Grand-Canonical Monte Carlo and Molecular-Dynamics Simulations

Jan 15, 2010 - Muthuramalingam Prakash , Navid Sakhavand , and Rouzbeh Shahsavari ..... Characterization of Zn q+ –imidazole (q = 0, 1, 2) organomet...
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J. Phys. Chem. C 2010, 114, 2171–2178

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Grand-Canonical Monte Carlo and Molecular-Dynamics Simulations of Carbon-Dioxide and Carbon-Monoxide Adsorption in Zeolitic Imidazolate Framework Materials Andrew Sirjoosingh, Saman Alavi, and Tom K. Woo* Centre for Catalysis Research and InnoVation, Department of Chemistry, UniVersity of Ottawa, Ottawa, Ontario K1N 6N5 ReceiVed: August 20, 2009; ReVised Manuscript ReceiVed: December 2, 2009

The nature of guest binding sites and selectivity in the zeolitic imidazolate framework (ZIF) 68 and 69 structures are studied by grand-canonical Monte Carlo and molecular-dynamics simulations. We have used the force field of Liu and co-workers to simulate CO2 and CO adsorption isotherms in the ZIF 68 and 69 structures at 273 K for pressures up to 1 atm. The experimental CO2 adsorption isotherms are reproduced with good accuracy, but the same force-field protocol overestimates the CO adsorption isotherms. In addition to the total guest adsorption in the unit cell of the ZIF structures from the adsorption isotherms, we determined the relative distribution of the guests in the pores and channels. The nature and number of the binding sites in the channels and pores are determined from the guest probability distributions in the ZIF structures. We find that the CO2 molecules associate strongly with the benzene rings of the benzimidazolate anion. The binding energies in the pores and channels for different numbers of CO2 and CO guests have been calculated from molecular-dynamics simulations. As expected, the binding energies of the CO guests in the lattice are much smaller than those of CO2. We have also studied the diffusion of the CO2 and CO guests in the pores and channels of the two ZIF structures. The size of the guest and the aperture size in lattice affect the diffusion rates considerably, and the guests do not diffuse through the pores and channels at equal rates. 1. Introduction Many applications of porous metal-organic framework (MOF) materials for CO2 capture and sequestration from mixtures with other gases have been recently proposed.1–11 Zeolitic imidazolate framework (ZIF) materials which have functionalized imidazolate (xIM) anions as the organic moieties with Zn linkers10 are a specific class of MOFs which have recently been suggested for CO2 capture. The Zn-xIM-Zn angle in the ZIFs corresponds to the Si-O-Si angle in zeolites, and many ZIFs synthesized to date have topologies analogous to zeolite structures. Yaghi and co-workers10,12 have shown that some ZIF structures have reversible and selective storage capabilities for large amounts of CO2, some as high as 83 L of CO2 per liter of ZIF.10 These materials also outperform the commonly used industrial substance, BPL carbon, for selectivity in CO2/CO absorption. Factors affecting selective CO2 adsorption by the ZIFs have been suggested to be the pore size, the pore aperture diameter, and the chemical functionality of the imidazole organic groups in the ZIFs. On the basis of these factors, three ZIF structures, namely, ZIF 68, 69, and 70, were highlighted for their large CO2 adsorption capacity and selectivity with respect to CO2/CO separation. Liu et al.13 recently studied the adsorption of CO2 in the ZIF 68 and 69 framework materials with grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations with a custom-designed classical force field. The GCMC calculations accurately reproduced the experimental CO2 adsorption isotherms in ZIF 68 and 69. The authors determined spatial probability distribution plots for the guests in the ZIF unit cells at different external pressures but did not analyze the chemical nature of individual binding sites. They also studied the total * Corresponding author. E-mail: [email protected].

