The Effects of Edge Functional Groups on Water Transport in

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Functional Nanostructured Materials (including low-D carbon)

The Effects of Edge Functional Groups on Water Transport in Graphene Oxide Membranes Ruosang Qiu, Shi Yuan, Jie Xiao, Xiao Dong Chen, Cordelia Selomulya, Xiwang Zhang, and Meng Wai Woo ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00492 • Publication Date (Web): 30 Jan 2019 Downloaded from http://pubs.acs.org on January 31, 2019

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ACS Applied Materials & Interfaces

The Effects of Edge Functional Groups on Water Transport in Graphene Oxide Membranes Ruosang Qiu†, Shi Yuan†, Jie Xiao§, Xiao Dong Chen§, Cordelia Selomulya†, Xiwang Zhang†, Meng Wai Woo†* † Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia §China-Australia Joint Research Center in Future Dairy Manufacturing, School of Chemical and Environmental Engineering, College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou, Jiangsu Province, 215123, PR China

KEYWORDS: graphene oxide, membrane, edge-functionalization, self-diffusion, water transport, molecular dynamics.

ABSTRACT: Graphene oxide (GO) membranes assembled by GO nanosheets exhibit high water flux because of the unique water channels formed by their functionalized layer-by-layer structure. Although water transport in GO membrane is in principle influenced by the functional groups at the edges of GO nanosheets, this has yet to be fully understood. To fill this knowledge gap, molecular dynamics simulation was employed in this work, to gain insights on the influences of three typical edge functional groups of GO nanosheets: carboxyl (COOH), hydroxyl (OH) and hydrogen (H). A well-controlled numerical analysis with complete isolation of the functional groups at the edges was undertaken. The results reveal that COOH group has negative impact on water transport due to its relatively large steric geometric structure, which resists water flow. By contract, OH group promotes water transport by uniquely ‘pulling’ water molecules across the nanosheet layer due to 1 ACS Paragon Plus Environment

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its relatively stronger interaction with water. H atom promotes water transport as well mainly due to its low resistance steric structure. Moreover, the size of inter-edge hub has apparent impact on the influence of these functional groups on water transport. The results suggest that in the design of high water flux GO membranes, it would be strategic to remove COOH edge functional groups while maintaining a mixture of OH and H edge functional groups.

INTRODUCTION Membrane-based separation technology is widely used in water treatment industry because of its high working efficiency and low energy consumption.1-3 Compared with traditional polymeric membranes, GO membranes can form a layer-by-layer structure via assembling GO nanosheets, which imparts little friction to water transport along the inter-layer spaces between neighboring GO nanosheets. Selective solute rejection is then imparted by size exclusion and interaction with functional groups of GO nanosheets as water molecules are transported across GO membranes.4 This kind of special ‘moving and sieving’ method could lead to higher water flux and separation efficiency.5-9 Experimental investigation on the influences of functional groups on water movement hitherto is currently limited to overall experimental observation involving mixtures of functional groups; current techniques do not allow complete isolation of different specific functional groups. In addition, experimental investigation cannot achieve detailed analysis on membrane internal channels to fully elucidate the mechanism on how different types of functional groups affect water transport. To circumvent this limitation, atom-scale numerical study has been used for fundamental mechanistic research. Using molecular dynamics simulation, functional groups can be ideally chosen and linked at specific positions on GO nanosheets, which can be further assembled into structured membranes. This method provides a controlled investigation into the effect of different functional groups on water transport behavior under equilibrium9-13 and dynamic pressure induced14-24 systems. Although the mechanisms of how water molecules move through the functionalized inter-layer channels inside GO membranes have been investigated in many studies,9, 13-14, 18-21, 23, 25-27 little attention had been paid until recently to the impact of different functional groups at the edges of GO nanosheets. For instance, 2 ACS Paragon Plus Environment

