Water desalination through fluorine-functionalized nanoporous graphene oxide membranes

Water desalination through fluorine-functionalized nanoporous graphene oxide membranes

Accepted Manuscript Water desalination through fluorine-functionalized nanoporous graphene oxide membranes Mostafa Hosseini, Jafar Azamat, Hamid Erfa...

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Accepted Manuscript Water desalination through fluorine-functionalized nanoporous graphene oxide membranes

Mostafa Hosseini, Jafar Azamat, Hamid Erfan-Niya PII:

S0254-0584(18)30952-0

DOI:

10.1016/j.matchemphys.2018.10.063

Reference:

MAC 21078

To appear in:

Materials Chemistry and Physics

Received Date:

08 September 2018

Accepted Date:

30 October 2018

Please cite this article as: Mostafa Hosseini, Jafar Azamat, Hamid Erfan-Niya, Water desalination through fluorine-functionalized nanoporous graphene oxide membranes, Materials Chemistry and Physics (2018), doi: 10.1016/j.matchemphys.2018.10.063

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Water desalination through fluorine-functionalized nanoporous graphene oxide membranes

Mostafa Hosseini a, Jafar Azamat b, Hamid Erfan-Niya a,* a

Faculty of Chemical and Petroleum Engineering, University of Tabriz, 51666-16471 Tabriz, Iran b

Department of Basic Sciences, Farhangian University, Tabriz, Iran

* Corresponding author. Tel.: +98 41 33392940; Fax: +98 41 33338497. E-mail address: [email protected] (H. Erfan-Niya).

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Abstract This study evaluates the application of fluorinated graphene-based water desalination membranes using molecular dynamics simulations. The studied membranes are fluorinated nanoporous graphene oxide (F–NPGO) and nanoporous graphene (F–NPG) sheets. The applied pressure, as a driving force, was used in the range of 5–150 MPa in order to transfer the water molecules through the reverse osmosis (RO) membranes. The obtained results show that the water permeability of F–NPGO membranes (G1 and G2) is much greater than that of F–NPG membranes (G3 and G4) due to the existence of hydrophilic groups on their surface. The maximum value of water permeability was obtained for the G2 system (i.e., 3345 L/(m2 hr bar)) at 150 MPa applied pressure. By fluorine functionalization of the pore edge, the passage of ions through the membrane, especially Cl- ions was prevented. This is the main issue of salt rejection performance. The minimum of obtained salt rejection percentage for F–NPGO membranes with the large pore (G2) was 94.31%, and small (G1) pore didn’t allow to crossing all of the ions. Many analyses such as water density map, water density profile, RDF, and PMF calculation for precisely understand and prove the performance of membranes systems was computed.

Keywords: Water desalination; Graphene-based membranes; Fluorine-functionalized pore; Molecular dynamics

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1. Introduction Even though about two-thirds of the Earth's surface is water-covered (in oceans, seas, lakes, rivers, etc.), the clean drinking water is not available sufficiently because oceans and seas, which constitute 97.5% of the Earth's water, contain salty and non-potable water [1]. Desalination of seawater is essential to solve the freshwater scarcity for surviving on the earth [2, 3]. But, desalination technology has been severely restricted from the beginning and the aim of many scientific research in the world is to eliminate the limitations and extend the water desalination industry [4]. The biggest challenge in water treatment technology during the last half-century is economic problem and all the challenges are due to the economic efficiency of freshwater production by seawater desalination; Because a method should be proposed to produce the highest amount of freshwater with lowest amount of energy and environmental pollution [5]. Membrane-based processes play a key role in the industry of water desalination. The processes of water desalination via membranes are classified on the basis solute size that are retained; and subsequently depend on membrane pore size and separation purpose, including: microfiltration, ultrafiltration, nanofiltration and reverse osmosis. Reverse osmosis (RO) method is a well-known water desalination technology that offers the most energy-efficient technique for industrial applications; therefore, more than half of all existing seawater desalination plants utilize RO technology [5, 6]. Low salt rejection and low water permeability were the problems of early membranes. The salt rejection reached to 98% by using cellulose acetate membranes [7]; but, the permeation rate remains an unresolved challenge. The water permeability reached near 1 L/(m2 h bar) using fully aromatic thin-film composite and hollow fiber membranes [8, 9]. This achievement has not been