self-diffusivity of the CO2 guests in the pores and channels of these two framework materials with MD simulations and determined that the self-diffusivity of CO2 in ZIF 68 is greater than that in ZIF 69. They related this observation to the larger aperture sizes of the ZIF 68 pores. Although CO2 adsorption was studied in ZIF 68 and 69 by Liu et al., CO adsorption in ZIFs has not been examined by molecular simulation. Integral to the use and rational design of framework material’s selective adsorption of gases is an understanding of their microscopic absorption mechanisms. The mechanism of guest adsorption in zeolites has been widely studied with Monte Carlo and MD simulations.14 In this work, we use MD and GCMC simulations to study the structure, dynamics, and adsorption isotherms of CO2 and CO in ZIF 68 and ZIF 69 with a force field identical to that used by Liu et al.13 Here, we focus on the microscopic details of the adsorption of these two gases with the goal of determining the specific mechanism for the selective adsorption of CO2 compared to CO in the ZIF phases. The relative importance of the functional groups in the ZIF structures in comparison to the structural features of the ZIF structures such as pore and aperture size will be studied in detail. We also study the details of the diffusion of these gases in the different parts of the ZIF structures. The pore space in the ZIF structures is composed of two independent regions (i.e., the pores and channels, see below), and it is important to separately determine the holding capacity and diffusion of the guests in these regions. The outline of this study is as follows. We first describe the computational methods used in the GCMC and MD studies of the CO2 and CO guest adsorption in the ZIFs. We then present the results of GCMC simulations for the adsorption isotherms. The distributions of guest molecules in the ZIF cages for accepted configurations of the GCMC simulations are analyzed to determine the adsorption sites of the guests in the framework.

10.1021/jp908058n  2010 American Chemical Society Published on Web 01/15/2010

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Sirjoosingh et al. in condensed phase to reduce simulation times.15 However, for the present systems, the large amount of empty pore and channel space in the ZIF phases and the small size of the CO2 and CO guests make guest insertion fairly efficient and lead to acceptable computation times for direct GCMC sampling. The acceptance criterion for each configuration of the guests at a specified temperature and pressure in the ZIF solid is that the chemical potential of the guest adsorbed in the solid, µSolid, must equal the chemical potential of the material in the gas phase, µGas. For example, when assuming that CO2 in contact with the ZIF solid is an ideal gas, at each temperature T and gas activity (fugacity) a, we have the following equilibrium condition,

(

µSolid(CO2) ) µGas(CO2) ) kTln Λ3 Figure 1. A 2 × 2 × 2 replica of the ZIF 69 unit-cell structure from X-ray structural determination. The c labels denote the channels, and the p labels denote the pores of the ZIF framework structure.

MD simulations of these systems are used to determine the binding energies of different guest loading in the ZIF channels and pores. We also study the dynamics of guest diffusion in the channels and pores of the ZIF phases.

)

(1)

where Λ is the thermal de Broglie wavelength of CO2 at T. This equilibrium condition allows us to determine acceptance criteria for Monte Carlo moves. In the present simulations, we will be dealing with CO2 and CO gases at 273 K and pressures up to 1 atm. For gases, the activity and pressure are related through the equation of state,

