PIM Mixed-Matrix Membranes

May 30, 2019 - An MMM obtained after annealing is periodic in all three dimensions and .... qualitative trends in computed properties than on absolute...
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Cite This: J. Phys. Chem. C 2019, 123, 15113−15121

An Atomistic Simulation Study on POC/PIM Mixed-Matrix Membranes for Gas Separation Xian Kong*,† and Jie Liu‡,§ †

Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576 Singapore § Key Laboratory for Green Chemical Process of Ministry of Education, School of Chemical Engineering and Pharmacy, Wuhan Institute of Technology, Wuhan 430073, P. R. China Downloaded via BUFFALO STATE on August 6, 2019 at 09:53:22 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: Although high flux membranes are indispensable to membrane-based gas separation technologies, enhancing membrane permeability proves to be difficult due to the trade-off between permeability and gas selectivity. Mixed-matrix membrane (MMM) is a promising route to break this limitation. Nevertheless, in sharp contrast to a myriad of experimental studies, only a few simulation studies on MMMs are available. In this work, we describe a molecular dynamics simulation scheme to model MMMs, including membrane construction through cyclic annealing and gas permeation simulation through a constant pressure difference setup. MMMs based on a typical porous organic cage (CC3) and a typical polymer of intrinsic microporosity (PIM-1) are probed. It is shown that discrete CC3 molecules mixed in PIM-1 afford no permeability enhancement, as the introduction of discrete CC3 changes neither the packing structure nor the gas movement mechanism. The presence of CC3 crystals in MMMs can promote gas permeability with a minor selectivity compromise by virtue of high gas diffusivities in CC3 crystals and high gas adsorption in PIM-1. In addition, perturbed packing of PIM-1 chains near an extremely flat CC3 surface gives rise to modestly large pores in the interface, which favors gas permeation. These understandings obtained from molecular models are useful for the rational design of advanced mixed-matrix membranes.

1. INTRODUCTION Gas separation is important in many industrial applications such as air purification, CO2 capture, and natural gas sweetening.1−4 Among a handful of technologies for gas separation, membrane-based is often preferred because of comparatively more energy efficiency, low capital cost, and easy scaling-up. Moreover, membrane-based separation processes are also relatively environmentally friendly. Currently, most of the membranes used for gas separation are synthesized from polymers. Although tremendous improvements have been achieved in the last several decades, the trade-off between permeability versus selectivity still curbs the performance improvement of polymer membranes.5 There are ongoing quests to go beyond this trade-off by developing new membranes toward the higher permeability with little sacrifice in selectivity or even with enhanced selectivity. A promising strategy to tackle this trade-off is to use mixedmatrix membranes (MMMs), in which a solid porous filler is embedded into a polymer matrix.6 The filler usually contains rigid cages or pores with well-defined size and shape and exhibits high selectivity. A properly designed MMM can integrate the high selectivity of the filler and the easy processability of the polymer. Different MMMs have been developed using a variety of fillers such as silicalite,7,8 zeolite,9−12 zeolitic imidazolate frameworks (ZIFs),13−15 metal−organic frameworks (MOFs),16−20 graphene,21 graphene oxide, ionic liquid, and inorganic nanoparticles.22 A © 2019 American Chemical Society

key issue in developing MMMs is the compatibility between the filler and polymer matrix.6,23 An incompatible and unfavorable interface between them may cause interfacial voids, a rigidified polymer layer, a deformed filler, and eventually a poor separation performance. Molecular insights into the interaction between the filler and polymer matrix are invaluable for the rational design of effective MMMs. Current theoretical studies of MMMs mostly rely on the Maxwell model or its derivatives.2,3 Although they are able to correlate flux measured in experiments and make predictions in similar systems, they only provide vague molecular-level information about the interaction between the polymer and filler and its effects on gas movement. Molecular simulation is able to provide such information and has been applied to study MMMs in recent years. Nevertheless, limitations on molecular simulation still exist. A popular strategy in molecular simulation is to study gas diffusion24 or adsorption in the bulk composite; permeability can only be obtained indirectly based on the solubility−diffusivity model.25−27 In these studies, a nanoscale filler comprising only several unit cells has to be used due to computation power limitation. This inevitably incurs concern whether this splinter sample can reflect the real porous structure, which Received: April 9, 2019 Revised: May 30, 2019 Published: May 30, 2019 15113