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Boukhvalov et al. found an increase in energy cost when water molecules moved from the hydroxyl functionalized inter-layer membrane channels to regions between hydroxyl functionalized edges, indicating the significance of edge functional groups on water flow.26 Despite this importance, most simulations reported in literatures only utilized non-oxidized edges (carbon atoms) without any functional groups.13, 17, 22-23, 25 One recent study by Kieu et al. compared the differences between carbon and hydrogen edges, and found that hydrogen edges relatively promoted water transport.14 Most recently, Safaei et al.16 attempted a more realistic approach and included six hydroxyls and three epoxies at the edges of 1.8 × 3 nm2 graphite nanosheets and Willcox et al.20-21 fully populated all the edges of 3.2 × 6.4 nm2 nanosheets with hydroxyl groups. The main premise of these studies, however, was on the investigation of the effect of inter-edge gap widths and interlayer distances on water transport. Therefore, a comprehensive study is still highly needed to investigate how different functional groups at the edges of GO nanosheets affect water molecule movement within GO membranes. In this work, to address this knowledge gap, multi-layered GO-base membranes functionalized with carboxyl (G-COOH), hydroxyl (G-OH) or hydrogen (G-H) on the edges of graphene (G) nanosheets, were numerically investigated in pure water. To minimize the interference of surface, as a more controlled study, all surface functional groups were omitted in the simulation. This work will provide a more fundamental and controlled investigation on the influence of functional groups at the edge of graphene nanosheets. The first part of this investigation was taken under equilibrium conditions to investigate the interactions between water molecules and edge functional groups inside GO membranes in the absence of external pressure. With the understanding obtained from the equilibrium analysis, the second part of this paper extended this numerical investigation to the movements of water molecules under the dynamic pressure induced conditions. COOH edge functional group, summarized from this work, negatively affects water permeance. OH and H edges, however, promote water transport via interactional “pulling” and low resistance steric structure, respectively. To the best of our knowledge, this is the first paper directly comparing the effects of three types of edge functional groups on water transport in GO membranes. The new understanding obtained from this work will provide insights to the development of high performance GO membranes for water processing. 3 ACS Paragon Plus Environment


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METHODOLOGY Molecular Structure The all-atom structures of GO nanosheets were built using VEGA_ZZ 3.1.1. COOH, OH or H functional groups were linked at all edge carbons of the honeycomb GO nanosheets with random orientations, respectively.

28-29

Their charge distributions were calculated with the Gasteiger Method30-31.

The

configuration and charge distributions are shown in Figure 1 and Table S1. The edge enhancement of C atoms was observed in all nanosheets’ models as edge C atoms carry more charges than the middle C atoms.32

Figure 1. Structures (Å) and charge distributions (e) of the (a) G-COOH, (b) G-OH and (c) G-H nanosheets. Membranes used in this numerical study were made by duplicating the nanosheets shown in Figure 1 and placing them with specific distance according to the cases to be investigated. An illustration is shown in Figure 2. For GO nanosheets with steric functional groups linked at their edges, the inter-layer distance was defined as the distance between C atoms of two vertically neighboring GO nanosheets while the inter-edge gap width was set as the distance between the closest atoms of two GO nanosheets in the same layer. The gap 4 ACS Paragon Plus Environment

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width at 7 Å (which allows the formation of two water layers within the gap) and 23 Å (the maximum width before the membrane structure becomes an open channel) were used in this work. For the inter-layer distance, 7 Å (which allows the formation of one water layer within the inter-layer space), 11 Å (which allows the formation of two water layers) and, 14 Å (which allows the formation of four water layers) were used (Figure S1 and S2). 7 Å was arbitrarily taken as the lower bound in the gap and inter-layer distance for this investigation following past reports in this area.14, 16-17, 20-21, 23-24 The upper bound of inter-layer distance at 14 Å was selected as any larger inter-layer distance will result in no water density aggregated layer in the middle of channel (between two aggregated water layers of each side, Figure S2d). This was an indication that there would be a minimal influence of the inter-layer surface of the nanosheets at such large distances.

Figure 2. Illustration of the layer-by-layer matrix of GO membranes. Placement of G-COOH, G-OH or G-H nanosheets (grey cross-linked beads) in water box (white-red lines) with same gap width and same inter-layer distance according to the layouts of the matrixes. The hub space, inter-layer channel and inter-edge gap are shown in dark red, blue and light red squares, respectively. After equilibrium, all redundant atoms external to the space bounded by the dashed lines in the x-axis and all water molecules outside the nanosheet matrix in the y-axis were removed. Periodic boundary condition was then applied to build a GO membrane. Finally, an impermeable sheet was put at the top of the system, which functioned to induce the pressure to push water molecules through the GO membrane.

