Zeolitic Imidazolate Framework Membranes for Organic Solvent

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Zeolitic-Imidazolate Framework Membranes for Organic Solvent Nanofiltration: A Molecular Simulation Exploration Wan Wei, Krishna M. Gupta, JIE LIU, and Jianwen Jiang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b08364 • Publication Date (Web): 11 Sep 2018 Downloaded from http://pubs.acs.org on September 16, 2018

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ACS Applied Materials & Interfaces

ZeoliticImidazolate

Framework

Membranes

for

Organic

Solvent

Nanofiltration: A Molecular Simulation Exploration Wan Wei, Krishna M. Gupta, Jie Liu, and Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576 Singapore

Abstract: Organic solvents are intensively used in chemical and pharmaceutical industries, their separation and recovery account for a significant portion of energy consumption and capital cost in many industrial processes. In this study, three microporous crystalline zeolitic-imidazolate frameworks (ZIF-25, -71 and -96) are investigated as organic solvent nanofiltration (OSN) membranes by molecular simulations. The fluxes of five solvents (methanol, ethanol, acetone, acetonitrile and n-hexane) are predicted. Despite the smallest aperture size among the three ZIFs, ZIF-25 exhibits the highest flux for polar solvents (methanol, ethanol, acetone and acetonitrile) due to its hydrophobic nature; whereas hydrophilic ZIF-96 shows the highest flux for nonpolar nhexane. The analysis of structural information and interaction energy reveals that the solventframework interaction is crucial to determine solvent permeation. Good correlations between solvent permeances and a combination of solvent properties are found. In the presence of a model solute (paracetamol), solvent permeances are marginally affected; moreover, the rejection of paracetamol is 100% for the three ZIF membranes in all the five solvents. This study highlights that the pore chemistry, in addition to pore size, plays an important role in solvent permeation; and it suggests that ZIFs are potential OSN membranes for the recovery of organic solvents. Keywords: organic solvent nanofiltration; zeolitic-imidazolate frameworks; membranes; permeation; molecular simulation

*E-mail: [email protected]

1

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1. Introduction Separation is crucial to a wide range of important applications in chemical, pharmaceutical and food industries. The separation process alone accounts for 40−70% of capital and operating costs,1 as well as nearly 50% of total industrial energy use.2 In traditional separation technologies such as distillation and crystallization, energy-intensive phase transition is involved. By replacing these thermal-driven technologies with membrane separation, energy consumption could be reduced by up to 90%.3-5 To date, membrane-based separation has been largely focused on gaseous and aqueous mixtures. Recently, there is considerable interest in organic solvent nanofiltration (OSN) for the recovery and reuse of organic solvents.6,7 Most of the experimentally tested OSN membranes are polymeric materials. For instance, ultrathin PIM-1 membranes were observed to exhibit exceptionally fast nheptane permeation with 90% rejection for hexaphenylbenzene; the maximum permeance was two orders of magnitude higher than a commercial polyimide OSN membrane.8 Chemically crosslinked polybenzimidazole (PBI) membranes were prepared from ionic liquids and tested for various solvents; the solute rejection was found to depend on solvent and the intricate interactions among solvent, solute and membrane.9 A hydrophilic monoamine was utilized to modify polyimide membranes, which led to the formation of sponge-like pores and 170% increase in isopropanol permeance with only slight decline in dye rejection.10 To achieve high-performance OSN, a narrow distribution of pore sizes is important for the discrimination of molecules of similar size, which however is difficult to be produced in polymeric membranes. In this context, microporous crystalline materials are of enormous potential to be developed into OSN membranes. Their highly ordered pore structure would allow solvents to permeate rapidly. In the last decade, zeolitic-imidazolate frameworks (ZIFs) have become a special class of nanoporous materials.11 With tetrahedral metal clusters and imidazolate ligands, they have high chemical and thermal stability. Moreover, the pore size and functionality of ZIFs can be readily tunable by judiciously selecting imidazolate ligands; thus ZIFs have been fabricated into membranes for separation.12,13 ZIF-8 membrane was tested for the separation of gas mixtures C2H4/C2H614 and C3H6/C3H8.15-20 By synergizing both simulation and experimental techniques, ZIF-8 was explored as a reverse osmosis (RO) membrane for seawater desalination and high performance was found.21,22 A number of ZIFs (ZIF-25, -71, -93, -96 and -97) were further 2