2. Computational Methods The initial structures of the ZIFs were taken from the X-ray structure analysis given by Banerjee et al.10 ZIF 68 and 69 have hexagonal unit-cell structures with the P63/mmc space group (number 194). The unit-cell lattice vectors of these phases are given in Table S1 in the Supporting Information. The formal stoichiometry of ZIF 68 is Zn(nIM)(bIM), where nIM is nitroimidazolate and bIM is benzimidazolate. The stoichiometry of ZIF 69 is Zn(nIM)(ClbIM), where ClbIM is chlorobenzimidazolate. A 2 × 2 × 2 replica of the hexagonal unit cell of ZIF 69 is shown in Figure 1. The ClbIM and nIM molecules line the walls and apertures of the large hexagonal pores (p in Figure 1) and the smaller hexagonal channels (c in Figure 1). In ZIF 69, the chlorine atoms are disordered among the four- and fivepositions of the benzene rings in ClbIM. In our simulations, we constructed an ideal structure with chlorine atoms distributed at the four-positions on the benzene rings throughout the framework. In our simulations, the ZIF frameworks are considered to be rigid. The details of the classical force field used for the ZIF 68, 69, and CO2 are similar to that of Liu et al. and are given in the Supporting Information. In summary, the Lennard-Jones (van der Waals) potential parameters for the lattice atoms and CO2 guests were taken from the Universal Force Field (UFF). The electrostatic point charges on the framework atoms and CO2 were determined by Mulliken analysis on periodic models of the ZIF 68 and ZIF 69 frameworks at the PW91/GGA level with the DND double numerical basis set.13 A similar methodology was applied to determine intermolecular potential parameters for CO (bond length 1.140 Å). The intermolecular potential parameters used in the simulations are given in Table S2 in the Supporting Information. GCMC simulations15 with an in-house developed set of scripts were performed to calculate gas adsorption isotherms of CO2 and CO in frozen ZIF frameworks. A script was written to generate guest moves, including displacement (translation and rotation), insertion, or annihilation in the rigid periodic ZIF frameworks. In general, it is more computationally efficient to use biased Monte Carlo sampling methods for guest insertion

a kT

ln

a ) p

Bp ∫0p (Z - 1) dpp ) RT

(2)

where Z ) pV/RT is the compressibility factor, V is the experimental molar volume, and B is the second virial coefficient.16a If the compressibility factor is close to 1 or equivalently, the second virial coefficient for a gas is small, the activity in eq 1 can be replaced by the pressure. For example, at 270 K and 1 bar pressure, the ideal gas density predicted for CO2 (1.9601 kg/m3) differs from the experimental value (1.9741 kg/m3) by less than 1%.16b The integrand in eq 2 is therefore small, and under these conditions, we can replace activity with the gas pressure p with an accuracy of about 1%. Moreover, partial pressures encountered in CO2 -capture applications in the ZIFs will be lower than 1 atm; therefore, nonideal effects for this gas can be neglected. The Monte Carlo routine was set up with equal probabilities for the processes of guest displacement, insertion, and annihilation. The acceptance criterion of a guest displacement from an initial configuration sN to a configuration generated by the MC move s′N for a framework with N guests is,15

accept(s f s') ) min{1, exp(-β[U(s'N) - U(sN)])}

(3)

where U(sN) is the total potential energy of the system. Guest molecules were inserted at all positions in the simulation cell with equal probability. The acceptance probability for guest insertion is,

accept(N f N + 1) ) pVsimulation min 1, exp(-β[U(N + 1) - U(N)]) (N + 1)kT

{

}

(4)

where Vsimulation is the volume of the simulation cell of the solid ZIF system. Similarly, the acceptance probability for guest removal from the solid ZIF phase is given by,

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accept(N f N - 1) ) NkT min 1, exp(-β[U(N - 1) - U(N)]) pVsimulation

{

}

(5)

