Theoretical study on Janus graphene oxide membrane for water transport

Abstract

Graphene oxide (GO) membranes have received considerable attention owing to their outstanding water-permeation properties; however, the effect of the membrane’s microstructures (such as the distribution of oxidized and pristine regions) on the transport mechanism remains unclear. In this study, we performed molecular simulations to explore the permeation of a water–ethanol mixture using a new type of Janus GO membranes with different orientations of oxidized and pristine surfaces. The results indicate that the oxidized upper surface endows the GO membrane with considerable water-capture capability and the in-built oxidized interlayer promotes the effective vertical diffusion of water molecules. Consequently, using the optimized Janus GO membrane, infinite water selectivity and outstanding water flux (~40.9 kg⋅m⁻²⋅h⁻¹) were achieved. This study contributes to explaining the role of oxidized regions in water permeation via GO membranes and suggests that Janus GO membranes could be used as potential candidates for water–ethanol separation.

Key words： graphene oxide membrane; molecular dynamics simulation; water permeation; water-ethanol separation; oxidized and pristine regions

1 Introduction

After Nair et al. demonstrated that graphene oxide (GO) membranes exhibit excellent water transfer properties [1], many researchers have been involved in studying their confined transport mechanism [2,3] and ultra-high water permeability [4,5]. Chen et al. reported that the water transport behavior through GO membranes was considerably affected by the thermophoretic [4] and rarefied effects [3] and that the flow rate could be tuned by varying the structural parameters of GO membranes [6]. In addition to the pore size [7,8], the interlayer distance [6,9], and the oxidized degree [10,11], the orientations of the oxidized and pristine regions in GO membranes play a vital role in the water–separation process [12], determining the number of empty spaces in the interlayer gallery and the wrinkles in GO nanosheets [13,14]. Both oxidized and pristine regions are highly interlaced in GO membranes [15]. Using molecular simulations, Willcox and Kim [16] and Ban [15] et al. demonstrated that the random locations of the oxidized and pristine zones blurred the water-transfer mechanism through GO membranes. Practically, it was found that the interlayer transport for water permeation was considered as plug flow in the pristine zone, whereas it was considered as Poiseuille flow in the oxidized zone [17]. Generally, the oxidized surface of GO membranes captured water from bulk solutions [18], while the pristine channels granted a low frictional resistance for the water slipping away [1]. To date, these two points are the primary explanations for the excellent permeation of water molecules through GO membranes. However, since the oxidized and pristine regions are not uniformly distributed in the GO membranes, one may doubt whether the nonresistance of capillary motion can still contribute to the quick permeation of water within these GO membranes. In addition to the interlayer transport, both aligned and straight pores represent another important pathway [19], which considerably stimulates pore penetration. Experimentally, it is necessary to increase the porosity and the alignment of the pores to enhance pore penetration [20]. Thus, with highly aligned tunnels, can the pristine interlayers still favor water permeation? Researches demonstrated that when the aligned pores were oxidized, the water flux was significantly enhanced compared to that of pristine pores [21], indicating that the oxidized tunnels favored water permeation. In a previous study, we reported that a monolayer GO membrane with 2.4 Å-sized pores, and an oxidized degree of 0.49 (C/O ratio) allowed fast water permeation while fully rejecting ethanol owing to both the sieving effect and the preferential adsorption of water over ethanol [22]. However, molecular insights into the effect of oxidized and pristine surfaces in GO membranes on water permeation remain unclear. Therefore, to understand the abovementioned effect, 2.4 Å-sized pores and an oxidized degree of 0.49 are adopted. Based on these optimal microstructures, it is important to realize a favorable water-selective permeation in a multilayer GO membrane, which would be more practical for scalable fabrication.

For producing bio-ethanol, which is a clean and renewable fuel, the separation of water and ethanol is a very important process [23]. Bio-ethanol can be considered as a substituent of fossil fuel and will help in the reduction of excessive emissions of greenhouse gases and contribute to a sustainable development. Traditional separation techniques, such as distillation, consume considerable amount of energy to separate the azeotropic mixture of water and ethanol. A promising alternative separation approach is the membrane technology, which is an environmentally friendly and lower energy-consuming process. One of the challenges of current membrane dehydration processes is developing membranes with both high water permeation and selectivity [24]. Therefore, this study aims to theoretically design a water-permselective GO membrane having high permeation flux and selectivity.

