Amorphous Porous Organic Cage Membranes for Water Desalination

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Amorphous Porous Organic Cage Membranes for Water Desalination Xian Kong, and Jianwen Jiang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11497 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 6, 2018

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The Journal of Physical Chemistry

Amorphous Porous Organic Cage Membranes for Water Desalination Xian Kong, Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore

ABSTRACT: Emerged as a new class of nanoporous materials, porous organic cages (POCs) possess salient features of solvent processibility and water stability, thus they are envisioned as promising membrane materials for water desalination. In this study, we propose a simulation protocol to construct atomic models of amorphous POC membranes and examine their desalination performance. Five membranes (AC1, AC2, AC3, AC16 and AC17) with similar cage structure but different periphery groups are considered. All the five membranes exhibit 100% salt rejection. In contrast to crystalline CC1 membrane that is impermeable to water, AC1 has a water permeability Pw of 3.6 × 10−8 kg·m/(m2·hr·bar). With increasing interconnected pores in AC2, AC3, AC16 and AC17, Pw increases. Due to the existence of hydroxyl groups in CC17 cages, AC17 exhibits the highest Pw of 3.17 × 10−7 kg·m/(m2·h·bar), which is higher than in commercial reverse osmosis membranes. Significantly, Pw is found to enhance in mixed AC3/AC17 and AC16/AC17 membranes with up to one-fold enhancement. The enhanced Pw is attributed to the counterbalance between water sorption and diffusion. This simulation study provides the bottom-up insights into the dynamics and structure of water in amorphous POC membranes, highlights their potential use for water desalination, and suggests a unique strategy to enhance desalination performance by tuning the composition of mixed POC membranes. Keywords: porous organic cages, amorphous membranes, water permeability, salt rejection, simulation

* [email protected]

1 Environment ACS Paragon Plus

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1. Introduction With rapid population increase and industrialization, water scarcity has escalated as an urgent issue worldwide.1 Desalination is a technically feasible and economically viable approach to harvest fresh water from seawater, which constitutes 95% of water on the Earth.2,3 Among available desalination techniques, membrane-based reverse osmosis (RO) has demonstrated to be the most attractive due to its comparatively lower capital cost.4 According to a recent estimation, RO accounts for 53% of current global desalination capacity.5 Nevertheless, RO processes are still energy intensive because of low water flux required to preserve high ion selectivity, which is a common dilemma in the widely used polymeric membranes. In a typical RO plant, energy consumption is ~ 45% of the total production cost.6 Therefore, membranes with high water flux and excellent salt rejection are indispensable to the optimization of RO processes. The quest for high performance RO membranes has been on-going for decades, primarily focusing on nanoporous materials such as zeolitic7,8 and carbonaceous materials,9-12 metal−organic frameworks (MOFs),13,14 as well as biological membranes.15,16 Zeolitic membranes manifest high water flux and good salt rejection, as attributed to their uniform pore network and high thermal stability; however, as inorganic materials, they are brittle and difficult to process. Membranes based on various carbon allotropes such as graphene and carbon nanotubes are promising alternatives, but their scalability hinders their practical applications. MOFs suffer from both stability and scalability issues because they are prepared through noncovalent assembly. Biological membranes are still under intensive exploration and far from ready for real applications. Recently, porous organic cages (POC) have emerged as a new class of porous materials.17,18 Unlike extended porous crystals such as zeolites and MOFs, POCs are discrete molecules with


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intrinsic cages that can persist in either crystals,19-21 amorphous solids