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developed and improved for many years. The first revolution in desalination technology has been occurred when a high rate of salt rejection as well as an adequate water permeability were achieved. Desalination processes are carried out with high cost and low water production. For example, classical RO membranes such as conventional polymeric membranes, exhibit a poor desalination performance due to membrane fouling which results in low water flux and high operational costs. Recently, new nanomaterials [10, 11] such as graphene [12-14], multilayer graphene oxide [15, 16], molybdenum disulfide [17] and boron nitride nanotube [18, 19] have been studied for water desalination. Water flux and permeability of two-dimensional (2D) membranes with a thin thickness [20] have improved significantly which make them more economically efficient membranes [21, 22]. Water desalination is performed slowly by a solution-diffusion process in conventional RO membranes, whereas, a fast-convective water flow is done through the well-defined pores in 2D nanoporous membranes. Carbon nanotubes have a low salt rejection [23, 24] whereas zeolites have a low water flux [25, 26]. Some surface properties can also affect the properties of nanostructures. Tao Li et al. investigated the wetting and coalescence of some liquids drops on carbon-based substrates. Their results emphasized the importance of the microstructure and surface topography of substrates in the coalescence process and also showed that the effect of substrate on coalescence is achieved by changing the wettability of the selected metals [27]. The main issue in scientific research is how to improve the performance of water desalination and reduce the capital and operating costs [5]. The answer to this question addresses the aim of the current study. To reduce the costs of water desalination and extend the process, it is essential to focus on energy consumption as well as capital and operational costs of the desalination plant [28]. The freshwater production cost in RO process is affected by energy consumption. Hence,

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recovery of energy or supply of energy from renewable sources have been explored in the water desalination industry [5, 28]. Also, improving the efficiency of desalination regarding the water permeability and salt rejection parameters needs to chemically modified 2D nanoporous membranes. Beyond atomistic simulations, recent progress in the development of multiscale and macroscale methods have enabled a more rigorous approach to study the relationship between molecular scale structure, material properties and ultimately system performance [29]. System simulations have an essential role to play in furthering our understanding of how NPGO (nanoporous graphene oxide) might fit into future RO-based technologies. Macroscopic simulations that draw from mechanical, chemical and systems engineering, as well as economics, have already been successfully applied in the field of desalination [30-32]. Moreover, CohenTanugi et al. [20] investigated the relationship between MD (molecular dynamics) simulation of ultra-permeable membrane (UPM) and macroscale desalination. By modeling the mass transport and fluid dynamics inside RO pressure vessels, they quantified how much a tripling in the water permeability of membranes would improve the feed pressure, recovery ratio, permeate production per vessel or number of membrane elements per vessel in a RO plant. They found that UPMs would allow for 63% fewer pressure vessels for a brackish water RO plant of a given capacity, and 55% fewer pressure vessels for a seawater RO plant, all other parameters being equal; and they demonstrated that membranes with 3x higher permeability could reduce the energy consumption of RO by 15-46% for seawater and brackish water respectively. Herein, we will show that increasing in water flux factor of the membrane could produce cheaper water, e.g. reduced system size of RO plant because the water flux is an important factor in the efficacy of RO plant. Also, we will demonstrate that there are less than 10% in water permeability results between our

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MD simulation of hydroxylated and hydrogenate NPGs and experimental fabricated NPGs by Surwade et al. [33]. This is an important reason about the accuracy of our simulation and MD simulation efficiency. Therefore, in this study, the chemically modified nanoporous graphene oxide (NPGO) and nanoporous graphene (NPG) membranes by fluorine (–F) are employed to investigate the membrane efficiency inside the desalination process by considering the water permeability and salt rejection. Increasing the efficiency of membranes and high freshwater production results in reducing the costs of the desalination plant. MD is a computational technique that solves the Newton’s equations of motion numerically for a system consisting of N particles (atoms and molecules) which interact through a force field. The trajectories of particles are calculated by MD simulation at molecular levels so that the macroscopic properties of the system are obtained from its microscopic behavior using statistical mechanics [34]. In this study, the molecular structure of fluorine-functionalized nanoporous graphene oxide (F–NPGO) and nanoporous graphene (F–NPG) membranes is constructed to study the performance of F–NPGO and F–NPG membranes in terms of water flux, permeability, and salt rejection as a function of applied pressure, pore-size and pore chemistry.

2. Methodology 2.1. Molecular structures The effects of pore-size and chemical function (fluorine) on the performance of graphenebased membranes were investigated in this study. For this purpose, four types of fluorinated pores with different sizes were created on the NPGO (G1 and G2) and NPG (G3 and G4) membranes in order to evaluate the water desalination across them. The pore diameter in G1 and 6

