PIM Mixed-Matrix Membranes

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

An Atomistic Simulation Study on POC/PIM Mixed-Matrix Membranes for Gas Separation Xian Kong, and Jie Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03318 • Publication Date (Web): 30 May 2019 Downloaded from http://pubs.acs.org on May 30, 2019

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The Journal of Physical Chemistry

An Atomistic Simulation Study on POC/PIM Mixed-matrix Membranes For Gas Separation Xian Kong1,*, Jie Liu2,3 1Department

of Chemical Engineering, Stanford University, Stanford, California 94305, United States

2Department

of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore

3Key

Laboratory for Green Chemical Process of Ministry of Education, School of Chemical Engineering and

Pharmacy, Wuhan Institute of Technology, Wuhan 430073, P. R. China

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 sharping 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’s 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 gas movement mechanism. The presence of CC3 crystals in MMMs can promote gas permeability with little selectivity compromise, by virtue of high gas diffusivities in CC3 crystals and high gas adsorption

*

[email protected]

1 Environment ACS Paragon Plus

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in PIM-1. In addition, perturbed packing of PIM-1 chains near 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.


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1. Introduction Gas separation is important in many industrial applications such as air purification, CO2 capture, and natural gas sweetening1-4. Among a handful of technologies for gas separation, membrane-based is often preferred because of comparatively more energy efficient, 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 membranes5. There is ongoing quests to go beyond this trade-off by developing new membranes toward higher permeability with little sacrifice in selectivity or even with enhanced selectivity. A promising strategy to tackle this trade-off is to use mixed-matrix 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 filler and the easy processability of polymer. Different MMMs have been developed using a variety of fillers such as silicalite,7-8 zeolite,9-12 zeoliticimidazolate frameworks (ZIFs),13-15 metal-organic frameworks (MOFs),16-20 graphene,21 graphene oxide, ionic liquid, inorganic nanoparticle.22 A key issue in developing MMMs is the compatibility between filler and polymer matrix.6, 23 An incompatible and unfavorable interface between them may cause interfacial voids, rigidified polymer layer, deformed filler, and eventually poor separation performance. Molecular insights into the interaction between filler and polymer matrix are invaluable for the rational design of effective MMMs. Current theoretical studies of MMMs mostly rely on Maxwell



model or its derivatives.2-3 Although they are able to correlate flux measured in experiments and to make predictions in similar systems, they only provide vague molecular level information about the interaction between 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 that whether this splinter sample can reflect the real porous structure, which extends to hundreds of nanometers. Slab model can be used to study the interface between filler and polymer matrix,28-29 but obviously, 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, ladder-type 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 assemble from discrete building blocks into 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 as well as 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


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now, Evan 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 Evan 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 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 (Fig. 1a), which can be synthesized by one-step condensation 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 (Fig. 1b) was built from ten repeated units with hydrogenterminated 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 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



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Two types of MMMs were investigated here namely the micro- and macro-mixed 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 macro-mixed MMM in our study. Two CC3 crystals, cut from CC3 crystal available in the crystallographic database,43 are used in this work. The tetrahedral CC3 crystal contains 55 CC3 molecules (Fig. 1c) and the octahedral CC3 crystal contains 83 CC3 molecules (Fig. 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 assembling process from identical molecular cage bricks.43 This self-similarity alleviates finite size effects due to the discrepancy between crystal size in simulation and in experiments.

(a)

(e)

(b)

(f)

(c)

(d)

(g)

(h)