Molecular Dynamics Simulation 5 ACS Paragon Plus Environment


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The simulations were undertaken via Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The interaction parameters between GO nanosheets and water atoms were adapted from the parameters used by Chen et al.17 and Lorentz-Berthelot mixing rules33 (as listed in Table 1). Periodic boundary condition was used in all directions. Water molecules was applied with the SHAKE Algorithm. The cut-off radius of Lennard-Jones potential was set at 9 Å and the long-range Coulombic potential was calculated using the kspace_style PPPM solver. After equilibrium conditions were achieved, the simulation was then adapted for the dynamic pressure modelling. Two simulation systems are illustrated below. Table 1. The interaction parameters used for simulation Interaction atoms

ε (kcal/mol)

σ (Å)

CGO-Ow

0.127697

3.5085

OGO-Ow

0.162484

3.1180

HGO-Ow

0

0

Ow-Ow

0.155300

3.1660

*-Hw

0

0

1. The Equilibrium System This series of simulations were undertaken to assess how different edge functional groups interact with water molecules inside GO membranes without external driving force. Three membrane layouts were used in this work as shown in Figure 2, which were 7 × 7, 7 × 11 and 7 × 14 (gap width × inter-layer distance). The membranes were initially solvated with SPC water molecules.34 The boundaries of all directions were over 25 Å away from GO nanosheets. Equilibration of the system was undertaken using the following schedule: NPT with a time step at 2 fs for 1 ns followed by NVT for 1 ns under 300 K. Once the equilibrium condition was achieved, equilibrium state analysis was undertaken by statistical sampling. 2. The Dynamic Pressure Induced System

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The second series of simulations were undertaken to assess the effects of edge functional groups on water transport behavior under external pressure. Membrane structures were adapted from the equilibrium system as shown in Figure 2. The 7 ×7 and 7 ×14 structured membranes were used in this case, in addition with the 23 × 7 membranes (Figure S3). Because the water boxes used in the equilibrium system were too large for the dynamic pressure induced system, redundant water molecules and GO nanosheet atoms were deleted (outside the dash lines in Figure 2 in the x-axis and outside the membrane in the y-axis), and periodic boundary condition was applied. The membrane surface areas are listed in Table S2. To induce the dynamic pressure, an impermeable sheet (akin to the surface of a piston) was implemented at the top boundary of the system, which was initially over 90 Å above the GO membranes.14, 16-17, 20-21, 24 The vacuum space between the impermeable sheet and equilibrated water box was then filled with water molecules to achieve a density of 0.97 g/cm³. Once the equilibrium condition was achieved with NVT, each atom of the impermeable sheet was then applied with a constant force of 1 kcal/(mol·Å) pointing towards the negative z-direction. Water molecules were pushed through the membranes by this impermeable sheet. The transmembrane differential pressure was around 2,500 bar (Table S2).

THEORETICAL ANALYSIS Water Density for Analysis Visual Molecular Dynamics (VMD) Density Profile Tool35 was employed in this work. Frames were recorded at every 200 fs during the simulations. For calculating the water (represented by O atom) distribution in a long period, larger frame step sizes were used to obtain a clearer water distribution analysis. Diffusion Coefficient of Water Molecules for the Equilibrium Analysis. Diffusion is caused by the Brownian motion in an equilibrium environment. By Fick’s law, diffusion states the flux of the diffusing species with the gradient in the concentration of solvate. When this is used for describing solvent molecules, the diffusion parameter measured is called self-diffusion.36



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In microscale, the slop of mean-squared displacement (MSD) versus time is proportional to the diffusion coefficient. 2

1

t 2 2 MSDxyz = ∑N i=1 ∑0 {[x(i)-x0 (i,t)] +[y(i)-y0 (i,t)] +[z(i)-z0 (i,t)] } N

Diffusion Coefficientxyz =

dMSDxyz

(1) (2)

6dt

For this analysis, simulation samples were undertaken at every 20 fs for 400 times. The MSD of the O atoms was calculated, representing the positions of the water molecules in the hub space. During this time most of the water molecules were still inside the same boundary of numerical sampling box.

Each

measurement was repeated 5 times. Radial Distribution Function for the Equilibrium Analysis Radial Distribution Function (RDF) is a type of curve that characterizes liquid state around a single atom or nanosheet component. It is a time independent ratio between the average densities of Ow or Hw atoms of water molecule at r distance away from the studying object.36 The RDFs of single atoms and all types of GO nanosheets were calculated by NPT simulation under 300 K with a time step at 2 fs for 3 ns and 1 ns, respectively. Pressure Determination for the Dynamic Analysis In the dynamic pressure induced system, the feed water density is much higher than the penetrant that brings in an external driving force that pushes water molecules transporting from high-density space to low-density space. This driving force was induced by the differential pressure between feed and penetrant. The pressure is determined by system temperature and atom interaction. The water densities caused by various pressures were determined apriority by NPT simulations with a time step at 2 fs for 40 ps under 300 K (Table S3). Based on the results, the feed or penetrant pressure was calculated through the water density with the statistic equation listed below: P = 113,097 ρ3 – 290,135 ρ2 + 262,479 ρ – 84,744