Rather than developing a new code to calculate the potential energy U(sN) of the periodic system, we have written scripts which produce input files for the ZIF-guest systems consistent with the format of the DL_POLY17 MD code. Each GCMC generated configuration is sent to DL_POLY for a single time step NVE ensemble calculation to evaluate the potential energy of the system. The details of the DL_POLY setup are similar to those described below for the MD simulations. At each external gas pressure, p, a total of 107 Monte Carlo accepted steps were used to generate the average number of CO2/CO guest molecules per simulation cell, 〈N(T,p)〉. In addition to the total number of guest molecules in the simulation cell, the partitioning of the guests among the pores or channels of the ZIF structures was determined. To determine binding energies of guest molecules in pore and channel sites, separate canonical constant volume-temperature NVT MD simulations were performed with the Nose´-Hoover thermostat algorithm18 on the periodic 2 × 2 × 2 replica of the ZIF unit cell. The DL_POLY MD program version 2.1817 was used for these simulations as well. Different numbers of CO2 and CO guest molecules were placed in the pores and channels of the frozen ZIF 68 and 69 frameworks to analyze the binding sites and binding energies of the guests. In the MD simulations, the equations of motion for the guest motions were integrated with a time step of 0.5 fs by using the Verlet leapfrog algorithm and a thermostat relaxation time of 0.1 ps. For all calculations, the total simulation time was 200 ps with the first 50 ps used for temperature-scaled equilibration. This simulation time was found to be sufficient for obtaining converged simulation energies. Long-range electrostatic interactions were calculated by using the Ewald summation method15,19 with a precision of 1 × 10-6, and all intermolecular interactions in the simulation box were calculated within a cutoff distance of Rcutoff ) 10.0 Å. For calculations of the guest mean-square displacement in the ZIF lattice, 1500 ps NVE simulations were performed on the previously equilibrated configurations from NVT simulations. All simulations were performed at 273 K. 3. Results and Discussions GCMC simulations are performed to calculate adsorption isotherms of CO2 and CO in ZIFs 68 and 69 in the pressure range of 0-1 atm at 273 K. The calculated isotherms are shown in Figure 2 along with experimental values.10 The agreement between the experimental results for the CO2 isotherm, the calculations of Liu et al.,13 and the present work is very good. Gas isotherms in MOFs should, however, be considered with some care, because there are many cases where the experimental gas capacity of the MOF depends on the method of pretreatment of the solid phase.20 Furthermore, using the same protocol for the force field of CO as what was used for CO2 gives rise to overestimation of the predicted adsorptions isotherms for CO in ZIF 69 when compared to experiments. In agreement with experimental results, the adsorption of CO2 in both ZIFs is computed to be much higher than that of CO. Spatial probability distributions of CO2 and CO in the ZIF 68 simulation cell from GCMC simulations at 273 K and 1 atm are shown in Figure 3. The density of the points in the framework is proportional to the probability of having guest molecules at the different positions. In ZIF 68 and 69, adsorption

Figure 2. (a) Isotherms for ZIF 68 at 273 K for CO2 and CO uptake. (b) Isotherms for ZIF 69 at 273 K for CO2 and CO uptake. Simulated results are shown as points plotted with error bars representing the standard deviation, and experimental results are plotted as solid lines. CO2 in blue, CO in red.

is observed in both pores and channels. The inhomogeneous placement of the CO2 molecules in the unit cell shows that the guest molecules associate with specific adsorption sites and are not distributed randomly in the free available pore or channel space. This is a characteristic of low-adsorption pressure conditions of the study. Close-ups of the distribution of the CO2 guests in a single hexagonal ZIF 68 pore are shown in Figure 4a where the view is looking down the c-direction of the unit cell. A careful analysis of the distribution of the guests in the pores shows that there are two different adsorption sites present in a 3:6 ratio. These are shown by the dashed and full ellipses in Figure 4a. In Figure 4b, we see three adsorption sites which lie in the equatorial region of the pores, between pairs of nIM molecules (dashed ellipses of Figure 4a). The CO2 molecules bound to these sites are aligned radially toward the center of the pore in the xy-plane. As seen in Figure 4b, these radial sites are staggered by 60° with respect to the radial binding sites (not circled) of the neighboring pores above and below it. The pores have two symmetry-distinct sites for the bIM molecules in their structure. The first group of bIM molecules lies in the pore equatorial plane and is aligned parallel to the c-direction of the unit cell. The second group of bIM molecules which cap the pore is aligned closer to the ab-plane and forms

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Figure 3. (a) Probability distribution for CO2 molecules in the ZIF 68 simulation cell at 1 atm pressure. Adsorption in both pores and channels is seen. There is a low probability for CO2 molecules in the center of the large pores. The probabilities represent accepted CO2 positions over 10 million attempted Monte Carlo trial steps. (b) Probability distribution for CO molecules in the ZIF 68 simulation cell at 1 atm pressure.