In this study, we report molecular simulations proposing a new type of Janus GO membranes for the selective permeation of water from its mixtures with ethanol to reveal the effects of the surface’s orientations on the water-permeation process and optimize the nanostructures of the GO membranes for water–ethanol separation. After the Introduction, the atomic models of the GO membranes and the separation systems are described in Section 2. In Section 3, we evaluate the water flux and characterize the water-sorption and dynamic properties in GO membranes. In particular, a radial distribution function (RDF) analysis is performed to compare the affinity of Janus GO membranes to water. Lateral and vertical diffusion, density contours, trajectories, and the potential of mean force (PMF) are evaluated to uncover the water permeation mechanism through the Janus GO membranes.

2 Experimental

A GO nanosheet with a pore diameter of 2.4 Å and an oxidized degree of 0.49, based on our previous work [22], was constructed using Amorphous Cell in Materials Studio 6.0 [25]. Each GO membrane had two nanosheets. With different surface orientations, the internal configuration of GO membranes was generally classified into three categories [15]: pristine-oxidized, pristine-pristine, and oxidized-oxidized. There are certain partial regions that isolate the pristine and oxidized surfaces on each side of the nanosheet. As shown in Figs. 1(a–d), it is important to focus on these regions; therefore, four GO membrane models with pristine and oxidized surfaces distributed on each side of the nanosheet were constructed. Figure 1(f) shows the criterion for the diameter definition of nanopores in which a van der Waals sphere is plotted and the diameter is calculated using the formula: d =\mathrm{2}\sqrt{(A/\mathrm{\pi })}. All pores were treated as flexible such that the water molecules could squeeze through, although the water molecular cluster is larger than the pore size [26]. The interlayer distance is an average value obtained by experimental characterization. In certain defects of the GO membrane (usually formed in the oxidized regions), this distance could be ~1.1–1.4 nm [27]. For freeing the movement of the water molecules, the interlayer distance in our simulation was set to 1.2 nm. Moreover, to ensure the primary pathway of pore penetration, the entrance and exit pores were aligned. Geometric optimizations were then performed using the COMPASS force field [28] with 5.0 × 10^-6 convergence in the Forcite module. After 800 iterations, the minimum energy states of three configurations (OPOP (POPO), POOP, and OPPO; O for the oxidized surface and P for the pristine surface) converged to 521.2, 532.6 and 537.8 eV, respectively. As shown in Fig. S1 (cf. Electronic Supplementary Material, ESM), the configuration of OPOP (POPO) had the lowest energy state, thus indicating the most stable orientation.

Molecular dynamic (MD) simulations were performed using the GROMACS package (version 4.5.5) [29]. As shown in Fig. 1(e), the Janus GO membrane was located at the center of the simulation box, thus dividing the box into two chambers. The left chamber was filled with 50 mol-% water–ethanol mixtures comprising ~960 water and 960 ethanol molecules. To collect the permeated molecules, the right one was treated as a vacuum. Two graphene plates were placed at both ends of the chambers. The right graphene was fixed to avoid molecules moving between periodic cells, while the right plate was exerted an external acceleration (a) along the positive direction of the z-axis to push the mixture through the GO membranes. The corresponding transmembrane pressure (60 MPa) was calculated using the equation: P= N·m·a/A [30], where A is the cross-section area of the graphene and N is the number of carbon atoms contained in the left plate. The potential energy of the framework atoms was calculated by the summation of electrostatic potentials and nonbonded Lennard-Jones (LJ). The LJ parameters and partial charges of the GO membranes were constructed as per our previous study [31]. The all-atom optimized potential for liquid simulations force field [32] was used for ethanol, and the intermolecular three-point potential model [33] was used to mimic the realistic water molecules. The combination rules [34] ({\epsilon }_{ij}={({\epsilon }_i{\epsilon }_j)}^{\mathrm{1}/\mathrm{2}},{\sigma }_{ij}={({\sigma }_i{\sigma }_j)}^{\mathrm{1}/\mathrm{2}}, where e is the well depth and s is the collision diameter) were applied to calculate the LJ potential parameters between non-bonded atoms.

