Effects of interlayer spacing and oxidation degree of graphene oxide nanosheets on water permeation: a molecular dynamics study

Graphene oxide (GO) membranes have shown great potential in the applications of water filtration and desalination. The flow behavior and structural properties of water molecules through GO nanochannels are still under debate. In this work, molecular dynamics simulations were performed to explore the effects of interlayer spacing and oxidation degree of GO nanochannels on water transport. The results show that GO nanosheets have strong adsorption capacity. The adsorbed layer of water molecules on GO surface is thermodynamically stable and not easy to flow. When the interlayer spacing falls into the range of 0.6 ~ 1.0 nm, water molecules form into single or double adsorbed layers between two GO nanosheets. When the interlayer spacing is bigger than 1.2 nm, the other water layers in the middle of nanochannel become disordered. Taking the separation performance based on size exclusion into consideration, the most suitable interlayer spacing for water nanofiltration is approximate 1.2 nm, which has one flowing layer of water molecules. Oxygen-containing groups are unfavorable for water permeation, as more and more hydrogen bonds prevent water flowing on GO surface with the increasing oxidation degree. Our simulation results may help to improve the design of GO nanofiltration membranes for water treatment.


Introduction
Graphene has unique optical, electronic, and mechanical properties as well as planar structure and can be used for nanofiltration, water treatment, supercapacitors, and photocatalysis [1][2][3][4][5]. Graphene-layered membranes are formed by stacking single layers of graphene with nanoscale interlayer spacing [6,7]. This special laminated structure allows the permeation of water molecules and rejects other molecules. The performance of desalination has been extensively studied by experimental and theoretical calculations [8,9]. Han et al. experimentally designed negatively charged ultrathin graphene nanofiltration membranes for water purification and found that pure water had high permeation rates and high rejection up to 99% for organic dyes and moderate rejection of 20 ~ 60% for salt ions [10]. In addition, since graphene is difficult to be exfoliated and easily agglomerated; its performance can be adjusted by introducing functional groups for efficient desalination, among which graphene oxide (GO) has been widely studied.
GO is the oxidation of pristine graphene (PG) with similar two-dimensional structure, which can be prepared by chemical and electrochemical oxidation methods [11,12]. There are various oxygen-containing groups on the surface of graphene oxide, such as hydroxyl, epoxy, and carboxyl groups, and different oxidation processes will affect the distribution of oxygen functional groups on GO's surface and the degree of oxidation [13,14]. GO [17]. Recent studies [18][19][20] showed that GO membranes were modified with different functional groups or intercalated by small molecules which could adjust their interlayer spacing to achieve the separation of specific organic molecules and ions in wastewater [21]. In order to further develop the above PG/GO membranes for practical processes, a fundamental understanding of the structures and properties of water or other molecules in PG/GO layered nanochannels is necessary. Furthermore, water or other fluids in these nanochannels exhibit distinctive nanoscale effects, and the continuous medium theory in fluid mechanics is not valid in nanoconfined spaces [22]. For example, ballistic molecular transport mechanisms were employed by Keerthi et al. to illustrate the fast and frictionless gas flow in angstrom-scale flat channels [23]. Since the molecular behavior in the confined space at such a nanoscale is not easily observed by existing experimental methods, thus molecular dynamics (MD) simulation has been an effective method to study the confined space at nanoscale [24][25][26][27][28][29][30]. It was previously reported [31,32] that MD was used to demonstrate the flow behavior of water molecules through membranes based on graphene nanochannels, and it was found that water molecules could undergo rapid transport, mainly due to the very weak interaction between graphene surface and water molecules. The study of water permeation in GO nanochannels showed that the large number of oxygen functional groups in the nanocapillary facilitated the formation of hydrogen bonds by water molecules, leading to the enhanced water adsorption and increased water flux in the membrane pores [33,34]. On the other hand, Yang et al. [35] found that the water flow rate in the GO membranes was low and the water molecules in the nanochannels became more disordered with the increase of oxidation, while the structure and kinetic behavior of water molecules changed significantly in 0.6-1.5 nm ultra-microporous pores [36]. Sun et al. investigated the effects of hydroxyl groups on the viscosity of water in GO channels. They found that the viscosity of water is hydroxyl-dependent and anisotropic, namely, higher in longitudinal direction and lower in perpendicular direction [37]. The study of their microscopic behavior in GO membranes is still a frontier in scientific society.
In this work, we explored the structural and kinetic behavior of water molecules in PG/GO nanochannels with varied interlayer spacing of 0.6-1.8 nm and oxidation degree of 0 ~ 40%, using MD simulations. The purpose is to find suitable interlayer spacing and oxidation degree for water permeation. The simulation results may be useful to improve the design of PG/GO nanochannels for the applications of water purification and desalination.

