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Microporous benzimidazole-linked polymer and its derivatives for organic solvent nanofiltration
Polymer xxx (xxxx) xxx
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Microporous benzimidazole-linked polymer and its derivatives for organic solvent nanofiltration Jie Liu, Jianwen Jiang * Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore
A R T I C L E I N F O
A B S T R A C T
Keywords: Microporous polymer membranes Organic solvent nanofiltration Solvent permeation Solute rejection Molecular simulation
Organic solvent nanofiltration (OSN) has emerged as a robust separation technology for solvent recovery and microporous polymer membranes are considered as promising OSN membranes. A molecular simulation study is reported here to investigate a new type of microporous membranes for OSN, including a benzimidazole-linked polymer (BILP-4) and its derivatives (PILP-1 and PILP-3). PILP-1 and PILP-3 are computationally designed, they consist of tetrahedral cores in BILP-4 and contorted linkers in polymer of intrinsic microporosity (PIM-1). From molecular dynamics simulations, three membranes are found to possess considerable stability in organic solvents (methanol, ethanol and acetonitrile). The mean pore sizes of the swollen membranes have a linear relationship with swelling degrees. Intriguingly, methanol, ethanol and acetonitrile exhibit distinctly different permeation behavior through the three membranes. Specifically, the permeation of methanol is solely governed by the pore size, whereas both the pore size and the membrane-solvent interaction play a role in the permeation of ethanol; for acetonitrile, the permeation is mainly determined by the membrane-solvent interaction. A dye molecule (methylene blue) is tested for OSN and complete rejection is observed by all the three membranes. This simulation study reveals the complex permeation behavior of different solvents, identifies the key factors gov erning permeation, and suggest the three microporous membranes as interesting candidates for OSN.
1. Introduction In the chemical and pharmaceutical industries, organic solvents are commonly used as raw materials, reaction media and cleaning agents. To recover them, efficient separation is required. Traditional separation technologies (e.g. distillation) are thermally driven and energy inten sive. Recently, membrane-based organic solvent nanofiltration (OSN) has emerged as an economical and viable technology for separation [1]. Among different materials tested as OSN membranes, polymer membranes show a great potential as both separating and supporting layers due to their structural diversity, good solvent resistance and low fabrication cost [2]. For instance, free standing polyamide nanofilms with thickness <10 nm were fabricated by Livingston and coworkers using controlled polymerization and further incorporated as separating layers in composite membranes; the permeance of acetonitrile was determined to be 112 L/(m2 h bar), which is more than two orders of magnitude higher than commercially available membranes [3]. They also used the polymers of intrinsic microporosity (PIM-1, PIM-7 and PIM-8) to produce OSN membranes and coated them on two different
supports (polyacrylonitrile and a crosslinked polyetherimide); the composite membranes exhibited typical molecular weight cut-off (MWCO) in the region of 500–800 Da [4]. Chung and coworkers pre pared chemically cross-linked polybenzimidazole (PBI) membranes 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 [5]. The same group further fabricated solvent resistant hollow fibers based on poly-2,20 -(m-phenylene)-5, 50 -bibenzimidazole, and achieved > 98% solute rejection as well as 3.5 and 7.1 L/(m2 h bar) permeances for methanol and hexane, respectively [6]. Vankelecom and coworkers synthesized 145 polyimide (PI) mem branes to remove a dye (Rose bengal) from iso-propanol; a wide variety of operating conditions were systematically examined such as polymer concentration, solvent type, co-solvent/solvent ratio, and evaporation time [7]. Liang et al. developed several conjugated microporous poly mers (CMP) membranes with superior structural rigidity and micropo rosity, and a 42-nm-thick CMP membrane offered good solute retention and high permeances for nonpolar hexane (32 L m 2 h 1⋅bar 1) and polar methanol (22 L m 2 h 1⋅bar 1) [8].
* Corresponding author. E-mail address: [email protected] (J. Jiang). https://doi.org/10.1016/j.polymer.2019.121932 Received 16 July 2019; Received in revised form 11 September 2019; Accepted 19 October 2019 Available online 22 October 2019 0032-3861/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Jie Liu, Jianwen Jiang, Polymer, https://doi.org/10.1016/j.polymer.2019.121932
J. Liu and J. Jiang
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Recently, a new type of microporous polymers namely benzimidazole-linked polymers (BILPs) have received attention due to their high chemical and thermal stability [9,10]. Unlike the contorted linkers in PIMs, they contain rigid tetrahedral cores and have been tested as potential sorbents for CO2 separation. Among the synthesized BILPs, BILP-4 possesses the highest CO2 uptake and superior sorption selec tivities for CO2-containing gas mixtures [10]. In our recent work, BILP-4 membrane and two computationally designed microporous membranes namely PILP-1 and PILP-3 were predicted to surpasses the Robeson’s upper bound for CO2/CH4 separation [11]. PILP-1 and PILP-3 are the hybrids of BILP-4 and PIM-1, composing of the tetrahedral cores as in BILP-4 and the contorted linkers as in PIM-1. To the best of our knowledge, these membranes have not been tested for OSN. Based on their rigid structures and microporous nature, nevertheless, we envision that they might be interesting candidates as OSN membranes. Therefore, we report a molecular simulation study herein to examine BILP-4 and two computationally designed membranes (PILP-1 and PILP-3) for their OSN performance. In Section 2, the models for the three membranes (BILP-4, PILP-1 and PILP-3), solvents (methanol, ethanol and acetoni trile), as well as solute (methylene blue, MB) are described; then mo lecular dynamics (MD) methods to simulate membrane swelling and solvent permeation are outlined. In Section 3, the swelling behavior of the membranes is firstly examined and compared with other mem branes; subsequently, the permeabilities of solvents are predicted. To provide microscopic insights, pore structures and membrane-solvent interactions in the membranes are analyzed. Moreover, the rejection of MB is quantified. Finally, the concluding remarks are summarized in Section 4. It is worthwhile to note that currently there are scarce molecular simulation studies on OSN. Only recently, we simulated the permeation of methanol and water through five PBI membranes with various mean pore sizes from 3.53 to 6.38 Å, and revealed the crucial role of large pores and their interconnectivity in solvent permeation [12]. Subse quently, we developed a simulation protocol for the efficient simulation of membrane swelling, then examined the permeation of four solvents (methanol, ethanol, acetonitrile and acetone) through PBI, PIM-1 and PI membranes, and found complete rejection of a dye (methylene blue) in the four solvents [13]. In this study, we further explore the capability of new membranes (BILP-4, PILP-1 and PILP-3) for OSN and the micro scopic insight provided is useful to facilitate the development of high-performance OSN membranes.
linker in PIM-1, PILP-1 and PILP-3 were designed [11]. A PILP-1 chain contained 8 TFPM and 16 PIM-1 linkers, while PILP-3 possessed 8 TFPM and 48 PIM-1 linkers. The models of BILP-4, PILP-1 and PILP-3 mem branes were composed of 6, 6 and 2 chains, respectively. The mem branes were constructed using a 7-step compression and relaxation scheme [14]. After equilibration, the sizes of BILP-4, PILP-1 and PILP-3 membranes were 4.15 � 4.15 � 9.20 nm3, 3.66 � 3.66 � 8.27 nm3 and 4.09 � 3.20 � 7.29 nm3, respectively. 2.2. Swelling It is important to understand membrane swelling in a solvent before the membrane is used for OSN. This is because the stability and structure of membrane are significantly affected by swelling. We simulated the swelling of BILP-4, PILP-1 and PILP-3 in three typical organic solvents (methanol, ethanol and acetonitrile) differing in molecular size, polarity and viscosity. An 8-step simulation protocol (Table S1) developed in our recent study [13] was adopted here. The protocol, which does not follow the naturally very slow swelling process, allows temperature variations, and thus accelerates the swelling process by nearly one order of magnitude compared with the normal simulation method. In addition, the protocol is independent of initial membrane configuration. For each membrane considered in the current study, the swelling was started from a dense (dry) membrane and followed by temperature variations of 30 cycles. The membrane after swelling exhibited a loose structure, hence the polymer density was not uniform, especially at the sol vent/membrane interface. Based on the concept of Gibbs dividing sur face, we have developed a methodology to characterize swollen membranes [15]. As shown in Fig. S2 for PILP-1 swelling in acetonitrile, the polymer density profile can be fitted by an error function � � � � �� 1 z z1 z z2 pffiffi pffiffi ρðzÞ ¼ ρ0 erf erf (1) 2 σ 2 σ 2 where ρ0 is the bulk polymer density of the swollen membrane, z1 and z2 are the positions of Gibbs surfaces, and σ is the standard deviation in length. The LGibbs and Lbulk represent the Gibbs and bulk thickness, respectively; Lbulk is considered as the actual thickness of the swollen membrane. To confirm the convergence of swelling process, the fitted density profiles at various simulation cycles are plotted in Fig. S3. Initially, the density is about 1037 kg/m3. At the 5th cycle, the density drops to 995 kg/m3. After 27th cycle, the density remains nearly a constant of about 743 kg/m3. This suggests that 30 cycles in the 8-step protocol are sufficient to simulate the swelling of PILP-1 in acetonitrile.