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Figure 1. Construction of CC3/PIM-1 MMMs. (a) CC3 cage. (b) PIM-1 chain. (c) Tetrahedral crystal with 55 CC3 cages. (d) Octahedral crystal with 83 CC3 cages. (e) Micromixed CC3/PIM-1 MMM. (f) Macro-mixed CC3/PIM-1 MMM. Some of the PIM-1 chains are not shown to show the crystal. (g) 2D MMM after removing the periodic boundary condition in the z direction. One graphene sheet is put at each side of the membrane. (h) 2D MMM after compression. Panels (a)−(f) are not to scale. Panels (g) and (h) have the same scale.

densation of 1,3,5-triformylbenzene with 1,2-diaminocyclohexane. It contains a tetrahedral cage with four triangular windows and six peripheries. The PIM is chosen to be PIM-1, which can be synthesized by a polycondensation reaction from 5,5′,6,6′tetrahydroxy-3,3,3′,3′-tetramethyl-1,1′-spirobisindane.37 The PIM-1 chain (Figure 1b) was built from 10 repeated units with hydrogen-terminated ends. The optimized potentials for liquid simulations all-atom (OPLS-AA) force field38 was adopted to describe the interaction of PIM-1 chains. The disperse interaction of the CC3 cage was also described by the OPLS-AA force field, and its atomic charges were estimated using density functional theory (DFT) calculations from our recent studies on water desalination through POC membranes.39,40 These force field and charges were found to reproduce the structure and energetics of PIM-141 and POCs.42 Two types of MMMs were investigated here, namely, the micro- and macromixed MMMs, constructed by adding discrete CC3 cages and a CC3 crystal, respectively, into a PIM-1 matrix. The CC3/PIM-1 MMMs prepared in previous experiments35 belong to the macromixed MMM in our study. Two CC3 crystals, cut from the CC3 crystal available in the crystallographic database,43 are used in this work. The tetrahedral CC3 crystal contains 55 CC3 molecules (Figure 1c), and the octahedral CC3 crystal contains 83 CC3 molecules (Figure 1d). They are large enough to act as crystals while requiring relatively affordable computational resources to simulate with MD. Larger CC3 crystals will render the model inaccessible for molecular dynamics simulations. A merit of POC crystals is that they are constructed by the assembling process from identical molecular cage bricks.43 This self-similarity alleviates finite size effects due to the discrepancy between the crystal size in simulation and that in experiments. CC3/PIM-1 MMMs are built by our improved cyclic annealing process, which is proposed by Abbott and Colina, to study amorphous porous organic polymers.31 Figure S1 schematically illustrates the construction approach for the two types of CC3/PIM-1 MMMs. For the micromixed one (Figure 1e), a certain number of CC3 cages and PIM-1 chains

extends to hundreds of nanometers. A slab model can be used to study the interface between the filler and polymer matrix,28,29 but obviously, the gas transport behavior cannot be studied with this model. Last but not least, the amorphous nature of MMMs poses a further difficulty for molecular simulation to generate physically representative models.30−32 We here develop a molecular dynamics (MD) simulation scheme to investigate the gas separation performance of a kind of MMM formed by the porous organic cage in polymers of intrinsic microporosity (POC/PIM). PIM has a rigid, laddertype structure, which is unfavorable for chain packing and leads to exceptionally high free volume.33 It is believed to be a potential polymer material for more efficient gas separation.3 POC is a nascent nanoporous material34 that can be assembled from discrete building blocks into a crystal with both intrinsic cavities and extrinsic voids. The building block is actually a single organic molecule that possesses an intrinsic/permanent pore. POC/PIM MMM has been experimentally shown to have enhanced CO2 and N2 permeability and good CO2/N2 selectivity.35 To develop new POC-contained MMMs, it is helpful to examine MMMs from a microscopic scale; however, such studies are scarce. Up to now, Evans et al. reported the only theoretical/simulation study to examine the performance of a series of POC-based MMMs for the separation of H2/N2, H2/CO2, CO2/N2, and CO2/CH4; the gas permeability in the MMM was estimated using the Bruggeman’s effective medium model.36 Unlike the phenomenological model used by Evans et al.,36 we explicitly construct the fully atomistic models of the POC/PIM MMMs, characterize their microscopic structures (e.g., free volumes and distributions), and calculate gas permeability from the MD simulations closely resembling experimental permeation measurements. The key factors governing CO2 capture by the POC/PIM MMMs are identified. These bottom-up insights are useful for the development of new MMMs.