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G3 membranes is 0.3 nm whereas in G2 and G4 membranes is 0.45 nm. The pore diameter is calculated according to the relation: d  2 A  where d and A are pore diameter and pore area, respectively [35]. The pristine graphene sheet was drilled to create small pore; after that functional groups were added to edge of pore. The structure of NPGO membrane was created via adding the hydroxyl and epoxy functional groups on the both sides of the NPG membrane. The functional groups in NPGO membrane were spatially distributed and randomly sampled over the oxidized region. Also, the ratio of hydroxyl/epoxy groups was adjusted as 1/1 on the graphene basal plane [36]. The concentration of oxygen in the NPGO was chosen about 20% in the current study. According to experimental studies, the minimum oxygen concentration in the GO sheet is about 20%. More reduction leads to a lower concentration of oxygen (12.5-0.04%) in the reduced graphene oxide (rGO). Moreover, the 20% O/C ratio is common in the theoretical studies in GO nanosheet and this ratio is useful for comparing results with the experimental works. In the current study, the O/C ratio can be higher than 20%, but the results obtained in the minimum concentration of NPGO membrane and we observed more improving in water flux and salt rejection, and hydrophilic property of membrane surface. This is clear that in the higher concentration, we will have better water flux. If we were taking upper ratio, we didn’t know about the NPGO performance in minimum ratio. It should be noted that there is the limitation in increasing the O/C ratio in water desalination application. We don’t have allowed to put the functional group on the edge of the membrane, because these groups have a low effect on desalination efficiency and adding these groups make the incorrect model for investigating of NPGO membrane. Figure 1 shows the molecular structure of the fluorinated NPGO and NPG membranes which are named as F–NPGO and F–NPG membranes.

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2.2. Molecular simulations First of all, the geometry optimization of the membranes was obtained by the density functional theory (DFT) method. The DFT calculations were carried out using the GAMESS software [37] at the B3LYP level with 6-311G basis-set in which the optimized structure and partial atomic charges of the F–NPGO and F–NPG sheets are attained. The obtained partial atomic charges were represented in Table 1 [38, 39]. Also, the partial atomic charges of the membranes are not affected by the pore-size. In order to describe the interactions between atomic species, the Lennard–Jones (L–J) interatomic potential was used. The actual parameters of L–J potential were determined for the water/F–NPGO, water/F–NPG, water/ion, ion/F–NPGO and ion/F–NPG interactions using the Lorentz-Berthelot combining rule [40, 41] and L–J parameters was collected in Table 1. All MD simulations were carried out using the NAMD 2.12 software [42] with a time-step of 1 fs. The vdW interactions between atoms were calculated within the cut-off radius of 12 Å. Also, the Particle Mesh Ewald (PME) method [43] was used to calculate the electrostatic interactions. All the analysis scripts were written by VMD software [44]. The simulated system consists of a F– NPGO or F–NPG membrane, water, and ions (Na+ and Cl-) with the salinity of ~ 0.6 M (seawater salinity). Periodic boundary condition (PBCs) were applied in whole progress. The size of the simulation box is 30 × 30 × 80 Å3 along the x, y, and z directions, respectively. In all MD simulations, the TIP3P water model [45] was used for aqueous solutions. The system was equilibrated at constant temperature and pressure (T = 298 K and P = 1 bar). The Langevin thermostat [46] and the hybrid Nosé-Hoover/Langevin piston barostat [47] were used to control the temperature and pressure of the system, respectively. After the initial equilibration to minimize the energy, all MD simulations were carried out in the NVT ensemble for 5 ns at 298

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K. A F–NPGO or F–NPG membrane was placed at the center of the simulation box. Also, a pristine graphene, as a barrier sheet, was located at z = -40 Å so that the molecules passing across the permeate side not re-enter to the feed side. All atoms of the functionalized membrane (F–NPGO or F–NPG) and barrier sheet (pristine graphene) were held fixed in the MD simulations whereas the water molecules and ions were free to move. The external forces were exerted on the water molecules to make a pressure drop across the functionalized membranes [48, 49]. The applied force exerted on the water molecules was calculated as: F

P  A n

(1)

where F is a constant force in the z direction, ∆P is the applied pressure, A is the cross-sectional region of the membrane, and n is the sum of water molecules. This method has been employed by many authors in pressure-driven flow [50, 51]. The range of the applied pressure was 5 to 150 MPa. The MD simulations were repeated 5–8 times for each applied pressure within 5 ns with different starting configurations so that the more accurate ensemble averages to be obtained. The ion permeation or rejection phenomenon across the fluorinated pores of NPGO and NPG membranes can be explained by calculating the potential of the mean force (PMF). Therefore, the simulation box was divided into windows with equal length in the z-axis of the system. The mean force distribution was obtained by sampling the force experienced by ions that were located in different positions. The ions were moved through positions from -10 Å to 0 Å (center of the membrane pore) with 0.1 Å increments, and the z-component of the ions was held in position using a tunable force constant of 15 kcal (mol Å2)-1 when the system was in equilibrium. The PMF curves were obtained by the umbrella sampling technique [52]. Each step or window

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was run for 1 ns and the obtained data were analyzed by the weighted histogram analysis method (WHAM) [53].