Materials and methods
As shown in Fig. 1A, to simplify GO model, we used epoxy and hydroxyl groups randomly distributed on both sides of GO surface to represent the oxidation of PG. The ratio of hydroxyl to epoxy groups was 1:1. The size of PG was 2.2 × 3.2 nm 2 . Following this model, the oxidation degree (OD) of GO was defined as OD = NO/NC × 100%, where NO and NC are the numbers of oxygen and carbon atoms. We constructed five kinds of GO nanosheets with varied OD, namely, 0% (PG), 10% (labeled as GO10), 20% (labeled as GO20), 30% (labeled as GO30), and 40% (GO40).
The configuration of the simulation system is presented in Fig. 1B. Two GO nanosheets placed parallelly with each other were employed as GO membrane. The interval between two sheets was used as nanochannel to transport water molecules. The interlayer spacing was set at 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, and 1.8 nm, respectively. Initially, the feed side (see Fig. 1A, Box1) was filled with pure water, while the right side (Box2) was empty. A plate was introduced into the left end of Box1 to block water from flowing between Box1 and Box2. During the water permeation process, the plate was pushed at a speed of 0.35 nm⋅ns −1 from left to right.
All MD simulations were performed under the canonical ensemble (NVT) using GROMACS software (version 5.1.4) Fig. 1 A Atomic structure of GO nanosheet with hydroxyl and epoxy groups. The red and white balls represent the oxygen and hydrogen atoms. B Side view of the simulation system composed of two GO nanosheets and two reservoirs [38,39] and OPLS-AA force field [40]. The parameters of PG were developed by Safaei et al. [41]. Water was depicted by the extended simple point charge (SPC/E) model [42]. During the simulation, PG and GO were position-restrained by a spring of 1000 kJmol −1 nm −2 . Periodic boundary conditions were applied in all directions. The long-range electrostatic interactions were calculated by Particle-Mesh Ewald method [43,44], and the van der Waals (vdW) interaction was computed with a cut-off of 1 nm. The bond lengths in PG/GO and water molecules were constrained by methods of LINCS [45] and SETTLE [46], respectively. A time step of 1 fs was used to acquire higher accuracy. The production run of each system lasted 20 ns to collect data for subsequent analysis.

Adsorption of water molecules on PG/GO surface
Prior to study the water transport through GO membranes, we should understand the adsorption features of water molecules on PG/GO surface. We therefore first performed simulations of water with single PG or GO nanosheets. Taking PG as an example, there are two peaks in the molecular number density profile, as shown in Fig. 2A. The first peak is localized at z = 0.33 nm, close to the vdW radii of carbon and oxygen atoms. The corresponding number density is 83.5 nm −3 , substantially bigger than that of bulk water (33.4 nm −3 ), confirming the strong adsorption ability of PG. The second peak exhibits much weaker, about 42.4 nm −3 at z = 0.63 nm. The two peaks indicate that there are two adsorbed layers of water on PG surface. To understand the adsorption stability of water for PG, the mean sojourn time (MST) of water molecules confined to their initial points in z-direction was analyzed, which is defined as where Δz(t) = | | z(t + t 0 ) − z(t 0 ) | | and Δ c is set at 0.01 nm [47]. MST is a good physical quantity for characterizing the adsorption intensity. MST profiles hold the same trend with those of number density (Fig. 2B). The maximal MST of PG is about 0.022 ns at 0.33 nm, which is well consistent with the molecular number density profile. This coincidence indicates that water molecules are thermodynamically stable in the first adsorbed layer. However, the second peaks in two profiles show much weaker, just slightly higher than those in bulk solution, implying that PG's adsorption intensity weakens quickly with the increasing distance from its surface. Water on GO surface exhibits similar results, which illustrate that PG and GO possess strong adsorption capacities close to their surface (d < 0.5 nm).