2. Models and methods 2.1. Atomic models
2.3. Nanofiltration
Fig. 1 depicts the atomic structures of BILP-4, PILP-1 and PILP-3, with their chemical structures in Fig. S1. Experimentally, BILP-4 was synthesized from tetrakis(4-for-mylphenyl)methane (TFPM) and 1,2,4,5-benzenetetramine tetrahydrochloride (BTA) [10]. Here, a BILP-4 chain was considered to contain 26 TFPM (tetrahedral core) and 52 BTA. Based on the tetrahedral TFPM core in BLIP-4 and contorted
Fig. 2 illustrates a simulation system for nanofiltration through a membrane. The membrane was positioned in the middle of the simu lation box sandwiched by two chambers, which were the feed and permeate sides on the left and right, respectively. The x-y dimension of each membrane was the same as that of dense membrane. The length in the z-dimension was about 60 nm to ensure that the box was sufficiently
Fig. 1. Atomic structures of BILP-4, PILP-1 and PILP-3. Carbon: cyan, oxygen: red, nitrogen: blue, hydrogen: white. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 2
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Fig. 2. A simulation system for nanofiltration. A dye solution is in the left chamber and a pure solvent is in the right chamber. A graphene plate is fixed as a support for the membrane and permeable for solvent and solute. The other two graphene plates are exerted under different pressures.
long to simulate nanofiltration. The feed contained an organic solvent with three MB molecules (~24 mM). A graphene plate was placed on the right side of the membrane, acted as a support with its position fixed during MD simulation, and it allowed only solvent and solute molecules to pass through. To eliminate the interactions between the graphene and membrane, the atoms on the graphene were neutral with a negligible interaction strength. Furthermore, two graphene plates existed at both ends of the box; they could be regarded as pistons and movable under pressures of 601 bar and 1 bar on the left and right, respectively. The transmembrane pressure gradient was thus 600 bar, which is nearly one order of magnitude higher than a practical nanofiltration process. This is a common setting in MD simulations in order to reduce the thermal noise and enhance the signal/noise ratio within a nanosecond timescale. For instance, extremely high pressures (up to 6000 bar) were used to simulate water permeation [16,17]. All the MD simulations were performed using GROMACS v5.0.6 [18]. The polymers, graphene plates, solvents as well as MB were described by the Optimized Potentials for Liquid Simulations all atom (OPLS-AA) force field [19]. The interactions of atoms were modeled by the combination of Lennard-Jones (LJ) and Coulombic potentials: �� �12 � �6 � X X σij σ ij qi qj 4εij (2) þ rij rij 4πε0 rij
solvents are quantified by SD wt %Þ ¼
msolvent � 100% mpolymer
(3)
where msolvent and mpolymer are the respective mass of solvent and polymer within the bulk region (i.e. Lbulk) of a swollen membrane [15, 21,22]. Table 1 lists the SDs of BILP-4, PILP-1 and PILP-3 in methanol, ethanol and acetonitrile. There are no experimentally measured data available for BILP-4, PILP-1 and PILP-3; instead, the SDs of PIM-1 and PBI from our previous study [13] are included in Table 1 for comparison. PIM-1 [4,22] and PBI [23,24] are commonly regarded as solvent-resistant membranes. Taking methanol as an example, the SDs of BILP-4, PILP-1 and PILP-3 are 76.9%, 45.3% and 56.2%, respectively, which are smaller than PIM-1 (86.6%) and comparable to PBI (68.3%). The same trend is also found in ethanol and acetonitrile. A smaller SD usually reflects a higher stability of a membrane [4]. Therefore, we infer that BILP-4, PILP-1 and PILP-3 membranes under this study possess good stability in the three solvents due to their relatively smaller SDs. It is intriguing to assess how the membrane structures vary upon swelling. As calculated from our in-house code, the pore size distribu tions (PSDs) of BILP-4, PILP-1 and PILP-3 are plotted in Fig. 3. Before swelling, the pore diameters in the three dense membranes are below 7 Å. Specifically, the PSDs in BILP-4 and PILP-1 exhibit a distinct peak at approximately 2 Å; while the peak in PILP-3 is at 3 Å. After swelling in any of the three solvents, the PSDs vary significantly and the pores are enlarged up to 14 Å, which is within the pore sizes of common nano filtration membranes from 5 to 20 Å [1,2]. Thus, swelling leads to a looser structure and the formation of larger pores, as attributed to sol vent sorption and polymer dilation during swelling. Similar phenome non was observed in our previous study for PIM-1, PBI and PI swelling in four solvents (methanol, ethanol, acetonitrile and acetone), in which the pore sizes of swollen membranes were substantially larger than the dense membranes [15]. To quantitatively understand the relationship between SD and pore R∞ size, we define the mean pore size dm ¼ 0 r PðrÞ dr, where r is the pore size and P(r) is the PSD. Fig. 4 shows the dm versus SD for swollen BILP-4, PILP-1 and PILP-3 membranes in methanol, ethanol and acetonitrile. The dm increases linearly with SD, and such a trend also exists for other polymer membranes [13]. This relationship is independent of the type of polymer or solvent. On this basis, the dm can be estimated given a SD or vice versa.
where rij is the distance between atoms i and j, εij and σ ij are respectively the LJ potential strength and diameter, qi is the atomic charge of atom i, and ε0 is the vacuum permittivity. First, each system was equilibrated with the steepest descent method with a maximum step size of 0.1 Å and a force tolerance of 1000 kJ/(mol⋅nm). Subsequently, the velocities were assigned according to the Maxwell-Boltzmann distribution at 300 K. For solvent permeation and nanofiltration, the temperature was kept at 300 K using the velocity-rescaling method [20] with a relaxation time of 0.1 ps. A time step of 2 fs was applied to integrate the equations of motion by the leapfrog algorithm. To calculate the LJ interactions, the cutoff was set at 14 Å. The Coulombic interactions were evaluated by the particle-mesh Ewald method with a real-space cutoff of 14 Å and a grid spacing of 1.2 Å. The simulation for nanofiltration was 200 ns and the trajectory was saved every 25 ps. 3. Results and discussion First, swelling degrees are examined for BILP-4, PILP-1 and PILP-3 membranes in three solvents, then correlated with the mean pore sizes of the swollen membranes. Next, solvent permeabilities are predicted; the structural and dynamic properties of solvents in the membranes such as the solvent-membrane interactions, mean-squared displacements and radical distribution functions are analyzed. Finally, the solute rejection is evaluated.
Table 1 SDs in different solvents.