the pore aperture. These latter bIM molecules are seen distinctly in Figure 4b. The oxygen atoms of CO2 molecules bound to the pore-capping bIM molecules are aligned out of the ab-plane, pointing toward the benzene rings. There are six such adsorption sites adjacent to the benzene rings of the bIM molecules (full ellipses in Figure 4a,c). At the pressures simulated in this study, there is a notable absence of CO2 guests in the central region of the pores. The CO2 molecules in the pore centers would interact weakly with the framework while suffering a large entropy penalty from being trapped in the small pore volume as compared to free gas phase CO2 molecules. Therefore, at the low pressures studied, free CO2 molecules in the centers of the guest pore are relatively rare. The spatial probability distributions of the CO2 molecules in the channels are shown in Figure 5. The distribution of the CO2 molecules viewed looking down the c-axis has a three-fold symmetry (Figure 5a). In a unit cell, there are two distinct segments to the ZIF 68 or 69 channels which can be seen clearly in Figure 5b. One segment is lined with three nIM molecules and can hold up to two CO2 molecules. The guest molecules in this region are primarily aligned parallel to the c-direction (shown in dashed ellipses in Figure 5b). The other channel segments are lined with bIM molecules and hold up to six CO2 molecules, with the oxygen atoms of CO2 pointing toward the benzene rings. The guest molecules in these latter segments have considerable translational mobility and readily exchange between

Sirjoosingh et al. binding sites. Snapshots of individual CO2 molecules in the channels are shown in the Supporting Information. In both pore and channel sites, there is a strong association of the CO2 molecules with the benzene rings. This suggests the importance of organic π-functionality in the CO2 adsorption capacity of the ZIF structures.10,12 The adsorption isotherms for CO2 in ZIF 69 are shown in Figure 2. The spatial probability distribution for CO2 guest molecules in the ZIF 69 simulation cell is similar to that shown in Figure 3. Despite the large differences in aperture and pore size between ZIF 68 and ZIF 69, they remain chemically similar (differing only in the Cl functional groups in ZIF 69), and the adsorption isotherms and guest distributions of CO2 in these materials are relatively similar. Therefore, it is apparent that in the low pressure regime with small guest molecules, the chemical functionality in the ZIF plays a more important role in gas adsorption than the aspects of the framework topology. The adsorption isotherms for CO in ZIF 68 and ZIF 69 are shown in Figure 2. The equilibrium adsorption of CO is substantially less than that of CO2, and the isotherm needs much larger pressures to show signs of plateauing. The spatialprobability-distribution plot for the CO molecules in ZIF 68 is shown in Figure 3b. The adsorption sites for CO are not as well defined as those of the CO2 adsorption sites. The radial adsorption sites in the pores (see Figure 4a) are occupied with CO guests. Similarly, the segments of the channels lined with nIM molecules are occupied with CO guests, but the segments lined with bIM molecules are not. The total uptake of CO2 and CO guest molecules in ZIF 68 and 69 at different pressures are given in Table 1. The ratio of guests in the pores and channels, nP/nC, at selected pressures are given in Table 2. Each unit cell is composed of two pores and two channels. By combining the total number of molecules in the unit cell and the ratio of the pore-to-channel occupancies, the average occupancy numbers of the pores, nP, and channels, nC, are calculated and given in Table 2. Although the overall adsorption per unit cell, 2(nP + nC), is about the same in ZIF 68 and 69, the ZIF 68 framework shows similar CO2 adsorption in the pores and channels, whereas ZIF 69 has a higher adsorption in the pores and a smaller adsorption in the channels. The smaller channel occupancies in ZIF 69 are expected because the larger van der Waals radii of the Cl molecules may hinder the accommodation of the CO2 molecules. In the pores, the enhanced van der Waals attraction of the Cl atoms and their stronger electrostatic interactions in ZIF 69 increase the occupancies of CO2 in the pores. To further analyze the binding of the guests in the ZIF frameworks, we performed NVT MD simulations on ZIF 68 and ZIF 69 at 273 K with set numbers of CO2 or CO guest molecules in the large pores or channels. The total energies of the systems were used to determine the binding energies of guests at the different ZIF 68 and 69 sites. In the first set of simulations, we placed from one to nine CO2 molecules in the pores of the ZIF 68 and 69 phases. The incorporation of the n gas-phase guests X in the ZIF framework is shown as,