(3)


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Where, P (atm) is the hydraulic pressure and ρ (g/cm3) is the density of SPC water molecules. SPC water density caused by various pressure had high similarity as the results reported by Francis W. Starr et al37 calculated with SPC/E water model. Water Permeance Computation for the Dynamic Analysis Water permeance, which is normalized water flux by dividing transmembrane pressure, is an important feature to measure the water transport process. It was calculated by the equation below: Water Permeance = ∆m/(∆t·S·∆P)

(4)

Where, ∆m is the penetrated water mass, ∆t is the penetrated time, S is the area of membrane (Table S2), ∆P is the driving transmembrane differential pressure (Table S2). Plotting the penetrated water mass versus time, the water fluxes (∆m/∆t) were computed via the linear gradient of the plot (Figure S9).

RESULTS AND DISCUSSION Equilibrium Water Self-Diffusion This part of the study was undertaken to assess how the edge functional groups affect water self-diffusivity inside GO membranes. Self-diffusivity is a measure of the Brownian motion of water molecules in an equilibrium environment as affected by the interaction with GO nanosheets. An initial hypothesis was that the self-diffusivity would delineate the behavior of water transport through membranes. Membrane hub spaces (Figure 3a) were chosen for the focus of this study because they are the regions where water movement will be influenced by edges functional groups when water molecules pass through: (1) the entrances/exits of the hubs formed by the surfaces and edges of GO nanosheets, and (2) the inter-edge gaps formed by two GO nanosheet edges (Figure 3a). The gap width was kept constantly at 7 Å in the equilibrium numerical analysis while the inter-layer distance was varied from 7, 11 to 14 Å (Figure 3a) to vary the influence of the nanosheet surface on the hub water.



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Figure 3. Characteristics of water molecules in GO membranes with different edge functional groups at diffusion equilibrium in the absence of external pressure. (a) Illustration of the layer-by-layer structure of GO membrane in the MD simulation. GO nanosheets are represented by grey squares. (b-g) Geometric and simplified structures of G-COOH, G-OH and G-H nanosheets. (h) Simplified illustration of ‘plate’ steric structure of the G-H nanosheet. (i) Simplified illustration of ‘pot’ structure of the G-COOH and G-OH nanosheets. (j) Water diffusion coefficients around the inter-edge gap in a constant water box thickness at 14 Å in the z-axis. (k) Water density of the 7 × 7 G-OH membrane corresponding to the region enclosed by the dashed black line in (a). (l) Water density of the 7 × 7 hubs along the z-axis corresponding to the region enclosed by the solid red line in (k). (m) Water density profile of the 7 × 14 G-OH membrane corresponding to the region enclosed by the dashed black line in (a). (n) Water density profile of the 7 ×14 hubs along the zaxis corresponding to the region enclosed by the solid red line in (m). Water densities of the G-COOH and G-H membranes are shown in Figure S4. As shown in Figure 3j, the water diffusivity around the inter-edge gaps increased when the inter-layer distance is extended from 7 to 14 Å, regardless of the edge functional groups. The lowest water self-diffusivity 10 ACS Paragon Plus Environment

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is observed in the OH inter-edge gap. Compared with the COOH inter-edge gap, water around the H interedge gap has higher diffusivity when the inter-layer distance is 7 Å. However, when the hub space is enlarged with larger inter-layer distance, the water self-diffusivity around the COOH inter-edge gap increases more significantly than that around the H inter-edge gap and eventually has a higher diffusivity at the inter-layer distance of 11 and 14 Å. To fully elucidate this behavior, it is important to firstly understand how the functional edges influence the movement of water molecules adjacent to the surfaces and the edges of GO nanosheets (especially in the interedge gaps). When located adjacent to the surfaces of GO nanosheets, water molecules have the highest water diffusivity on the G-H nanosheet because they could move randomly on the ‘plate’ structure (Figure 3f, 3g, 3h and S5b). Water molecules adjacent to the surfaces of G-COOH and G-OH nanosheets, however, are constrained in a steric ‘pot’ structure (Figure 3i), trapped by the edge functional groups of these GO nanosheets (Figure 3b, 3c, 3d and 3e) and the self-diffusivities are reduced to some extent (Figure S5b). G-OH nanosheet has relatively opened steric ‘pot’ structure than G-COOH nanosheet (Figure 3d and 3e) that results in slightly higher water self-diffusivity on the surface (Figure 3b, 3c and S5b). Meanwhile, when the water molecules are adjacent to the functionalized edges, especially in the inter-edge gaps where is under the minimal influence from the surfaces of the nanosheets, the interaction effect between the nanosheet edges and water molecules become more significant. Higher level of interaction (attraction) from the edge of GO nanosheets is denoted by lower water self-diffusivity and vice versa. Lower selfdiffusivity translates to slower water molecule movement leading to denser molecular clustering and subsequently higher water density. Along this line, the water diffusivity around the inter-edge gap follows the order of COOH>H>OH (Figure S5c) with a corresponding water density order of OH>H>COOH (Figure 3l and 3n). These indicate that the water affinity on the edges of the nanosheets is of the following order OH>H>COOH. However, this observation would not be expected if the water affinity on functional groups were to be deduced by the reducing number of hydrogen bonds between them. Previous reports using this form of analysis for systems with single functional group suggested that the water affinity of these functional groups 11 ACS Paragon Plus Environment