2. MODELS AND METHODS 2.1. Membrane Model. The POC in this study is CC3 (Figure 1a), which can be synthesized by one-step con15114

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was placed in the middle of the simulation box with one graphene plate fixed ∼10 nm from its surface on each side. A vacuum of 3 nm was added outside of the two graphene plates to diminish periodic images effects. A CO2/N2 mixture with composition (CO2/N2 = 0.15:0.85) representing flue gas was added on one side (i.e., feed) of the membrane, whereas the other side (i.e., permeate) was a vacuum with a length of 10 nm in the z direction. A “constant pressure difference” MD simulation was conducted with the fixed box volume. The membrane was position restrained with a force constant of 10 kJ/(mol·nm2) along the z direction to avoid membrane drift. Due to the pressure difference, gas molecules started to permeate through the membrane from the feed to permeate side; meanwhile, the pressure (which is positively proportional to number of gas molecules) dropped in the feed side and rose in the permeate side, thus reducing the pressure difference. To maintain the same pressure difference, after a certain time interval τ, the number of CO2 and N2 molecules in the feed chamber was counted, and additional gas molecules were added in the feed to keep the numbers of CO2 and N2 molecules corresponding to the flue gas composition. Gas velocities in the feed chamber were also regenerated from the Maxwell distribution at 300 K. Meanwhile, the gas molecules permeated into the permeate side was removed. The gas molecules sorbed in the membrane (which were defined as gas molecules within 0.54 nm of membrane atoms) were retained. At the steady state, the pressure in the feed side was estimated from the ideal gas law, while the pressure in the permeate side was close to zero; thus, a constant pressure difference was maintained. We note that the constant pressure difference simulation (CPDMD) is a simplified version of dual control volume grand canonical molecular dynamics (DCVGCMD),44,45 in which Monte Carlo simulations are applied to regenerate the feed and permeate chambers. As the pressure in our work is low enough to legitimate the application of ideal gas law (Figure S3), we used it to describe the equation of state of the gas in the feed and permeate chambers, which would speed up the simulation compared with DCV-GCMD. 2.3. MD Simulation. All the MD simulations were performed using the GROMACS v5.0.6 package.46 The periodic boundary conditions were applied in all the three directions. The electrostatic interactions were evaluated by the particle mesh Ewald method, whereas the Lennard-Jones interactions were truncated at 12 Å in conjunction with a switching function. The temperature was maintained by the Nosé−Hoover thermostat with a relaxation time of 0.2 ps. In the NPT step, the pressure was controlled by the Parrinello− Rahman barostat with a relaxation time of 1.0 ps. A time step of 2 fs was used in the leap-frog algorithm to integrate the equations of motion.