ZIF(s) + nX(g) f ZIF[nX](s)

(6)

The binding energy for the ZIFs with nCO2 or nCO molecules per unit cell is defined as,

Ebinding ) E(ZIF + guests)-E(ZIF)-nE(guests)

(7)

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Figure 4. (a) Adsorption sites for CO2 in the ZIF 68 pores at 273 K and 1 atm. The view looks downward along the c-axis of the unit cell. The radial sites are shown with the dashed ellipses, and each pair of tilted sites are shown by the solid ellipses. (b) Ideal radial adsorption sites adjacent to the equatorial linkers in two overlying neighbor ZIF 68 pores. The three radial sites in the top pore are shown with dashed circles, and the sites of the pore underneath it are not circled. (c) Details of the adsorption sites of CO2 in the ZIF 68 pores viewed perpendicular to the c-axis. The CO2 radial sites are shown with dashed circles, and the tilted sites are shown with full circles.

The average binding energies as a function of the number of guest molecules per pore and channel of the ZIF structure are plotted in Figures 6 and 7, respectively. In the pores (Figure 6), the binding energies of CO2 (full lines) are stronger than those of CO (dashed lines), regardless of the guest population in the pores. For the CO2 molecules in the ZIF 68 pores, the binding energy is relatively constant up to occupancies of nine per pore. In ZIF 69, the magnitudes of the binding energies are lower than those of CO2 in ZIF 68 and decrease after occupancies of six CO2 molecules per pore. The relative binding energy of CO2 in the two ZIF phases may partially explain the observations from Table 2 that ZIF 69 holds a larger fraction of the CO2 guests in the pores when compared to ZIF 68. As seen in Figure 7, the binding of CO2 guests in the ZIF 68 channels is stronger than that in the ZIF 69 channels. This can be a factor determining the smaller uptake of CO2 in the ZIF 69 channels compared to that in ZIF 68 channels. Furthermore, the binding energies of CO2 in the channels are smaller than the pores for both ZIF 68 and ZIF 69. This is also a factor in the smaller uptake of CO2 guests in the channels compared to the pores (see Table 2). The different binding energies associated with the pores and channels indicate that adsorption involves multiple binding sites. It is thus expected that the CO2 adsorption isotherm in the ZIFs will not obey the simple Langmuir isotherm. Consistent with this observation, the experimental adsorption isotherms of this guest have been fit to Toth isotherm and virial expansion forms.10

In the MD simulations with frozen framework structures, CO2 and CO guest molecules in ZIF 68 and 69 do not interdiffuse between pores and channels. A typical trace of the center of mass of a CO2 molecule in a ZIF 68 pore with single occupancy during a MD simulation is shown in Figure 8. At this low occupancy, guest molecules diffuse with a hopping mechanism. The guests do not move freely in the ZIF framework but rather spend most of the time at adsorption sites, as might be expected. After an average lifetime, thermal motions lead to the release of the guest and its motion to another adsorption site. This is clearly seen in the view along the c-direction of Figure 8a. Furthermore, as seen in the view parallel to the c-direction shown in Figure 8b and sampling of other guest trajectories and mean square displacement curves (see below), the guests at single pore occupancy do not diffuse between neighboring pores. The diffusion between pores is not observed, even though the aperture radius between pores is large enough to allow diffusion. The diffusion trace for a single CO2 molecule in the case where the occupancy of the pores is six is shown in Figure 8c,d. We can see that the motion of the CO2 molecule inside the pore is limited to fewer binding sites because some of the binding sites will be occupied by other CO2 guests in the same pore, and furthermore, the guest spends more time in the central pore region. This can be due to collisions with other guests and lead to diffusion of the CO2 molecules between pores. This is reflected in the larger mean-square-displacement (MSD) values for the guests in the higher-occupancy cases (see below).