3. Results and Discussion 3.1. Water Flux and Permeability Coefficient In the present work, fluorine (–F) as a chemical function was used to modify the pores of NPGO and NPG membranes. Therefore, the small and large fluorinated-pores (F–pores) were created on the membranes in order to study the effect of pore-size and chemistry on the water flux and ion rejection through the membranes. Figure 2 reveals the water flux through the various types of pores on the F–NPGO and F–NPG membranes versus the applied pressure. The water flux unit indicates the number of transferred water molecules across the membrane pores per nanosecond (# ns-1) [17]. A comparison between the obtained results of F–NPGO and F– NPG membranes reveals that the F–NPGO is more efficient membrane due to the existence of hydrophilic groups on its surface. In order to study the water permeation, the F–NPGO (G1 and G2) pores were compared with the F–NPG (G3 and G4) pores which have approximately equivalent accessible pore areas. As shown in Figure 2, the water flux of F–NPGO membranes was higher than that of F–NPG membranes in all MD simulations. At P < 50 MPa, the water permeability of F–NPGO (G1 and G2) membranes was much greater than that of F–NPG (G3 and G4) membranes at the same size. It is due to existence of hydrophilic functional groups on the surface of F–NPGO membrane that can form the hydrogen bonding with water molecules. Therefore, the energy barrier decreases for water flux across the F–NPGO pores which results in increasing the overall water flux. But, the difference in water permeability was slight and gradually going down at P > 50 MPa. Therefore, the functional groups show less effect on the improvement of water flux and its permeability at P > 50 MPa. As can be seen in Figure 2, when 10

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pressures of 5 and 10 MPa was exerted to the system G3, the water flux was not observed while the value of applied pressure was more than the osmotic pressure difference between two sides of the simulation box. A similar condition was occurred for system G4 at pressure of 5 MPa. This phenomenon can be explained by increasing the hydrophobic property of NPG membrane surface via addition of fluorine (–F) to the pore edge. Theoretically, the osmotic pressure difference of 29 bar for 0.6 M NaCl was considered as a driving force for crossing the water molecules [54]. At high pressures (P > 50 MPa), the effect of these interactions is negligible due to the existence of high driving force for water flow. Also, there is the repulsive electrostatic interactions between oxygen atoms of water molecules and fluorine atoms which are very important at low pressures. It should also be noted that the water flux through G4 membrane with all-hydrogenated pore was significant at applied pressures of 5 and 10 MPa [54]. Also, this figure shows that the water flux increases with an increase in pore area which is in good agreement with Hagen-Poiseuille’s law. At the region of low pressures (P < 50 MPa), the water flux of F–NPGO with smaller pore-size (G1) is greater than that of F–NPG with larger pore-size (G4). The low-pressure zone is more important. Because the high applied pressures in membrane-based water desalination result in high operating cost. Hence, G1 system can be considered as a promising candidate for new generation of membranes with high permeability and salt rejection. Therefore, the comparison of water flux between F–NPGO and F–NPG membranes shows the importance of designing new generation of membranes. Because, the water flux increases significantly by adding chemical functions to the surface of membranes. Also, Figure 2 shows that for a desired water flux (e.g., 28 #ns-1), a smaller applied pressure is required for G2 membrane (10 MPa) in comparison with G4 membrane (65 MPa) and therefore, the operating costs is reduced. Comparing the water flux of fluorinated NPGO in this work and

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hydroxylated NPGO in our previous work [54] demonstrated that the permeability of (F–H–F) group at the pore edge of F–NPGO is the same as the permeability of (OH–H–OH) group at the pore edge of OH–NPGO and the hydrophilic feature of both arrangements is the same. The different behavior of water molecules in four membranes are calculated by water density map along the x-axis of the simulation system. The water density maps were obtained using the VolMap plugin in VMD software. Figure 3 illustrates the water density maps of G1, G2, G3, and G4 membranes with different arrangements. Water molecules are attracted toward the surface of F–NPGO membranes that leads to an increase in water flux. While, a similar phenomenon is not observed in F–NPG membranes. Also, the water molecules passed from near the pore edge and there is not significant struggle in pore center for passing. High dense passageway in pore center of F-NPG may cause reversely attraction of water molecules toward the functionalized pores after passing the pores and drag the water molecules into the pores and return to the feed side. The water density map snapshots clearly confirm that the water molecules were distributed on the surface of F–NPGO after passing through the membrane. This behavior of F–NPGO is due to its hydrophilic surface that increases its wettability property. But, the mentioned behavior of water molecules was not observed in the F–NPG membranes in which the water molecules are transferred through the pore center and accumulated near the pore due to its hydrophobic surface. Also, the water molecules in G1 and G2 systems distribute to the membrane surface homogeneously and pass easily through the membranes; but, in G3 and G4 systems, there is a disturbance in high-density water passageway for passing across the pore. Hence, the water flux in F–NPG (G3 and G4) membranes is lower than F–NPGO (G1 and G2) ones. As illustrated in Figure 4 for water density maps, the regime of water flow across the pores in the F–NPGO and F–NPG membranes is different at the same conditions of pore size, functional