Fig.1 Configurations of the simulation system: (a–d) Atomistic structures of Janus GO membranes with different surface orientations (O for oxidized surface and P for pristine surface); (e) The simulation system for 50 mol-% water–ethanol mixtures permeating through a GO membrane; (f) The effective pore diameter of the GO nanosheet, i.e., the “green” area.

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First, to remove close contacts between the atoms, the separation system was subjected to energy minimization using the steepest descent method with a force tolerance of 1 kJ·mol⁻¹·Å⁻¹ and a maximum step size of 0.1 Å. Then, velocities were generated based on the Maxwell-Boltzmann distribution. After energy minimization, 5 ns NPT ensemble and 1.013 × 10⁵ Pa were implemented to reach the equilibrium state of simulation systems. In subsequent simulations, NVT calculations were performed to integrate the trajectories using the leapfrog scheme with a time step of 1 fs. The absolute temperature was then controlled at 300 K using a Nose–Hoover thermostat with a relaxation time of 0.1 ps. Long-range electrostatic interactions were computed by the particle mesh Ewald method [35] with a grid spacing of 1.2 Å and a fourth-order interpolation, whereas short-range van der Waals interactions were truncated at 1.2 nm. To prevent the GO membranes from drifting along the permeation direction, harmonic constraints with a spring constant of 1000 kJ·mol⁻¹·nm⁻² were imposed on the randomly selected sp² carbon atoms in the GO membrane. Periodic boundary conditions were then imposed in all three directions to mimic an infinitely large system; coordinates were stored every 1 ps and the total simulation time was 80 ns.

3 Results and discussion

Under a fixed transmembrane pressure, the water flux through four GO membranes was calculated by tracking the permeated water molecules on the vacuum chamber. Then, we presented the effect of the surface’s orientation on the water flow. The sorption amount on the upper surface and the diffusion property in the interlayer gallery were systematically analyzed to study the transport mechanism. Finally, the dynamic structure and permeation pathway of water molecules were examined by hydrogen bond and trajectory analyses, respectively. Note that with a microstructure having a pore diameter of 2.4 Å and an oxidized degree of 0.49, the GO membrane could completely reject ethanol molecules [22]. Therefore, the following discussions primarily focus on water permeation.

3.1 Water permeation flux

The water flux can be obtained by fitting the linear relationship between the permeated number of molecules and the simulation time. Figure 2 shows the water fluxes of 50 mol-% water-ethanol mixtures through four GO membranes after 80 ns. There is a clear increasing trend for the water flux in the order: OPPO<POPO<POOP<OPOP. In particular, the OPOP membrane achieved the maximum water flux of ~40.9 kg·m^-2·h^-1, while the OPPO membrane had the lowest, namely, ~20.1 kg·m^-2·h^-1. In current industrial water-ethanol separation processes, the commercial membranes, primarily based on polyvinyl alcohol (PVA), show a relatively low flux (<0.5 kg·m^-2·h^-1) [36]. Inorganic membranes, such as NaA zeolite membranes, have been applied for industrial water-ethanol separation and show a flux of up to 10 kg·m^-2·h^-1 [37]. GO is considered as a new-generation membrane for water–ethanol separation. Our recent study [38] demonstrated that the water flux and separation factor through an experimentally prepared GO membrane were 3.6 kg·m^-2·h^-1 and 260, respectively. Compared with state-of-the-art polymeric membranes, inorganic membranes, and GO-based membranes, the water–ethanol separation performance achieved in our simulated GO membrane (flux: 20–40 kg·m^-2·h^-1) is considerably higher. The first reason could be that we adopted suitable pores based on our previous simulation such that ethanol could be completely rejected. The second reason for the high water flux can be attributed to the ultra-thin membrane thickness (only 2.0 nm) constructed in our simulation work.

