Dipeptide Crystals as Reverse Osmosis Membranes for Water

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Dipeptide Crystals as Reverse Osmosis Membranes for Water Desalination: An Atomistic Simulation Study Zeyu Zhao, Krishna M. Gupta, Zhongjin He, and Jianwen Jiang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11863 • Publication Date (Web): 01 Mar 2018 Downloaded from http://pubs.acs.org on March 3, 2018

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The Journal of Physical Chemistry

Dipeptide Crystals as Reverse Osmosis Membranes for Water Desalination: Atomistic Simulation Zeyu Zhao, Krishna M. Gupta, Zhongjin He and Jianwen Jiang* Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore

ABSTRACT: An atomistic simulation study is reported to investigate the capability of dipeptide crystals as reverse osmosis (RO) membranes for water desalination. Eight dipeptides are considered, namely Ala-Val (AV), Val-Ala (VA), Ala-Ile (AI), Ile-Ala (IA), Val-Ile (VI), Ile-Val (IV), Val-Val (VV) and Leu-Ser (LS). It is revealed that water flux is governed by both pore size and helicity. With a relatively larger pore size, AV, AI, VV and LS exhibit a higher water flux than VA, IA, VI and IV. Despite similar pore size in AI and VA, a higher flux is observed in AI due to a smaller helicity. On the other hand, VI, LS, IV and IA possess higher salt rejection (> 90%, and 100% for VI) than the rest (< 70%). The salt rejection is determined by the electric potential difference across the membrane, induced by the staggered arrangement of -NH3+ and COO− groups in the dipeptides. This unique arrangement of charge groups is not observed in other types of RO membranes. A higher electric potential difference allows more ions to pass through the membrane, leading to a lower salt rejection. The lifetime of hydrogen bonding of water in LS membrane is shorter than in VI and IV, which follows the decreasing trend of water flux. An Arrhenius relationship is found between water flux and temperature in LS and VI, and the activation energies are predicted to be 27.72 and 33.42 kJ/mol, respectively. Furthermore, the membrane flexibility is examined; a correlation between water flux and position restraint force constant is obtained. This simulation study provides microscopic insights into the important structural and dynamic properties of water in dipeptide membranes, and suggests their potential use as RO membranes for water desalination.

Email: [email protected]

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1. Introduction The rapid increase of world population and economic development have caused inadequate supply of fresh water.1,2 In recent years, a number of seawater desalination plants have been built in water-stressed countries to augment water supply.3-5 The commonly used desalination technologies include thermal distillation, reserve osmosis (RO) and electrodialysis, etc.1 Particularly, membrane-based RO is efficient to produce fresh water suitable for human consumption and irrigation.6-11 Currently, RO comprises of 60% of desalination capacity worldwide and represents 75-85% of new desalination projects.12 In a RO process, the membrane used is of central importance to desalination performance. Since the operation of the first RO plant, polymeric membranes have been commercially employed.13 Nevertheless, polymeric membranes suffer from several drawbacks including oxidation, fouling and abrasion, which reduces their stability and efficiency. To enhance desalination performance, it is indispensable to develop new membranes with high water flux and salt rejection, which could potentially reduce capital cost and energy consumption in RO. Towards this end, a great deal of studies have been conducted. With uniform pore structure, zeolites exhibit high water flux and good salt rejection, but they are fragile and not easily reproducible.14,15 Carbon nanotubes appear to be superior in water desalination, whereas their durability and scalability remain a practical bottleneck for large-scale RO.16-18 Recently, dipeptide crystals have emerged as an interesting type of porous materials. Due to the inefficient packing of dipeptides and the lack of topological self-complementarity, dipeptide crystals contain very high density of one-dimensional (1D) straight pores ranging from 3 to 10 Å, which are desirable for molecular level adsorption, transport and separation.19,20 High adsorption capacity of Xe in AV and VA crystals was experimentally reported.21 The storage of CH4, CO2 and H2 in VA, AV, IV and VI crystals were tested.22 Extremely high selectivities for O2/N2 and O2/Ar were observed in AA crystal.23 Proton transport in dendritic dipeptides was found to be facilitated, while impeding Li+, Na+ and Cl− transport.24 The presence of 1D nanosized pores suggests dipeptide crystals might be potentially useful for water desalination. In this work, we report an atomistic simulation study to investigate eight dipeptide crystals as RO membranes and evaluate their desalination performance. The eight candidates include Ala-Val (AV), Val-Ala (VA), Ala-Ile (AI), Ile-Ala (IA), Val-Ile (VI), Ile-Val (IV), Val-Val (VV) and Leu-Ser (LS).25 The pores are formed through a 3D hydrogen bond network by dipeptides with two fairly small hydrophobic side chains, thus the inner pore surfaces 2 ACS Paragon Plus Environment