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groups and applied pressure. Green, red and again green colors near the fluorinated pores indicate the regular and uniform water flow near the functionalized pore; also, blue color of pore center shows a less accumulation and disturbance for water flow through the pore center. With increasing the pore size in G2 and G4 membranes, more space will be available for passing the water molecules through the pore cross-sectional area between the pore center and near the pore edge. Moreover, the orientation of oxygen atoms of water molecules was affected by the partial charges of functional groups near the pore edge and the maximum water flow was observed near the three points (H–F–H) group. This phenomenon can be explained due to the overall positive charge of (H–F–H) group in comparison with (F–H–F) group of functional groups in the pore edge. Therefore, (H–F–H) group can easily attract the oxygen of water molecules with negative charge to pass across the pore. This is the reason for using the combination of fluorinated and hydrogenated pores as the pore functional groups. Unlike the F–NPGO, the water molecules are uniformly passed near the functional groups of the pore edge of the F–NPG. This fact can be seen in Figure 4, wherein a combination of red and green colors alongside is observed near the pore edge not a single-color spectrum. Also, the amount of green color at pore center of F–NPG is lower than F–NPGO system which causes a disturbance in passage of water molecules through the pore of F–NPG membranes. So, the irregular and non-uniform water flow leads to the reduction in water flux. Figure 4 illustrates the role of functional groups at pore edge and the behavior of water molecules passing through the pore. Also, the water density map in the present work can be compared with our previous work. The water flux (JW) can be calculated using the following equation [55]: JW  A  P   

(2)

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where A is the permeability coefficient of water, ∆P is the applied pressure, and ∆π is the osmotic pressure. When ∆P > ∆π, water molecules flow from a region of higher concentration to a region of lower concentration. In order to compare the water permeability between the studied membranes and the other membranes, the units in the results of Figure 2 should be converted to (L/(m2 hr bar)). The water permeability for G1, G2, G3, G4 systems are almost 774, 956, 133, 497 L/(m2 hr bar), respectively at the applied pressure of 50 MPa and pore density of 0.111 nm-2. The obtained MD results demonstrated that the water flux in G1 and G2 membranes is 77% and 88%, respectively which is better than that in G3 and G4 membranes. These values are higher at lower applied pressures; i.e., ~ 2–5 order of magnitude greater than the current reverse osmosis membranes [1]. The maximum value for water permeability of the investigated membranes is 3345 L/(m2 hr bar), that belongs to G2 system at the applied pressure of 150 MPa.

3.2. Effect of temperature Temperature is one of the most important parameters that influences the chemical potential and its change can affect the water flux in RO membranes [55]. As the temperature increases, the chemical potential of the system decreases as much as the entropy of the system. This phenomenon causes to increase the effect of the applied pressure; and as a result, the water flow increases from the saline water side to the fresh water side and eventually leads to an increase in water flux across the membrane. For this purpose, to investigate the effect of temperature, the G2 system was studied at the temperatures of 283, 288, 298, 308, 318, 328, and 333 K. The temperature of 283 K was chosen to study the reduction of temperature in water desalination system.

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Many experimental results of water desalination by membrane processes were reported at temperatures about 313 K [1, 14], which is close to the simulated temperature of 318 K. It should be

noted

that

temperatures

above

333

K

were

rise and lack of economic justification. According to the Figure 5, at the applied pressure of 10 MPa, as the temperature rises, the water flux increases; so that by increasing the temperature from 298 to 333 K, the water flux increases ~ 74%. This increasing in the temperature is equivalent to an approximate increasing of 60 MPa in applied pressure. Also, molecular dynamics simulations were performed at 150 MPa and same temperatures (see Figure 5) which revealed an increase in water flow through the membrane with increasing the temperature at high pressures. The results of MD simulations at the applied pressure of 10 MPa for G4 system demonstrate the passage of 6 water molecules over the simulation time. The temperature rising did not show significantly effect on the water flux through the G4 membrane at the applied pressures near the osmotic pressure. It should be noted that an increase in the temperature has no effect on the separation performance of membranes; and therefore, the salt rejection rate remains almost constant. 3.3. Salt Rejection Ion separation ability is one of the most important factors in the performance of RO membranes; because, the ultimate goal is the separation of ions from saline water. In the present study, the simulation time of 5 ns is an enough time to investigate the salt rejection rate of membranes. In operating conditions, some of the feed water in the system is taken as the concentrate or retentate water according to the recovery rate; then, the salt rejection rate is measured. In commercial RO systems, the recovery rate is almost near 30-50%. Recovery rate is obtained from the ratio of the permeate water to the feed water [55]. It should be noted that the