22,23

or even moderate-

sized solvents forming porous liquids.24 As organic molecules, POCs have excellent solvent processibility and can be easily fabricated into membranes including supported 2D crystalline membranes through layer-by-layer assembly.25 supported amorphous membranes through spin coating26 and moreover mixed matrix membranes through co-solution casting.27 In addition, some POCs have remarkable water stability. For example, CC3 crystal can remain stable for more than 4 hours in boiling water.28 On the other hand, the chemical stability of imine-based POCs could be improved by reducing imines into amines, while the structure persistence could be preserved by tying carbonyls at the cage vertices.29 The salient features of solvent processibility and water stability suggest that POCs might be promising membrane materials for desalination. Recently, we conducted a molecular dynamics (MD) simulation study to examine the desalination performance of five crystalline POC membranes (CC1, CC2, CC3, CC16 and CC17).30 As shown in Figure S1, the five POCs share a similar [4+6] tetrahedral cage (Figure S1a) containing four triangular windows and six peripheries. The presence of various periphery groups (Figure S1b) leads to different crystal packings in the five POCs.19,31 Our simulation study revealed that the crystal packing significantly affects water permeation; CC2 was identified to possess the best desalination performance with a high water permeability of 2.05×10-6 kg·m/(m2·hr·bar) and complete salt rejection.30 Nevertheless, the preparation of crystalline POC membranes is nontrivial and their long-term stability is unclear. In contrast, amorphous POC membranes have been experimentally fabricated and tested for gas permeation, e.g., molecular sieving capability was observed for H2-containing mixtures such as H2/N2, H2/CO2 and H2/CH4.26 In this study, we thus further investigate water



desalination through amorphous CC1, CC2, CC3, CC16 and CC17 membranes (coined as AC1, AC2, AC3, AC6 and AC17). It is important to note the key differences from our previous study: (1) while the crystalline and amorphous POC membranes contain the same type of cages, the packing of cages and pore morphology are different; as we find herein, the desalination performance is substantially different. (2) the structures of crystalline POCs are experimentally available; however, the structures of amorphous POCs are not and they can only be computationally constructed. In this study, a simulation protocol is proposed and tested to construct amorphous POCs. (3) Unlike the crystalline POCs, the amorphous POCs exhibit a strong system size effect; this effect is comprehensively examined here. Therefore, this study is not simply incremental from our previous study. In Section 2, we first describe a simulation protocol to construct amorphous POC membranes, then characterize their pore morphologies and outline the method to simulate a RO process. In Section 3, water flux, permeability and salt rejection are presented for the AC membranes and compared with crystalline counterparts; water structure and dynamics in the AC membranes are discussed; we also propose to use mixed POC membranes to improve performance. Finally, the concluding remarks are summarized in Section 4.

2. Models and Methods Gas diffusion and storage in AC membranes were examined by a few simulation studies.32,33 To construct AC membranes, Jiang et al. first loaded POCs into a simulation box with a low density; after 500 ps MD simulation in a micro-canonical ensemble, several clusters were formed and then subjected to 8 ns MD simulation in an isothermal-isobaric ensemble with temperature and pressure of 300 K and 1 bar, respectively.32 Rather than 1 bar, Evans et al. ran MD simulation at a very high pressure (1000 bar) for 1 ns to accelerate the compression.33 To


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examine the effect of pressure P, we simulated the density and root-mean squired deviation (RMSD) for both crystalline and amorphous CC3 membranes by varying P. For crystalline CC3 membrane, as shown in Figure S2, the density remains nearly constant at P ≤ 100 bar and then rises gradually; the RMSD is about 0.04 nm at P ≤ 1000 bar and increases marginally to 0.05 nm at 10000 bar. For amorphous CC3 (AC3) membrane, the density is lower due to inefficient packing and exhibits a similar trend with P; nevertheless, the RMSD increase continuously with P. This indicates that the cage structure is not preserved and even distorted upon compression, particularly at a high P, thus reducing intrinsic porosity. To overcome this, we propose a new protocol to construct the AC membranes. As summarized in Table S1, the first two steps are similar to previous studies. The key difference is in the implement of distance restraint on individual cage during high-pressure compression (step 3). With such a distance restraint, the POCs preserve their cage structure much better (see Figure S2b). The last step 4 includes MD simulation at 1 bar for 1 ns without distance restraint to relax the membranes. Using this protocol, five AC membranes were constructed (AC1, AC2, AC3, AC16 and AC17) each with six configurations. Table 1 lists the averaged density and thickness for each membrane. In CC1, CC2, CC3 and CC16 cages, the peripheral groups are alkyl based and the size increases as CC1 < CC2 < CC3 < CC16; as a consequence, the packing efficiency and density of the AC membranes follow the opposite trend, i.e., AC1 > AC2 > AC3 > AC16. An exception is AC17, in which CC17 cages are relatively more compact due to the favorable hydrogen bonding between hydroxyl groups. The typical pore morphologies of the five AC membranes were analyzed by Zeo++ package34 with a probe diameter of 2.65 Å, which is the kinetic diameter of water.35 Figure 1 illustrates the interconnected and disconnected pores in the



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AC membranes. Visually, there are a small portion of interconnected pores in AC1, an increased portion in AC2, and a large portion in the other three membranes.