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Figure 6. Binding energies of CO2 (full symbols) and CO (open symbols) guests in the pores of ZIF 68 (black) and ZIF 69 (red) framework materials. The top graph shows the total binding energy per unit cell (consisting of two pores), and the bottom graph is the binding energy per guest molecule.

Figure 5. Two views of the probability distributions of the CO2 molecules in the ZIF 68 channels. (a) As seen looking down from the unit cell c-axis, the distribution of the guest molecules has a three-fold symmetry. (b) The view parallel to the ab-plane shows that the channels have different fragments lined with nIM groups (shown with dashed ellipses) and lined with bIM groups. The distribution of the CO2 guests in these fragments is not similar.

TABLE 1: Uptake in Terms of Molecules Per Unit Cell (Along with Standard Deviation) Of CO2 and CO Guests in ZIF 68 and ZIF 69 at 273 K and Different Pressures (mmHg) pressure

CO2/ZIF 68

CO2/ZIF 69

CO/ZIF 68

CO/ZIF 69

0 38 76 114 152 190 380 570 760

0 3.0 (0.5) 5.1 (0.7) 7.0 (0.8) 8.7 (0.9) 10.2 (0.9) 16 (1) 20 (1) 22 (1)

0 4.4 (0.6) 7.0 (0.8) 9.2 (0.8) 10.8 (0.9) 12.4 (0.9) 18 (1) 21 (1) 24 (1)

0 0.4 (0.2) 0.8 (0.3) 1.1 (0.4) 1.6 (0.4) 1.8 (0.5) 3.6 (0.6) 5.0 (0.7) 6.4 (0.8)

0 0.5 (0.2) 1.0 (0.3) 1.5 (0.4) 1.9 (0.5) 2.4 (0.5) 4.4 (0.7) 6.2 (0.8) 7.8 (0.9)

TABLE 2: Distribution of the Guests among the Pores and Channels at 273 K and Selected Pressures (mmHg) pressure

nP/nC

nP

nC

190 380 760

CO2/ZIF 68 0.878 2.4 0.993 4.0 1.056 5.6

2.7 4.0 5.3

190 380 760

CO/ZIF 68 0.802 0.4 0.776 0.8 0.8531 1.5

0.5 1.0 1.7

pressure

nP

nC

190 380 760

CO2/ZIF 69 1.905 4.1 1.844 5.8 1.679 7.5

nP/nC

2.1 3.2 4.5

190 380 760

CO/ZIF 69 1.016 0.6 1.094 1.1 1.151 2.1

0.6 1.0 1.8

Figure 8 shows the trace of a CO2 molecule in the ZIF 68 pore, and Figure 9 shows the same for a CO2 molecule in the channel. We see that the CO2 guest diffuses along bIM-lined

Figure 7. Binding energies of CO2 (full symbols) and CO (open symbols) guests in the channels of ZIF 68 (black) and ZIF 69 (red) materials. The top graph shows the total binding energy per unit cell (consisting of two channels), and the bottom graph is the binding energy per guest molecule.

binding sites in each channel and undergoes relatively fast diffusion through the nIM-lined parts of the channels. According to Figures 6 and 7, the binding energies of the guests to the pore sites are stronger than those of the channel sites. This could explain the greater mobility of the CO2 molecules parallel to the c-direction in the channels. MSD plots of the CO2 and CO guests in the pores and channels for guest loadings corresponding to Table 2 in ZIF 68 and 69 at 250 K and 1 atm pressure are shown in Figure 10. Each MSD curve is an average over three trajectories that were run for ∼2 ns. As expected, because of the large aperture of the pores, MSDs for CO2 guest molecules in the pores are considerably larger than those in the channels. The CO guests are geometrically smaller and have smaller binding energies than the CO2 guests. The CO molecules are observed to have larger MSD values than the more strongly bound CO2 guests. The MSD of the CO2 guests for different occupancies has a complex behavior. In Figure 10, we observe that the MSD for CO2 in ZIF 69 with the most probable occupancy of 8 is larger than the MSD of CO2 in ZIF 68 pores with the most probable occupancy of 6. Despite the smaller aperture size and greater