at a given weight percentage (wt %) were mixed randomly in a simulation box with a target density of 0.6 g/cm3 (Figure S1a). The system was then subject to equilibration. As listed in Table S1, the equilibration consisted of seven-step compression and relaxation: (1) energy minimization at 0 K with a tolerance force of 1000 kJ/(mol·nm), (2) isothermal and isobaric (NPT) MD simulation at 300 K and 3000 bar for 300 ps, (3) isothermal and isochoric (NVT) MD simulation at 800 K for 100 ps, (4) NVT MD simulation at 300 K for 100 ps, (5) NPT MD simulation at 300 K and 1000 bar for 300 ps, (6) repeat steps (3)−(5) 29 times, and finally (7) NPT MD simulation at 300 K and 1 bar for 10,000 ps. It should be noted that a high pressure or temperature during equilibration was artificially applied to accelerate the compression or relaxation; consequently, the CC3 cages might be distorted, thus reducing the internal porosity. As discussed in the Supporting Information (Figure S2), distance restraint was thus added in steps (2), (3), and (5) to prevent distortion. After equilibration, the box size was approximately 6 nm × 6 nm × 10 nm in the x, y, and z directions depending on the weight percentage of CC3 cages in the MMM, respectively. For the macromixed MMM (Figure 1f), one tetrahedral or octahedral crystal was first placed at the center of a simulation box with a size of 20 nm × 20 nm × 20 nm, and then PIM-1 chains were added randomly around the crystal (Figure S1b). There were 115 or 113 PIM-1 chains added in each case, corresponding to 11.6 or 17.8 wt % of CC3 cages, respectively. Finally, the system was subject to the compression and relaxation steps for equilibration. After equilibration, the box sizes were 10.3 nm × 10.3 nm × 10.3 nm and 10.5 nm × 10.5 nm × 10.5 nm for the MMM with the tetrahedral and octahedral crystals, respectively. For comparison, six pristine PIM-1 membranes (125 PIM-1 chains, box size is about 10 nm × 10 nm × 10 nm), one crystalline CC3 membrane39 (3 × 3 × 4 supercell containing 288 CC3 molecules, box size is 7.44 nm × 7.44 nm × 9.92 nm), and six amorphous CC3 membranes40 (400 CC3 molecules, box size is about 9.7 nm × 9.7 nm × 9.7 nm) were also built. An MMM obtained after annealing is periodic in all three dimensions and cannot be used directly for gas permeation simulation in the next section. To build a 2D periodic membrane that is only periodic in the x and y directions, the simulation box containing a 3D periodic membrane was extended along the z direction, and two impenetrable graphene plates were added on both sides of the membrane (Figure 1g). Then, a pressure of 1 bar was exerted on both graphene plates to compress the membrane, resulting in relatively flat membrane interfaces (Figure 1h). 2.2. Constant Pressure Difference MD Simulation (CPDMD). Figure 2 illustrates the simulation setup for gas permeation through a 2D periodic membrane. The membrane

3. RESULTS AND DISCUSSION First, we explore factors that can influence the CPDMD using pure PIM-1 membranes. Next, the structural characteristics, permeability, and selectivity of the CO2/CH4 mixture through the micro- and macromixed MMMs are presented. 3.1. Gas Permeation from CPDMD. Figure 3 shows the numbers of CO2 and N2 molecules sorbed in the PIM-1 membrane with a thickness of about 10 nm as well as the numbers permeated through the membrane. The adding/ removing gas time interval τ used was 200 ps. There are several interesting observations: (i) In the early stage, gas molecules start to be sorbed into the membrane, and the number of

Figure 2. Simulation setup for gas permeation. Red arrows represent adding and removing gas molecules to maintain a constant pressure difference across the membrane. 15115

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Apparently, the adding/removing gas interval τ is a parameter playing an important role in the constant pressure difference MD simulation. To examine its sensitivity, Figure 4

Figure 3. Numbers of CO2 and N2 molecules sorbed in and permeated through the PIM-1 membrane versus time for the CO2/N2 mixture at the total pressure pt = 7.2 bar (τ = 200 ps). Figure 4. Numbers of CO2 molecules sorbed in the PIM-1 membrane at different time frequencies. pt = 7.2 bar for the CO2/N2 mixture.