Table 1. Membrane density and thickness, water permeation and hydrogen bonds. Membrane

Density (g/cm3)

Membrane thickness (nm)

Permeation duration (ns)

Specific permeation duration (ns/nm)

Hydrogen bonds per water

AC1

0.949 ± 0.005

5.18 ± 0.01

20.14 ± 5.87

3.89 ± 1.13

2.66 ± 0.02

AC2

0.892 ± 0.004

5.47 ± 0.01

12.47 ± 4.74

2.28 ± 0.87

2.73 ± 0.02

AC3

0.818 ± 0.006

6.10 ± 0.02

12.82 ± 4.27

2.10 ± 0.70

2.86 ± 0.01

AC16

0.793 ± 0.004

6.46 ± 0.01

8.56 ± 3.27

1.32 ± 0.51

2.65 ± 0.01

AC17

0.873 ± 0.006

6.29 ± 0.01

17.10 ± 5.31

2.72 ± 0.84

2.58 ± 0.01

AC1

AC2

AC3

AC16

AC17

Figure 2. Pore morphologies in AC membranes. Green: interconnected and red: disconnected. Water desalination through an AC membrane was simulated in a system illustrated in Figure 2. There were two chambers, a feed chamber with seawater and a permeate chamber with pure water, separated by the membrane. The seawater was mimicked by an aqueous NaCl solution of 0.6 M. Along the z direction, the lengths of the feed and permeate chambers were 6.0 and 3.0 nm, respectively. The large size of the feed chamber was to assure that seawater concentration would not alter appreciably during simulation. In the two chambers, two graphene plates were added and they could adjust their positions during simulation under hydraulic pressures. The


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periodic boundary conditions were exerted in the x, y and z directions, and a vacuum of 6 nm was added on each side of the system to eliminate the effect of periodic images along the z direction. The POCs were described by the Optimized Potentials for Liquid Simulations all atom (OPLSAA) force field,36 which has been demonstrated to be reliable to reproduce the structure and energetics of POCs.24 To incorporate the flexibility of cages, the stretching, bending and torsional contributions were included in the bonded potentials. The nonbonded potentials included the Lennard-Jones (LJ) and electrostatic terms. The atomic charges of POCs were calculated using density functional theory (DFT) implemented in GAUSSIAN 09.37 Based on individual cages, the DFT calculations used the Becke exchange plus Lee-Yang-Parr functional (B3LYP) and 6-311++g(d,p) basis set. By fitting the electrostatic potentials, the atomic charges -

were estimated.30 Na+ and Cl ions were described as charged LJ particles with parameters from the OPLS-AA, water was mimicked by the 3 point-transferable intermolecular potential (TIP3P).38 The carbon atoms on graphene plates were modeled with parameters as used for carbon nanotubes.39

Figure 2. A simulation system for water desalination. For each membrane, initially energy minimization was conducted using the steepest descent method, then velocities were assigned according to the Maxwell-Boltzmann distribution at 300 K, Finally, MD simulation was conducted at 300 K for 60 ns, with the system size kept as



constant and temperature controlled by the Nosé-Hoover thermostat with a relaxation time of 0.2 ps. The two graphene plates were exerted pressures of 601 and 1 bar, leading to a pressure difference of 600 bar. Such a high pressure is commonly used in non-equilibrium MD simulations to enhance the sampling while still capturing underlying physics.40,41 To incorporate membrane flexibility, the membrane atoms were allowed to fluctuate but the heavy atoms were restrained along the z direction with a force constant of 1 kJ/(mol·nm2). It should be pointed out that, as already demonstrated, the magnitude of force constant has an insignificant effect on water flow.30 The carbon atoms of graphene plates were restrained in the x and y directions with a force constant of 1000 kJ/(mol·nm2), while they were movable along the z direction. A cutoff of 12 Å was used to calculate both LJ interactions and electrostatic interactions, and the particlemesh Ewald method was used to evaluate the long-range electrostatic interactions with grid spacing of 1.2 Å. The time step was 2 fs for integration and the trajectory was saved every 2 ps. For each membrane, three configurations were used for simulations. GROMACS v.5.0.6 was used for all the simulations.42 In our previous study for water desalination through crystalline POC membranes, the system size was found to have an indiscernible effect. With increasing either membrane area or thickness, water permeability remains almost identical.30 However, the situation is substantially different for AC membranes. Evans et al. reported that if the number of POCs < 100, unphysical structural correlations might exist due to limited system size and the pore structure in AC membranes could not be effectively sampled.33 To test if this phenomenon occurs here, water desalination through AC3 membranes was simulated by varying the number of CC3 cages (nCC3) in the system. Specifically, 54, 100, 200 and 400 CC3 cages were used to constructed four AC3 membranes with similar thickness of approximately 6.10 nm but differing in area. For each