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simulated for desalination and the highest water permeances were predicted to be one - two orders of magnitude higher than commercial RO membranes.23 The separation of alcohol/water and dimethyl carbonate/methanol was conducted by pervaporation through ZIF-71 membrane, which displayed good integrity and high permselectivity.24 Recently, different types of ZIF membranes as well as metal-organic framework (MOF) membranes have been developed for OSN. (i) The first type is thin-film nanocomposite (TFN) membranes. Notably, Livingston and coworkers produced TFN membranes containing ZIF-8, MIL-53, NH2-MIL-53 and MIL-101 nanoparticles in a polyamide thin-film layer on top of polyimide supports, then evaluated their OSN performance on the basis of methanol and tetrahydrofuran permeances and rejection of styrene oligomers.25 Zhong and coworkers modified UiO-66-NH2 nanoparticles with long alkyl chains and used them to prepare TFN membranes on polyamide; and found significant enhancement in methanol permeance without comprising tetracycline rejection.26 (ii) The second type is mixed-matrix membranes (MMMs) with fillers dispersed in a polymer phase. Basu et al. incorporated ZIF-8, MIL-47, MIL-53 and HKUST-1 in polydimethylsiloxane, applied them in the separation of Rose Bengal from iso-propanol, and found higher permeance but lower retention compared with unfilled membranes.27 From non-solvent induced phase separation, Zhu et al. produced MMMs using MIL-53 and aromatic poly(mphenyleneisophthalamide), and observed a significant increase in ethanol permeance while a slight reduction in the rejection of brilliant blue G.28 (iii) The third type is continuous membranes, which are comparatively less investigated. Li et al. prepared continuous ZIF-8 membranes on porous polyethersulfone supports and confirmed the membrane integrity by SEM, TEM and ATR-FTIR; these membranes exhibit high performance in the removal of Rose Bengal from water, ethanol and iso-propanol.29 Livingston and coworkers used interfacial synthesis to fabricate a thin layer of HKUST-1 within polyimide support and observed better OSN performance compared with HKUST-1 grown above the support.30 In this study, we report a molecular simulation study to explore three continuous ZIF membranes (ZIF-25, -71 and -96) for OSN. The three ZIFs have the same topology and similar pore size, but differ in functional groups. Therefore, the effect of ZIF functionality will be explicitly elucidated. Five organic solvents are considered including four polar (methanol, ethanol, acetonitrile and acetone) and one non-polar (n-hexane). Moreover, a model solute, paracetamol 3



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(PRM), is used to test OSN performance. Following this introduction, the atomic models of ZIFs, solvents and solute are described in Section 2. In Section 3, the solvent fluxes, permeances and permeabilities are presented; then, the interplay between solvent property and membrane chemistry is discussed; finally, the rejection of solute is examined. In Section 4, the concluding remarks are summarized, along with limitations in the simulations.

2. Models and Methods The atomic structures of three ZIFs (ZIF-25, -71 and -96) are shown in Figure 1. They share the same metal cluster (ZnN4) but with different imidazolate linkers: dimethyl imidazolate (dmeIm), dichloro imidazolate (dcIm) and cyanideamine imidazolate (cyamIm).31 Truncated cuboctahedra (-cages) exist in the structures arranged in a cubic body-centred manner. As listed in Table 1, dmeIm and dcIM contain –CH3 and –Cl, respectively, thus ZIF-25 and -71 are hydrophobic. With the presence of –NH2 and –CN in cyamIm, however, ZIF-96 is hydrophilic. A simulation study on water adsorption has confirmed this classification.32 As presented below, the hydrophobic/hydrophilic framework is crucial to solvent permeation. The pore morphologies and radii along the z-direction in the three ZIFs were analyzed by the HOLE program.33 As shown in Figure S1, there are two distinct pores present in each ZIF, which consist of alternating cage and aperture with slightly different sizes. Table 1 lists the cage and aperture diameters (dc and da). Permeation is primarily governed by da rather than dc. The da are 4.3  4.9 Å in ZIF-25, slightly smaller than 5.2  5.5 Å in ZIF-71 and 5.5 Å in ZIF-96. As discussed below, the pore size is not the only factor to govern permeation.