sorbed molecules continues to increase. While N2 sorption is rapidly saturated (about 60 molecules) after 4 ns, it takes approximately 42 ns for CO2 to reach saturation (about 280 molecules). The faster initial adsorption of N2 is due to its higher diffusivity in PIM-1 (Table 1) and higher molar fraction in the feed gas. Apparently, CO2 is more preferentially sorbed than N2 in the membrane due to the favorable interaction between CO2 and the membrane. (ii) Gas permeation appears to occur at about 14 ns prior to the saturation of CO2 sorption; as a consequence, the number of permeated CO2 molecules in the next several nanoseconds is fewer than N2 because N2 has reached saturation in the membrane. (iii) With increasing time, more CO2 molecules are sorbed in the membrane; meanwhile, more CO2 and N2 molecules are permeated through the membrane. At 42 ns, when CO2 sorption approaches saturation, the number of permeated CO2 molecules is greater than N2. (iv) Further extending the simulation, a steady state is achieved with CO2 and N2 molecules sorbed in the membrane remain nearly constant. From the Ni−t slope for permeated gas i, the permeability Pi can be estimated as Pi =

(Ni /N0)l AΔtpi

shows the numbers of sorbed CO2 (Nsorbed CO2 ) in the PIM-1 membrane by varying τ from 50 to 250 ps. When τ = 50 ps, the maximal Nsorbed is slightly over 100, and the saturation is CO2 indeed not achieved even after 60 ns. The reason is that adding/removing is too frequent and gas molecules in the feed have an insufficient time to move toward the membrane to be sorbed. With increasing τ to 80 and 100 ps, Nsorbed CO2 continues to increase. Further increasing τ to 150, 200, and 250 ps, no obvious change in Nsorbed CO2 is observed. Therefore, τ ≥ 150 ps is required for sorption to reach saturation. In the results discussed below, τ is equal to 200 ps. In addition to the adding/removing frequency, we also found that gas permeation is sensitive to the model and simulation parameters. To get in-depth insights, we examined two key factors: (i) membrane thickness and (ii) position restraint force constant. We studied two PIM-1 membranes with different thicknesses (6 and 10 nm). The 6 nm membrane predicts twice higher gas permeability than the 10 nm membrane (Figure S4a). The thickness-dependent permeability is also found experimentally, probably due to factors such as chain movement, interfacial effects, gas plasticization effects, etc.47,48 More discussions can be found in the Supporting Information. Position restraint on the membrane

(1)

where N0 is the Avogadro’s constant (6.022 × 10 ), l and A are the membrane thickness and area, respectively, and pi is the partial pressure in the feed side. 23

Table 1. Summary of Selectivity and Diffusivity diffusivitya (10−9 m2/s) membrane pristinec

micromixed

macromixedd

selectivity PIM-1 AC3 CC3 6.9%-MMM 14.8%-MMM 48.1%-MMM 35%-MMM 48.1%-MMM MMM-83 MMM-55

6.2 18.1 25.2 5.7 6.8 6.2 6.5 6.3 10.4 10.1

b

CO2 0.12 0.61 1.60 0.15 0.14 0.13 0.12 0.14

± ± ± ± ± ± ± ±

0.06 0.23 0.14 0.08 0.07 0.06 0.06 0.05

N2 0.27 1.35 3.40 0.24 0.24 0.25 0.26 0.27

± ± ± ± ± ± ± ±

0.12 0.27 0.11 0.07 0.13 0.14 0.13 0.12

a

Diffusivity was estimated from 100 ns MD simulation for a single gas molecule in a bulk membrane. Macro-MMMs have two different regions, rendering this single molecule estimation incapable to reflect gas diffusion in different regions. Therefore, no diffusivity is shown for macro-MMMs. b Selectivity: PCO2/PN2 averaged over several configurations. Total feed gas pressure is ∼7 bar. The errors are about ±2. cAC3, amorphous CC3 membrane; CC3, crystalline CC3 membrane dMMM-55 is MMM with the tetrahedral crystal, and MMM-83 is MMM with the octahedral crystal. 15116