Fig.2 Water flux of 50 mol-% water–ethanol mixtures through four Janus GO membranes.

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3.2 The permeation mechanism

The permeation mechanisms of water through the Janus GO membranes are governed by two main reasons: the first one is preferential adsorption [39]. The orientation of the oxidized surface does affect the affinity of the GO membrane toward water molecules. From the RDF analysis in Fig. S2(a) (cf. ESM), the affinity increases in the order: OPPO<POPO ≈ POOP<OPOP. The membrane of OPOP has a strong affinity toward water, which can easily capture water from the feed tank to form a sorption layer [40]. The first peak (located at r = 0.45 nm) in Fig. S2(a) is to denote the first adsorption layer [41] of water on the membrane surface. Together with the water density contours on the cross-section of the GO membrane in Fig. S2(b), the thickness of the first adsorption layer is assumed to be 0.45 nm. The preferential water-adsorption layer on the GO surface is appeared in the region I with a thickness of 0.45 nm, as shown in the yellow rectangle region (Fig. 3, inset). By averaging the number densities of water molecules in this thin layer in GROMACS, the preferential water adsorptions on four Janus GO membranes are shown in Fig. 3. The oxidized upper surface (OP) endows GO membranes with the largest water adsorption amount (~4.5 molecule·nm^-2). However, the pristine upper surface (PO) has a low water capture capability, where the adsorption amount is only 2.8 molecule·nm^-2. To understand the capturing mechanism better, water density contours (N_w/uc refers to the number of molecules per unit grid, and the unit of density is 1/(1.25 ų)) on GO membranes are plotted in Fig. S3 (cf. ESM). As shown in Figs. S3(a,d), water has a slightly broader distribution on the oxidized surface owing to strong affinity. Furthermore, it is interesting to report that water molecules are highly assembled in the pore’s territory, where its surroundings have an extremely low water-density distribution (<30.0 N_w/uc). This is primarily because the primary pathway of pore penetration picks most water molecules from the surroundings into the pores. In particular, the OPOP membrane is much more attractive to water molecules, where the water density in the pore’s territory is up to 180.0–200.0 N_w/uc. The water-density contours on the GO membranes revealed that the oxidized upper surfaces promoted the water molecules to preferentially occupy the pore’s territory.

Fig.3 Preferential adsorption amount (molecule·nm^-2) of water molecules on four Janus GO membranes (Inset: Preferential water-adsorption region I with a thickness of 0.45 nm, marked by the yellow rectangle).

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The other important dominant factor for water permeation is ascribed to selective diffusion [42]. Once the water molecules have entered into the interlayer gallery from the adsorption layer, the diffusion coefficients are evaluated. Note that there are two types of diffusion modes in the interlayer gallery. One is the lateral diffusion parallel to the GO surface, and the other is the vertical diffusion along the direction of pore penetration. Using the following equations, the lateral (Eqs. (1) and (2)) and vertical (Eqs. (3) and (4)) diffusion coefficients of the water molecules in the interlayer galleries were computed by mean square displacement (MSD), where N is the total number of water molecules. The boundary conditions of lateral and vertical diffusions were set as follows: x(y) = 0.0–3.0 nm, z = 13.2–14.4 nm, x(y) = 1.2–1.8 nm, z = 13.2–14.4 nm, respectively.

(1)MS{D}_{xy}(t)={\displaystyle \frac{\mathrm{1}}{N}}\langle {\displaystyle {\sum }_{i=\mathrm{1}}^N{[x_i(t)-x_i(t_{\mathrm{0}})]}^{\mathrm{2}}+y_i(t)-y_i(t_{\mathrm{0}}){]}^{\mathrm{2}}}\rangle ,

(2)D_{xy}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}\underset{t\to \infty }{\lim }{\displaystyle \frac{\mathrm{d}MS{D}_{xy}(t)}{\mathrm{d}t}},

(3)MS{D}_z(t)={\displaystyle \frac{\mathrm{1}}{N}}\langle {\displaystyle {\sum }_{i=\mathrm{1}}^N{[z_i(t)-z_i(t_{\mathrm{0}})]}^{\mathrm{2}}}\rangle ,

(4)D_z={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\underset{t\to \infty }{\lim }{\displaystyle \frac{\mathrm{d}MS{D}_{xy}(t)}{\mathrm{d}t}}.