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are hydrophobic. In the eight dipeptide crystals, the pore size ranges from 3.7 to 5.0 Å, well suited for water desalination. In Section 2, the atomistic models of the dipeptides and RO systems are described, and followed by simulation methods. In Section 3, desalination performance is assessed on the basis of water permeability and salt rejection. The dynamic and structural properties of water in the dipeptides are analyzed. We also examine the effects of temperature and membrane flexibility on water transport. Finally, the concluding remarks are summarized in Section 4.

2. Models and methods The crystal structures of the eight dipeptides as shown in Figure S1 were constructed from experimental X-ray crystallographic data.25 Table 1 lists their structural characteristics. The pore sizes were calculated using the HOLE program,26 with the largest diameter of 5.0 Å in AV and the smallest of 3.7 Å in VI and IA. Also listed is the helicity, which will be discussed below. For each structure, water molecules were added into the pores and equilibrium molecular dynamics (EMD) simulation was conducted for 10 ns to examine water diffusion. Table 1. Structural characteristics of eight dipeptide crystals.

The circles in the top and side views represent the pore surfaces.



To simulate water desalination through each dipeptide membrane, a system illustrated in Figure 1 was used. Two chambers containing NaCl solution and pure water were separated by a membrane. The membrane thickness was approximately 40 Å (except 43 Å for LS). The concentration of NaCl solution was 0.5 M, which is close to the salt concentration in seawater. There were two graphene layers in the left and right chambers, and their positions could be selfadjusted along the z-axis upon external pressures Pleft and Pright, respectively. The periodic boundary conditions were applied along all the x, y and z directions and thus the membrane was mimicked to be infinitely large. The dipeptide atoms, Na+ and Cl− ions were represented by the optimized potentials for liquid simulation (OPLS).27 Water was modeled by the three-point transferable interaction potential (TIP3P) model.28 The carbon atoms in graphene layers were described as used for carbon nanotubes.29 The system was initially energy minimized by utilizing the steepest descent method with a maximum step size of 0.5 Å and a force tolerance of 1.0 kJ mol-1 nm-1. Then, velocities were assigned according to Maxwell-Boltzmann distribution at 300 K. Subsequently, non-equilibrium MD (NEMD) simulation was performed for 40 ns with Pleft = 90.1 MPa and Pright = 0.1 MPa (ambient pressure) to examine water desalination. While most MD simulations were at 300 K, additional simulations were also carried out at 290 and 310 K to estimate the activation energy of water transport through two membranes (LS and VI). The temperature was controlled by velocity-rescaled Berendsen thermostat with a relaxation time of 0.1 ps. Compared with a practical situation, the pressure gradient used here was approximately one order of magnitude lager, which is commonly used in NEMD simulations to reduce the influence of thermal noise.30,31 During both EMD and NEMD simulations, the heavy atoms (C, O and N) of dipeptides were position restrained with a force constant of 1000 kJ/(mol⋅nm2). To explore the effect of membrane flexibility, other force constants of 2000 and 200 were also tested. The two graphene layers were frozen along the x and y directions but flexible along the z direction. A cutoff of 14 Å was used to evaluate the Lennard-Jones interactions, and the electrostatic interactions were calculated using the particle-mesh Ewald (PME) method with a grid spacing of 1.2 Å and a fourth-order interpolation. A time step of 2 fs was used and the trajectory was saved every 2 ps. For each system, three independent simulations were performed and found to give close results. All the simulations were run using Gromacs v.5.0.4.32