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Figure 5. (a) Densities, (b) void size distributions, (c) free volumes, (d) and CO2 permeabilities in POC/PIM-1 MMMs versus CC3 wt % at pt = 7.2 bar. AC3 represents the amorphous CC3 membrane. Error bars are standard deviations from six different assembly models in panels (a), (c), and (d). The error bars in panel (b) are indicated by the shaded region, in which each data point was based on 10 frames in the last 1 ns for each of the six configurations, that is, averaged over 60 frames.

each MMM, six different initial configurations were generated, and all the results were averaged over the six configurations. Figure 5a presents the densities in the MMMs versus CC3 wt %. The simulated densities of the pristine PIM-1 and amorphous CC3 (AC3) membranes are (976±28) and (818 ± 6) kg/m3, respectively, which are consistent with the reported values.30,49−53 With increasing CC3 wt % and hence more porous CC3 cages present in the membrane, the density gradually drops. Void size distribution was calculated to characterize pore structures in the membranes. To obtain void size distribution, the box of the 3D periodic membrane was divided into fine grids. At a given grid, the void size was determined as the diameter of maximum cavity that enclosed the grid and had no overlap with any membrane atom. The criteria of judging overlap took into account the size of the membrane atoms. The void size distributions in Figure 5b also show an evolution from the pristine PIM-1 to AC3 membrane with increasing CC3 wt %, most notably in the void size below 4 Å and between 6 and 9 Å. However, there exist large pores >9 Å in the AC3 membrane, which are not seen in the pristine PIM-1 and the MMMs. The large pores in the AC3 membrane are not the internal CC3 cages with a diameter of 4.9 Å54,55 (Figure 7); instead, they are the interstitial voids among CC3 cages. In the AC3 membrane, due to the shape persistence of CC3 cages, molecular packing is not efficient and leads to the formation of the pores >9 Å. Nevertheless, these pores are absent in the MMMs with the presence of PIM-1. This is because the PIM-1 chains are relatively softer and more flexible than CC3, thus filling the interstitial voids among CC3 cages. The free volumes in the MMMs are plotted in Figure 5c. With increasing CC3 wt %, the interconnected free volume rises,

was applied to prevent membrane drift. This is achieved by imposing an external potential Vpr = 1/2kpr(zi − zi0),2 where kpr is the force constant, zi is the actual z coordinate of heavy atom i in the membrane, and zi0 is the targeted (or initial) z coordinate of atom i. Figure S4b shows that gas permeability decreases with increasing force constant. As an amorphous membrane, PIM-1 needs to be flexible to allow gas permeation, since the gas moves in transient pores.6 With larger force constant, the membrane becomes less flexible, leading to a reduction in the gas permeation. To exclude artificial trends introduced by the position restraint, we used two different force constants for the main simulation studies. It turns out that the trend in the membrane properties persists with different position restraint force constants (Figure S5). Six PIM-1 membranes were built and simulated at a constant pressure difference. CO2 permeability through the PIM-1 membrane was predicted to be 15,557.5 ± 2045 barrer at pt = 7.2 bar. This is located in the wide range of experimentally measured data. It is known that accurate and repeatable determination of gas permeability through amorphous membranes is nontrivial either experimentally or theoretically (see Table S2 for comparison with available data from the literature). The large error bar is an intrinsic character of amorphous materials, which has been found in other amorphous systems.30,49 Based on the above discussions, quantitative comparison of simulation results is not straightforward and should be careful. Therefore, in the following, we focus our discussions more on the qualitative trends in computed properties than on absolute values. 3.2. Micromixed MMMs. A series of micromixed POC/ PIM-1 MMMs with varying wt % of CC3 were simulated. For 15117

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Figure 6. Performance of different membranes. (a) Gas permeability and (b) steady-state gas adsorption amount versus total feed gas pressure. Gas adsorption is calculated for the middle membrane region that is 1.5 nm from membrane surfaces. In both panels, error bars are about the size of the symbols.