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followed the order of COOH>OH>H.38-39 Analysis in the current work from the angle of geometric structures reveals an alternative view on this phenomenon. All types of single charged O atoms of edge-functionalized G nanosheets have stronger interaction with water molecules shown by their higher water density at a closer spherical radius when compared with single charged and neutral C atoms (Figure S8, obtaining RDF of H atom is not possible as its Van der Waal interaction is negligible). After incorporation into the edge functional group structures, both H and O of the OH groups have tighter and higher RDF peaks than those in the H and COOH groups (Figure 4b and 4c). Although COOH group has two O atoms, large repulsion force among the COOH edge groups results in their dispersion into two sides of GO nanosheets. This largely decreases the O density (red beads in Figure 3b and Figure S6a) and therefore reduces the water attraction by O atoms. Moreover, because of these repulsion forces among COOH groups, their hydrophobic C2COOH atoms (purple beads in Figure 1a)40 are exposed to the water molecules in the inter-edge gaps. This is supported by the fact that this C2COOH atom has a similar RDF distribution as bare C+0.2926 atom, however, its RDF peak is lower than C1COOH whose radial reach of RDF peak was extended by the COOH groups (Figure 4a and S8). The exposure of C2COOH atom further increases the hydrophobicity of the COOH edge. Thus, water molecules have higher affinity on OH edge than on the other two edges. Because of the tiny volume of H atom, its Van der Waal interaction is negligible, and it only interacts with other atoms with long distance electrostatic interaction. Therefore, its RDF peak is formed by the charge it carried and the atoms linked with (Figure 4c). Because HH directly points towards to the inter-edge gap (Figure 1c) and it has higher water density within a closer sphere region than all atoms of the COOH groups (Figure 4), water molecules have higher affinity on the H edge than the COOH edge. This difference is further confirmed by the higher and closer RDF peak of CH when compared to that of C2COOH (Figure 4a). Therefore, this RDF analysis provides more evidence supporting that the water affinity on the functionalized edges of GO nanosheets is in the order of OH>H>COOH. More explanations about the geometric and interaction effects on the water diffusivity were undertaken using simplified single layer nanosheet simulations, which are provided in the Supplementary Information (Supplementary Part 2: Single layer nanosheet simulation).


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Figure 4. Radial distribution functions of G-COOH, G-OH and G-H nanosheets including (a) C atoms, (b) O atoms and (c) H atoms. HW is H atom of water molecule. OW is O atom of water molecule. C1COOH is the C atom of GO nanosheet linked with COOH group. C2COOH is the C atom of COOH functional group linked with GO nanosheet. COH is the C atom of GO nanosheet linked with OH group. CH is the C atom of GO nanosheet linked with H atom. O1COOH is the O atom of COOH edge functional group linked with C2COOH with double bonds. O2COOH is the O atom of COOH edge functional group linked with both C1COOH and HCOOH. OOH is the O atom of OH edge functional group. HCOOH is the H atom of COOH edge functional group linked with O1COOH atom. HOH is the H atom of OH edge functional group linked with OOH. HH is the edge H atom of H edge functional group linked with CH.