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obtained recovery rates in the MD simulations are almost in the range of 30-50%. Figure 6 displays the percentage of rejected salt by the F–NPGO and F–NPG membranes versus applied pressures. As shown in the figure, the ion rejection at P < 50 MPa is about 100% for all types of the F–NPGO membranes. Also, the rejection rate at all pressures was 100% for G2 membrane. The salt rejection decreases with increase of the applied pressure and pore-size and reaches to a minimum value of 90.9% for G4 pore at 150 MPa. In the case of large pores (G2 and G4), ions pass through the pore and reduce the salt rejection with increase of the pressure. At higher pressures, higher forces are induced on the ions and cause to more ions movements from one side of membrane to another side, leading to a decrease in ions rejection. Also, the salt rejection of F–NPGO membranes is somewhat better than that of F–NPG ones at the same conditions. Many studies in the field of water desalination through graphene-based membranes have been carried out by hydrogenated and hydroxylated pores [12-14]. According to previous studies on hydroxylated graphene [54], two considerable issues were observed. The first one is the high passage of chlorine ions across the pore in comparison with sodium ions due to the large size of chlorine ions with respect to sodium ions; because, the chlorine ions with larger size are most influenced by the propulsion force of the water molecules and pass through the membrane more than sodium ions. The second issue is accumulation of chlorine ions near the pore edge and their interactions with hydroxylated functional groups of the pore edge. This effect is related to the fact that hydroxyl (–OH) functional groups make the hydrogen bonds with salt ions, more similar to what water molecules do, which leads to a lower free energy barrier for ionic passage, increasing the probability of ions passage and decreasing the water permeability due to the accumulation in front of the pore. Therefore, in order to solve the mentioned problems, the fluorine (–F) with negative partial charge and hydrogen (–H) with positive partial charge were

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used to modify the pores. The addition of fluorine atoms and well defining of the pores, two basic problems were completely solved; therefore, the pore fluorination in nanoporous membranes is one of the best recommended options for increasing the performance of water desalination. In this work, fluorination of pore edge improved the salt rejection compared to our previous work [54]. In order to accurately investigate the membrane selectivity and the efficiency of the functionalized pores, the PMF functions were calculated along the z-axis of the simulations box with and without applied pressure. Figure 7 shows the PMF values of ions in the studied systems. The free energy profile for permeation of ions is positive; so, in the absence of external forces to the simulation box, ions do not pass through the pore. While, with regarding the applied pressure to the system, the external forces are given to ions by water molecules wherein some ions overcome the potential barrier and pass through the pore with water molecules. It can be also noted that the amount of force exerted on the ions increases with increase of applied pressure; as a result, the salt rejection decreases with increasing the applied pressure to the system. Three common phenomena in both types of membranes are observed: (I) by approaching the pore openings, the PMF is increased and reached a maximum value at the pore center. This is due to the interactions between ions and functional groups of the pore edge. While the interactions between ions and water molecules is negligible inside the pore. (II) the energy barrier for passage of Cl- ions is greater than Na+ ions; on the other hand, there is a strong energy barrier to prevent Cl- ions entering the pore due to the existence of fluorine with the negative charge in the pore edge. (III) with increasing the pore size in membranes, PMFs are decreased and a low energy barrier is needed for ions passage; hence, the salt rejection rate is decreased by increasing the pore size. In F–NPGO membranes, the PMFs of both ions (Cl- and Na+) are

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greater than F–NPG membranes. Therefore, the barrier energy of G2 membrane with bigger pore size is greater than that of G3 with smaller pore size (see Figure 7). The obtained MD simulation results confirm the capability of the F–NPGO membranes in salt rejection with respect to F–NPG ones. Finally, the fluorination of the pore edge prevents the more passage of Cl- ions; because, Cl- ions are more affected by the force to pass through the pore due to their larger size with respect to Na+ ions. Radial distribution function (RDF) or g(r) can be employed to describe the structure of the water molecules around the ions. The RDF calculations were computed for all membrane systems at all applied pressures but the obtained results show that the RDFs of ions–water were similar by changing the membrane types and applied pressures; therefore, the RDFs of ions– water almost depend on the nature of ions and water. On the other hands, the RDFs of Cl-–water and Na+–water show the different results. Hence, the RDFs of Cl-–water and Na+–water were reported for G2 membrane at the applied pressure of 10 MPa. As illustrated in Figure 8, g(r) is zero at short distances less than the atomic diameter, because of the strong repulsive forces between atoms. The first peak in the RDF of Cl-–water is closer to membrane surface and has higher intensity than that of Na+–water. This different behavior demonstrates the different hydration number of ions and the probability for the passage of Cl- ions is more than Na+ ions in simulation box. This phenomenon is controlled by using fluorine atoms at the pore edge. The arrangement of water molecules around the membrane can be revealed by the density profile. Figure 9 displays the density profile of water molecules in both sides of G1 membrane in the simulation box. In the G1 system, water molecules concentrated in the region of ±0.35 nm between the left and right sides of the membrane. This phenomenon was observed in the all of the simulation systems. This behavior of water molecules exhibits two sharp peaks at various