ZIF-25

ZIF-71

ZIF-96

Figure 1. Atomic structures of three ZIFs. Color code: ZnN4, orange; O, red; N, blue; Cl, green; C, cyan and H, white. 4


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Table 1. Characteristics of three ZIFs. ZIF-25

ZIF-71

ZIF-96

dmeIm 26.6825 15.8 4.9 16.2 4.3

dcIm 28.5539 17.4 5.5 17.0 5.2

cyamIm 28.5291 16.8 5.5 16.7 5.5

Organic linker

a = b = c (Å)31 dc (Å) Pore 1 da (Å) dc (Å) Pore 2 da (Å)

The interactions of ZIF atoms were modeled by the Lennard−Jones (LJ) and electrostatic potentials

Unonbonded

    4 ij  ij  rij 

12 6    ij   qi q j        4 0 rij   rij  

(1)

where rij is the inter-distance between atoms i and j, εij and σij are the LJ potential strength and diameter, qi is the atomic charge of atom i, and ε0 is the vacuum permittivity. Table S1 lists the atomic charges, which were estimated from density functional theory calculations on fragmental clusters (see Figure S2), as described in our previous work.32 Table S2 lists the LJ parameters adopted from the DREIDING force field.34 All the five solvents (methanol, ethanol, acetonitrile, acetone and hexane) and solute (PRM) were described by the OPLS force field.35 The physical properties of solvents and solute are listed in Table S3. Figure 2 demonstrates a simulation system for solvent permeation through a ZIF membrane. The feed and permeate chambers, each containing solvent molecules, were separated by the ZIF membrane. The graphene plates in the two chambers were under pressures pleft and pright, respectively. The carbon atoms in graphene plates were mimicked with potential parameters as used for carbon nanotubes.36 The membrane was represented by 3 × 3 × 2 unit cells in x, y, and z direction, respectively. The membrane area was calculated by 9 times the area of a unit cell on the xy plane. To examine the OSN performance, the rejection of PRM was further simulated. For this case, 0.05 M of PRM was added into the left chamber. It is worthwhile to note that we did not use common dye molecules to test solute rejection. This is because dye molecules usually have a size 5



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larger than 10 Å, and the aperture size of the three ZIFs under study is only around 5 Å. In contrast, PRM has a size comparable to the aperture size.

pleft

graphene

pright

feed

membrane

permeate

graphene

Figure 2. A simulation system for solvent permeation. The feed and permeate chambers contain solvent molecules (yellow: feed; pink: permeate). Two graphene plates are exerted under pressure pleft and pright, respectively.

Initially, the system was subjected to energy minimization by the steepest descent method with a maximum step of 0.5 Å and a force tolerance of 1000 kJ/(mol∙nm). Then, velocities were assigned according to the Maxwell−Boltzmann distribution at 300 K. Finally, molecular dynamics (MD) simulation was conducted at 300 K with pleft = 501 bar and pright = 1 bar. It should be noted that the pressure gradient applied here was about one order of magnitude higher than in practical OSN. This is common in MD simulations in order to reduce thermal noise and enhance signal/noise ratio within a nanosecond simulation timescale. For example, high pressures (up to 6000 bar) were used to simulate water permeation.37,38 The velocity-rescaling thermostat with a relaxation time of 0.1 ps was adopted to control the system temperature. The ZIF atoms were frozen during the simulations. The LJ interactions were calculated with a cutoff of 14 Å, while the electrostatic interactions were calculated by the particle-mesh Ewald method. The time step was 2 fs and the trajectory was saved every 50 ps. All the simulations were conducted using Gromacs v.5.0.6,39 and the results were analyzed using Gromacs commands and an in-house code.

3. Results and Discussion The flows and fluxes of five solvents through the three ZIF membranes are first presented, the interplay between solvent polarity and membrane functionality is comprehensively discussed, then the dynamics and structure of solvents in the membranes are revealed. Next, the correlation 6


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between solvent permeances with a combination of solvent properties is attempted. Furthermore, the predicted permeabilities are compared with literature data. Finally, the rejection of the model solute PRM is examined. 3.1. Solvent flows and fluxes Under the pressure gradient Δp, there is a net flow of solvent from the left chamber to the right. Figure 3 shows the number of solvent molecules Ns permeated through the three ZIF membranes at Δp = 500 bar. The Ns generally increases linearly with time after a certain time lag. This happens because the membrane is initially dry, thus solvent molecules need to fill in the membrane before permeating. For the same solvent, the time lag depends on the membrane. Taking methanol as an example, the time lag is the shortest in ZIF-25 and the longest in ZIF-96. On the other hand, the time lag in the same membrane varies with solvent. In ZIF-96, hexane exhibits the shortest time lag, followed by ethanol and methanol; whereas acetone and acetonitrile appear to be trapped therein with very long time lag. 1200