3.1. Swelling The swelling degree (SD) of BILP-4, PILP-1 and PILP-3 in different 3
Membrane
methanol
ethanol
acetonitrile
BILP-4 PILP-1 PILP-3 PIM-1 [13] PBI [13]
76.9 45.3 56.2 86.6 68.3
30.3 27.8 79.7 104.2 70.1
54.2 46.6 46.9 83.8 53.5
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Fig. 3. Pore size distributions of swollen and dense membranes.
From the slopes of Ns ~ t in Fig. 5, solvent permeabilities can be estimated by Ps ¼
ðNs =N0 Þ⋅Ms ⋅l A⋅Δt⋅Δp⋅ρ
(4)
where N0 is the Avogadro constant (6.022 � 1023), Ms is the molecular weight of solvent, l and A are the membrane thickness and cross-section area, respectively, Δt is the time duration, ρ is the density of solvent. For each case, the permeability was estimated from the last 50 ns trajectory. The Ps of methanol, ethanol and acetonitrile through BILP-4, PILP-1 and PILP-3 membranes are plotted in Fig. 6. Clearly, the three solvents exhibit different Ps as discussed below. 3.2.1. Methanol The permeabilities of methanol through the three membranes in crease as PILP-1 < PILP-3 < BILP-4. Apparently, the trend is different from Fig. 5, in which the net flows of methanol follow PILP-1 < BILP-
Fig. 4. Relationship between mean pore size (dm) and swelling degree (SD).
3.2. Solvent permeation Under a transmembrane pressure difference Δp, there is a net solvent flow from the feed to permeate side. Fig. 5 shows the number of solvents (Ns) through the three membranes versus time at Δp ¼ 600 bar. The Ns generally increases linearly with time after a certain lag time except for ethanol through BILP-4 and PILP-1. The occurrence of lag time is because the solvent molecule needs a certain time to enter then pass through the membrane. For the same solvent, the lag time varies with the membrane. A faster flow leads to a shorter lag time. For example, methanol flow through PILP-3 is the fastest, then followed by BILP-4 and PILP-1. As a consequence, the lag time is the shortest for PILP-3 and increases for BILP-4 and PILP-1, which is clearly seen in Fig. S4. This phenomenon was also seen previously, a shorter lag time was ascribed to a faster flow through a membrane with a larger pore size [12]. For ethanol, the lag time is very long as there is no discernible flow through BILP-4 and PILP-1.
Fig. 6. Solvent permeabilities (Ps) through three membranes.
Fig. 5. Solvent flows through three membranes. 4
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4 < PILP-3. This is because the net flow depends on membrane thickness and a thinner membrane results in a faster flow. However, the perme ability is independent of membrane thickness or it is thicknessnormalized flux. The thicknesses of BILP-4, PILP-1 and PILP-3 swollen in methanol are 10.1, 8.6 and 6 Å, respectively. The net flow through the thinnest PILP-3 is the fastest. Fig. 7a shows the mean pore sizes (dm) of the swollen membranes in methanol. The dm increases in the order of PILP-1 (5.3 Å) < PILP-3 (5.9 Å) < BILP-4 (7.3 Å), which is consistent with the increasing trend of permeability. From the PSDs in Fig. S5, we can see that there are large pores of 12–15 Å in BILP-4; while the PSDs in PILP-1 and PILP-3 are generally similar and 8–12 Å sized pores are more populated in PILP-3 than in PILP-1. Thus, the dm is the largest in of BILP-4, followed by PILP-3 and PILP-1. We also calculated the interaction energies of methanol with the membranes. As shown in Fig. 7c, the total energies (including both LJ and Coulombic) are quite close for the three mem branes. Therefore, it can be concluded that the permeability of methanol is predominantly governed by the pore size, rather by the membranesolvent interaction.
the VAVF in both BILP-4 and PILP-1 are nonzero, suggesting that ethanol may permeate through these two membranes if simulation is sufficiently long; nevertheless, its permeability is vanishingly low. Fig. 7d shows the interaction energies of ethanol with the membranes. Unlike methanol, the total energies here decrease as BILP-4 > PILP-1 > PILP-3. The strong interactions of ethanol with BILP-4 and PILP-1 also contribute to the low permeability. The permeability of ethanol through PILP-3 is 0.85 � 10 7 L/(m⋅hr⋅bar), substantially lower compared with 6.5 � 10 7 L/(m⋅hr⋅bar) of methanol. One reason is that ethanol is larger than methanol in size; specifically, they have the kinetic diameters of 4.5 and 3.8 Å [25], respectively. In addition, ethanol has a higher viscosity (1.17 mPa s) than methanol (0.49 mPa s) [26,27]. With a higher vis cosity, the permeability is obviously lower, as found experimentally [3, 8]. 3.2.3. Acetonitrile A low permeability of 0.2 � 10 7 L/(m⋅hr⋅bar) is observed for acetonitrile through BILP-4. Comparatively, the permeabilities through PILP-1 and PILP-3 are 4.9 � 10 7 and 3.2 � 10 7 L/(m⋅hr⋅bar), respec tively. Interestingly, the extremely low permeability through BILP-4 is not because the pores in BILP-4 are very small. As shown in Fig. S6, indeed, BILP-4 has a close (even slightly larger) dm to PILP-1 and PILP-3. To elucidate this non-intuitive behavior, we calculated the meansquared displacements (MSDs) of acetonitrile in the membranes along z-axis
3.2.2. Ethanol Within 200 ns, ethanol permeation is observed through PILP-3 but not BILP-4 and PILP-1 (Figs. 5 and 6). This is largely due to different pore sizes of the three membranes in ethanol. Fig. 7a shows the dm of PILP-3 (7.1 Å) is much larger than BILP-4 (4.1 Å) and PILP-1 (4.4 Å). On this basis, the accessible volume fractions (VAVF) are different among the three membrane. The VAVF is defined as VAV VAVF ¼ Vmem
MSDz ðtÞ ¼
(5)
N 1 X 〈jzi ðtÞ N i¼1
zi ð0Þj2 〉
(6)
where t is time, N is the number of molecules, zi(t) is the position of molecule i, and 〈:::〉 is the ensemble average. As shown by Fig. 8a, the MSDs of acetonitrile in the three membranes follow the trend of PILP1 > PILP-3 > BILP-4. Thus, acetonitrile has the slowest mobility in BILP4. Furthermore, we estimated the interaction energies of acetonitrile with the membranes. From Fig. 8b, the total energy between acetonitrile
where VAV and Vmem are the accessible and total volume of a membrane, respectively. The VAV represents the available space to accommodate solvent and the Vmem is the total pore volume within a membrane. As shown in Fig. 7c, the VAVF in PILP-3 is the largest. It should be noted that
Fig. 7. (a) Mean pore sizes of membranes in methanol and ethanol. (b) Interaction energies of methanol with membranes. (c) Accessible volume fractions of membranes in ethanol. (d) Interaction energies of ethanol with membranes. 5
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and BILP-4 is the strongest. If separating the energy into LJ and Coulombic contributions, the LJ contribution in the three systems is similar, while the Coulombic contribution between acetonitrile and BILP-4 is distinctly stronger than the other two systems. It is instructive to understand the structure of solvent near mem branes. To quantify, the radial distribution functions were evaluated by gij ðrÞ ¼
Nij ðr; r þ ΔrÞ V 4 πr2 Δr Ni Nj
through polyamide TFC nanofilm [3]. One thing we should note is that the three membranes in this study are initially dense membranes and the large pores are formed solely by swelling. In experiments, however, intrinsic large pores can be formed during a fabrication process [1]. By taking this into account, the permeabilities through three membranes would be further enhanced.
