. Accordingly, the insets of Figure 6 show the corresponding relaxation times at different loadings, which are well consistent with the loading-dependent


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diffusion coefficients for all kinds of gas molecules shown in Figure 1. For example, when the loading is from 4 to 16 molecules/UC, the relaxation time of CH4 molecules in ZIF-10 decrease with loading while the relaxation times of both CO2 and SO2 molecules display a clear increase. The phenomena should also arise from the change of HBs between CO2 (or SO2) molecules and ZIF-10. As shown in Figure 2c, the average HB numbers of both CO2 and SO2 molecules slightly decrease with the loading. More importantly, there is a large decrease in their HB strength from 4 to 16 molecules/UC as shown in Figures 2d and 2e. Such weakened HB interactions between CO2 (or SO2) molecules and ZIF-10 can decrease the collision frequency between gas molecules and ZIF-10 and surpass the unfavorable influence of increasing collision frequency among gas molecules on their diffusion motions. In addition, the binding effects from strong HBs will cause the hydrogen-bonded gas molecules to aggregate in a small space around the imidazolate ligands of ZIF-10 in which the collision frequency among gas molecules as well as that between gas molecules and ZIF-10 can increase. Therefore, the strong HBs between CO2 (or SO2) molecules and ZIF-10 cause the Di values of both CO2 and SO2 molecules to be less than that of CH4 molecules at low loadings. Additionally, the weakened HBs at high loadings result in a smaller deviation in the Di values among different gas molecules, as shown in Figure 1. 3.2. Binary equimolar mixtures in ZIF-10 We have also investigated the diffusion behavior of CH4/CO2, CH4/SO2, and CO2/SO2 binary mixtures in ZIF-10, respectively. For better comparisons, equimolar


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gas mixtures with the same loadings as pure gas molecules are considered here. Figure 7 presents the variation of their self-diffusion coefficients Di with the loading. We can find from this figure that the Di values of CH4 molecules decrease monotonically with the loading in the cases of both CH4/CO2 and CH4/SO2 mixtures, while all Di values of both CO2 and SO2 molecules initially have a slight increase and follow a slow decrease as the loading increases in their binary mixtures. These diffusion phenomena of CH4, CO2, and SO2 molecules in binary mixtures are almost identical to those in the cases of pure gas molecules in ZIF-10 and suggest similar interaction mechanisms between gas molecules and ZIF-10 in both cases of pure gases and binary mixtures. As shown in Figure 8, the average interaction energies between CH4 molecules and ZIF-10 also remain nearly in CH4/CO2 and CH4/SO2 mixtures and are less than one third of the corresponding values of CO2 and SO2 molecules due to the absence of HBs. Meanwhile, the average interaction energies of both CO2 and SO2 molecules in binary mixtures are also found to decease rapidly with the loading at low loadings and follow a slow decrease at high loadings. Nevertheless, it should be noted that the deviations of Di values in binary mixtures are less than those in the cases of pure gas molecules in ZIF-10, especially at the highest loading of 80 molecules/UC. This is because the presence of CO2 and SO2 molecules can block the diffusion path of ZIF-10 and slow down the diffusion motion of CH4 in CH4/CO2 and CH4/SO2 mixtures, respectively, as shown in Figures S9 and S10 of the Supporting Information. In addition, Figure 9a shows that the average number of HBs of CO2 molecules in


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both CH4/CO2 and CO2/SO2 mixtures are found to remain nearly constant from 4 to 16 molecules/UC and follow a clear drop from 16 to 32 molecules/UC. However, the value in CH4/CO2 mixture is higher than that in CO2/SO2 mixture when the loading is more than 32 molecules/UC. This is due to the presence of HB competition between CO2 and SO2 molecules in CO2/SO2 mixture. Meanwhile, the corresponding average HB lifetimes in CH4/CO2 and CO2/SO2 mixtures initially decrease and follow an increase with the loading, as shown in Figures 9b and 9c. Compared to CO2 molecules in their mixtures, on the other hand, we can find from Figures 9d-9f that SO2 molecules in CH4/SO2 and CO2/SO2 mixtures display similar HB behavior with the loading. The HB phenomena of both CO2 and SO2 molecules in binary mixtures are almost identical with those in the cases of pure gases in ZIF-10, only associated with the presence of HB competition between CO2 and SO2 molecules in CO2/SO2 mixture, which supports similar diffusion and interaction mechanisms between pure gases and binary mixtures in ZIF-10.