2500

Ethanol

Methanol 1000

2000 1500

ZIF-25

800

ZIF-71

Ns (t)

Ns (t)

ZIF-25 ZIF-96 1000

ZIF-71 600

ZIF-96

400 500

200

0

0 0

10

20

30

40

50

0

50

t (ns) 800

Acetonitrile

1500

800

Ns (t)

ZIF-96

500

ZIF-71 400

ZIF-96

0 30

t (ns)

40

50

ZIF-25 400

ZIF-71

0

0 20

ZIF-96

200

200

10

n-hexane

600

ZIF-25

600

ZIF-71

0

150

Acetone

ZIF-25

1000

100

t (ns)

Ns (t)

2000

Ns (t)

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

10

20

30

40

50

t (ns)

Figure 3. Solvent flows through three ZIFs.

7


0

10

20

30

t (ns)

40

50


15 ZIF-25 ZIF-71

Js (104 kg/m2∙h)

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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ZIF-96

10

5

0

methanol

ethanol acetonitrile acetone

n-hexane

Figure 4. Solvent fluxes through three ZIFs. From the slopes of Ns ~ t in Figure 3, solvent fluxes Js can be calculated by

Js 

 Ns / NA  M w A t

(2)

where NA is the Avogadro constant (6.022 × 1023), Mw is the molecular weight of solvent, A is the membrane cross-section area, and Δt is time duration. The Δt is from 100 to 150 ns for ethanol, and from 30 to 50 ns for other solvents. As shown in Figure 4, the four polar solvents (methanol ethanol, acetonitrile and acetone) exhibit a decreasing trend of Js through the three membranes ZIF-25 > -71 > -96. For the non-polar hexane, Js decreases as ZIF-96 > -25 > -71. As discussed earlier, ZIF-25 has the smallest da (4.3  4.9 Å) compared with ZIF-71 (5.2  5.5 Å) and ZIF-96 (5.5 Å). Apparently, the decreasing trend of Js for both polar and non-polar does not simply follow the order of da in the ZIFs. Moreover, a negligible or no flux is observed for acetonitrile through ZIF-96 and for acetone through ZIF-71 and -96. All these results reveal that there are other important factors governing Js, as elucidated below for different solvents. 3.1.1. Methanol and ethanol The Js of methanol and ethanol are inversely proportional to da. Similar phenomenon was observed in our pervious simulation of seawater desalination through ZIFs.23 Given the similar polar and hydrogen-bonding nature between alcohols and water, we postulate that methanol and ethanol would behave similarly to water: the interaction of solvent with membrane plays an

8


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important role in determining the Js. To unveil this behavior, the packing of solvent molecules in the membranes is quantified by radial distribution functions

gij  r  

N ij  r, r  r V

(3)

4 r 2r N i N j

where r is the distance between atoms i (solvent molecule) and j (framework atom), Nij(r, r + Δr) is the number of atom j around i within a shell from r to r + Δr, V is the volume of the membrane, and Ni and Nj are the numbers of atoms i and j, respectively. Figures 5 and S3 show the g(r) of methanol and ethanol around the framework atoms of ZIFs, respectively. For methanol, the first peak appears at 4.5 Å in ZIF-25 and -71, while in ZIF-96 the first peak is at around 3.0 Å and followed by a more pronounced peak at 3.9 Å. The peak intensity rises in the order of ZIF-25 < 71 < -96. Due to the similar structural and chemical properties between methanol and ethanol, it is not surprising to find that the g(r) of ethanol have similar pattern. These results are caused by different functional groups in the three ZIFs. With the nonpolar (–CH3) and weakly polar (–Cl) groups respectively, ZIF-25 and -71 are hydrophobic; however, ZIF-96 contains the polar –NH2 and –CN groups with high affinity for methanol and ethanol. Thus, we can infer from the structural analysis that the affinity for methanol and ethanol becomes stronger in the order ZIF-25 < -71 < 96. This is further confirmed by our previous adsorption study, in which the isosteric heat of ethanol was predicted to be the highest in ZIF-96 and the lowest in ZIF-25.32 Upon entering the membrane, alcohol molecules are most strongly bonded onto ZIF-96, thus resulting in the lowest flux among the three ZIFs, and vice versa for ZIF-25. 2

2

2

ZIF-71

ZIF-25 1.5

ZIF-96

1.5

1

1.5

g(r)

g(r)

g(r)

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


1

Zn1

Zn

Zn

0.5

1

0.5

C2

N2

0.5

C2

N3 C3

Cl

C4

0

0 0

0.5

1

r (nm)

1.5

2

0 0

0.5

1

1.5

r (nm)

2

0

0.5

1

r (nm)

Figure 5. g(r) of methanol around the framework atoms of three ZIFs.

