Ionic Sieving Properties of Graphene Oxide (GO) Membranes

ABSTRACT: We characterized the ionic sieving properties of graphene oxide (GO) membranes by performing classical molecular dynamics (MD) simulations. The Lerf-Klinowski model is used for GO nanosheets structure. The Optimized Potentials for Liquid Simulations for all atoms (OPLS-AA) force field is used for GO potential. The SPC/E model is used for water molecules. We show that GO membranes can act as reverse osmosis (RO) membranes, although the water flow in GO membranes is hundred times faster than RO membranes. In this work two important factors in ionic sieving process are studied. First the GO layers separation and second the pressure of water. Each simulation runs until at least half of the water molecules are desalinated. The water flux, permeability, salt rejection, potential of mean force (PMF), and radial distribution function (RDF) are measured. We show that the GO membranes can be the appropriate choice for desalination of seawater in future due to the simplicity in production, low cost, fast water flow, and great ion rejection ability.

“By 2030 nearly half the global population could be facing water scarcity, with demand outstripping supply by 40 percent”, said United Nations Secretary General Ban Ki-Moon.Over 97% of the water on the Earth is saline water and only three percent is fresh water and about two thirds of this fresh water is frozen.So in the near future the only way to provide fresh water is desalination of seawater. There are common ways to desalinate seawater like reverse osmosis (RO) or methods based on distillation. In the RO method an applied pressure is used to overcome natural osmotic pressure so water passes through a semi-permeable membrane leaving salt behind. In the Distillation methods seawater is evaporated and then condensed to produce freshwater. Both methods require a lot of energy and are very costly.

Recently nanotube-based membranes and graphene-based membranes have attracted many interests for their potential in water desalination due to their high permeability and great ion rejection.  Although these membranes have a great theoretical advantages, the problem of synthesis and fabrication is a major challenge for producing cost effective membranes.

Graphene oxide (GO) is a chemical derivative of graphene with several functional groups such as epoxide and hydroxyl that is produced from graphite by the Hummer’s method. GO has been synthesized and fabricated in the forms of papers and films in the industrial-scale. Functional groups and layers separation of GO membranes can optimized simply during synthesis process to achieve best performance for desalination.

In the GO membranes, water molecules permeate through the nanochannels between oxidized regions (pristine regions), which are provided by the hydrophobicity of functional groups. Particles that have a smaller size than the GO nanochannels can permeate in the GO membrane with speed orders of magnitude greater than common membranes.

Dry GO membranes have a layers separation of ~5±1 angstroms which only lets water vapor molecules permeate through the nanochannels. When a GO membrane is immersed in water, it is swelled so the layers separation is increased to ~12±1 angstroms. Na⁺ is the smallest ion in the saline water which has a hydrated diameter of 9 Å. Therefore after swelling of the membrane, small ions such as Na⁺ can permeate easier which leads to reduction of ion rejection. Several methods have been tried to prevent swelling of GO membranes, such as physical confinement, and crosslinking of nanosheets

In this paper we present a next generation of ultrathin membranes which have remarkable abilities like high permeability, good ion rejection, and great resistance to blockage. Furthermore the simple and cheap methods for synthesis of GO membranes make them energy efficient.

We performed Classical molecular dynamics (MD) simulations using the large-scale atomic molecular massively parallel simulator (LAMMPS).The VMD and OVITO were used for analysis and visualization. All simulations were carried out in NVT ensemble with a Nosé-Hoover thermostat and a damping constant of 10 femtoseconds. The equations of motion were integrated with a time step of 1 femtosecond using the velocity-verlet algorithm. The periodic boundary conditions (PBC) were applied for all three directions.