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Figure 1. A system for water desalination. An aqueous NaCl solution (0.5 M NaCl) and pure water are on the left and right chambers of the membrane, respectively. Two graphene layers in the two chambers are exerted under pressures Pleft and Pright, respectively. C: cyan, H: white, N: blue, O: red, Na+: blue, Cl-: cyan; water molecules in left and right chambers: orange and purple. 3. Results and discussion First, water diffusion in the eight dipeptide crystals is presented. Then, water permeation and salt rejection through the dipeptide membranes are examined in a RO process. The performance of the eight membranes for water desalination are compared with other membranes reported in the literature. The dynamic and structural properties of water molecules in the membranes are discussed. Finally, the effects of temperature and membrane flexibility on water transport through the membranes are investigated. 3.1. Water diffusion Water diffusion along the z-axis in the eight dipeptide crystals is examined by the meansquared displacement (MSD) MSD =

1 N

N

∑ 〈| z (t ) − z (0) | 〉 2

i

i

(1)

i =1

where N is the number of water molecules and zi(t) is the position of ith molecule at time t. For better statistical accuracy, the multiple time-origin method was used to estimate the MSDs. As plotted in Figure 2, the hierarchy of MSD is VI > IV > AI > IA ≥ VV > AV > LS > VA. Apparently, the MSD depends on the pore size, as well as the alignment of water molecules in the pore quantified by helicity. Illustrated in Table 1, the helicity is defined as the angle formed between water alignment and the pore axis. Among VI, IV and IA, they have similar pore size (3.7 – 3.9 Å); nevertheless, the MSD in VI is the largest due to the lowest helicity (12°) and followed by IV (37°) and IA (42°). A similar trend is observed among AI, VA and LS with a close pore size (4.7 – 4.9 Å), in which AI with the lowest helicity (27°) exhibits the largest MSD compared with LS (30°) and VA (51°). On the other hand, with a similar helicity, water diffusion 5 ACS Paragon Plus Environment


appears to be faster in a smaller pore; for instance, IV (3.9 Å) has a larger MSD than VV (4.4 Å), and AI (4.7 Å) than AV (5.0 Å). The reason for the observed trend of MSD versus the helicity and pore size is that water molecules are more easily to align head-to-tail in a pore with a smaller size or a lower helicity, leading to faster diffusion. Oppositely, two or more water layers may form in a pore with a larger size or a higher helicity, thus water molecules have to move side-byside causing slower diffusion. Among the eight dipeptides, VI has the smallest pore size (3.7 Å) and lowest helicity (12°); therefore, water diffusion in VI is the fastest. 120

VI IV AI IA VV AV LS VA

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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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80 60 40 20 0

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Figure 2. Mean-squared displacements of water in dipeptide crystals. 3.2. Water flow and salt rejection Upon initiating simulation, water exchange occurs in two chambers for the system in Figure 1. Due to the presence of pressure gradient, there is net water flow from the left to right mimicking a RO process. Figure 3a shows the water flows Nw (i.e. the net transferred water molecules) through the eight dipeptides at ∆P = 90 MPa. Generally, the Nw increases linearly with time after a short time lag. Nevertheless, non-linear behavior is found in AV, AI and VV, which will be discussed below. The appearance of time lag is because the membrane is initially dry, thus water needs to fill in the membrane before permeation. From the slope, water flux Jw can be estimated by Jw = Nw/(A∆t), where A is the cross-section area of the membrane and ∆t is the time duration. As shown in Figure 3b, the Jw generally rises when the pore size increases. For AI and VA with an identical pore size (4.7 Å), the Jw is larger in AI due to a smaller helicity (27°). Similar behavior is also observed in VI and IA with an identical pore size (3.7 Å). Therefore, the pore-size dependence of water permeation under a pressure gradient is different from that of water diffusion. As discussed above, water tends to diffuse faster in a small pore at 6 ACS Paragon Plus Environment