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membrane, six different configurations were constructed. As shown in Figure 3, if nCC3 = 54, water flow Nw/A (where Nw is the number of net transferred water molecules through a membrane and A is the cross-section area of membrane on the xy plane) is largely different among the six configurations. With increasing nCC3, the difference of Nw/A is reduced and becomes marginal if nCC3 = 400. This suggests the effect of system size is large but becomes negligible if nCC3 = 400. Therefore, 400 POCs were used to construct all the membranes in this study; initially, the simulation box in the x/y direction was twice of that in the z direction. 25

25 nCC3 = 100

nCC3 = 54 20 -2

NW/A (nm )

-2

NW/A (nm )

20 15 10

15 10

5 0 0

5

10

20

30

0 0

40

10

t (ns)

20

30

40

30

40

t (ns)

25

25

nCC3 = 200

nCC3 = 400

20 -2

NW/A (nm )

20

-2

NW/A (nm )

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


15

15

10

10 5

5 0 0

10

20

30

40

0 0

t (ns)

10

20

t (ns)

Figure 3. Effect of system size on water flow through AC3 membranes. The curves in each figure correspond to different configurations.

3. Results and Discussion



3.1. AC Membranes Figure 4 shows the normalized net water flow = λ/ (λ is the membrane thickness) versus time t through the five AC membranes at the pressure gradient of 600 bar. For all the membranes, the slope of is nearly zero within the first few ns (about 5 ns). This is because the membranes are initially dry and water molecules need to fill in before entering the permeate chamber. The slope gradually increases implying the occurrence of a RO process. At about 30 ns, a steady state is approached. Despite chemically similar structure, the five AC membranes exhibit different magnitude of . Apparently, due to the presence of a small portion of interconnected pores (Figure 1), AC1 exhibits the lowest among the five membranes. With increased portion of interconnected pores, AC2 has an intermediate . The other three membranes, AC3, AC16, and AC17, allow more water to flow, in accordance with their highly interconnected pore structures. 60 AC1 AC2 AC3 AC16 AC17

50

NW (nm-1)

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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40 30 20 10 0 0

10

20

30

40

50

60

t (ns)

Figure 4. Normalized net water flow versus time. The transparent shades indicate standard errors based on three different membrane configurations.

It is instructive to examine how water and ions are located in the membranes. Figure 5 and Figure S3 shows the density profiles of water in the five membranes as a function of time. Initially, no water exists in the membrane interior. Along with time, water permeates


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progressively into and passes through the membrane. It takes 20 ns for the density profile to attain a steady state in AC17 membrane, while 40 ns is required in other membranes. On the other hand, the density in AC17 is the highest among the five membranes. The fastest permeation and highest density of water in AC17 are attributed to the existence of hydroxyl groups in the periphery of CC17 cages, which enhances the hydrophilicity of AC17 membrane with strong affinity for water. The density profiles of ions near the end of simulation are plotted in Figure S4. Most of the ions reside in the feed chamber, specifically, at the membrane/solution interface. Some ions can move into the membrane interior, particularly AC16 and AC17, but the ions are trapped in the membrane and cannot enter the permeate chamber.

Figure 5. Density profiles of water along the z direction in AC16 and AC17 membranes.