(7)
3.3. Solute rejection To examine the OSN performance of BILP-4, PILP-1 and PILP-3, the rejection of MB was simulated. Fig. 10 shows the trajectories of MB molecules along the z-axis in methanol. The positions of MBs are based on their center-of-mass. Obviously, no MB molecule is observed to penetrate into any of the membranes within 200 ns simulation duration. This suggests 100% dye rejection, an ideal performance for OSN mem brane. Solute accumulation on the membrane/solution interface is un desirable, as it slows down solvent permeation [24]. As shown in Fig. 10, the MB molecules are not bonded onto the membrane interface, instead, they can move back into the feed solution. This implies that the blockage of membrane interface is insignificant and solvent permeation can be fairly well maintained.
where r is the distance between atom i (solvent molecule) and j (mem brane atom), Nij (r, r þ Δr) is the number of atom i around j within a shell from r to r þ Δr, V is the volume of the membrane, and Ni and Nj are the number of atoms i and j, respectively. Fig. 9 shows the g(r) for nitrogen atoms of acetonitrile around specific membrane atoms. A significant peak is seen at 1.9 Å in BILP-4, but the peaks in PILP-1 and PILP-3 are negligible. This is attributed to different functional groups in the three membranes. The nitrogen atoms of acetonitrile are negatively charged and prefer to interact with the positively charged (N)H atoms in BILP-4; however, the interactions with the negatively charged O1, O2 and (C)N in both PILP-1 and PILP-3 are not appreciated. Thus, the strong Coulombic interaction between acetonitrile and BILP-4 in Fig. 8b is due to the presence of –NH groups in BILP-4. Upon entering the membrane, acetonitrile molecules are most strongly bonded onto BILP-4, resulting in the lowest permeability among the three membranes. Such a phe nomenon was also seen previously, in which PBI had the strongest attraction with four solvents than PI and PIM-1, thus the permeability through PBI was the lowest [13]. From the above structural and energetic analyses, the permeation of three solvents through BILP-4, PILP-1 and PILP-3 membranes is revealed to depend on membrane structure and/or membrane-solvent interac tion. For methanol, the permeation is almost solely governed by the pore size. Nevertheless, the pore size and membrane-solvent interaction both come into play in ethanol permeation. Interestingly, the pore size has no discernible effect on acetonitrile permeation, which appears to be dominated by membrane-solvent interaction especially the Coulombic interaction. These phenomena underline the complex nature of organic solvent permeation through polymer membranes. In Table S2, we list the characteristics of BILP-4, PILP-1 and PILP-3 with other membranes reported in the literature. The three mem branes in this study exhibit comparable permeabilities with the experi mental membranes. Taking methanol as an example, the permeabilities through BILP-4, PILP-1 and PILP-3 are predicted to be 7.58, 4.51 and 6.49 � 10 7 L/(m⋅hr⋅bar), which are higher than 0.72 � 10 7 L/ (m⋅hr⋅bar) through graphene-based HLGO membrane [28], close to 9.45 � 10 7 L/(m⋅hr⋅bar) through conjugated microporous polymer (CMP) membranes [8], but lower than 39 � 10 7 L/(m⋅hr⋅bar) through PBI/P84 hollow fiber membrane [24] and 49.5 � 10 7 L/(m⋅hr⋅bar)
4. Conclusions Molecular simulations have been performed to examine the perme ation of three solvents (methanol, ethanol and acetonitrile) through three microporous polymer membranes (BILP-4, PILP-1 and PILP-3). PILP-1 and PILP-3 are designed derivatives of BILP-4. Moreover, the rejection of a dye (methylene blue) is considered. The membranes are swollen in the solvents and their structures become loose. A linear relationship is found between their mean pore sizes and swelling de grees. Compared with other membranes (e.g. PBI and PIM-1), the swelling degrees of the three MPMs are smaller, which indicates their physical stability in the solvents. The predicted permeabilities are comparable with other reported membranes. Among the three mem branes, BILP-4 has the highest methanol permeability; the fastest acetonitrile permeation occurs in PILP-1; ethanol permeation is only observed through PILP-3. The solvent permeation is governed by the pore size and/or membrane-solvent interaction in a complex manner. While methanol permeation appears to be exclusively dominated by the pore size, ethanol permeation is affected by the pore size as well as the membrane-solvent interaction; nevertheless, acetonitrile permeation is determined by the membrane-solvent interaction. Despite the largest pore size, BILP-4 exhibits the slowest permeation for acetonitrile, due to the strong Coulombic interaction of acetonitrile with –NH groups in BILP-4. The rejection of dye is observed to be 100% by all the three membranes. This study provides molecular level understanding for solvent permeation through the new microporous membranes and
Fig. 8. (a) Mean-squared displacements of acetonitrile in the membranes along the z-axis. (b) Interaction energies of acetonitrile with membranes. 6
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Fig. 9. Radical distribution functions for acetonitrile around membrane atoms (indicted by the insets).
Fig. 10. Trajectories of MB molecules. The dashed line indicates the membrane/solution interface in the feed side. The solvent is methanol.
suggests their potential use as OSN membranes.
[5] D.Y. Xing, S.Y. Chan, T.S. Chung, The ionic liquid as a solvent to fabricate stable polybenimidazole membranes for organic solvent nanofiltration, Green Chem. 16 (2014) 1383–1392. [6] A. Asadi Tashvigh, T.-S. Chung, Robust polybenzimidazole (pbi) hollow fiber membranes for organic solvent nanofiltration, J. Membr. Sci. 572 (2019) 580–587. [7] P. Vandezande, X. Li, L.E. Gevers, I.F. Vankelecom, High throughput study of phase inversion parameters for polyimide-based srnf membranes, J. Membr. Sci. 330 (2009) 307–318. [8] B. Liang, H. Wang, X. Shi, B. Shen, X. He, Z.A. Ghazi, N.A. Khan, H. Sin, A. M. Khattak, L. Li, Z. Tang, Microporous membranes comprising conjugated polymers with rigid backbones enable ultrafast organic-solvent nanofiltration, Nat. Chem. 10 (2018) 961–967. [9] M.G. Rabbani, H.M. El-Kaderi, Template-free synthesis of a highly porous benzimidazole-linked polymer for CO2 capture and H2 storage, Chem. Mater. 23 (2011) 1650–1653. [10] M.G. Rabbani, H.M. El-Kaderi, Synthesis and characterization of porous benzimidazole-linked polymers and their performance in small gas storage and selective uptake, Chem. Mater. 24 (2012) 1511–1517. [11] J. Liu, J.W. Jiang, Molecular design of microporous polymer membranes for the upgrading of natural gas, J. Phys. Chem. C 123 (2019) 6607–6615. [12] J. Liu, X. Kong, J.W. Jiang, Solvent nanofiltration through polybenzimidazole membranes: unravelling the role of pore size from molecular simulations, J. Membr. Sci. 564 (2018) 782–787. [13] J. Liu, Q.S. Xu, J.W. Jiang, A molecular simulation protocol for swelling and organic solvent nanofiltration of polymer membranes, J. Membr. Sci. 573 (2019) 639–646. [14] Q. Shi, K. Zhang, R. Lu, J.W. Jiang, Water desalination and biofuel dehydration through a thin membrane of polymer of intrinsic microporosity: atomistic simulation study, J. Membr. Sci. 545 (2018) 49–56. [15] Q.S. Xu, J.W. Jiang, Computational characterization of ultrathin polymer membranes in liquids, Macromolecules 51 (2018) 7169–7177. [16] M.E. Suk, N.R. Aluru, Water transport through ultrathin graphene, J. Phys. Chem. Lett. 1 (2010) 1590–1594. [17] D. Cohen-Tanugi, J.C. Grossman, Water desalination across nanoporous graphene, Nano Lett. 12 (2012) 3602–3608. [18] M.J. Abraham, T. Murtola, R. Schulz, S. P� all, J.C. Smith, B. Hess, E. Lindahl, Gromacs: high performance molecular simulations through multi-level parallelism from laptops to supercomputers, Software 1 (2015) 19–25. [19] W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc. 118 (1996) 11225–11236. [20] G. Bussi, D. Donadio, M. Parrinello, Canonical sampling through velocity rescaling, J. Chem. Phys. 126 (2007) 014101.