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equilibrium condition. Under a pressure gradient, however, water permeates faster in a larger pore. This is because water permeation depends on not only diffusion, but also capacity (i.e., the number of water molecules in the pore). Here, the pore size is in a narrow range (3.7 ~ 5 Å) and water capacity increases with the pore size. On the other hand, the pore helicity has the same effect on both water diffusion and permeation. The smaller the helicity, the faster water diffuses and permeates. With the smallest helicity (12°), VI possesses water flux higher than IV (37°) even though the latter has a larger pore size.

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Figure 3. (a) Water flows and (b) water fluxes. Along with water permeation, salt may also enter the membrane and permeate. Figure 4 shows the number distributions of Na+ and Cl− ions along the pore axis at the end of 40-ns simulation. In all the eight systems, Cl− ions are completely blocked by the membrane. However, several Na+ ions can pass through the membrane except VI. By defining salt rejection as (cleft – cright)/cleft × 100%, where cleft and cright are the concentrations of Na+ ions in the left and right chambers, respectively. The salt rejections in VI, LS, IV and IA (over 90%, and 100% for VI) are higher than in AV, VA, AI and VV (< 70%).



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Figure 4. Number distributions of Na+ and Cl- ions at 40 ns. Each membrane is between the two dashed lines. It is interesting to observe that AV and LS have a similar pore size (5.0 and 4.9 Å), but the salt rejection is quite different. This suggests that other intrinsic properties also affect ion transport. Taking AV as an example, the main-chain -NH3+ and -COO− terminal groups are arranged in a staggered pattern in its crystal structure (Figure S2a and S2b). Although the positions of C, N and O atoms were not fixed during the RO simulation, the average number distributions of -NH3+ and -COO− groups are still staggered (Figure S2c). Consequently, the positive and negative charge densities display a sinusoidal pattern as in Figure 5a, where q = 1.6×10-19 C is the elementary charge of a proton. However, AV has a higher charge density than LS. Based on the charge density, the electric potential φ along the z-axis can be calculated from the Poisson equation based on the Gauss’s Law: ∇2φ = −ρ/ε0, where φ = 0 at the reference point z = 0, ρ is the charge density and ε0 is the vacuum permittivity. As shown in Figure 5b, AV, VA, AI and VV possess a larger electric potential difference between the left and right side of the membrane, which induces more ions to pass through the membrane and thus a lower salt rejection (< 70%). Nevertheless, the electric potential difference is relatively lower across VI, LS, IV and IA, and hence the salt rejection is higher (over 90%). This result reveals that the salt rejection is affected by pore size as well as the arrangement of charged groups, a phenomenon not observed in other types of RO membranes.


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Figure 5. (a) Average charge densities in VI and AV membranes along z-axis. (b) Electric potentials along the z-axis. The non-linear water flow (see Figure 3, particularly in AV membrane) is also related to the electric potential difference. Under an electric potential, water molecules are packed more tightly and thus water flow is impeded, as observed for water in carbon nanotubes under electric fields.33 In AV membrane, salt rejection is the lowest (~ 50%) among the eight membranes. As shown in Figure S3, when ions are permeated from the left to right of AV membrane, an electric potential is generated by the ions and opposite to the one generated by dipeptides. Thus, the total electric potential difference drops (as seen from 2 to 30 ns), thus promoting water flow. In other words, water flow becomes faster along with ion permeation. This non-linear behavior is also observed in AI and VV membranes but less obvious.