hence conduct our discussions based on the cases with 10 kJ/ (mol·nm2) as the position restraint force constant. Gas permeability is shown in Figure 6a. For comparison, gas permeabilities through the crystalline CC3 membrane (CC3) and pristine PIM-1 membrane are also shown. Gas permeability in CC3 depends on the feed gas pressure more significantly than PIM-1 and MMMs. This is due to the relatively low gas adsorption saturation amount in CC3, as evidenced by the adsorbed gas amount (Qgas) in Figure 6b. The adsorption amount in CC3 shows saturation at 7.5 bar. According to the solubility−diffusivity relation, gas permeability is related to gas diffusivity (D) and apparent solubility (S), Pgas ∝ S·D. S is proportional to the equilibrium adsorption over gas pressure, S ∝ A/P. Below saturation, increasing P usually leads to the increase in A proportionally (see the gas adsorption amount vs feed gas pressure for PIM-1 and MMMs in Figure 6b), leaving S relatively constant. Once gas adsorption is saturated, A cannot increase with increasing P (see the gas adsorption amount vs feed gas pressure for CC3 in Figure 6b); thus, S decreases versus increasing pressure, so as gas permeability. Nevertheless, gas permeability in CC3 is still higher than either PIM-1 or MMMs. This is benefited from fast gas diffusion in CC3, as gas diffusivity in CC3 is nearly one order of magnitude higher than in PIM-1 (Table 1). Apparently, this can be attributed to the structured tetrahedral 3D channel network in CC3.43,54 Both macro-MMMs show elevated gas permeability than PIM-1, manifesting the synergic effects of the composite. PCO2 in both MMMs is about twice in PIM-1, approximating the 3fold increase in the experiments.35 Also in line with experimental findings, PCO2 is higher in MMMs with higher CC3 wt % (17.8 wt % in MMM-83 vs 11.6 wt % in MMM-55), despite the fact that the large statistical error and different crystal shapes may make this argument less evident. Gas adsorption in MMMs is comparable to PIM-1 (Figure 6b), with no indication of saturation in the studied gas pressure range. MMMs show a higher gas selectivity than PIM-1 (Table 1), different from experimental findings. This is probably because PIM-1 and MMM are subjected to different extent of plasticization in the experiment, while plasticization is minimal in simulation due to position restraint. From the above observations, it can be seen that the improved performance of MMMs can result from high diffusivity in CC3 and high adsorption in PIM-1. What is more, the interface between the CC3 crystal and PIM-1 matrix should also be important, since the interfacial region can entail a remarkable portion of the nanocomposite membrane. The

whereas the disconnected counterpart reduces, consistent with the decrease of membrane density with increasing CC3 wt %. Figure 5d shows CO2 permeabilities in the MMMs versus CC3 wt % and in pristine PIM-1 and AC3 membranes. Apparently, the permeability in the AC3 membrane is higher than in the PIM-1 membrane due to the higher gas diffusivity in AC3 (Table 1) caused by the presence of pores >9 Å. Gas diffusivities are similar within the allowance of error for micromixed MMMs and PIM-1. Consistently, within the statistical uncertainty, there is no significant difference among the permeability in the MMMs and PIM-1. Ideally, with increasing CC3 in the MMMs, we may expect that the CO2 permeability increases. Due to the small difference between the permeability of PIM-1 and CC3 compared to the large variances in the data, however, we do not have a distinct increase in permeability in the micromixed MMMs. This is perhaps because gas movement in the membrane is determined not only by the interconnected free volume but also by other factors such as pore size and pore topology. Although interconnected free volume increases with increasing CC3 amount, the pore structure does not change too much, as evidenced by the void size distribution in Figure 5b. Therefore, we infer that when CC3 are mixed as discrete cages with PIM1, there is no significant enhancement in gas permeability. Consequently, gas selectivity is also similar for micromixed MMMs and PIM-1 membranes. These findings suggest that in an MMM of CC3/PIM-1, no performance improvement should be expected to result from introducing discrete CC3 cages. 3.3. Macromixed CC3/PIM-1 MMMs. It is found experimentally35 that when CC3 nanocrystals are embedded in PIM-1 (CC3 wt % = 17%), the MMM has a CO2 (N2) permeability of 9730 (540) barrer, which is a huge improvement from the pristine PIM-1 membrane (2790 and 120 barrer for CO2 and N2). To get molecular insight into the macromixed CC3/PIM-1 MMM, we study MMMs formed by CC3 crystals surrounded by PIM-1 chains. The tetrahedral crystal and octahedral crystal contain 55 and 83 CC3 molecules, respectively. MMMs containing the tetrahedral crystal or octahedral CC3 crystal have CC3 wt % of 11.6 and 17.8%, respectively. Six independent packing structures were prepared and simulated. All results were averaged over all six cases. To exclude the possible dependence on the simulation parameter, we conducted permeation simulations with two position restraint force constants of 10 and 250 kJ/(mol·nm2) (Figure S5). Although absolute values of the results are dependent on the force constant, the trends are similar. We 15118