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applied pressures near the G1 membrane (Figure 9). Also, this figure shows that the water flux increases with increasing of the applied pressure. The layered arrangement of high-density water was detected in a region near the membranes; but, in the region far away from the membranes, the water density was 1 g/cm3. This observation was confirmed by RDFs between oxygen– oxygen water molecules inside a region of ±0.35 nm around the G1 and in the whole system (Figure 10). Figure 11a shows the effect of pore size on the arrangement of water molecules at the same membrane type and applied pressure (10 MPa). The first peak of G1 system is greater than G2 due to higher accumulation of water molecules in the left side of G1 membrane; therefore, G1 membrane plays a more barrier role for water flux with respect to G2 membrane. But, Figure 11b indicates the effect of membrane type on the arrangement of water molecules at the same pore size and applied pressure (150 MPa). According to this figure, F–NPGO membrane is more permeable than F–NPG membrane; because, the second peak of G1 is greater than G3. While, the first peak of G3 is greater than G1 which demonstrates higher accumulation of water molecules behind the F–NPG with respect to F–NPGO. Therefore, the barrier role of F–NPGO for water flux is less than F–NPG. Finally, the F–NPGO membranes have high water permeability due to the existence of hydrophilic groups on the surface and their atomic thickness. Moreover, full salt rejection was obtained by fluorination of pore edge. The high-water permeability and full salt rejection at low pressures indicate the capability of F–NPGO membranes with respect to F–NPG and conventional reverse osmosis membranes. These types of membranes need lower energy requirements and operating cost for a given water output; because, they work at lower operating

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pressures. Therefore, these membranes can be used in large number of operating RO units in the world in order to improve the efficiency of water desalination plants.

4. Conclusion In this study, fluorine-functionalized NPGO and NPG membranes with the pore size of 0.3-0.45 nm were investigated by molecular dynamics simulations for application in water desalination. Hydrophilic functional groups on the surface of F–NPGO membrane cause to increase the water permeability in comparison with F–NPG membrane. These functional groups affect the water flow regime. The water molecules in the F–NPGO systems approach uniformly to the membrane surface and pass through the pore edge with a more specific pathway than the F–NPG membrane. While in the F–NPG systems, the water molecules pass across the pore in a non-specific pathway along with more collisions among molecules which is explained by the water density map analysis. The hydration of ions and probability of finding an ion with respect to the membrane was determined by RDF analysis. It was found that Cl- ions are more affected by the driving force exerted on the water molecules to cross the membrane in MD simulations. The passage of Cl- ions was largely prevented by fluorine (–F) functionalization of pore edge which led to increase in salt rejection rate of the membranes. The chemically functionalization of pores by fluorine (–F) owns the advantages of both hydroxyl (–OH) in increasing the water permeability and hydrogen (–H) in increasing the rate of salt rejection simultaneously. The increase in the energy barrier against the passage of ions (especially the Cl- ion in the PMF analysis) was explained. Also, salt rejection rate and water flux of F–NPGO systems were more than F–NPG systems. In the G1 system, the passage of ions was not observed at all applied pressures while the minimum salt rejection of 94.31% was obtained in the G2 system at 150 MPa. The effects of pore size, type of membrane and different applied pressures on the water 20

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permeability was clarified by water density profile across the pore. Also, the water flux increases with increasing the temperature while no significant change occurs in salt rejection rate. The water flux was increased almost 74% by increasing the feed side temperature from 298 K to 333 K in the G2 system which is equivalent to a change in the applied pressure from 10 to ~70 MPa. Therefore, the effect of temperature on water permeability and salt rejection is promising to increase the efficiency and reduce the capital cost of water desalination units by simultaneously using optimum temperature and pressure. Finally, the fluorine-functionalized NPGO membrane not only increases the water flux due to hydrophilic functional groups on its surface but also increases the salt rejection due to existence of fluorine (–F) atoms on the pore edge which make it applicable as a reverse osmosis membrane in water desalination industry.

Conflict of interest We wish to confirm that there are no known conflicts of interest associated with this publication.

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Tables.

Table 1. Partial atomic charges in fluorine-functionalized NPGO and NPG membranes calculated by DFT method and Lennard- Jones parameters. Element

C (sp2)

CCOH

HCOH

OCOH

CCO

OCO

HCH

CCH

FCF

CCF

Na+

Cl-

Partial charge

+0.0039

+0.2463

+0.3631

-0.6095

+0.1636

-0.3273

+0.221

-0.221

-0.2813

+0.2813

+1

-1

ε (Kcal/mol)

0.086

0.070

0.00

0.155

0.069

0.142

0.030

0.046

0.135

0.046

0.168

0.012

σ (Å)

3.39

3.55

0.00

3.07

3.39

2.90

2.42

2.98

1.45

1.48

2.26

5.16

references

[56]

[57]

[57]

[57]

[38]

[38]

[58]

[58]

[39]

[39]

[59]

[59]

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Figures.