4．CONCLUSIONS In this work, a series of classical MD simulations have been carried out to systematically investigate the diffusion behavior of CH4, CO2, SO2, and their binary equimolar mixtures in ZIF-10 at six different loadings. Our simulations show that CH4 molecules display a different loading-dependent diffusion mechanism from those of CO2 and SO2 molecules in the cases of both pure gas and binary mixtures in ZIF-10, where the self-diffusion coefficients Di of CH4 molecules decrease sharply and


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monotonically with the loading while those of both CO2 and SO2 molecules initially display a slight increase at low uptakes and follow a slow decrease at high uptakes. Such different diffusion behavior with respect to the loading among CH4, CO2, and SO2 molecules can be attributed to different interaction mechanisms between gas molecules and ZIF-10. In the case of CH4 molecules in ZIF-10, the interaction energies between gas molecules and ZIF-10 are found to be almost constant regardless of the loading. However, the interaction energies between CO2 (or SO2) and ZIF-10 decease rapidly at low amount of gas molecules and then follow a slow decrease with the loading. In the loading range from 4 to 16 molecules/UC, a rapid decrease in the interaction between CO2 (or SO2) molecules and ZIF-10 lead to much less restriction on gas molecule. Consequently, the unfavorable contribution on diffusion from the increasing interaction among gas molecules themselves is overcome, so that their Di values display a slight increase with the loading. Furthermore, our simulations reveal that such a rapid decrease in the interaction between CO2 (or SO2) molecules and ZIF-10 arises from the considerable changes of corresponding HB behavior at low loadings, and is significantly different from the case of CH4 molecules in ZIF-10 in which there is an absence of HBs. Through a detailed analysis on HBs in the cases of both CO2 and SO2 molecules in ZIF-10, we find that both the number and the strength of HBs between gas molecules and ZIF-10 decrease with the loading at low loadings. On the contrary, their HB strength shows an obvious increase with loading at high loadings, although the average number of HBs per gas molecule still decreases with the loading. Similar loading-dependent


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phenomena in diffusion, interaction, and HB behavior can be observed in the cases of their binary mixtures in ZIF-10, only associated with some competition between CO2 and SO2 molecules in the case of CO2/SO2 mixture. In addition, our simulations also illustrate that the relevant loading-dependent collision frequency of gas molecules in ZIF-10 is well consistent with the corresponding diffusion behavior. The simulation results in this work provide a molecular-level picture of the diffusion mechanism of different gas molecules in ZIF-10, and is of great importance for experimental scientists to design and prepare new ZIFs and their membranes for high gas adsorption and separation performance.

ASSOCIATED CONTENT Supporting Information 1. Lennard-Jones parameters and partial atomic charges used in this work; 2. MSD curves and diffusion coefficients of pure gas molecules in ZIF-10; 3. Interaction energies between pure gas molecules; 4. Definition of HB formation; 5. Coordination number profiles of gas molecules around Zn atom; 6. MSD curves, diffusion coefficients, density distribution, and VACF curves of binary equimolar mixtures in ZIF-10. The information is available free of charge via the Internet at http://pubs.acs.org/.

AUTHOR INFORMATION Corresponding Author


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*E-mail: [email protected] (Z. Y.) *E-mail: [email protected] (X.S.C.) *E-mail: [email protected] (L.L.H.)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21306070, 21463011, and 21476099), Natural Science Foundation of Jiangxi Province (Nos. 20171BAB203012 and 20151BAB203014), Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University.

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Dynamics Simulations of Hydrogen Bond Dynamics and Far-Infrared Spectra of Hydration Water Molecules around the Mixed Monolayer-Protected Au Nanoparticle. J. Phys. Chem. C 2015, 119, 1768−1781. (70) Fu, F. J.; Li, Y. Z.; Yang, Z.; Zhou, G. B.; Huang, Y. P.; Wan, Z.; Chen, X. S.; Hu, N. Li, W.; Huang, L. L. Molecular-Level Insights into Size-Dependent Stabilization Mechanism of Gold Nanoparticles in 1-Butyl-3-methylimidazolium Tetrafluoroborate Ionic Liquid. J. Phys. Chem. C 2017, 121, 523−532. (71) Zhou, G. B.; Yang, Z.; Fu, F. J.; Huang, Y. P.; Chen, X. S.; Lu, Z. H.; Hu, N. Molecular-Level Understanding of Solvation Structures and Vibrational Spectra of Ethylammonium Nitrate Ionic Liquid around Single-Walled Carbon Nanotubes. Ind. Eng. Chem. Res. 2015, 54, 8166−8174.


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Figure Captions Figure 1. Variation of the self-diffusion coefficients Di with the loading for pure CH4, CO2, and SO2 molecules in ZIF-10.

Figure 2. (a) Average interaction energy of pure CH4, CO2, and SO2 molecules in ZIF-10 at different loadings, (b) schematic illustrations for the definitions of HBs between CO2 (left), SO2 (right) and the imidazolate ring of ZIF-10, (c) average number of HBs for CO2 and SO2 molecules in ZIF-10, continuous TCFs SHB(t) for the HBs of (d) CO2 and (e) SO2 molecules in ZIF-10, and the insert shows the corresponding HB lifetimes. Lines colored in green, orange, magenta, red, blue and blank correspond to the loadings from 4 to 80 molecules/UC in turn. Figure 3. (a) Two dimensional structure in the x-y plane of ZIF-10 framework, and two-dimensional density distribution in the x-y plane for pure (b) CH4, (c) CO2, and (d) SO2 molecules in ZIF-10 at the loading of 4 molecules/UC.