Supporting information Chemical structures of BILP-4, PILP-1 and PILP-3; simulation pro tocol for membrane swelling; density profile of PILP-1 swelling in acetonitrile; fitted density profiles of PILP-1 swelling in acetonitrile; lag times of methanol flows; pore size distributions of swollen membranes in methanol; mean pore sizes of swollen membranes in acetonitrile; com parison of different membranes. Acknowledgements We gratefully acknowledge the National Research Foundation of Singapore (NRF-CRP14-2014-01) and the National University of Singapore (R-279-000-474-112) for financial support. JL would also acknowledges the National Natural Science Foundation of China (No. 21706197). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.polymer.2019.121932. References [1] P. Marchetti, M.F. Jimenez Solomon, G. Szekely, A.G. Livingston, Molecular separation with organic solvent nanofiltration: a critical review, Chem. Rev. 114 (2014) 10735–10806. [2] X.Q. Cheng, Y.L. Zhang, Z.X. Wang, Z.H. Guo, Y.P. Bai, L. Shao, Recent advances in polymeric solvent resistant nanofiltration membranes, Adv. Polym. Technol. 33 (2014) 21455. [3] S. Karan, Z. Jiang, A.G. Livingston, Sub-10 nm polyamide nanofilms with ultrafast solvent transport for molecular separation, Science 348 (2015) 1347–1351. [4] M. Cook, P.R. Gaffney, L.G. Peeva, A.G. Livingston, Roll-to-roll dip coating of three different pims for organic solvent nanofiltration, J. Membr. Sci. 558 (2018) 52–63.
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[21] K.M. Gupta, J. Liu, J.W. Jiang, A molecular simulation study for efficient separation of 2,5-furandiyldimethanamine by a microporous polyarylate membrane, Polymer 175 (2019) 8–14. [22] D. Fritsch, P. Merten, K. Heinrich, M. Lazar, M. Priske, High performance organic solvent nanofiltration membranes: development and thorough testing of thin film composite membranes made of polymers of intrinsic microporosity, J. Membr. Sci. 401 (2012) 222–231. [23] I.B. Valtcheva, P. Marchetti, A.G. Livingston, Crosslinked polybenzimidazole membranes for organic solvent nanofiltration: analysis of crosslinking reaction mechanism and effects of reaction parameters, J. Membr. Sci. 493 (2015) 568–579. [24] S.-P. Sun, S.-Y. Chan, W. Xing, Y. Wang, T.-S. Chung, Facile synthesis of dual-layer organic solvent nanofiltration hollow fiber membranes, ACS Sustain. Chem. Eng. 3 (2015) 3019–3023.
[25] S. Van der Perre, T. Van Assche, B. Bozbiyik, J. Lannoeye, D.E. De Vos, G.V. Baron, J.F.M. Denayer, Adsorptive characterization of ZIF-68: a complex structure with amphiphilic properties, Langmuir 30 (2014) 8416–8424. [26] B.E. Poling, J.M. Prausnitz, J.P. O’connell, The Properties of Gases and Liquids, vol. 5, Mcgraw-hill, New York, 2001. [27] A. Buekenhoudt, F. Bisignano, G. De Luca, P. Vandezande, M. Wouters, K. Verhulst, Unravelling the solvent flux behaviour of ceramic nanofiltration and ultrafiltration membranes, J. Membr. Sci. 439 (2013) 36–47. [28] Q. Yang, Y. Su, C. Chi, C. Cherian, K. Huang, V. Kravets, F. Wang, J. Zhang, A. Pratt, A. Grigorenko, Ultrathin graphene-based membrane with precise molecular sieving and ultrafast solvent permeation, Nat. Mater. 16 (2017) 1198.
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Polymer journal homepage: http://www.elsevier.com/locate/polymer
Microporous benzimidazole-linked polymer and its derivatives for organic solvent nanofiltration Jie Liu, Jianwen Jiang * Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore
A R T I C L E I N F O
A B S T R A C T
Keywords: Microporous polymer membranes Organic solvent nanofiltration Solvent permeation Solute rejection Molecular simulation
Organic solvent nanofiltration (OSN) has emerged as a robust separation technology for solvent recovery and microporous polymer membranes are considered as promising OSN membranes. A molecular simulation study is reported here to investigate a new type of microporous membranes for OSN, including a benzimidazole-linked polymer (BILP-4) and its derivatives (PILP-1 and PILP-3). PILP-1 and PILP-3 are computationally designed, they consist of tetrahedral cores in BILP-4 and contorted linkers in polymer of intrinsic microporosity (PIM-1). From molecular dynamics simulations, three membranes are found to possess considerable stability in organic solvents (methanol, ethanol and acetonitrile). The mean pore sizes of the swollen membranes have a linear relationship with swelling degrees. Intriguingly, methanol, ethanol and acetonitrile exhibit distinctly different permeation behavior through the three membranes. Specifically, the permeation of methanol is solely governed by the pore size, whereas both the pore size and the membrane-solvent interaction play a role in the permeation of ethanol; for acetonitrile, the permeation is mainly determined by the membrane-solvent interaction. A dye molecule (methylene blue) is tested for OSN and complete rejection is observed by all the three membranes. This simulation study reveals the complex permeation behavior of different solvents, identifies the key factors gov erning permeation, and suggest the three microporous membranes as interesting candidates for OSN.
1. Introduction In the chemical and pharmaceutical industries, organic solvents are commonly used as raw materials, reaction media and cleaning agents. To recover them, efficient separation is required. Traditional separation technologies (e.g. distillation) are thermally driven and energy inten sive. Recently, membrane-based organic solvent nanofiltration (OSN) has emerged as an economical and viable technology for separation [1]. Among different materials tested as OSN membranes, polymer membranes show a great potential as both separating and supporting layers due to their structural diversity, good solvent resistance and low fabrication cost [2]. For instance, free standing polyamide nanofilms with thickness <10 nm were fabricated by Livingston and coworkers using controlled polymerization and further incorporated as separating layers in composite membranes; the permeance of acetonitrile was determined to be 112 L/(m2 h bar), which is more than two orders of magnitude higher than commercially available membranes [3]. They also used the polymers of intrinsic microporosity (PIM-1, PIM-7 and PIM-8) to produce OSN membranes and coated them on two different
supports (polyacrylonitrile and a crosslinked polyetherimide); the composite membranes exhibited typical molecular weight cut-off (MWCO) in the region of 500–800 Da [4]. Chung and coworkers pre pared chemically cross-linked polybenzimidazole (PBI) membranes 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 [5]. The same group further fabricated solvent resistant hollow fibers based on poly-2,20 -(m-phenylene)-5, 50 -bibenzimidazole, and achieved > 98% solute rejection as well as 3.5 and 7.1 L/(m2 h bar) permeances for methanol and hexane, respectively [6]. Vankelecom and coworkers synthesized 145 polyimide (PI) mem branes to remove a dye (Rose bengal) from iso-propanol; a wide variety of operating conditions were systematically examined such as polymer concentration, solvent type, co-solvent/solvent ratio, and evaporation time [7]. Liang et al. developed several conjugated microporous poly mers (CMP) membranes with superior structural rigidity and micropo rosity, and a 42-nm-thick CMP membrane offered good solute retention and high permeances for nonpolar hexane (32 L m 2 h 1⋅bar 1) and polar methanol (22 L m 2 h 1⋅bar 1) [8].