The all-atom optimized potential for liquid simulations (OPLS-AA) is used for graphene oxide (GO) and salt ions.This potential contains many-body terms, including bond stretching, bond angle bending, van der Waals, and electrostatic interactions. In addition, OPLS uses a geometric combining rule for the Lennard-Jones coefficients. The extended simple point charge model (SPC/E) is used for water molecules, following previous studies on similar systems. The force field parameters are given in the table S1 to table S4 completely (see supporting information).

The SHAKE algorithm is applied for water molecules to reduce high frequency vibrations that require shorter time steps. The interaction between water and GO includes both van der Waals and electrostatic terms. The van der Waals forces are truncated at 1.0 nm, and the long-range Coulomb interactions are computed by using the particle-particle particle-mesh (PPPM) algorithm.

As it is seen in the figure S1 (see supporting information), in our model of GO, both hydroxyl and epoxide groups are considered, following the Lerf−Klinowski model that is the most well-known model for GO.

The structure of the single sheet of GO was considered as 1.5Ã-3 nm² containing 18 epoxide and 25 hydroxyl groups. The oxygen functional groups were distributed on both sides of GO sheet. The single sheet of GO contains 206 carbon atoms and 43 oxygen atoms. Therefore, the ratio of C/O is about 4.8 which is in consistent with the Lerf−Klinowski model. The size of simulation box in the x, y and z directions were about 17, 37 and 11 nm respectively. For preventing the membrane from movement, carbon atoms in the edges of the sheets were fixed.

In the first step, a membrane was designed with 13 GO sheets and two layers according to the GO membranes structure proposed in previous studies. Distance between the edges was considered 2 nm. Figure S2 shows the designed membrane (see supporting information).

Simulations were carried out for multiple values of layers separation from 7 to 8.5 angstroms with increment of 0.5 angstroms. For each choice of layers separation, three simulations were run for different nominal water pressures of 500 atm, 1000 atm, and 2000 atm. These numbers are nominal pressures but in the feed side of simulation box using voronoi atom volume estimation, feed pressure determined as 600 atm, 980 atm, and 1600 atm.

Water pressure on the feed side of the membrane was enforced by applying specified and uniform forces in the z-direction to the piston atoms, thus ensuring that the water pressure was kept constant. Figure S3 shows the membrane with the layers separation of 8.5 angstroms, water, salt ions, and the piston (see supporting information). In the Figure S3a after 0.1 ns water molecules are in the pressure of 2000 atm and in the Figure S3b after 14 ns, we have 94 percent salt rejection and more than half of water molecules purified.

In our simulations, saltwater was generated on the feed side of the membrane, consisted of 4800 water molecules and 52 Na⁺/Cl^− pairs, corresponding to a salt concentration of 35.5 g/L, which is close to the normal salinity of seawater (~35 g/L).

Figure 1a shows the flux of water (volume per unit of time per area) passing through the membrane as a function of applied pressure and layers separation. In our simulations, we had to use high pressures in compare to typical pressures that is needed for desalination, because we have a time scale limit in molecular dynamics. We can solve this problem with calculating permeability (volume per unit of time per area per pressure) of membrane that is shown in figure 1b. Another possible method is extrapolating the graphs in figure 1a to low pressures like 10 atm, so we can reach to appropriate flux due to approximately linear relation (R²=0.99). In figure 1b it is obvious that with increasing the layers separation, the membrane permeability increases linearly (R²=0.98). As it is expected the numbers for membrane permeability are in consistent with other reports.Figure 1c shows salt rejection for the membranes with different layers separation and different water pressures. Salt passage was calculated from proportion of filtered salt ions number at time t (t is the time that half of the water molecules passed from membrane) to initial salt ions number in the feed side. So we have “salt rejection = (1 – salt passage)”. As it is seen in the figure 1c, with increasing the pressure or layers separation, salt rejection reduces which is expected. It is clear that with using lower water pressures like 10 atm, we can achieve higher ion rejection.