Figure 6 shows the performance of the eight dipeptides and other RO membranes in terms of salt rejection versus water permeability. The permeability was calculated from Pw = Jwl/∆P, where l is the membrane thickness. In AV, AI, VV and VA, the salt rejection is too low (< 70%) and not suitable for water desalination. The Pw in LS is comparable with graphene,30 graphyne34 and high-flux RO membrane,35 higher than in seawater and brackish RO membranes.35 The other three dipeptides (VI, IV and IA) possess Pw similar to seawater RO membrane, but the salt rejection in IV and IA is a bit low. Considering both the permeability and salt rejection, LS and VI are the best among the eight dipeptides. Particularly, VI exhibits 100% salt rejection and Pw nearly the same as seawater RO membrane, suggesting its potential for water desalination.



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Permeability (kg .m/m2. hr .bar) Figure 6: Salt rejection versus permeability for dipeptide and other membranes (graphene,30 graphyne,34 commercial RO and MFI zeolite35). 3.3. Water dynamics and structure It is instructive to understand water dynamics and structure in the membranes. Figure 7 shows the trajectories of randomly selected water molecules through three membranes (LS, VI and IV). The speed of water transport through the membranes is proportional to water flux. In LS with a large pore size (4.9 Å), most selected water molecules can pass though the membrane within 5 ns. Upon comparison, most water molecules in VI need a longer time (10 to 20 ns) to pass though, and some water molecules jump back and forth staying in the membrane. The reason is VI has a smaller pore size (3.7 Å). Nevertheless, the helicity also comes into play. IV has a slightly larger pore size (3.9 Å) than VI, but almost all the selected water molecules reside in the membrane for more than 20 ns and keep jumping before leaving the membrane. This is attributed to a higher helicity (37°) in IV compared with VI (12°), which inhibits water transport. 20

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z (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

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Figure 7: Trajectories of water molecules through LS, VI and IV membranes. Each membrane is between the two dashed lines. 10 ACS Paragon Plus Environment

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To characterize water structure, hydrogen bonds are calculated on the basis of two geometrical criteria: (1) the distance between a donor and an acceptor ≤ 0.35 nm and (2) the angle of hydrogen-donor-acceptor ≤ 30°.36 The relaxation of hydrogen bonds is quantified by autocorrelation function (ACF)36,37 c (t ) =

hij ( t0 ) hij (t 0 + t )

(2)

hij ( t0 ) hij ( t0 )

where h(t ) = 1 if two water molecules are hydrogen bonded at time t and h(t ) = 0 otherwise. The

ensemble average ... is on all the pairs of hydrogen bonded water molecules. The ACF describes the probability of two molecules being bonded at both time t = 0 and t, thus it can reveal the relaxation rate of a hydrogen bond. Shown in Figure 8 are the c(t) in LS, VI, IV and bulk phase. Compared with those in dipeptides, c(t) in bulk phase is much lower, because the membrane confinement and interaction restrict water motion and slow down the relaxation of hydrogen bonds. Additionally, c(t) in LS, VI and IV are inversely proportional to water flux. Among the three dipeptides, water flux through LS is the largest and thus hydrogen bonds are mostly relaxed. The lifetime of hydrogen bonds τHB can be calculated from c(t = τHB) = e-1. In LS, VI and IV, the τHB are 2.4, 2.5 and 2.9 ps, respectively. Compare with the case in ZIFs (e.g. 1.7, 1.8 and 2.2 ps in ZIF-25, -71 and 96),38,39 the lifetime in the three peptides is longer since water molecules are more strongly confined in one-dimensional dipeptide pores than in the threedimensional porous network of ZIFs.39 1.0

LS VI IV in bulk

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c(t)

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Figure 8. Autocorrelation function c(t) in LS, VI and IV membranes and bulk phase, respectively. 11 ACS Paragon Plus Environment


3.4. Effects of temperature and membrane flexibility Figure 9 shows water fluxes through LS and VI membranes as a function of inverse temperature 1000/T. The activation energy Ea of water transport can be estimated from the Arrhenius equation