The behavior of the water molecules around the inter-edge gap inside hub spaces can be well explained by the effect of steric structure and water affinity on water molecule self-diffusivity at the regions adjacent to the surface and between the edges. In the 7 × 14 hubs, water molecules are distributed relatively ‘evenly’ across the height of the hub space as denoted by the density distribution (Figure 3n, relative to the density distributions in 7 × 7 hubs shown in Figure 3l). Therefore, the self-diffusivity order around the 7 × 14 interedge gaps (Figure 3j) follows the order between the edge of different functionalized GO nanosheet, which is 13 ACS Paragon Plus Environment


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COOH>H>OH (Figure S5c). When the inter-layer distance is decreased from 14 Å to 11 Å, the first aggregated water layers on the upper and bottom nanosheets are still located outside of the inter-edge gap space (Figure S2c, S4d, S4e and S4f). It means that most of water molecules are under the influence of edge interaction resulting in similar behavior between the 11 Å and the 14 Å inter-layers. When the inter-layer distance is further decreased from 11 Å to 7 Å, more water molecules are accumulated adjacent to the surfaces (Figure 3l, 3n, S4a, S4b and S4c). It results in the overall diffusivities around the inter-edge gaps to be more represented by water molecules located adjacent to the surfaces of the nanosheets. In the H inter-edge gap, the remarkably high water diffusivity on the G-H nanosheet surface (Figure S5b) results in the H inter-edge gap water having the highest diffusivity (Figure 3j). However, the difference between the geometric effects of the COOH and OH surfaces is relatively small (Figure S5b). This behavior could have been partly augmented by the higher water affinity to OH edge than to the COOH edge, resulting in lower OH inter-edge gap diffusivity, due to the close proximity between the nanosheet surfaces and edges that formed the 7 × 7 hub spaces (Figure 3k, 3l and S4). The above analysis provides a baseline analysis on the mobility of the water molecules in the GO systems evaluated. As elucidated earlier, it is initially hypothesized that water molecules with lower self-diffusivity, due to higher steric hindrance or higher affinity with the GO nanosheet edges, may have lower fluxes as more energy is required to overcome these associated barriers to movement. In the next section, the water transport processes of the three types of edge-functionalized membranes are further investigated under dynamic pressure conditions to assess this hypothesis.

The Dynamic Water Transport Layer-by-layer membranes of the 7 × 7, 7 × 14 and 23 × 7 layouts were used for this part of study (Figure S3). These three geometrical membrane layouts cover the following situations: the membranes that have (1) narrow inter-edge gaps only (7 ×14), (2) both narrow inter-edge gaps and narrow inter-layer channels (7 ×7) and (3) narrow inter-layer channels only (23 × 7). The first two cases correspond to the geometrical cases 14 ACS Paragon Plus Environment

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used in the equilibrium analysis. The last case, as an addition in this part of the report, represents a scenario where there is a staggered layer structure with minimum geometric overlap in the layers. 7 × 14 Nanosheet-Based Membrane – The Interaction Effect The 7 ×14 membranes provide a scenario of relatively wide inter-layer channels and narrow inter-edge gaps (Figure 5a and S3). The water permeance order of the three types of membranes is OH>H>COOH under the transmembrane pressure at around 2,500 bar (Figure 5b). Surprisingly, the water permeance order is opposite to the equilibrium self-diffusivity order of COOH>H>OH presented in the preceding section. It indicates that water self-diffusivity, as an indication of ‘resistance to movement’, might not be directly applicable to denote the water permeance behavior under the dynamic pressure system. Hence, there must be some other factors controlling water transport, which will be discussed in the following sections.

Figure 5. Water transport within the 7 × 14 membranes at 2,500 bar. (a) Illustration of the 7 × 14 membrane system. (b) Water permeance. (c-h) Water distributions within the (c, d) G-COOH, (e, f) G-OH and (g, h) GH membranes corresponding to the region enclosed by the dashed line in (a). These dark blue areas in (c) (e) (g) show the effective boundaries of the GO nanosheets. The vertical dashed lines in (c-h) show the geometric sizes of the middle layer nanosheets and the inter-edge gaps that are illustrated by the grey and red squares in (a), respectively. (d) (f) (h) Water distributions averaged from the region whose thickness at 4 Å along the x-