From the linear relationship between and t in a steady state, water permeability Pw can be estimated by =

/ ∙ ∙λ ∙∙ ∆

(1)

where N0 is the Avogadro constant (6.022 × 10²³), Mw is the molecular weight of water (18.015 g/mol), ∆p is pressure gradient (600 bar), and π is the osmotic pressure of 0.6 M NaCl solution



(about 30 bar). In addition to water permeability, salt rejection is another important metric to evaluate desalination performance. Here, salt rejection is calculated from

 N Ip /( N Wp + N Ip )  × 100% 1 − 0 0 0   N I /( N W + N I ) 

(2)

where N Wp and N Ip are the numbers of permeated water molecules and ions, respective, while N w0 and N I0 are the numbers in the feed chamber before RO process. The performance of the

five AC membranes is plotted in Figure 6 and compared with other membranes.

Graphene

100

Graphyne ZIF-25

Salt rejection (%)

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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98 96 94 92 90

ZIF-71 CC2

ZIF-96

CC3

ZIF-93

CC16

ZIF-97

CC17

Seawater RO

AC1

Brackish RO

AC2

High-flux RO

AC3

ZIF-8

AC16

CTF-1

AC17

CTF-1-Cl CTF-1-CH3 Polyamide

88 10-7

10-6

Permeability (kg. m/m2. h .bar)

Figure 6. Performance of POCs and other membranes (graphene,40 graphyne,43 CTFs,44 polyamide,45 commercial RO46 and ZIFs47-49).

All the five AC membranes show complete ion rejection during our simulation. The Pw in AC1 is 3.6 × 10−8 kg·m/(m2·hr·bar), different from its crystalline counterpart, which is impermeable to water.30 This indicate the amorphous assembly of CC1 enhances porosity. In AC2, AC3 and AC16, the Pw are 1.25 × 10−7, 2.65 × 10−7 and 3.04 × 10−7 kg·m/(m2·hr·bar), respectively. It appears that the Pw increase as the membrane density drops and becomes more porous. The Pw in AC17 is 3.17 × 10−7 kg·m/(m2·h·bar) and the highest among the five AC membranes. The Pw in


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AC3, AC16 and AC17 are higher than current seawater RO membranes, but lower than in most 2D membranes such as graphene,40 graphyne43 and CTF-1.44 Compared with the crystalline counterparts, AC2, AC3 and AC17 have lower Pw. Thus, the crystallinity plays in important role in water permeability through the POC membranes. The 2D membranes benefit from their ultrathin thickness, while crystalline POC membranes benefit from the regular pores. However, both 2D membranes and crystalline POC membranes are notably difficult to prepare. Therefore, the AC membranes are still promising alternative to RO. In particular, as we shall see below, the Pw can be tuned and enhanced in mixed AC membranes.

0.3

0.15

Interconnected Disconnected

(a)

(b) AC1 AC2 AC3 AC16 AC17

3

Pore Volume (cm /g)

0.2

0.10

PSD

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


0.1

0.05

0.0 0.00

AC1

AC2

AC3

AC16

AC17

0

Membrane

5

10

15

d (Å)

Figure 7. (a) Pore volume (b) Pore size distribution of AC membranes. The five AC membranes differ in pore morphology and exhibit different desalination performance. Therefore, it is necessary to conduct a quantitative characterization of pore structure. Figure 7 plots the pore volume (PV) and pore size distribution (PSD), estimated from Zeo++ and in-house code, respectively. The PV increases when the peripheral groups become bulkier. Consistent with Figure 2, AC1 exhibits the lowest PV and greatest disconnected pores. AC2 has more interconnected pores than AC1. AC3, AC16 and AC17 possess high PV, due to the large substitutes at the periphery of cages. Moreover, interconnected pores are dominant in



these three membranes, which is in favor of water permeation. In terms of PSD, AC1 and AC2 contain primarily small pores with size < 4 Å; while there are greater probability of larger pores in AC3, AC16 and AC17. It should be noted although the pores in all the AC membranes are larger than the size of Na+/Cl− (~ 5.0 Å), the salt rejection is 100%. The reason is the pore structure is rather tortuous and irregular, thus even some ions can enter the membrane interior but they cannot pass through (see Figure S4). 3.2. Water dynamics and structure in AC membranes It is useful to provide microscopic insight into water dynamics and structure in the membranes. Figure 8 shows the trajectories of randomly selected water molecules along the z direction. Generally, water molecules exhibit similar behavior in the five AC membranes. After moving into the membrane from the feed chamber, depending on the membrane, a water molecule may stay in the membrane for about 5 ~ 30 ns before entering the permeate chamber. Occasionally, a few water molecules may move back to the feed chamber, demonstrating the stochastic nature of water dynamics.