9


1.5

2


It is important to point out the above discussion on the role of solvent-membrane interaction works for crystalline membranes with well-defined pores. For amorphous polymer membranes, however, the role is different. There are no regular pores in polymer membranes, solvent permeation is largely governed by the entry of solvent molecules into polymer network. For example, water can enter a hydrophilic polymer membrane more easily than a hydrophobic counterpart due to favorable interaction; thus hydrophilic polymer membranes are widely used for water desalination. Such behavior was also observed in our recent simulation study for water permeation through two amorphous carbon membranes,40 in which water permeation through the hydrophilic membrane was faster. 3.1.2. Acetonitrile As shown in Figure 3, there is no flux of acetonitrile through ZIF-96, despite larger aperture size in ZIF-96 than in ZIF-25 and -71. Figure 6a-c show the trajectories of random selected acetonitrile molecules. The acetonitrile molecules are observed to permeate through ZIF-25 and 71 membranes after residing there for a certain amount of time. The residence time in ZIF-71 is longer than in ZIF-25, which translates to a lower flux through ZIF-71. The reason is that acetonitrile possesses stronger interaction with ZIF-71, as illustrated by the g(r) in Figure 6d-e. However, after entering ZIF-96 membrane, acetonitrile molecules remain therein with almost no local motion (nearly constant z) throughout 50 ns simulation. This is attributed to the existence of –CN groups in both acetonitrile and ZIF-96, leading to strong polar interaction between them; which corresponds to the pronounced peaks around the N3 and C4 atoms of ZIF-96, as shown in Figure 6f.

10


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30

30

25

ZIF-71

b

25

20

z (nm)

z (nm)

15

15 10

10

5

5

5 0

0 0

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50

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20

30

40

0

50

2

f

ZIF-71

g(r)

g(r) Zn C2 C3

0.5

1

1.5

ZIF-96

Zn2 N2 N3 C4

2

1

C2 Cl

0

0 1

50

Zn 0.5

0 0.5

40

3

1.5

1

30

4

e

1.5

0

20

t (ns)

2

ZIF-25

d

10

t (ns)

t (ns)

g(r)

15

10

0

ZIF-96

c

25

20

20

z (nm)

30

ZIF-25

a

2

0

0.5

1

1.5

2

0

0.5

r (nm)

r (nm)

1

1.5

2

r (nm)

2500

g Energy (kJ/mol)

2000 1500 1000 ZIF-25 ZIF-71

500

ZIF-96

0 0

10

20

30

40

h

Coulombic

30

Ns

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


Lennard-Jones Total 20

10

0

50

ZIF-25

t (ns)

ZIF-71

ZIF-96

Figure 6. (a-c) Trajectories of selected acetonitrile molecules. Each membrane is between the two dashed lines. Each color represents a random selected acetonitrile molecule. (d-f) g(r) of acetonitrile around the framework atoms. (g) Number of accumulated acetonitrile molecules in the membranes. (h) Interaction energies of acetonitrile with the membranes.

Figure 6g shows the number of accumulated acetonitrile molecules in the ZIF membranes. The number becomes constant in ZIF-25 and -71 after 3 ~ 4 ns, indicating the flow reaches a steady state and there is solvent flux across the membrane; whereas in ZIF-96, the number keeps increasing throughout 50 ns simulation. A much longer simulation until 400 ns was then conducted. As shown in Figure S4, the number of acetonitrile molecules in ZIF-96 reaches 11