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Figure 8. Trace of the center of mass of sample CO2 molecules moving in the ZIF 68 pore over 200 ps. (a) Trace for the case of one CO2 per pore occupancy. The pore is viewed looking down the c-direction. (b) Trace for the case of one CO2 per pore occupancy. The pore is viewed looking parallel the c-direction. (c) Trace of a guest molecule for the case of six CO2 per pore occupancy. The pore is viewed looking down the c-direction. (d) Trace of a guest molecule for the case of one CO2 per pore occupancy. The pore is viewed looking parallel the c-direction.

Figure 9. Trace of the center of mass of sample CO2 molecules moving in the ZIF 68 channel over 200 ps for the case of single channel occupancy. (a) The channel is viewed looking down the c-direction. (b) The channel is viewed looking parallel the c-direction.

probability of guest-guest collisions, the higher occupancy of binding sites in the pores of ZIF 69 allows CO2 guests to move more readily among pores. A log-log plot based on the time variation of the MSD with time has been prepared to determine the diffusion coefficient for CO2 and CO in these ZIF phases. The slope of the log-log plots, however, was found to not equal 1. This could be due to the short time of the simulations or to the single file motion of

the molecules through the pore apertures and channels.14c A more thorough analysis of the MSD curves and diffusion in the ZIFs will remain for further studies. 4. Summary and Conclusions The importance of functional groups in the ZIF framework on the adsorption and retention of CO2 and CO guest molecules

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Sirjoosingh et al. of the binding mechanism for the different gases. In this work, we studied the effect of the nature of the binding sites on the gas adsorption. In upcoming work, we will study the effect of the nature of the guest molecules on adsorption and gas separation in more detail. Acknowledgment. We thank NSERC of Canada and the Canada Research Chairs Program for funding. We are also grateful to CFI, the Ontario Research Fund, and IBM Canada for providing computing resources. Supporting Information Available: Details of the classical force field for the ZIF and guest molecules, and figure of CO2 binding in ZIF 68 channels. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 10. MSD of CO2 and CO in the pores (full lines) and channels (dashed lines) of ZIF 68 and 69 at 273 K and ambient pressure. The occupancies of the guests in the pores and channels are similar to mostprobable-occupancy values given in Table 2.

has been demonstrated in these simulations. It is often stated that gas uptake by porous materials is mainly dictated by pore volume and aperture size. In the low-pressure range of the simulations, the presence of binding sites in the framework is observed to be more important than the geometric structure of the framework material in determining the uptake of guest molecules. In the cases of the ZIF 68 and 69 phases, the benzene rings of bIM and the imidazole groups of nIM functional groups determine the nature of the adsorption sites. The aromatic functional groups on the linkers are the sites of the adsorption, and only a small fraction of the guest molecules reside in the central pore space. Two groups of binding sites are observed in the ZIF 68 and 69 pores. The three radial sites are associated with the imidazolate ring of the nIM groups in the equatorial region of the pores, and the six tilted sites are associated with the benzene rings of the bIM or ClbIM groups in the pore polar regions. The channels in these two ZIF structures also have two distinct segments. The segments lined with nIM groups hold up to two guest molecules, and those lined with the bIM or ClbIM hold up to six guests. These distinct sites are determined by GCMC calculations, and their binding energies are indirectly determined. The CO2 and CO guests in the ZIF 68 and 69 pores and channels have different MSD behaviors. The MSD in each case depends strongly on the pore or channel occupancy. At low occupancies, a hopping mechanism seems to be in effect where the guest molecules jump between binding sites in the pores or channels. As the occupancy of the pores increases, the likelihood of encountering free binding sites decreases, and a diffusing molecule moves longer distances before reattaching to the lattice. This leads to an increase in the MSD at higher occupancies. In designing porous materials for specific gas storage or separation applications, it is important to understand the nature

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