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Figure 8. Trajectories of randomly selected water molecules through AC membranes. The dashed lines indicate membrane interfaces.

The time for water molecules permeating through a membrane is quantified by permeation duration. Table 1 lists the permeation durations in the five AC membranes averaged over all permeated water molecules, as well as the membrane-thickness normalized specific permeation durations τsp. For AC1, AC2, AC3 and AC16, the τsp decreases as AC1 > AC2 > AC3 > AC16, following the decreasing trend of membrane density. This is because water permeates faster in a less dense membrane. Due to the presence of hydroxyl groups, water permeation in AC17 membrane is restricted and thus the τsp is longer than in most of the AC membranes (except AC1).

1.0

2

0.6

bulk AC1 AC2 AC3 AC16 AC17

1.0

AC1 AC2 AC3 AC16 AC17

0.8

ACF

0.8

MSDz(nm )

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


0.4

0.6

0.40 0.38 0.36 0.34 0.32 0.30

0.4

2.6

2.8

3.0

3.2

3.4

t (ps)

0.2

0.2

(b)

(a) 0.0 0

0.0 200

400

600

800

1000

0

5

t (ps)

10

t (ps)

15

20

Figure 9. Water dynamics in AC membranes. (a) MSDz and (b) Autocorrelation functions of HBs.

We also examine the mean-squared displacements (MSDs) of water molecules in the membranes along the z direction MSDz ( t ) = zi ( t0 + t ) − zi ( t0 )

2

i∈Ω


(3)


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where zi is the z-coordinate of atom i, Ω is a set of water molecules staying in the membrane from t0 to (t0 + t), and ... denotes ensemble average. As shown in Figure 9a, the MSD decreases in the order of AC16 > AC3 > AC17 > AC2 > AC1, which largely follows the increasing trend of specific permeation duration in Table 1 (except AC17). Although water diffusion in AC17 is not the fastest, water density therein is the highest among the five membranes (see Figure 5) due to the presence of hydroxyl groups. Based on the solution-diffusion mechanism, AC17 has the highest water permeability. Therefore, we infer that the performance of AC membranes is largely governed by their peripheral groups, which can affect two competing factors, namely solubility and diffusivity; furthermore, this suggests the performance can be tuned by altering the peripheral groups. Water structure in the membranes is characterized by hydrogen bonds (HBs). Two geometrical criteria were implemented to define a HB: (1) the distance between a donor and an acceptor ≤ 0.35 nm and (2) the angle of hydrogen-donor-acceptor ≤ 30°.50 Apparently, as listed in Table 1, the number of HBs per water in each membrane is reduced compared with that in bulk phase (~3.5). This desolvation effect exerts a barrier for water entry into the membrane, which thus requires an external pressure to facilitate water permeation. In general, the number of HBs in the five membranes is close, suggesting similar water structure. This is in contrast to crystalline POC membranes where the number of HBs in CC2 and CC17 is relatively greater, because their larger pore and porous network. The dynamics of HBs can be quantified by the autocorrelation function50,51 c (t ) =

hij (t0 ) hij (t0 + t ) hij (t 0 ) hij (t0 )


(4)

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where h(t) = 1 if two water molecules are hydrogen bonded at time t and h(t ) = 0 otherwise. Shown in Figure 9b, the c(t) in all the five membranes drop with increasing time, implying fewer water molecules remain hydrogen bonded over a longer period. Compared with the case in bulk phase, the c(t) are larger because the confinement and interaction of the membranes restrict water movement and hence the lifetime of HBs is longer. Although the c(t) in the five membranes is largely similar, a decreasing trend of AC17 > AC1 > AC2 > AC3 > AC16 is observed from the inset. Except for AC17, this trend follows the decreasing trend of specific permeation duration. The longest lifetime in AC17 is attributed to the strong affinity of hydroxyl groups for water. Again, this further reveals water dynamics is affected by the peripheral groups.