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axis, which corresponding to the middle nanosheet layer as bounded by the horizontal dashed lines in (c) (e) (g), respectively. The water densities (Figure 5d, 5f and 5h) in narrow inter-edge gaps reveal different attractions from three types of edge functional groups. For COOH and OH inter-edge gaps, two water paths across the nanosheets are revealed by two peaks in Figure 5d and 5f. The H inter-edge gap, however, is different from that of the COOH and OH inter-edge gaps. There is only one water path formed because the main attraction inside this channel is long distance electrostatic interaction from HH rather than Van der Waal interaction from O or C atom (Figure 5h). Comparing water permeance among three types of 7 × 14 membranes for identifying the effect of different edge groups on water transport, water permeance order of OH>H>COOH could be observed (Figure 5b). It appears that the OH edge interaction relatively promotes the water permeance although the attraction between water molecules and OH groups is the highest, evidenced by the lowest diffusivity around OH inter-edge gap (Figure 3j). In contrast, the COOH and H edge interactions have relatively higher effect on reducing the water permeance, despite higher water diffusivities are observed in COOH and H inter-edge gaps (Figure 3j). This contradiction could be explained by the nature of the edge functional groups. As discussed earlier, the low water attraction of the COOH edge is due to its steric structure, which is exposed the hydrophobic C2COOH to the edge of the nanosheet. In contrast, the OH edge does not have such steric structure and thus is relatively more hydrophilic, giving it a stronger attraction to the water molecules. For the H edge, although the hydrophobic CH is shielded by HH, it exhibits weaker attraction than the OH edge. Compared with the HOH and OOH of the OH groups, HH has lower water density around it (Figure 4b and 4c). Thus, the order of water affinity on three types of edge functional groups is OH>H>COOH. Under the pressure induced system, water densities in the inter-edge gaps became less structured (Figure 5 c-h) than in the equilibrium system (Figure 3m and S4) because of their high speed pressure-driven movements. Higher attraction of edge functional groups could help pull water molecules passing through the narrow inter-edge gap with high regularity. Consequently, the hydrophilic interaction of the G-OH membrane exhibits a ‘pulling effect’ on attracting and 16 ACS Paragon Plus Environment

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allowing easier passage of water molecules. In contrast, the hydrophobic interaction of the COOH edge exhibits a ‘blocking effect’ on the dynamic movement of the water molecules.

7 × 7 Nanosheet-Based Membranes – The Dominance of the Geometric Effect The 7 × 7 membranes were assembled as a scenario of relatively narrow inter-layer channels and narrow inter-edge gaps (Figure 6a and S3). Similar to the observation with the 7 × 14 membranes, the water permeance order of H>OH>COOH from the 7 × 7 membranes (Figure 6b) did not follow the equilibrium diffusivity order of OHCOOH in such small hub entrance/exit scenario, is mainly determined by the geometric volumes of the functional groups. Meanwhile, same size of the inter-edge gaps of the 7 × 7 membranes as the 7 ×14 membranes suggests that the interaction effect may also have influence on water transport in the 7 ×7 membranes. Following the same scenario as the 7 ×14 membranes, there are two clear water paths inside both COOH and OH inter-edge gaps and only one water path inside the H inter-edge gap (Figure 6d, 6g and 6j). These special water paths inside the inter-edge gaps mean that the interaction effect also works inside the 7 ×7 membranes, although it played less dominated role than the physical steric blockage on affecting the transmembrane water permeance.


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23 × 7 Nanosheet-Based Membranes – The Geometric Effect The 23 × 7 membranes were assembled as a scenario of relatively narrow inter-layer channels with wide inter-edge gaps (Figure 7a and S3). It was designed to provide a layer-by-layer membrane that had similar entrance/exit geometric steric blocking effect as the 7 ×7 membranes but with the minimum interaction effect induced by the edge functional groups on water molecules in the inter-edge gaps. This was intended to give additional evidence to the mechanism discovered from the 7 × 7 membranes. The water permeance of the 23 × 7 membranes follows the same order as the 7 × 7 membranes with H>OH>COOH. Compared with the 7 × 7 membranes, regardless of the edge functional groups, the water permeance of the 23 × 7 membranes significantly increases because wider inter-edge gap distance removes the limitation of narrow inter-edge gaps (Figure 6b and 7b). The higher water permeance is a clear indication that the effective edge functional group-water interaction effect is minimized at wide inter-edge gaps.

Figure 7. Water transport within the 23 × 7 membranes at 2,500 bar. (a) Illustration of the 23 × 7 membrane system. The white and yellow arrows mark the positions of the hub entrances and exits, respectively. (b) Water permeance. (c-h) Water distributions within the (c, d) G-COOH, (e, f) G-OH and (g, h) G-H membranes corresponding to the region enclosed by the dashed line in (a). These dark blue areas in (c) (e) (g) show the effective boundaries of the GO nanosheets. The vertical dashed lines in (c-h) show the geometric sizes of the nanosheets as illustrated in grey squares in (a). (d) (f) (h) Water distribution averaged from the region whose thickness at 3 Å in the z-axis along the x-axis, which corresponding to the region between the entrance and 19 ACS Paragon Plus Environment