Figure 4. Two-dimensional density distribution in the x-y plane of pure (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10: (a1-c1) 16 molecules/UC, (a2-c2) 32 molecules/UC, (a3-c3) 48 molecules/UC, (a4-c4) 64 molecules/UC, and (a5-c5) 80 molecules/UC.

Figure 5. Enlarge the circle region of site 2 (as shown in Figure 3) for (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10 at the loading of 4 molecules/UC, the corresponding region of (d) CH4, (e) CO2, and (f) SO2 molecules in ZIF-10 at the loading of 16 molecules/UC.

Figure 6. VACF curves of pure (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10 at different loadings. Lines colored in green, orange, magenta, red, blue and blank correspond to the loadings from 4 to 80 molecules/UC in turn. The insert shows the corresponding relaxation times.


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Figure 7. Variation of the self-diffusion coefficients Di with the loading for binary (a) CH4/CO2, (b) CH4/SO2, and (c) CO2/SO2 mixtures at 303.0 K.

Figure 8. Average interaction energy of binary (a) CH4/CO2, (b) CH4/SO2, and (c) CO2/SO2 mixtures in ZIF-10 at different loadings.

Figure 9. (a) Average number of HBs for CO2 molecules in their binary mixtures, continuous TCFs SHB(t) for the HBs of CO2 molecules in (b) CH4/CO2 and (c) CO2/SO2 mixtures, and the inserts show the corresponding HB lifetimes. And (d-f) same as (a-c) but for SO2 molecules in their binary mixtures. Lines colored in green, orange, magenta, red, blue and blank correspond the loading from 4 to 80 molecules/UC.


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Figure 1. Variation of the self-diffusion coefficients Di with the loading for pure CH4, CO2, and SO2 molecules in ZIF-10.


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Figure 2. (a) Average interaction energy of pure CH4, CO2, and SO2 molecules in ZIF-10 at different loadings, (b) schematic illustrations for the definitions of HBs between CO2 (left), SO2 (right) and the imidazolate ring of ZIF-10, (c) average number of HBs for CO2 and SO2 molecules in ZIF-10, continuous TCFs SHB(t) for the HBs of (d) CO2 and (e) SO2 molecules in ZIF-10, and the insert shows the corresponding HB lifetimes. Lines colored in green, orange, magenta, red, blue and blank correspond to the loadings from 4 to 80 molecules/UC in turn.


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Figure 3. (a) Two dimensional structure in the x-y plane of ZIF-10 framework, and two-dimensional density distribution in the x-y plane for pure (b) CH4, (c) CO2, and (d) SO2 molecules in ZIF-10 at the loading of 4 molecules/UC.


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Figure 4. Two-dimensional density distribution in the x-y plane of pure (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10: (a1-c1) 16 molecules/UC, (a2-c2) 32 molecules/UC, (a3-c3) 48 molecules/UC, (a4-c4) 64 molecules/UC, and (a5-c5) 80 molecules/UC.


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Figure 5. Enlarge the circle region of site 2 (as shown in Figure 3) for (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10 at the loading of 4 molecules/UC, the corresponding region of (d) CH4, (e) CO2, and (f) SO2 molecules in ZIF-10 at the loading of 16 molecules/UC.


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Figure 6. VACF curves of pure (a) CH4, (b) CO2, and (c) SO2 molecules in ZIF-10 at different loadings. Lines colored in green, orange, magenta, red, blue and blank correspond to the loadings from 4 to 80 molecules/UC in turn. The insert shows the corresponding relaxation times.


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Figure 7. Variation of the self-diffusion coefficients Di with the loading for binary (a) CH4/CO2, (b) CH4/SO2, and (c) CO2/SO2 mixtures at 303.0 K.


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Figure 8. Average interaction energy of binary (a) CH4/CO2, (b) CH4/SO2, and (c) CO2/SO2 mixtures in ZIF-10 at different loadings.


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Figure 9. (a) Average number of HBs for CO2 molecules in their binary mixtures, continuous TCFs SHB(t) for the HBs of CO2 molecules in (b) CH4/CO2 and (c) CO2/SO2 mixtures, and the inserts show the corresponding HB lifetimes. And (d-f) same as (a-c) but for SO2 molecules in their binary mixtures. Lines colored in green, orange, magenta, red, blue and blank correspond the loading from 4 to 80 molecules/UC.


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Molecular Dynamics Simulations for Loading-Dependent Diffusion of

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