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The Journal of Physical Chemistry C void size distributions (Figure 7) reflect the CC3/PIM-1 interface with the appearance of pores with a diameter of 9−13

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Cyclic annealing procedures, construction of CC3/PIM1 MMMs, shape persistence of CC3 during high pressure compression, comparison of reported CO2 permeability in PIM-1, validation of ideal gas law, influences of membrane thickness and position restraint force constant on CO2 permeability, and gas permeability and adsorption amount with a position restraint force constant of 250 kJ/(mol·nm2) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xian Kong: 0000-0001-5602-6347 Jie Liu: 0000-0002-5138-5348

Figure 7. Void size distributions in CC3, PIM-1, MMM-55, and MMM-83 membranes. The shaded regions are standard errors.

Notes

The authors declare no competing financial interest.

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Å since neither the CC3 crystal nor PIM-1 shows pores larger than 9 Å. Pores larger than 9 Å are absent in micromixed MMMs (Figure 5b). This suggests that although PIM-1 can pack tightly around the single CC3 cage, it cannot pack as tightly near the CC3 crystal, whose surface is molecularly flat (Figure 1c,d).56 Pores larger than 9 Å also appear in amorphous CC3. In spite of these relatively large pores, the selectivity of the AC3 membrane is still quite high among all examined membranes (Table 1). This suggests that these pores while being able to permit faster gas diffusion will not sacrifice gas selectivity significantly. This helps to improve the gas separation performance of the macromixed MMMs.

ACKNOWLEDGMENTS We gratefully acknowledge Professor Jianwen Jiang for constructive discussions. This work is funded by the National Natural Science Foundation of China (no. 21706197).

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4. CONCLUSIONS We describe a systematic methodology to study mixed-matrix membranes (MMMs) using all-atom molecular dynamics (MD) simulation. This includes constructing MMM models using cyclic annealing and examining gas separation using constant pressure difference MD (CPDMD) simulation, which mimics the experimental setup of membrane gas separation. We applied this methodology to MMMs based on a typical porous organic cage (CC3) and a typical polymer of intrinsic microporosity (PIM-1). Two types of CC3/PIM-1 MMMs are constructed. In the micromixed MMMs, where discrete CC3 molecules are dispersed in the PIM-1 matrix, no significant enhancement of gas permeability is found. Although the porosity increases slightly with increasing CC3 percentage in the micromixed MMMs, there is no significant change in the void size distribution and gas diffusivities are low. In contrast, for the macromixed MMMs, where CC3 crystals are mixed with PIM-1, remarkable gas permeability enhancement can be achieved without any selectivity sacrifice (compared to PIM1). This benefits from high gas diffusivities in CC3 crystals and high gas adsorption in PIM-1. In addition, modestly large pores appear in the interface between PIM-1 and CC3 crystals due to the loose packing of PIM-1 chains near the flat CC3 crystal surface. This also benefits gas permeation. This molecular-level understanding of MMMs is necessary for the rational design of mixed-matrix membranes.

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REFERENCES

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03318. 15119

DOI: 10.1021/acs.jpcc.9b03318 J. Phys. Chem. C 2019, 123, 15113−15121

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