Figure 1. Four types of functionalized pores on the NPGO (G1 and G2) and NPG (G3 and G4) membranes. The pore diameter in G1 and G3 membranes is 0.3 nm while in G2 and G4 membranes is 0.45 nm. (The carbon, fluorine, oxygen and hydrogen atoms are represented by cyan, pink, red and white colors, respectively.)

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80

G1 G2 G3 G4

70

Water flux (#ns -1)

60 50 40 30 20 10 0 0

25

50 75 100 Applied pressure (MPa)

125

150

Figure 2. Water flux as a function of applied pressures for F–NPGO (G1, G2) and F–NPG (G3, G4) membranes

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G1

G2

G3

G4

Figure 3. Water density map for F–NPGO (G1 and G2) and F–NPG (G3 and G4) membranes. The x-axis snapshot of water density map analysis clearly shows that water molecules distribute on the membrane surface (hydrophilic surface) after reaching to the NPGO surface. They pass regularly through the pore under the influence of applied pressure (driving force) and functional groups in the pore edge without any accumulation around the pore. Red regions show the highest probability of finding water molecules while blue regions show the zero-probability. But in F– NPG (G3, G4) membranes, the water molecules do not distribute very well on the surface and have not regular flow regime which results in accumulation around the pore.

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G1

G2

G3

G4

Figure 4. Water density map for F–NPGO (G1 and G2) and F–NPG (G3 and G4) membranes at the z = 0; The water flow through the pores of F–NPGO membranes is very uniform and regularly.

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90 80

G2 at 150 MPa G2 at 10 MPa

Water flux (#ns -1)

70 60 50 40 30 20 273 278 283 288 293 298 303 308 313 318 323 328 333 338 Temperature (K) Figure 5. Water flux versus temperature for G2 membrane at low (10 MPa) and high (150 MPa) pressures; The results show that the water flux significantly increases with increasing the temperature of feed side at both low- and high-pressure regions.

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100

Salt rejection (%)

98 96 94

G1 G3

92

G2 G4

90 88 0

25

50 75 100 Applied pressure (MPa)

125

150

Figure 6. The salt rejection percentage for F–NPGO (G1, G2) and F–NPG (G3, G4) membranes at different applied pressures; The results show that at the same conditions of applied pressure and pore size, the rejection rate of F–NPGO membranes is better than that of F–NPG ones.

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100 G1 G2 G3 G4

90 80 70 60 50 40

PMF (kcal/mol)

a

30 20 10 0 -7

-6

-5 -4 -3 Axial position (Å)

-2

-1

0 120

G1 G2 G3 G4

b

110 100 90 80 70 60 50 40

PMF (kcal/mol)

-8

30 20 10 0 -8

-7

-6

-5 -4 -3 Axial position (Å)

-2

-1

0

Figure 7. The potential of mean force (PMF) of F–NPGO and F–NPG membranes for (a) Na+ and (b) Cl- ions. Fluorine atoms in the pore edge provide high energy barrier for flow of ions through the membrane pore, especially for Cl- ions.

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14 Cl-water

12

Na-water 10

g(r)

8 6 4 2 0 0

1

2

3

4 r (Å)

5

6

7

8

Figure 8. The radial distribution function (RDF) for ion-water inside the G2 system at the applied pressure of 10 MPa.

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Water density (g/cm3)

2

Applied pressure (MPa) 5 10 50 100 150

1.5

1

0.5

0 -15

-10

-5

0 5 Axial position (Å)

10

15

Figure 9. Density profile of water molecules in the F–NPGO (G1) system at different applied pressures

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60 in selected region

50

in whole system

g(r)

40 30 20 10 0 0

1

2

3

4 r(Å)

5

6

7

8

Figure 10. The radial distribution functions (RDFs) between oxygen–oxygen of water molecules inside a region of ± 0.35 nm around the G1 and in the whole system

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2

a

1.8

G1 at 10 MPa G2 at 10MPa

Water density (g/cm3)

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -15 2

-10

-5

0 5 Axial position (Å)

b

1.8

15

G1 at 150 MPa G3 at 150MPa

1.6

Water density (g/cm3)

10

1.4 1.2 1 0.8 0.6 0.4 0.2 0 -15

-10

-5

0 5 Axial position (Å)

10

15

Figure 11. Water density profile, (a): the effect of pore size on the water density profile by comparing G1 and G2 systems, (b): the effect of membrane type on the water density profile by comparing G1 and G3 systems 38

ACCEPTED MANUSCRIPT  Highlights:

 The capability of functionalized graphene oxide for desalination was investigated.  The effect of functional groups on the graphene oxide for desalination was investigated.  Fluorine atoms of pore edge were very good choice for improving salt rejection.  Hydrophilic groups on the surface make the NPGO as an ultra-permeable membrane.  The effect of increasing or decreasing temperature was explained on the water flux.