constant after 200 ns. Within the whole 400 ns, negligible acetonitrile molecules permeate through ZIF-96, indicating vanishingly small permeation. This phenomena can be elucidated by Figure 6f and further by Figure 6h. The interaction energy between acetonitrile and ZIF-96 is almost twice of that with ZIF-25 and -71. This distinct difference mainly comes from the significantly higher electrostatic interaction between the polar –CN groups in both acetonitrile and ZIF-96. The interaction is so strong that acetonitrile molecules are essentially trapped in ZIF-96 membrane; as a consequence, no flux is observed through ZIF-96 membrane. 3.1.3. Acetone Acetone exhibits a large flux through ZIF-25, a vanishingly small flux through ZIF-71, and no flux through ZIF-96. This seems implausible as ZIF-25 has the smallest da among the three ZIFs. From the trajectories shown in Figure S5, we can see that acetone molecules do enter all the three membranes; however, only through ZIF-25 does permeation occur. In ZIF-71 and -96, acetone molecules show almost no local motion in the z direction till the end of the simulation. This observation is again rooted at how acetone interacts with the membranes. Figure 7 shows the interaction energies of acetone with pore 1 and 2 in three membranes. The total energy is dominated by LJ contribution, like the case in Figure 6h. Due to the slight difference in radius (Figure S1), the total energies are not identical in both pores. In ZIF-25, the total energy ranges from –35 to 40 kJ/mol in pore 1, but up to 1400 kJ/mol in pore 2. This extremely high repulsive energy in pore 2 is attributed to the small da (4.3 Å), which is even smaller than the kinetic diameter of acetone (4.7 Å).41 Consequently, there is a high energy barrier for acetone to enter pore 2 and only pore 1 in ZIF-25 is accessible as illustrated by Figure S6. In ZIF-71, the pore size is larger than 4.7 Å and in principle, the interaction energy with acetone should be attractive. We do find the total energy is attractive mostly in pore 1 and largely in pore 2; however, at a few positions in pore 2 (z = 0.2, 2.8, 3.2 and 5.4 nm), the energy is repulsive. This is because both the pore size and the kinetic diameter are approximate quantities; therefore, we cannot determine the interaction by solely comparing the pore size and kinetic diameter. In ZIF-96, the total energy is always attractive in pore 1 and 2. Overall, both pores in ZIF-71 and -96 are accessible to acetone as seen from Figure S6. However, once entering ZIF-96, acetone molecules are strongly bound onto the membrane and cannot easily permeate. Consequently, no discernable flux is observed through ZIF-71- and 96 even after 400 ns (Figure S7). 12


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Pore 1

Pore 2

60 Coul LJ

40

Coul

1400

Energy (kJ/mol)

Energy (kJ/mol)

ZIF-25

Total 20 0 -20 -40

LJ Total

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Energy (kJ/mol)

Energy (kJ/mol)

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Coul LJ

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Energy (kJ/mol)

Energy (kJ/mol)

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 -20 Coul

-40

LJ

20 0 -20 Coul

-40

LJ Total

Total

-60

-60 0

1

2

3

4

5

0

6

1

2

3

z (nm)

z (nm)

Figure 7. Interaction energies of acetone with pore 1 and 2 in the ZIFs along the z direction.

13



Furthermore, the diffusion of acetone molecules in the membranes can be examined by the mean-squared displacement (MSD)

MSD  t  

1 N

N

 i 1

zi  t   zi  0 

2

(4)

where t is time, N is the number of molecules, zi(t) is the displacement of molecule i from its initial position, and  is ensemble average. Figure 8a shows the MSDs of acetone along the z direction in the three ZIF membranes. In ZIF-71 and -96, the MSD quickly reaches a plateau indicating the small mobility of acetone in the membranes. This underpins the above observation that acetone molecules are trapped in the two membranes with negligible flux. 2

2.5

(a) acetone

(b) hexane

2

1.5

MSDz (nm2)

ZIF-25

MSDz (nm2)

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

Page 14 of 23

ZIF-71

1.5

ZIF-96

1

ZIF-96 ZIF-25 ZIF-71

1

0.5

0.5 0

0 0

1000

2000

3000

4000

5000

0

t (ps)

1000

2000

3000

4000

5000

t (ps)