Distribution of water in nanochannels
Then, we take two sets of systems as examples to investigate the effects of interlayer spacing and oxidation degree on water permeation through GO membranes, namely, the fixed oxidation degree (OD = 20%, GO20, Fig. 3A) with different interlayer spacing (0.6 ~ 1.8 nm) and the same interlayer spacing (d = 1.2 nm, Fig. 3B) with different oxidation degrees (0 ~ 40%). Figure 3C and 3D show the number density of water molecules in the nanochannels along the thickness direction (z-axis). When the interlayer spacing is only 0.6 nm, there is just one layer of water molecules in the nanochannel. Moreover, the molecular number density is highest 200 nm −3 . Except d = 0.6 nm, the peaks of the density profiles are close with each other and symmetrical about bilayer center at a fixed OD, falling in the range of 88 ~ 108 nm −3 , which are slightly bigger than that on single PG/GO surface. This is because the pressure in the nanochannels is much greater than 1 bar, when water molecules are pushed by the plate at a constant speed. The symmetrical two peaks correspond to the adsorption layers clinging to the GO surface. When d = 0.8 and 1.0 nm, water molecules form into two layers in the nanochannel. The structure of these single or double layers of water sandwiched by PG/GO is ice-like. Hence, these layers of water are not easy to flow on PG/GO surface. When d = 1.2 nm, water molecules form into three layers. However, when d is greater than 1.4 nm, Fig. 2 A Molecular number density profiles of water molecules in z direction (normal to PG/GO surface). B Mean sojourn time for water molecules with respect to their initial z coordinates the water structures become gradually disordered in the middle of the interlayer gallery (Fig. 3C). At a fixed interlayer spacing of 1.2 nm, the density profiles are coincident that there are three layers of water between two GO20 sheets.
The main difference is that the peak values drop slightly with the increasing OD (see Fig. 3D) because of steric effects, as more and more oxygen-containing groups are evenly distributed on graphene surface. On the other hand, the middle peaks are much lower, since the adsorption intensity weakens with the increasing distance to GO surface.