Figure 2a shows the number of water molecules versus time in the membrane part. For each value of separation there is a limit for number of water molecules that can be in the membrane. In the simulations with higher pressures, the membrane gets filled faster as it is shown in figure 2b. Furthermore in longer times (about 15 ns) the separation value controls the number of water molecules in the membrane. Therefore, without attention to the water pressure, anyway the membrane is filled with water completely.

Figure 3 indicates number of filtered water molecules against time. The graphs are plotted at the time that half of the water molecules are desalinated. According to the figure 3b, it is obvious that after about 5 ns the membrane is filled approximately. So we can see a stable flow due to linear relationship between filtered molecules and time. Figure 3a shows water flow for different layers separation and figure 3b shows water flow for different pressures in constant separation value.

Figure 4 is the 3D color map for potential of mean force (PMF) for a particle passing through two sheets of GO. The PMF was calculated from steered molecular dynamics (SMD). We used harmonic potential U = K(x − x)²/2, where K is 20 Kcal/mole-angstrom² and end of spring moving with velocity of 0.00005 angstrom/femtosecond that is enough for reversible pulling. For checking the reversible pulling, the SMD was performed in X direction and -X direction at same width, but the results were same. Also using umbrella sampling and weighted histogram analysis method (WHAM) give us the same results as SMD for PMF calculation. For creating each PMF map, 30 simulations were performed to cover all of the GO layers width. We have done these simulations for 3 different layers separation. So we have a PMF map that shows barriers and valleys of energy all over the GO layers completely.

In figure 4a, 4b, and 4c the PMF are plotted for Cl ion that passing from one side of GO layers to another side. In each path, Cl ion sees many barriers that prevent from movement of the ions. Also the ions can stuck in the valleys of energy between the barriers. Figure 4d, 4e, and 4f show PMF map for Na ion. In comparison to Cl ion, the barriers are shorter and valleys have a higher depth. So the Na ions in the valleys can move out with lower energy than Cl ions. PMF for H₂O molecule in figure 4g, 4h, and 4i are shown. Flat surfaces indicate easy movement of H₂O molecules across GO layers without encountering any barriers or valleys. As we can see in all of the plots, with increasing the layers separation, height of barriers and depth of valleys are reduced so the ions and water molecules move easier.

Figure 5 shows salt concentration in the three part of feed, membrane, and filtered against time. In figure 5a the simulation is selected with layers separation of 8 angstroms and pressure of 2000 atmosphere. At the first of all simulations the salt concentration is 35.5 g/lit in the feed part which is same as sea water salinity. Salt concentration of feed part is slightly increased until reach to 90 g/lit at the time that half of the water molecules are desalinated. In the filtered part there are some peaks showing passage of ions through membrane. After the each peak, the salt concentration is reduced until the next peak because of passing water molecules from membrane into filtered part. Salt concentration in the membrane part fluctuates around the mean value of 17 g/lit until the end of simulation. So this fluctuation is enough to ensure that the membrane blockage does not occur even in higher salt concentrations like 90 g/lit. In figure 5b the layers separation is 8.5 angstroms with the water pressure of 2000 atmosphere. As we can see the behavior of plots is similar to figure 5a except number of peaks in the filtered part.

Figure S4 indicates radial distribution function (RDF) for water and functional groups in GO layers (see supporting information). Figure S4a shows correlation between oxygen and hydrogen in water. Figure S4b presents RDF between oxygen in water and hydrogen in hydroxyl groups. Figure S4c shows RDF between hydrogen in water and oxygen in hydroxyl groups. Figure S4d shows correlation between hydrogen in water and oxygen of epoxide groups. The first peak in all of the plots in figure S4 shows length of hydrogen bond. As we can see in the figure the longest hydrogen bond is belong to hydrogen of water and oxygen of epoxide.

We show that nanometer-scale pores in single-layer freestanding graphene can effectively filter NaCl salt from water. Using classical molecular dynamics, we report the desalination performance of such membranes as a function of pore size, chemical functionalization, and applied pressure.