z


1 bar

1 bar

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Figure. 1. Construction of CC3/PIM-1 MMMs. (a) A CC3 cage. (b) A PIM-1 chain. (c) A tetrahedral crystal with 55 CC3 cages. (d) An octahedral crystal with 83 CC3 cages. (e) A micromixed CC3/PIM-1 MMM. (f) A 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 z direction. One graphene sheet is put at each side of the membrane. (h) 2D MMM after compression. (a)-(f) are not to scale. (g) and (h) have the same scale. CC3/PIM-1 MMMs are built by our improved cyclic annealing process which is proposed by Colina et al. to study amorphous porous organic polymers.31 Fig. S1 schematically illustrates the construction approach for the two types of CC3/PIM-1 MMMs. For the micro-mixed one (Fig. 1e), a certain number of CC3 cages and PIM-1 chains at a given weight percentage (wt%) were mixed randomly in a simulation box with a target density of 0.6 g/cm3 (Fig. S1a). The system was then subject to equilibration. As listed in Table S1, the equilibration consisted of 7-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 step (35) 29 times, finally (7) NPT MD simulation at 300 K and 1 bar for 10000ps. It should be noted that a high pressure or temperature during the 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 supplementary information, (Fig. S2), distance restraint was thus added in step 2, 3 and 5 to prevent the distortion. After equilibration, the box size was approximately 6 nm × 6 nm × 10 nm in the x, y, and z directions depending on the wt% of CC3 cages in the MMM. For the macro-mixed MMM (Fig. 1f), one tetrahedral or octahedral crystal was first placed at the center of a simulation box with size of 20 nm × 20 nm × 20 nm, then PIM1 chains were added randomly around the crystal (Fig. S1b). There were 115 or 113 PIM-1 chains



added in each case, corresponding to 11.6 wt% or 17.8 wt% of CC3 cages. Finally, the system was subject to the compression and relaxation steps for equilibration. After equilibration, the box size was 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 crystal, 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. A 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 xy 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 (Fig. 1g). Then, a pressure of 1 bar was exerted on both graphene plates to compress the membrane, resulting in relatively flat membrane interfaces (Fig. 1h). 2.2. Constant pressure difference simulation (CPDMD) Fig. 2 illustrates the simulation setup for gas permeation through a 2D periodic membrane. The membrane 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 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.


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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 , 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 flue gas composition. Gas velocities in the feed chamber were also regenerated from 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 CPDMD is a simplified version of dual control volume grand canonical molecular dynamics (DCV-GCMD),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 (Fig. S3), we used it to describe the equation of state of gas in feed and permeate chambers, which would speed up the simulation compared with DCVGCMD.

z adding gas

removing gas

permeate

feed

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



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 LJ 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. 3. Results and Discussions First, we explore factors that can influence the CPDMD using pure PIM-1 membranes. Next, the structural characteristics, permeability and selectivity of CO2/CH4 mixture through the microand macro-mixed MMMs are presented. 3.1. Gas permeation from CPDMD Fig. 3 shows the numbers of CO2 and N2 molecules sorbed in a 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  used was 200 ps. There are several interesting observations: (1) In the early stage, gas molecules start to be sorbed into the membrane and the number of 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. (2) Gas permeation appears to occur at


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about 14 ns, prior to the saturation of CO2 sorption; as a consequence, the number of permeated CO2 molecules in the next several ns is fewer than N2 because N2 has reached saturation in the membrane. (3) 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. (4) 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

Pi 

( N i / N 0 )l A t p i

(1)

where N0 is the Avogadro constant (6.022 × 10²³), l and A are the membrane thickness and area, pi is partial pressure in the feed side. 300

sorbed CO2 permeated CO2 sorbed N2 permeated N2

200

N

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


100

0

0

10

20

30

t (ns)

40

50

60

Fig. 3. Numbers of CO2 and N2 molecules sorbed in and permeated through PIM-1 membrane versus time for CO2/N2 mixture at total pressure pt = 7.2 bar ( = 200 ps). Apparently, the adding/removing gas interval  is a parameter playing an important role in the constant pressure difference MD simulation. To examine its sensitivity, Fig. 4 shows the numbers



sorbed of sorbed CO2 ( N CO ) in the PIM-1 membrane by varying  from 50 to 250 ps. When  = 50 ps, 2

sorbed the maximal N CO is slightly over 100 and the saturation is indeed not achieved even after 60 ns. 2

The reason is that the adding/removing is too frequent, gas molecules in the feed have insufficient sorbed time to move toward the membrane to be sorbed. With increasing  to 80 and 100 ps, N CO 2

sorbed continues to increase. Further increasing  to 150, 200 and 250 ps, no obvious change in N CO 2

is observed. Therefore,  ≥ 150 ps is required for sorption to approach saturation. In the results discussed below,  is equal to 200 ps. 300

