and in those simulations only hydroxyl or epoxy functional groups are considered for the modeling of the GO nanosheets [107, 108, 109, 110, 281]. However, along with the hydroxyl and epoxy functional groups, GO nanosheets also contain carboxyl functional groups which are mainly located at the edges of the GO nanosheets [5, 46].
In the present work, we consider carboxylic functional group along with the epoxy and hydroxyl functional groups for the modeling of the GO nanosheets and our study suggested that carboxylic functional group also plays and important role in the dy- namics of water molecules and ions while permeating through the layered GO mem- branes. Although GO nanosheets have previously been employed as a coating material to improve the functionality of thin-film composite (TFC) FO membrane [282], the influence of internal structure of GO on the membrane performance has not been ad- dressed in the FO mode. We aim to address this question with the help of large scale fully atomistic simulations by considering three different membrane configurations where each configuration has a different pore offset distance (W). The dynamics of water molecules, pathways of water/ions inside the membrane and membrane perfor- mance are discussed in detail to have an atomistic insight of layered GO membrane in FO applications.
the GO nanosheets are as follows:
∙ 20.0×49.0 Å2
∙ 30.0×49.0 Å2
∙ 40.0×49.0 Å2
∙ 50.0×49.0 Å2
The epoxy and hydroxyl groups are located on the basal plane of the GO nanosheet, while the carboxylic groups are located on the edges. We did not consider any pore in the GO nanosheet. The chemical composition of this GO nanosheet is C10O1(OH)1(COOH)0.5 [46, 5]. With these GO nanosheets as the constructing unit, 3 different configurations of GO membranes are modeled as shown in Figure 4-1. In all the three configurations the initial interlayer distance (H) and the dimension of the pores (D) are10.0Å [13, 18] and 7.0×49.0 Å2 respectively. However these three membrane configurations differ in their pore offset distance (W). For configuration- 1 W = 25.0 Å (Figure 4-1a), for configuration-2 W = 8.0 Å (Figure 4-1b) and for configuration-3 W = 0 Å (Figure 4-1c). In other words for configuration-3 the pores of the respective GO layers in the membrane are perfectly aligned. Form an experimental point of view configuration-1 can be considered as GO membranes com- posed of GO nanosheets of very large lateral dimensions, configuration-2 refers to GO membranes composed of GO nanosheets of medium lateral dimensions, whereas configuration-3 resembles GO membranes consisting of GO nanosheets of very small lateral dimensions [35, 102].
4.2.2 Simulation System
After the membranes were constructed they are properly hydrated by solvating them in a water box of size 77.0×49.0×55.0 Å3 (Figure 4-2a). All the water molecules within 2.0 Å distance from the GO sheets are removed. The total number of water molecules in this solvating water box are 6500. To mimic the osmotic pressure of seawater (27.0 𝑎𝑡𝑚) a 0.56 molar solution of sodium chloride (NaCl) is considered
(a)
(b)
(c)
Figure 4-1: The three membrane configurations (a) Configuration-1 (b) Configuration-2 (c) Configuration-3. The green color is for hydrogen atoms, the red color is for oxygen atoms and the cyan color is for carbon atoms.
as the feed solution. This 0.56𝑀 NaCl solution contains 10000 water molecules, 108 Na+ ions and 108 Cl− ions (Figure 4-2b). A solution of 1.0 𝑀 MgCl2 and 0.05
(a) (b) (c)
(d)
Figure 4-2: (a) Hydrated membrane (configuration-3) (b) Feed solution (c) Draw solution (d) Simulation setup. The green color is for hydrogen atoms, the red color is for oxygen atoms, the cyan color is for carbon atoms, the blue color is for Cl− ions, the magenta color is for Na+ ions, the orange color is for Mg2+ ions, the black color is for Al3+ ions, the yellow color is for sulfur atoms.
𝑀 Al2(SO4)3 is considered as the draw solution [283]. This draw solution contains 15000 water molecules, 246 Mg2+ ions, 492 Cl− ions, 26 Al3+ ions and 39 (SO4)2−
ions (Figure 4-2c). For the simulation system the draw solution box is placed in between the two hydrated membranes and the feed solution boxes are placed ouside the membranes as shown in Figure 4-2d. This type of FO configurations are simulated successfully by Raghunathan and Aluru [284].
4.2.3 Simulation Methodology
We performed all the non-equilibrium MD simulations using NAMD 2.11 [285] em- ploying OPLS-AA force field [45] with a time step of 1.0𝑓 𝑠. For the water molecules TIP3P water model is used [286]. The bond length of the water molecules are con-
strained using SETTLE algorithm [287]. The van der Waals interactions are cal- culated through Lennard-Jones potential with a cut-off distance of 12.0 Å. For the calculation of the long range electrostatic interactions, Particle mesh Ewald (PME) method is implemented [288].
After the simulation system was constructed, energy minimization was performed to remove any internal stress within the system. After that, the system was equi- librated for 1.0 𝑛𝑠 at a temperature of 300.0 𝐾 and 1.0 𝑎𝑡𝑚 pressure. Then the production runs of the non-equilibrium MD simulations were carried out for 25.0 𝑛𝑠 in a𝑁 𝑃 𝑇 ensemble with periodic boundary condition (PBC) in all the directions for configuration-1 and configuration-2. However to get a better insight of the water per- meability and salt rejection of the membrane, the production run for configuration-3 was carried out for 64.0 𝑛𝑠 with the same set of parameters as for configuration-1 and configuration-2 (i.e. 𝑁 𝑃 𝑇 ensemble with PBC in all directions). Simulation data were saved at every 20.0 𝑝𝑠. During the simulations the temperature was held constant using Langevin dynamics with a damping factor of 5.0 𝑝𝑠−1. Pressure was kept constant using modified Nosé-Hoover method where barostat oscillation time and damping factors both were set to 0.3 𝑝𝑠.
Previous simulation studies on layered GO membrane were performed mainly in RO mode and in most of those simulations GO sheets are constrained in all the three (𝑋, 𝑌, 𝑍) directions. However, these kind of constrains are not there in an experiment.
So, to have a better resemblance to the experiments, in this study we constrained the GO nanosheets only in the 𝑋𝑌 plane. We did not apply any constrain to the mem- brane in the 𝑍 direction (permeating direction). This allows the GO nanosheets of the membrane to move (or fluctuate) in the𝑍 direction during the course of the sim- ulations. We apply harmonic constrain to all the carbon atoms of the GO membranes in the 𝑋𝑌 plane, so that the layered structure of the GO membranes are retained throughout the simulations with predefined value of W for each configurations. This allows us to effectively study the effect of internal structure of the layered GO mem- brane on is performance. The carbon atoms of the GO membranes are constrained in the𝑋𝑌 plane with a force constant of 1.0 𝑘𝑐𝑎𝑙/(𝑚𝑜𝑙 Å2). For each of the 3mem-
brane configurations 3 independent simulations are performed with different initial configurations ( or initial arrangements of atoms) and the results are averaged over the 3 simulations for each of the membrane configurations.