* Corresponding author. E-mail address: [email protected] (J. Jiang). https://doi.org/10.1016/j.polymer.2019.121932 Received 16 July 2019; Received in revised form 11 September 2019; Accepted 19 October 2019 Available online 22 October 2019 0032-3861/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Jie Liu, Jianwen Jiang, Polymer, https://doi.org/10.1016/j.polymer.2019.121932
J. Liu and J. Jiang
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Recently, a new type of microporous polymers namely benzimidazole-linked polymers (BILPs) have received attention due to their high chemical and thermal stability [9,10]. Unlike the contorted linkers in PIMs, they contain rigid tetrahedral cores and have been tested as potential sorbents for CO2 separation. Among the synthesized BILPs, BILP-4 possesses the highest CO2 uptake and superior sorption selec tivities for CO2-containing gas mixtures [10]. In our recent work, BILP-4 membrane and two computationally designed microporous membranes namely PILP-1 and PILP-3 were predicted to surpasses the Robeson’s upper bound for CO2/CH4 separation [11]. PILP-1 and PILP-3 are the hybrids of BILP-4 and PIM-1, composing of the tetrahedral cores as in BILP-4 and the contorted linkers as in PIM-1. To the best of our knowledge, these membranes have not been tested for OSN. Based on their rigid structures and microporous nature, nevertheless, we envision that they might be interesting candidates as OSN membranes. Therefore, we report a molecular simulation study herein to examine BILP-4 and two computationally designed membranes (PILP-1 and PILP-3) for their OSN performance. In Section 2, the models for the three membranes (BILP-4, PILP-1 and PILP-3), solvents (methanol, ethanol and acetoni trile), as well as solute (methylene blue, MB) are described; then mo lecular dynamics (MD) methods to simulate membrane swelling and solvent permeation are outlined. In Section 3, the swelling behavior of the membranes is firstly examined and compared with other mem branes; subsequently, the permeabilities of solvents are predicted. To provide microscopic insights, pore structures and membrane-solvent interactions in the membranes are analyzed. Moreover, the rejection of MB is quantified. Finally, the concluding remarks are summarized in Section 4. It is worthwhile to note that currently there are scarce molecular simulation studies on OSN. Only recently, we simulated the permeation of methanol and water through five PBI membranes with various mean pore sizes from 3.53 to 6.38 Å, and revealed the crucial role of large pores and their interconnectivity in solvent permeation [12]. Subse quently, we developed a simulation protocol for the efficient simulation of membrane swelling, then examined the permeation of four solvents (methanol, ethanol, acetonitrile and acetone) through PBI, PIM-1 and PI membranes, and found complete rejection of a dye (methylene blue) in the four solvents [13]. In this study, we further explore the capability of new membranes (BILP-4, PILP-1 and PILP-3) for OSN and the micro scopic insight provided is useful to facilitate the development of high-performance OSN membranes.
linker in PIM-1, PILP-1 and PILP-3 were designed [11]. A PILP-1 chain contained 8 TFPM and 16 PIM-1 linkers, while PILP-3 possessed 8 TFPM and 48 PIM-1 linkers. The models of BILP-4, PILP-1 and PILP-3 mem branes were composed of 6, 6 and 2 chains, respectively. The mem branes were constructed using a 7-step compression and relaxation scheme [14]. After equilibration, the sizes of BILP-4, PILP-1 and PILP-3 membranes were 4.15 � 4.15 � 9.20 nm3, 3.66 � 3.66 � 8.27 nm3 and 4.09 � 3.20 � 7.29 nm3, respectively. 2.2. Swelling It is important to understand membrane swelling in a solvent before the membrane is used for OSN. This is because the stability and structure of membrane are significantly affected by swelling. We simulated the swelling of BILP-4, PILP-1 and PILP-3 in three typical organic solvents (methanol, ethanol and acetonitrile) differing in molecular size, polarity and viscosity. An 8-step simulation protocol (Table S1) developed in our recent study [13] was adopted here. The protocol, which does not follow the naturally very slow swelling process, allows temperature variations, and thus accelerates the swelling process by nearly one order of magnitude compared with the normal simulation method. In addition, the protocol is independent of initial membrane configuration. For each membrane considered in the current study, the swelling was started from a dense (dry) membrane and followed by temperature variations of 30 cycles. The membrane after swelling exhibited a loose structure, hence the polymer density was not uniform, especially at the sol vent/membrane interface. Based on the concept of Gibbs dividing sur face, we have developed a methodology to characterize swollen membranes [15]. As shown in Fig. S2 for PILP-1 swelling in acetonitrile, the polymer density profile can be fitted by an error function � � � � �� 1 z z1 z z2 pffiffi pffiffi ρðzÞ ¼ ρ0 erf erf (1) 2 σ 2 σ 2 where ρ0 is the bulk polymer density of the swollen membrane, z1 and z2 are the positions of Gibbs surfaces, and σ is the standard deviation in length. The LGibbs and Lbulk represent the Gibbs and bulk thickness, respectively; Lbulk is considered as the actual thickness of the swollen membrane. To confirm the convergence of swelling process, the fitted density profiles at various simulation cycles are plotted in Fig. S3. Initially, the density is about 1037 kg/m3. At the 5th cycle, the density drops to 995 kg/m3. After 27th cycle, the density remains nearly a constant of about 743 kg/m3. This suggests that 30 cycles in the 8-step protocol are sufficient to simulate the swelling of PILP-1 in acetonitrile.
2. Models and methods 2.1. Atomic models
2.3. Nanofiltration
Fig. 1 depicts the atomic structures of BILP-4, PILP-1 and PILP-3, with their chemical structures in Fig. S1. Experimentally, BILP-4 was synthesized from tetrakis(4-for-mylphenyl)methane (TFPM) and 1,2,4,5-benzenetetramine tetrahydrochloride (BTA) [10]. Here, a BILP-4 chain was considered to contain 26 TFPM (tetrahedral core) and 52 BTA. Based on the tetrahedral TFPM core in BLIP-4 and contorted
Fig. 2 illustrates a simulation system for nanofiltration through a membrane. The membrane was positioned in the middle of the simu lation box sandwiched by two chambers, which were the feed and permeate sides on the left and right, respectively. The x-y dimension of each membrane was the same as that of dense membrane. The length in the z-dimension was about 60 nm to ensure that the box was sufficiently
Fig. 1. Atomic structures of BILP-4, PILP-1 and PILP-3. Carbon: cyan, oxygen: red, nitrogen: blue, hydrogen: white. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 2
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Fig. 2. A simulation system for nanofiltration. A dye solution is in the left chamber and a pure solvent is in the right chamber. A graphene plate is fixed as a support for the membrane and permeable for solvent and solute. The other two graphene plates are exerted under different pressures.
long to simulate nanofiltration. The feed contained an organic solvent with three MB molecules (~24 mM). A graphene plate was placed on the right side of the membrane, acted as a support with its position fixed during MD simulation, and it allowed only solvent and solute molecules to pass through. To eliminate the interactions between the graphene and membrane, the atoms on the graphene were neutral with a negligible interaction strength. Furthermore, two graphene plates existed at both ends of the box; they could be regarded as pistons and movable under pressures of 601 bar and 1 bar on the left and right, respectively. The transmembrane pressure gradient was thus 600 bar, which is nearly one order of magnitude higher than a practical nanofiltration process. This is a common setting in MD simulations in order to reduce the thermal noise and enhance the signal/noise ratio within a nanosecond timescale. For instance, extremely high pressures (up to 6000 bar) were used to simulate water permeation [16,17]. All the MD simulations were performed using GROMACS v5.0.6 [18]. The polymers, graphene plates, solvents as well as MB were described by the Optimized Potentials for Liquid Simulations all atom (OPLS-AA) force field [19]. The interactions of atoms were modeled by the combination of Lennard-Jones (LJ) and Coulombic potentials: �� �12 � �6 � X X σij σ ij qi qj 4εij (2) þ rij rij 4πε0 rij
solvents are quantified by SD wt %Þ ¼
msolvent � 100% mpolymer
(3)
where msolvent and mpolymer are the respective mass of solvent and polymer within the bulk region (i.e. Lbulk) of a swollen membrane [15, 21,22]. Table 1 lists the SDs of BILP-4, PILP-1 and PILP-3 in methanol, ethanol and acetonitrile. There are no experimentally measured data available for BILP-4, PILP-1 and PILP-3; instead, the SDs of PIM-1 and PBI from our previous study [13] are included in Table 1 for comparison. PIM-1 [4,22] and PBI [23,24] are commonly regarded as solvent-resistant membranes. Taking methanol as an example, the SDs of BILP-4, PILP-1 and PILP-3 are 76.9%, 45.3% and 56.2%, respectively, which are smaller than PIM-1 (86.6%) and comparable to PBI (68.3%). The same trend is also found in ethanol and acetonitrile. A smaller SD usually reflects a higher stability of a membrane [4]. Therefore, we infer that BILP-4, PILP-1 and PILP-3 membranes under this study possess good stability in the three solvents due to their relatively smaller SDs. It is intriguing to assess how the membrane structures vary upon swelling. As calculated from our in-house code, the pore size distribu tions (PSDs) of BILP-4, PILP-1 and PILP-3 are plotted in Fig. 3. Before swelling, the pore diameters in the three dense membranes are below 7 Å. Specifically, the PSDs in BILP-4 and PILP-1 exhibit a distinct peak at approximately 2 Å; while the peak in PILP-3 is at 3 Å. After swelling in any of the three solvents, the PSDs vary significantly and the pores are enlarged up to 14 Å, which is within the pore sizes of common nano filtration membranes from 5 to 20 Å [1,2]. Thus, swelling leads to a looser structure and the formation of larger pores, as attributed to sol vent sorption and polymer dilation during swelling. Similar phenome non was observed in our previous study for PIM-1, PBI and PI swelling in four solvents (methanol, ethanol, acetonitrile and acetone), in which the pore sizes of swollen membranes were substantially larger than the dense membranes [15]. To quantitatively understand the relationship between SD and pore R∞ size, we define the mean pore size dm ¼ 0 r PðrÞ dr, where r is the pore size and P(r) is the PSD. Fig. 4 shows the dm versus SD for swollen BILP-4, PILP-1 and PILP-3 membranes in methanol, ethanol and acetonitrile. The dm increases linearly with SD, and such a trend also exists for other polymer membranes [13]. This relationship is independent of the type of polymer or solvent. On this basis, the dm can be estimated given a SD or vice versa.