Push forces and hydrogen bonds
Although we push the plate at the same speed, the push forces vary with different interlayer spacing and oxidation degree, as shown in Fig. 4. In general, with the fixed OD, the cumulative average push forces are getting weaker with the increasing interlayer spacing. The push forces continue to weaken from 6.5 × 10 5 kJ/mol/nm to 3.0 × 10 3 kJ/mol/nm, corresponding to the channel widening from 0.6 to 1.8 nm (see Fig. 4A). This is simply because the wider the channels are, more easily water molecules can pass. It should be noted that the interlayer spacing of GO membrane with one layer water molecules is larger than 0.8 nm, which is confirmed by XRD experiments [15,16]. Therefore, water cannot spontaneously permeate into the nanochannel, when d = 0.6 nm, thus only exerting a huge pressure that can water pass through such narrow channel. Furthermore, at a fixed channel width, the push forces become stronger with the increasing OD. In Fig. 4B, the push forces strengthen continually from 2.2 × 10 3 kJ/mol/nm to 1.3 × 10 4 kJ/mol/nm with the OD rising from 0 to 40%. It has been reported that water transport through interlayer gallery is inhibited by a dominant side-pinning effect originated from the oxidized regions of GO [48]. Here, the sidepinning effect refers to the hydrogen bonds formed between water molecules and oxygen-containing groups on GO surface and acted as anchors preventing water permeation. We therefore count the number of hydrogen bonds formed between GO nanosheets and water in the nanochannels, as Fig. 3 A Atomic structures of water molecules between two GO20 sheets with varied interlayer spacing from 0.6 to 1.8 nm. B Atomic structures of water molecules between PG/ GO sheets with varied OD from 0 to 40%. C,D The number density profiles along the thickness direction z, corresponding to panels (A) and (B), respectively  Fig. 5. In general, the number of hydrogen bonds is close with each other regardless of different interlayer spacing at a fixed OD, except the case of d = 0.6 nm (Fig. 5A). In this case, the number of hydrogen bonds reaches highest 97, while the average value of 0.8 ~ 1.8 nm is 66. Obviously, at a fixed interlayer spacing, the number of hydrogen bonds increase gradually with the increase of oxidation degree. For example, the numbers of hydrogen bonds are 0, 46, 67, 76, and 88, corresponding to the OD of 0, 10%, 20%, 30%, and 40% at a fixed d = 1.2 nm (Fig. 5B). Furthermore, we analyzed the contributions of epoxy and hydroxyl groups to form hydrogen bonds, as shown in Fig. 5C. We find that the number of hydrogen bonds from hydroxyl groups is approximately twice that from epoxy groups, since hydroxyl groups are both hydrogen bond donors and acceptors, while epoxy groups are just donors. In general, the influence of epoxy groups on GO surface cannot be ignored. Both epoxy and hydroxyl groups play an important role in water permeation through GO channels.
Eventually, we depict the relationship between hydrogen bonds and push forces. The results further confirm the sidepinning effect. In detail, the push forces become weaker with the increasing interlayer spacing at a fixed OD (Fig. 6A). The push forces decrease from 6.6 × 10 5 kJ/mol/nm at d = 0.6 nm to 3.0 × 10 3 kJ/mol/nm at d = 1.8 nm. Interestingly, there is a huge drop of the number of hydrogen bonds between d = 0.6 nm and d = 0.8 nm. This is because there is only one layer water molecules in the GO bilayer when the interlayer spacing is fixed at 0.6 nm, and all water molecules in the channel can interact with both the upper and lower GO sheets. The average distance between water molecules and bilayer is about 0.3 nm, which falls in the range of the length of hydrogen bonds (< 0.35 nm). Thus, water molecules in single layer are easier to form hydrogen bonds with oxygen-containing groups on both the upper and lower GO sheets. However, when d increases from 0.8 to 1.0 nm, the number of water molecules in each layer in the channel also increases. Therefore, the number of hydrogen bonds at 1.0 nm is more than that at 0.8 nm. On the other hand, the push forces get stronger with the increasing OD at a fixed interlayer spacing (Fig. 6B), since more and more hydrogen bonds are formed and prevent water molecules passing the channel. Hence, stronger forces are required to push the plate at a stable speed. And the push forces are directly proportional to the number of hydrogen bonds (Fig. 6C). The push forces linearly increase from 5.4 × 10 4 kJ/mol/nm when the number of hydrogen bonds is 46 to 1.3 × 10 5 kJ/mol/nm when the number of hydrogen bonds is 88. As a result, higher OD is not favorable to water transport through PG/GO nanochannels.

Conclusions
In summary, MD simulations have been conducted to investigate the effects of interlayer spacing and oxidation degree on water permeation through GO membranes. The MD results show that there is only one layer of water in the nanochannel when d = 0.6 nm. When the interlayer spacing falls in the range of 0.8 ~ 1.0 nm, two layers of water molecules formed between GO sheets. GO possesses strong adsorption capacity so that these two layers of water are hard to flow on GO surface. When the interlayer spacing continues to increase, the structure of water molecules in the middle of nanochannel becomes disordered. We propose that the most suitable interlayer spacing for water flow is approximate 1.2 nm, as there are just three layers of water formed between two GO sheets, and the middle layer of water molecules is relatively easy to flow. On the other hand, with the increasing oxidation degree, more and more hydrogen bonds are formed and prevent water flowing on GO surface. That is, oxygen-containing groups are unfavorable for water permeation. Further study should focus on the separation performance of GO membranes taking interlayer spacing and oxidation degree into consideration.
Author contribution Q.T. and Y.F. performed the simulations and wrote the paper. Z.S. analyzed the results and prepared all figures. J.C. and L. C. reviewed and revised the manuscript. All authors gave final approval for publication. Availability of data and material All data relevant to this work are deposited at the Dryad Data Repository: https:// datad ryad. org/ stash/ share/ LlXuH 17HtV EgmW2 If2mp GJZ2x Nt5lo RdSM9 iVH2f sZo.
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