Figure 8. MSDs of (a) acetone and (b) hexane along the z direction in ZIF membranes. 3.1.4. Hexane Despite the long alkyl backbone, hexane has a small kinetic diameter of 4.3 Å.41 As shown in Figure 4, hexane exhibits unique permeation behavior compared with other solvents. The flux decreases as ZIF-96 > -25 > -71, which follows the trend of MSD in Figure 8b. That is, the diffusion of hexane along the z direction is the fastest in ZIF-96, then in ZIF-25 and -71. The unique feature is likely to be originated from the non-polar nature of hexane. Figure 9 plots the g(r) of hexane in the ZIFs. In contrast to polar solvents, hexane experiences weak interaction with hydrophilic ZIF-96. Given the largest aperture size of ZIF-96, hexane permeates through ZIF-96 the fastest among the three membranes. In ZIF-25 and -71, the aperture is larger than 4.3 Å and hexane can freely diffuse. Nevertheless, the pore in ZIF-25 is smaller than in ZIF-71, which prevents diverging flow and facilitates the permeation of linear hexane molecules. Thus, hexane 14


Page 15 of 23

has a higher MSD in ZIF-25 than in ZIF-71, as seen in Figure 8b. Even though the interaction of hexane with ZIF-25 is stronger than with ZIF-71, overall the flux through ZIF-25 is larger. 2

3

2

ZIF-25

ZIF-71 Zn

2

C2

1.5

C3

1.5

ZIF-96 1.5

g(r)

2.5

g(r)

g(r)

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


1

1

Zn

0.5 0 0.5

1

1.5

2

0

0.5

r (nm)

1

1.5

N2 N3

Cl

0 0

Zn2

0.5

C2

0.5

1

0 2

0

0.5

r (nm)

1

1.5

2

r (nm)

Figure 9. g(r) of hexane around the framework atoms of three ZIFs. 3.2. Solvent permeances and permeabilities The solvent permeances can be calculated by Ps = Js/Δp. Table 2 lists the permeances of five solvents through ZIF-25, -71 and -96. In the literature, experimental studies were reported to correlate solvent permeances through microporous silica membranes42 and ceramic membranes43 with solvent properties. It is recognized that permeance is not solely dependent on a single solvent property, but determined jointly by solvent size, viscosity, molecular interaction, etc. Here, we attempt to correlate the permeances with a combination of solvent properties44

Ps 

s

2 s d m,s

(5)

where δs, μs and dm,s are the solubility parameter, viscosity and diameter of solvent, respectively, as listed in Table S3. Figure 10 plots the correlations between permeances and the combination of solvent properties in ZIF-25 and -71. In ZIF-25, a fairly good correlation is found except hexane. It is not surprising that hexane does not fit into Eq. (5) well, which was also observed previously in polyacrylonitrile membrane.45 Because of the linear shape, the cross-section size of hexane is overestimated by its molecular diameter dm,s. Furthermore, only pore 1 in ZIF-25 is accessible to hexane, as visualized by a video in the Supporting Information. In ZIF-71, a good correlation is found for four solvents (excluding acetone due to its negligible permeance). Different from that in ZIF-25, hexane fits nicely in the correlation because it can enter both pore 1 and 2 in ZIF-71, thus interacting with the 15



entire pore in the membrane. From this observation, we again reiterate the important role of solvent-membrane interaction in determining permeation. Table 2. Solvent permeances (L/h/m2/bar) without and without PRM. ZIF-25

ZIF-71

ZIF-96

Solvent Pure

With PRM

Pure

With PRM

Pure

With PRM

acetonitrile

322.04

312.22

200.17

202.00

-

-

methanol

373.10

354.04

180.11

194.55

108.96

110.35

n-hexane

193.91

176.95

32.31

38.12

379.69

379.32

ethanol

85.18

84.46

20.75

19.33

8.87

10.44

acetone

202.08

194.85

-

-

-

-

250

400 methanol

ZIF-25 300

Permeance (L/h/m2/bar)

Permeance (L/h/m2/bar)

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

Page 16 of 23

acetonitrile

200

n-hexane

acetone

100 ethanol

ZIF-71

acetonitrile

200 methanol 150 100 50 ethanol

n-hexane

0

0 0

100

200

0

300

50

100

150

200

250

300

δs μs-1dm,s-2 (x 10-3)

δs μs-1dm,s-2 (x 10-3)