2

sorbed

200

NCO

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

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100

0

50 ps 80 ps 100 ps

0

10

20

30

t (ns)

150 ps 200 ps 250 ps

40

50

60

Fig. 4. Numbers of CO2 molecules sorbed in PIM-1 membrane at different time frequencies. pt = 7.2 bar for CO2/N2 mixture. 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 (1) membrane thickness and (2) position restraint force constant. We studied two PIM-1 membranes with different thickness (6 and 10 nm). The 6 nm membrane predicts twice higher gas permeability than the 10 nm membrane (Fig. S4a). Thickness-dependent permeability is also found experimentally, probably due to factors such as chain movement, interfacial effects, gas


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plasticization effects, etc. 47-48 More discussions can be found in the SI text. Position restraint on the membrane was applied to prevent membrane drift. This is achieved by imposing an external potential Vpr = ½ kpr(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. Fig. S4b shows that gas permeability decreases with increasing force constant. As an amorphous membrane, PIM1 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 constant (Fig. S5). Six PIM-1 membranes were built and simulated at constant pressure difference. CO2 permeability through the PIM-1 membrane was predicted to be 15557.5±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 non-trivial, either experimentally or theoretically (see Table S2 for comparison with available data from 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. Micro-mixed MMMs A series of micro-mixed POC/PIM-1 MMMs with varying wt% of CC3 were simulated. For each MMM, six different initial configurations were generated and all the results were averaged



over the six configurations. Fig. 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) kg/m3 and (818 ± 6) kg/m3, respectively, which are consistent with 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 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 Fig. 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 6-9 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 (Fig. 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 Fig. 5c. With increasing CC3 wt%, the interconnected free volume rises whereas the disconnected counterpart reduces, consistent with the decrease of membrane density with increasing CC3 wt%.


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1050

(a)

Density (kg/m3)

1000 950 900 850

AC3

(b)

0% 6.9% 14.8% 24.1% 35.0% 48.1%

0.2

0.1

AC3

800

0.0 0

25

50

0

100

wt% CC3

0.15

AC3

25000

4

6

8

10

12

14

16

d (Å)

(d)

AC3

20000 15000

2

PCO (barrer)

Interconnected Disconnected

0.10

2

30000

(c) Void volume (cm3/g)

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


Void size distribution

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0.05

10000 5000

0.00 0

25

50

100

0

0

wt% CC3

25

50

100

wt% CC3

Fig. 5. (a) Densities (b) void size distributions (c) free volumes (d) CO2 permeability in POC/PIM1 MMMs versus CC3 wt% at pt = 7.2 bar. AC3 means amorphous CC3 membrane. Error bars are standard deviations from 6 different assembly models in (a), (c), (d). The error bars in (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 6 configurations, i.e., averaged over 60 frames. Fig. 5d shows CO2 permeabilities in the MMMs versus CC3 wt%, as well as in pristine PIM1 and AC3 membranes. Apparently, the permeability in AC3 membrane is higher than in 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 micro-mixed 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 of permeability in the micro-mixed 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 micro-mixed MMMs and PIM-1 membrane. These findings suggest that in a MMM of CC3/PIM-1, no performance improvement should be expected to result from introducing discrete CC3 cages. Table 1. Summary of selectivity and diffusivity Diffusivityd (10-9 m2/s) CO2 N2 PIM-1 6.2 0.12 ± 0.06 0.27 ± 0.12 a Pristine AC3 18.1 0.61 ± 0.23 1.35 ± 0.27 CC3 25.2 1.60 ± 0.14 3.40 ± 0.11 6.9%-MMM 5.7 0.15 ± 0.08 0.24 ± 0.07 14.8%-MMM 6.8 0.14 ± 0.07 0.24 ± 0.13 6.2 0.13 ± 0.06 0.25 ± 0.14 Micro-mixed 24.1%-MMM 35%-MMM 6.5 0.12 ± 0.06 0.26 ± 0.13 48.1%-MMM 6.3 0.14 ± 0.05 0.27 ± 0.12 MMM-83 10.4 Macro-mixedb MMM-55 10.1 a AC3: amorphous CC3 membrane, CC3: crystalline CC3 membrane bMMM-55 is MMM with the tetrahedral crystal and MMM-83 is MMM with the octahedral crystal. c Selectivity: P CO2/PN2 averaged over several configurations. Total feed gas pressure is ~7 bar. The errors are about ±2. d Diffusivity was estimated from 100ns 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. Membrane