Fig.4 Water diffusion coefficients for the two types of diffusion modes in GO interlayer galleries: (a) Lateral diffusion parallel to the GO surface; (b) vertical diffusion along the direction of pore penetration.

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Figure S4 (cf. ESM) shows two types of MSD curves. By fitting the linear slope during the time interval of 10–60 ps, the diffusion coefficients through four Janus GO membranes were obtained with the formatting of 10^-6 cm²·s⁻¹, which agreed well with Devanathan’s work [9], while slightly lower than that in carbon nanotubes (CNTs) [43], probably because of the superhydrophobic channels of the CNTs. The pristine interlayer gallery forces the water into a fast lateral diffusion. As shown in Fig. 4(a), the water molecules are slipping transversely at an extremely high speed (20.28 × 10^-6 cm²·s⁻¹) in the OPPO membrane, where the in-built gallery comprised of sp² carbon atoms is pristine. With more oxidized regions built-in interlayers, the lateral diffusion properties of the water molecules are considerably reduced. Since the lateral resistance is generated by large LJ interactions between water and oxygen-containing functional groups, there is a decrease in the lateral diffusion coefficients as follows: D_xy(OPPO)>D_xy(OPOP) ≈ D_xy(POPO)>D_xy(POOP). In particular, equipped with both oxidized and pristine interlayer galleries, the GO membranes of OPOP and POPO have acceptable diffusion coefficients for lateral water transport. Remarkably, if the entrance and exit pores are highly aligned to form columnar pores, the directed diffusion is inspired and the tortuosity of the membrane is reduced [19,20], which demonstrates that the pore-to-pore transport (i.e., vertical diffusion) is the most effective and direct pathway for crossing the membranes. Interestingly, this vertical diffusion is stimulated by the oxidized interlayer galleries (Fig. 4(b)); e.g., in the OPOP membrane, the partially oxidized channels promote the pore-to-pore transport and then endow water with large vertical diffusion. However, the pristine interlayer in the OPPO membrane has the lowest vertical water diffusion coefficient (2.24 × 10^-6 cm²·s⁻¹). Therefore, the higher water flux in OPOP compared to OPPO can be attributed to the fast vertical diffusion of the water molecules in the columnar pore. With a large correlation time in Fig. S4(b), the vertical diffusion coefficients increase as follows: D_z(OPPO)<D_z(POPO)<D_z(POOP)<D_z(OPOP). This trend is similar to that of the water fluxes in Fig. 2. Under these conditions, the pristine interlayer gallery reduces the water flux because of the extended interlaminar pathway in the OPPO membrane, even with a great lateral diffusion. However, the oxidized galleries stimulate water from the entrance to energetically exit while restraining the long interlaminar movement, thereby contributing to a larger water flux. Therefore, with highly aligned pores in the Janus GO membrane, the large water flux is primarily attributed to vertical rather than lateral diffusion.

Figure 5 shows the accommodations of water molecules in four interlayer galleries via density contours. Water molecules concentrated in aligned pores (100.9–117.7 N_w/uc), generating the primary pathway for pore penetration, while this pore penetration was considerably more confined in OPPO membranes in which the narrowest density distribution (~84.1–100.9 N_w/uc) of water was observed. However, the oxidized galleries possibly collect water molecules in the pore’s territory (Figs. 5(a–c)). Nevertheless, as for their surroundings, the situation is quite different. Figure 5(d) shows that the pristine gallery surrounding the pore possesses the largest water distribution, indicating that the water molecules are wandering in this pristine interlayer rather than do the vertical permeation effectively, thus resulting in a low water flux. Note that the little difference in water distribution between OPOP and POPO in Figs. 5(a,c) is primarily attributed to these two membranes having the same partial oxidized channel. The larger preferential adsorption aroused by the upper surface (Fig. 3) introduces a higher water flux in OPOP compared to POPO.