Figure 10. Correlations between permeances and a combination of solvent properties in ZIF-25 and -71. The solvent permeabilities can be estimated by Js/Δp (: the membrane thickness). As an intrinsic membrane property, permeability is independent of transmembrane pressure and membrane thickness. Table S4 compares the permeabilities through the ZIFs in this study with those reported in the literature. For acetonitrile, ZIF-25 and -71 have permeabilities comparable with PBI/P84 and β-CD TFC, higher than HPEI-GA/mPMIA, but lower than PA TFC activated. For methanol, ZIF-25 and -71 are superior to many other membranes, though inferior to PBI/P84, PA TFC activated and GO@nylon 6. For ethanol, the permeability through ZIF-25 is close to that through β-CD TFC, β-CD/TMC/Matrimid, p-CMP, m-CMP and o-CMP on PAN. For acetone, ZIF-25 possesses permeability higher than HPEI-GA/mPMIA, PAR-BHPF and PAR-TTSBI, but 16


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lower than PA TFC activated and S-rGO-18. Finally, for n-hexane, ZIF-96 exhibits higher permeabilities than many other membranes. 3.3. Solute rejection To examine the OSN performance of ZIF-25, -71 and -96, the rejection of PRM was simulated. All the three membranes exhibit perfect rejection of PRM in all the five solvents. In the presence of PRM, solvent permeances can be calculated by Ps = Js/(ΔP – Π), where Π is the osmotic pressure of 0.05 M solution (about 1.24 bar). As shown in Table 2, the solvent permeances are marginally varied when PRM is present. The variations are due to the thermal noise and fluctuation in simulation, as well as the approximation to estimate Π. Overall, the presence of solute has a negligible effect on solvent permeation. The ZIF membranes exhibit the capability of perfect solute rejection without compromising solvent permeances.

4. Conclusions A molecular simulation study is reported to examine solvent permeation and solute rejection through ZIF-25, -71 and -96 membranes. The fluxes decrease as ZIF-25 > -71 > -96 for polar solvents (methanol ethanol, acetonitrile and acetone), and as ZIF-96 > -25 > -71 for non-polar solvent (n-hexane). With nonpolar –CH3 groups, ZIF-25 is hydrophobic and interacts weakly with polar solvents. However, ZIF-96 tends to be hydrophilic with polar –NH2 and –CN groups, thus has weak interaction with n-hexane. Based on the radial distribution functions and interaction energies, the framework affinity for solvent is revealed to be crucial in governing solvent permeation. Due to the strong interaction with framework, acetonitrile has no flux through ZIF-96 and acetone exhibits a vanishingly small flux through ZIF-71 and -96. A phenomenological model is used to correlate solvent permeances with a combination of solvent properties, and good correlations are found. The ZIF membranes show perfect rejection for paracetamol with only slight change in solvent permeances. From this simulation study, the ZIF membranes are revealed to be potentially useful for OSN. Nevertheless, it is worthwhile to point out the assumptions and limitations associated with the simulations: (1) The ZIF structures were assumed to be stable and rigid in the solvents. If the structural flexibility is incorporated, which we plan to do in our future study, the solvent permeance and solute rejection may be influenced. (2) To observe the OSN process within a time scale of 100 ns, the pressure gradient exerted was quite high; the predicted fluxes and permeances were thus on 17



the high end. (3) The membranes used were only several nm in thickness, substantially thinner than experimental samples of m scale; therefore, the simulation results might not be straightforwardly compared with experimental measurements. However, the intrinsic permeabilities are, in principle, independent of pressure gradient and membrane thickness, and they could be reasonably well predicted. (4) Fouling is an important factor for a practical membrane application as it has an adverse effect on membrane performance. The simulations here were focused on membrane performance in a short-time duration and did not consider fouling. Even with these assumptions and limitations, the simulation study provides quantitative microscopic understanding for various solvents in different ZIFs, reveals the important role of functional groups in solvent permeation, and would assist the rational design of new crystalline membranes for high-performance OSN.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Pore morphologies and radii in ZIFs, fragmental clusters of ZIFs, atomic charges and force field parameters of ZIFs, physical properties of solvents and solute, radial distribution functions of ethanol, number of acetonitrile molecules in and through ZIF-96, trajectories of acetone molecules, snapshots of acetone molecules, number of acetone molecules in and through ZIF-71 and -96, comparison of different membranes. A video for hexane permeation through ZIF-25. Acknowledgements We gratefully acknowledge the National Research Foundation of Singapore (R-279-000-468-281) and the National University of Singapore (R-279-000-474-112) for financial support, and the National Supercomputing Centre Singapore for providing part of the computational resources used in this work.

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Table of Contents Graphic

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Zeolitic Imidazolate Framework Membranes for Organic Solvent

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