Selectivityc

3.3. Macro-mixed 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


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improvement from the pristine PIM-1 membrane (2790 and 120 barrer for CO2 and N2). To get molecular insight into the macro-mixed 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. MMMs containing tetrahedral 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 obtained from average over all six cases. To exclude possible dependence on the simulation parameter, we conducted permeation simulations with two position restraint force constants of 10 and 250 kJ/(mol∙nm2) (Fig. S5). Although absolute values of results are dependent on the force constant, the trends are similar. We hence conduct our discussions based on the cases with 10 kJ/(mol∙nm2) as position restraint force constant. Gas permeability is shown in Fig. 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 feed gas pressure more significantly than PIM-1 and MMMs. This is due to relatively low gas adsorption saturation amount in CC3, as evidenced by the adsorbed gas amount (Qgas) in Fig. 6b. 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 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 Fig. 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 Fig. 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 3-D 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 threefold increase in 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 large statistical error and different crystal shapes may make this argument less evident. Gas adsorption in MMMs is comparable to PIM-1 (Fig. 6b), with no indication of saturation in studied gas pressure range. MMMs show 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 experiment, while plasticization is minimal in simulation due to position restraint.

CC3 PIM-1 MMM-83 MMM-55

60000

CO2

40000

20000

N2

0

5

10

(b) Qgas (cm3[STP] cm-3)

(a) 80000 Pgas (barrer)

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

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5 4


CO2

3 2 1 0

P (bar)

N2 5

10 P (bar)

Fig. 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 middle membrane region that is 1.5 nm from membrane surfaces. In both panels, error bars are about the size of the symbols.


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From 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’s more, the interface between CC3 crystal and PIM-1 matrix should also be important, since the interfacial region can entail a remarkable portion of the nano-composite membrane. The void size distributions (Fig. 7) reflect the CC3/PIM-1 interface with the appearance of pores with diameter of 9~13 Å since neither CC3 crystal nor PIM-1 shows pore larger than 9 Å. Pore larger than 9 Å is absent in micro-mixed MMMs (Fig. 5b). This suggests that although PIM-1 can packing tightly around single CC3 cage, it cannot pack as tightly near CC3 crystal, whose surface is molecularly flat (Fig.1 c, d). 56 Pores larger than 9 Å also appear in amorphous CC3. In spite of these relatively large pores, the selectivity of 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 macro mixed MMMs.


0.4

Void size distribution

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


0.3

interstitial cavity cage cavity

0.2 0.1 0.0

0

5

10

15

d (Å)

Fig. 7. Void size distributions in CC3, PIM-1, MMM-55, and MMM-83 membranes. The shaded regions are standard errors. 4. Conclusions



We describe a systematic methodology to study mixed-matrix membranes (MMMs) using allatom 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 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 PIM-1 matrix, no significant enhancement of gas permeability is found. Although the porosity increases slightly with increasing CC3 percentage in the micro-mixed MMMs, there is no significant change in the void size distribution and gas diffusivities are low. In contrast, for the macro-mixed MMMs, where CC3 crystals are mixed with PIM-1, remarkable gas permeability enhancement can be achieved at no selectivity sacrifice (compared to PIM-1). 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 crystal due to the loose packing of PIM-1 chains near 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.

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

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI:… Cyclic annealing procedures; construction of CC3/PIM-1 MMMs; shape persistence of CC3 during high pressure compression; comparison of reported CO2 permeability in PIM-1; 20 Environment ACS Paragon Plus

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PIM Mixed-Matrix Membranes

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