where rij is the distance between atoms i and j, εij and σ ij are respectively the LJ potential strength and diameter, qi is the atomic charge of atom i, and ε0 is the vacuum permittivity. First, each system was equilibrated with the steepest descent method with a maximum step size of 0.1 Å and a force tolerance of 1000 kJ/(mol⋅nm). Subsequently, the velocities were assigned according to the Maxwell-Boltzmann distribution at 300 K. For solvent permeation and nanofiltration, the temperature was kept at 300 K using the velocity-rescaling method [20] with a relaxation time of 0.1 ps. A time step of 2 fs was applied to integrate the equations of motion by the leapfrog algorithm. To calculate the LJ interactions, the cutoff was set at 14 Å. The Coulombic interactions were evaluated by the particle-mesh Ewald method with a real-space cutoff of 14 Å and a grid spacing of 1.2 Å. The simulation for nanofiltration was 200 ns and the trajectory was saved every 25 ps. 3. Results and discussion First, swelling degrees are examined for BILP-4, PILP-1 and PILP-3 membranes in three solvents, then correlated with the mean pore sizes of the swollen membranes. Next, solvent permeabilities are predicted; the structural and dynamic properties of solvents in the membranes such as the solvent-membrane interactions, mean-squared displacements and radical distribution functions are analyzed. Finally, the solute rejection is evaluated.
Table 1 SDs in different solvents.
3.1. Swelling The swelling degree (SD) of BILP-4, PILP-1 and PILP-3 in different 3
Membrane
methanol
ethanol
acetonitrile
BILP-4 PILP-1 PILP-3 PIM-1 [13] PBI [13]
76.9 45.3 56.2 86.6 68.3
30.3 27.8 79.7 104.2 70.1
54.2 46.6 46.9 83.8 53.5
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Fig. 3. Pore size distributions of swollen and dense membranes.
From the slopes of Ns ~ t in Fig. 5, solvent permeabilities can be estimated by Ps ¼
ðNs =N0 Þ⋅Ms ⋅l A⋅Δt⋅Δp⋅ρ
(4)
where N0 is the Avogadro constant (6.022 � 1023), Ms is the molecular weight of solvent, l and A are the membrane thickness and cross-section area, respectively, Δt is the time duration, ρ is the density of solvent. For each case, the permeability was estimated from the last 50 ns trajectory. The Ps of methanol, ethanol and acetonitrile through BILP-4, PILP-1 and PILP-3 membranes are plotted in Fig. 6. Clearly, the three solvents exhibit different Ps as discussed below. 3.2.1. Methanol The permeabilities of methanol through the three membranes in crease as PILP-1 < PILP-3 < BILP-4. Apparently, the trend is different from Fig. 5, in which the net flows of methanol follow PILP-1 < BILP-
Fig. 4. Relationship between mean pore size (dm) and swelling degree (SD).
3.2. Solvent permeation Under a transmembrane pressure difference Δp, there is a net solvent flow from the feed to permeate side. Fig. 5 shows the number of solvents (Ns) through the three membranes versus time at Δp ¼ 600 bar. The Ns generally increases linearly with time after a certain lag time except for ethanol through BILP-4 and PILP-1. The occurrence of lag time is because the solvent molecule needs a certain time to enter then pass through the membrane. For the same solvent, the lag time varies with the membrane. A faster flow leads to a shorter lag time. For example, methanol flow through PILP-3 is the fastest, then followed by BILP-4 and PILP-1. As a consequence, the lag time is the shortest for PILP-3 and increases for BILP-4 and PILP-1, which is clearly seen in Fig. S4. This phenomenon was also seen previously, a shorter lag time was ascribed to a faster flow through a membrane with a larger pore size [12]. For ethanol, the lag time is very long as there is no discernible flow through BILP-4 and PILP-1.
Fig. 6. Solvent permeabilities (Ps) through three membranes.
Fig. 5. Solvent flows through three membranes. 4
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4 < PILP-3. This is because the net flow depends on membrane thickness and a thinner membrane results in a faster flow. However, the perme ability is independent of membrane thickness or it is thicknessnormalized flux. The thicknesses of BILP-4, PILP-1 and PILP-3 swollen in methanol are 10.1, 8.6 and 6 Å, respectively. The net flow through the thinnest PILP-3 is the fastest. Fig. 7a shows the mean pore sizes (dm) of the swollen membranes in methanol. The dm increases in the order of PILP-1 (5.3 Å) < PILP-3 (5.9 Å) < BILP-4 (7.3 Å), which is consistent with the increasing trend of permeability. From the PSDs in Fig. S5, we can see that there are large pores of 12–15 Å in BILP-4; while the PSDs in PILP-1 and PILP-3 are generally similar and 8–12 Å sized pores are more populated in PILP-3 than in PILP-1. Thus, the dm is the largest in of BILP-4, followed by PILP-3 and PILP-1. We also calculated the interaction energies of methanol with the membranes. As shown in Fig. 7c, the total energies (including both LJ and Coulombic) are quite close for the three mem branes. Therefore, it can be concluded that the permeability of methanol is predominantly governed by the pore size, rather by the membranesolvent interaction.