3.3. Mixed AC membranes One merit of amorphous AC membranes is that the composition of cages can be readily controlled, e.g., by mixing different POCs during the preparation of casting solution for spin coating.21,22 In this context, we investigate water desalination in two mixed AC membranes AC3/AC17 and AC16/AC17. Figure 10a presents water permeability Pw through these two membranes with varying composition xAC17 (i.e. hydrophilicity). With increasing xAC17, the Pw first rises, passes a maximum and then drops. The maximal Pw in AC3/AC17 and AC16/AC17 are observed at xAC17 = 0.4 and 0.7, respectively. Surprisingly, the Pw in the mixed membranes is enhanced from pristine membranes, and the maximal enhancement is nearly one-fold. Intuitively, one may speculate that the enhanced Pw is due to increased pore volume or pore size in the mixed AC membranes. As shown in Figure 10b, however, the interconnected pore volume does not vary significantly with xAC17, particularly in AC16/AC17 membrane. Also shown in Figure S5, there is no substantial difference in the pore size distribution between the mixed and pristine membranes.



We find that the enhanced permeability in the mixed membranes can be elucidated by the counterbalance between water sorption and diffusion. Figure S6 shows the density profiles of water and MSDz in AC3/AC17 and AC16/AC17. On this basis, water density and diffusivity in the membranes are plotted in Figure 10c and 10d. With increasing xAC17, water density rises monotonically in both AC3/AC17 and AC16/AC17. This suggests water sorption is enhanced with more CC17 in the mixed membranes because CC17 cages consist of hydroxyl groups and have strong affinity for water. On the other hand, water diffusivity drops with increasing xAC17. Both sorption and diffusion contribute to permeation. With increasing xAC17, water sorption is enhanced while water diffusion is inhibited; as a consequence, a maximum is observed in water permeability. This demonstrates the remarkable advantage of POCs, which allows one to change the composition or hydrophilicity of POC membranes and subsequently tailor membrane performance.


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-1 -7

-1

-1

6 5 4 3

0.00

0.25

0.50

0.75

(b)

3

Interconnected Pore Volume (cm /g)

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7

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0.00

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xCC17

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400

D (10 cm /s)

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-6

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(d)

12

3

Density (kg/m )

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PW (10 kg·m ·h ·bar )

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200 AC3/AC17 AC16/AC17

8

6

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100 0.00

0.25

0.50

xAC17

0.75

1.00

4

0.00

0.25

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xAC17

0.75

1.00

Figure 10. (a) Water permeability (b) Interconnected pore volume (c) Water density (d) Water diffusivity along the z direction in mixed membranes AC3/AC17 and AC16/AC17. The dashed lines are to guide the eye. The error bars are based on three different membrane configurations.

4. Conclusions We have simulated water desalination through five amorphous POC membranes (AC1, AC2, AC3, AC16 and AC17). To construct the amorphous membranes, a protocol is proposed by implementing distance restraint on individual cage and thus the cage structure is well preserved. With increasing size of peripheral groups, the packing efficiency and density of the AC membranes generally drop. The effect of system size is found to be substantial but becomes negligible when the number of cages is sufficiently large (e.g. 400). All the five membranes show complete salt rejection. When the membrane density drops and hence becomes more porous, water permeability increases. The permeability in AC3, AC16, and AC17 outperforms



current seawater RO membranes, endorsing their potential use as RO membranes. The high permeability in hydrophobic AC16 and AC3 is primarily attributed to fast water diffusion, whereas the high permeability in hydrophilic AC17 benefits from strong water sorption by hydroxyl groups. Although water permeability in the amorphous membranes is lower than in their crystalline counterparts, the latter are not readily to be prepared. Intriguingly, the mixed membranes possess higher water permeability compared with pristine membranes. By optimizing the composition of hydrophobic/hydrophilic cages in mixed membranes, water permeability can be enhanced by up to one-fold. This provides a unique opportunity to design and fabricate new POC membranes to tailor water permeability and improve desalination performance.

Acknowledgements We gratefully acknowledge the A*STAR (R-279-000-475-305 and R-279-000-431-305) for financial support.

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Table of Contents Graphic

An atomistic simulation study is reported for water desalination through amorphous porous organic cage membranes.


Amorphous Porous Organic Cage Membranes for Water Desalination

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