Fig.5 Density contours of water in the interlayer of GO membranes. The unit of density (N_w/uc) is 1/(1.25 ų).

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To analyze the permeation pathway and residence time of molecules crossing the Janus GO membranes, we investigated the permeation trajectories. Considering POOP (oxidized gallery) and OPPO (pristine gallery) as examples, randomly selected water and ethanol molecules are represented by different color lines (Fig. 6). Indeed, water molecules are forcefully enchanted by pristine galleries and restricted between the dotted lines in Fig. 6(c) for a long time. The residence time of the selected water molecule, represented by a green line in Fig. 6(c), is ~50 ns. Owing to the in-built hydrophobic carbons, water molecules prefer to wander in the long interlaminar pathway with little resistance compared to the pore-to-pore transport. This wandering is an ineffective permeation, which brings about a low water flux in the case of the OPPO membranes. However, in the oxidized interlayer, the water molecules jump the gallery within a relatively short time (Fig. 6(a)) owing to the directed vertical diffusion along the pores. It is difficult for ethanol to cross through the studied GO membranes because the GO nanosheet (with a pore size of 2.4 Å and an oxidized degree of 0.49) can completely reject ethanol [22].

Fig.6 Trajectories of randomly selected water and ethanol molecules (represented by different colors) through the oxidized and pristine interlayers: (a) and (b) Trajectories through POOP; (c) and (d) trajectories through OPPO.

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To visualize the permeation process, the equilibrium snapshots of four GO membranes are shown in Fig. 7. Ethanol has been entirely rejected and water molecules are abundantly captured by the oxidized upper surface (Figs. 7(a,c)). Because of the interlayers in Fig. S5(a) (cf. ESM), two water layers are formed to thoroughly free water diffusion. With more oxidized regions, hydrogen bonds between the water and the interlayer can be easily formed to stabilize the structure, as shown in Fig. S7(b) (cf. ESM). Importantly, the OPOP membrane inspired directed pore penetration for water molecules, as shown in Fig. S6(a) (cf. ESM). The PMF calculation in Fig. S(8) (cf. ESM) shows that it is the OPOP membrane that achieves the lowest total energy barrier for water permeation. Therefore, owing to the oxidized upper surface and the oxidized gallery, the Janus GO membrane with OPOP orientation exhibits the largest adsorption capacity and vertical diffusion for water molecules, which synergistically contributes to the highest water flux in the vacuum side in Fig. 7(a).

Fig.7 Snapshots of water–ethanol mixtures permeating via four Janus GO membranes. The water and ethanol molecules are represented by green and orange balls, respectively.

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4 Conclusions

MD simulations were performed to investigate the permeation of water-ethanol mixtures through Janus GO membranes with different orientations of oxidized and pristine surfaces. The oxidized upper surface had considerable ability to capture water molecules from aqueous solutions. When the pores were aligned, vertical diffusion was the most direct and effective mode for water passing through the GO membranes, especially in the oxidized channels. While in the pristine channels, the fast lateral diffusion enchanted water to wander in the extended interlaminar pathway, resulting in a low water flux (~20.1 kg·m^-2·h^-1) in the OPPO membrane. Owing to the oxidized upper surface and oxidized gallery, the water flux doubled (~40.9 kg·m^-2·h^-1) in this type of Janus GO membrane with an OPOP orientation. The density contours, trajectories, and dynamic properties of the water molecules demonstrated that the water flux could be largely enhanced by flipping the oxidized and pristine surfaces. This simulation study provides a microscopic understanding of water permeation via Janus GO membranes. It highlights the important role of the oxidized upper surface and the interlayer galleries in water crossing through the aligned pores for selective water transport. The results in this work could be instructive for separating aqueous solutions containing volatile organic compounds (larger than ethanol) such as propanol, butanol, ethyl acetate, and dimethyl carbonate.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 21922805, 21776125). We are grateful to the High-Performance Computing Center of Nanjing Tech University for supporting the computational resources.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11705-020-1954-5 and is accessible for authorized users.

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