the VAVF in both BILP-4 and PILP-1 are nonzero, suggesting that ethanol may permeate through these two membranes if simulation is sufficiently long; nevertheless, its permeability is vanishingly low. Fig. 7d shows the interaction energies of ethanol with the membranes. Unlike methanol, the total energies here decrease as BILP-4 > PILP-1 > PILP-3. The strong interactions of ethanol with BILP-4 and PILP-1 also contribute to the low permeability. The permeability of ethanol through PILP-3 is 0.85 � 10 7 L/(m⋅hr⋅bar), substantially lower compared with 6.5 � 10 7 L/(m⋅hr⋅bar) of methanol. One reason is that ethanol is larger than methanol in size; specifically, they have the kinetic diameters of 4.5 and 3.8 Å [25], respectively. In addition, ethanol has a higher viscosity (1.17 mPa s) than methanol (0.49 mPa s) [26,27]. With a higher vis cosity, the permeability is obviously lower, as found experimentally [3, 8]. 3.2.3. Acetonitrile A low permeability of 0.2 � 10 7 L/(m⋅hr⋅bar) is observed for acetonitrile through BILP-4. Comparatively, the permeabilities through PILP-1 and PILP-3 are 4.9 � 10 7 and 3.2 � 10 7 L/(m⋅hr⋅bar), respec tively. Interestingly, the extremely low permeability through BILP-4 is not because the pores in BILP-4 are very small. As shown in Fig. S6, indeed, BILP-4 has a close (even slightly larger) dm to PILP-1 and PILP-3. To elucidate this non-intuitive behavior, we calculated the meansquared displacements (MSDs) of acetonitrile in the membranes along z-axis
3.2.2. Ethanol Within 200 ns, ethanol permeation is observed through PILP-3 but not BILP-4 and PILP-1 (Figs. 5 and 6). This is largely due to different pore sizes of the three membranes in ethanol. Fig. 7a shows the dm of PILP-3 (7.1 Å) is much larger than BILP-4 (4.1 Å) and PILP-1 (4.4 Å). On this basis, the accessible volume fractions (VAVF) are different among the three membrane. The VAVF is defined as VAV VAVF ¼ Vmem
MSDz ðtÞ ¼
(5)
N 1 X 〈jzi ðtÞ N i¼1
zi ð0Þj2 〉
(6)
where t is time, N is the number of molecules, zi(t) is the position of molecule i, and 〈:::〉 is the ensemble average. As shown by Fig. 8a, the MSDs of acetonitrile in the three membranes follow the trend of PILP1 > PILP-3 > BILP-4. Thus, acetonitrile has the slowest mobility in BILP4. Furthermore, we estimated the interaction energies of acetonitrile with the membranes. From Fig. 8b, the total energy between acetonitrile
where VAV and Vmem are the accessible and total volume of a membrane, respectively. The VAV represents the available space to accommodate solvent and the Vmem is the total pore volume within a membrane. As shown in Fig. 7c, the VAVF in PILP-3 is the largest. It should be noted that
Fig. 7. (a) Mean pore sizes of membranes in methanol and ethanol. (b) Interaction energies of methanol with membranes. (c) Accessible volume fractions of membranes in ethanol. (d) Interaction energies of ethanol with membranes. 5
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and BILP-4 is the strongest. If separating the energy into LJ and Coulombic contributions, the LJ contribution in the three systems is similar, while the Coulombic contribution between acetonitrile and BILP-4 is distinctly stronger than the other two systems. It is instructive to understand the structure of solvent near mem branes. To quantify, the radial distribution functions were evaluated by gij ðrÞ ¼
Nij ðr; r þ ΔrÞ V 4 πr2 Δr Ni Nj
through polyamide TFC nanofilm [3]. One thing we should note is that the three membranes in this study are initially dense membranes and the large pores are formed solely by swelling. In experiments, however, intrinsic large pores can be formed during a fabrication process [1]. By taking this into account, the permeabilities through three membranes would be further enhanced.
(7)
3.3. Solute rejection To examine the OSN performance of BILP-4, PILP-1 and PILP-3, the rejection of MB was simulated. Fig. 10 shows the trajectories of MB molecules along the z-axis in methanol. The positions of MBs are based on their center-of-mass. Obviously, no MB molecule is observed to penetrate into any of the membranes within 200 ns simulation duration. This suggests 100% dye rejection, an ideal performance for OSN mem brane. Solute accumulation on the membrane/solution interface is un desirable, as it slows down solvent permeation [24]. As shown in Fig. 10, the MB molecules are not bonded onto the membrane interface, instead, they can move back into the feed solution. This implies that the blockage of membrane interface is insignificant and solvent permeation can be fairly well maintained.
where r is the distance between atom i (solvent molecule) and j (mem brane atom), Nij (r, r þ Δr) is the number of atom i around j within a shell from r to r þ Δr, V is the volume of the membrane, and Ni and Nj are the number of atoms i and j, respectively. Fig. 9 shows the g(r) for nitrogen atoms of acetonitrile around specific membrane atoms. A significant peak is seen at 1.9 Å in BILP-4, but the peaks in PILP-1 and PILP-3 are negligible. This is attributed to different functional groups in the three membranes. The nitrogen atoms of acetonitrile are negatively charged and prefer to interact with the positively charged (N)H atoms in BILP-4; however, the interactions with the negatively charged O1, O2 and (C)N in both PILP-1 and PILP-3 are not appreciated. Thus, the strong Coulombic interaction between acetonitrile and BILP-4 in Fig. 8b is due to the presence of –NH groups in BILP-4. Upon entering the membrane, acetonitrile molecules are most strongly bonded onto BILP-4, resulting in the lowest permeability among the three membranes. Such a phe nomenon was also seen previously, in which PBI had the strongest attraction with four solvents than PI and PIM-1, thus the permeability through PBI was the lowest [13]. From the above structural and energetic analyses, the permeation of three solvents through BILP-4, PILP-1 and PILP-3 membranes is revealed to depend on membrane structure and/or membrane-solvent interac tion. For methanol, the permeation is almost solely governed by the pore size. Nevertheless, the pore size and membrane-solvent interaction both come into play in ethanol permeation. Interestingly, the pore size has no discernible effect on acetonitrile permeation, which appears to be dominated by membrane-solvent interaction especially the Coulombic interaction. These phenomena underline the complex nature of organic solvent permeation through polymer membranes. In Table S2, we list the characteristics of BILP-4, PILP-1 and PILP-3 with other membranes reported in the literature. The three mem branes in this study exhibit comparable permeabilities with the experi mental membranes. Taking methanol as an example, the permeabilities through BILP-4, PILP-1 and PILP-3 are predicted to be 7.58, 4.51 and 6.49 � 10 7 L/(m⋅hr⋅bar), which are higher than 0.72 � 10 7 L/ (m⋅hr⋅bar) through graphene-based HLGO membrane [28], close to 9.45 � 10 7 L/(m⋅hr⋅bar) through conjugated microporous polymer (CMP) membranes [8], but lower than 39 � 10 7 L/(m⋅hr⋅bar) through PBI/P84 hollow fiber membrane [24] and 49.5 � 10 7 L/(m⋅hr⋅bar)
4. Conclusions Molecular simulations have been performed to examine the perme ation of three solvents (methanol, ethanol and acetonitrile) through three microporous polymer membranes (BILP-4, PILP-1 and PILP-3). PILP-1 and PILP-3 are designed derivatives of BILP-4. Moreover, the rejection of a dye (methylene blue) is considered. The membranes are swollen in the solvents and their structures become loose. A linear relationship is found between their mean pore sizes and swelling de grees. Compared with other membranes (e.g. PBI and PIM-1), the swelling degrees of the three MPMs are smaller, which indicates their physical stability in the solvents. The predicted permeabilities are comparable with other reported membranes. Among the three mem branes, BILP-4 has the highest methanol permeability; the fastest acetonitrile permeation occurs in PILP-1; ethanol permeation is only observed through PILP-3. The solvent permeation is governed by the pore size and/or membrane-solvent interaction in a complex manner. While methanol permeation appears to be exclusively dominated by the pore size, ethanol permeation is affected by the pore size as well as the membrane-solvent interaction; nevertheless, acetonitrile permeation is determined by the membrane-solvent interaction. Despite the largest pore size, BILP-4 exhibits the slowest permeation for acetonitrile, due to the strong Coulombic interaction of acetonitrile with –NH groups in BILP-4. The rejection of dye is observed to be 100% by all the three membranes. This study provides molecular level understanding for solvent permeation through the new microporous membranes and
Fig. 8. (a) Mean-squared displacements of acetonitrile in the membranes along the z-axis. (b) Interaction energies of acetonitrile with membranes. 6
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Fig. 9. Radical distribution functions for acetonitrile around membrane atoms (indicted by the insets).
Fig. 10. Trajectories of MB molecules. The dashed line indicates the membrane/solution interface in the feed side. The solvent is methanol.
suggests their potential use as OSN membranes.
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