J w ∝ e − Ea / RT

(3)

where R and T are gas constant and temperature. Through LS and VI, the Ea are about 27.72 and 33.42 kJ/mol, respectively. The reason for a lower Ea through LS is that LS has a larger pore than VI and hence water can more easily transport. As a comparison, the Ea through (6, 6), (7, 7) and (8, 8) carbon nanotubes with a similar pore size are much lower (1.6 kJ/mol).40 This is because the pores in carbon nanotubes are extremely smooth, which facilitates fast water transport. In spite of one-dimensional, the pores in the dipeptide membranes are rough and helical, thus leading to higher Ea. 3.5 3.0 LS 2.5 2.0

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lnJw(10 kg hr m )

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VI

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1000/T (K )

Figure 9. Water fluxes through LS and VI membranes vs inverse temperature (1000/T) at ΔP = 90 MPa. The dashed lines fit to the Arrhenius equation. All the above results are based on position restrained dipeptide membranes with a force constant of 1000 kJ/(mol·nm2) on the heavy atoms, which is the default value in Gromacs. To examine the effect of membrane flexibility, the force constant was varied to 200 and 2000 kJ/(mol·nm2). A smaller force constant denotes the atoms are less restrained, i.e., the membrane is more flexible. Figure 10 shows that water flow through VI membrane drops with decreasing force constant. This is because the pore size is governed, to a certain extent, by the force constant. As shown in Figure S4, at a smaller force constant, the membrane is more flexible and


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there is a larger fluctuation in the pore diameter during simulation. Specifically, the pore diameter becomes smaller in most of the regions; consequently, water flux is reduced. 1800 VI 1500

kb = 2000 kb = 1000 kb = 200

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Figure 10. Water flows through VI membrane with position restraint force constants of 2000, 1000 and 200, respectively. 4. Conclusions Water desalination through eight dipeptide membranes AV, VA, AI, IA, VI, IV, VV and LS has been investigated. Due to the staggered arrangement of -NH3+ and -COO− groups, an intrinsic electric potential difference exists between the membrane interfaces and determine salt rejection. With a smaller electric potential difference, VI, LS, IV and IA show higher salt rejection (over 90%) than AV, VA, AI and VV (< 70%). Water flux is in the order of AV > LS > AI > VV > VA > VI > IV > IA, depending on the pore size and helicity. The higher flux through AV, LS, AI and VV is based on their large pore size. Despite a similar pore size in AI and VA, a higher flux is observed through AI because of its lower helicity. Among LS, VI and IV, the lifetime of hydrogen bonds in LS is the shortest, which follows a decreasing trend of water flux. The activation energies of water transport through LS and VI are approximately 27.72 and 33.42 kJ/mol, larger than through carbon nanotubes as a result of the rough and helical pore surface in dipeptides. Moreover, water flux is found to drop with increasing membrane flexibility. This simulation study suggests that the dipeptide crystals might be intriguing RO membranes for water desalination. Nevertheless, several limitations associated with the simulations should be noted: (1) The pressure gradient applied is much higher than practical cases. This is a common practice in simulation studies in order to observe the RO process within nanosecond timescale. (2) The model membranes are very thin and not straightforwardly comparable with realistic membranes. Despite these limitations, the study provides the molecular-level 13 ACS Paragon Plus Environment


understanding of water behavior in dipeptides, unravels the significant role of pore size and helicity in water transport, and would facilitate the rational design of new porous materials toward high-performance water desalination.

Supporting Information Atomic structures of eight dipeptides; Arrangement of -NH3+ and -COO− groups in AV dipeptide, number distributions of -NH3+ and -COO− groups; Ion distributions and electric potentials in AV system; Diameters of one pore in VI membrane at various position restraint force constants.

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

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TOC Graphic


Dipeptide Crystals as Reverse Osmosis Membranes for Water

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