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middle, and middle and exit layers of membranes (locations are shown in Figure 2) as illustrated in purple squares in (a). The red arrows in (d) and (f) highlight the low water densities corresponding to the positions of the hub entrances/exits. The geometric effect, which is another effect summarized from the 7 × 7 membranes and is delineated by the low water densities at the entrances/exits of the hub spaces, can be clearly observed in the 23 × 7 membranes (Figure 7d, 7f and 7h). It corresponded to the completely closed COOH edges (Figure 3b and 3c), relatively opened OH edges (Figure 3d and 3e) and fully opened H edges (Figure 3f and 3g). In this way, this observation via the 23 × 7 membranes provides more evidence to the geometric effect observed via the 7 × 7 membranes: when there is only one water layer at the entrances/exits of the hub spaces, the main resistance to water flux is contributed by geometric blockage caused by the edge functional groups. The Contribution of Edge Functional Groups Figure 8 summarizes the contributions of the three kinds of edge functional groups on the water transport processes inside structured GO membranes. For the G-COOH membrane, because of the completely closed ‘pot’ geometric structure formed by the COOH edge functional groups, the narrow horizontal channel at the entrance/exit of the hub space (when only one water molecule passes through), is greatly blocked by that particular edge group (Figure 8e and 8h). At the same time, water molecules have the least affinity on COOH edges, which is caused by large repulsion among COOH groups that disperses the attraction of the O atoms and exposes the hydrophobic C atoms. This does not provide sufficient interaction to ‘pull’ water molecules across the inter-edge gaps (Figure 8b and 8h). The negative influence caused by both geometric and interaction effects results in the most inefficient water transport inside the G-COOH membrane. For G-OH membrane, the relatively opened ‘pot’ structure formed by the OH functional groups partly enlarge the hub entrance/exit compared to the one formed by the COOH edge (Figure 8f and 8i). Concurrently, water molecules have the highest affinity to the OH edges allowing them to be easily ‘pulled’ into the inter-edge gaps (Figure 8c and 8i). This ‘pulling effect’, however, is highly dependent on the sizes of the inter-layer channel and the inter-edge gap. Similarly, the G-H membrane also promotes water flux due to its opened 20 ACS Paragon Plus Environment

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structure at the entrance/exit of the hub space (Figure 8g and 8j). The low water attraction by the H edge provides less ‘pulling force’ compared to the OH edge (Figure 8d and 8j). Consequently, COOH edge functional groups reduce the water transport in the GO membrane while the effect of OH and H edge functional groups are controlled by their geometric or interaction effect that is highly determined by the size of interlayer channel.

Figure 8. Summary of the individual influences of the three kinds of edge functional groups on water transport under different geometric membrane structures. (a) Illustration of the membrane system.

Geometric

structures of the membranes are (b-d) 7 ×14, (e-g) 23 ×7, and (h-j) 7 ×7. While their edge functional groups are (b) (e) (h) COOH, (c) (f) (i) OH and (d) (g) (j) H. Green, orange, red and white parts of arrows illustrate the promoted, neutral, restricted and not obvious influences from the edge functional groups, respectively.

CONCLUSION In this numerical study, the effect of highly compacted layer-by-layer GO membranes, functionalized with COOH, OH or H at the edge, on the water transport mechanism was investigated in both equilibrium and dynamic pressure conditions. Hub-water self-diffusivity in the equilibrium condition, delineating resistance to water flow, is not suitable as a sole parameter to quantify or characterize the potential dynamic flux of edge functionalized membrane. When the inter-layer channels are small, to the order of only allowing a single 21 ACS Paragon Plus Environment


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water layer, the water flux is largely determined by the entrances/exits formed by the edge functional groups. Meanwhile, the high attraction from the edges of the GO nanosheets, particularly which is functionalized by the OH groups, helps to ‘pull’ water molecules to promote high flux when they are passing through the interedge gaps. Therefore, membranes functionalized with a mixture of OH and H edge will potentially have higher water flux. The results from this work can be used as a basis for further work in developing strategies to tailor the functionalization of GO membranes in practice to achieve higher fluxes particularly for industrial applications.

ASSOCIATED CONTENT Supporting Information: Extra simulations using single layer GO nanosheet and the supplementary figures and tables for the Methodology section and the induced pressure analysis.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This project was supported by the Australian Government Department of Industry, Innovation, and Science through the Australia-China Science and Research Fund (ACSRF48154), and is conducted as part of the research program of the Australia-China Joint Research Centre in Future Dairy Manufacturing (http://acjrc.eng.monash.edu/).

Soochow University acknowledges The National Key Research and

Development Program of China (International S&T Cooperation Program, ISTCP, 2016YFE0101200) for support of the Australia-China collaboration.


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37. Starr, F. W.; Sciortino, F.; Stanley, H. E., Dynamics of Simulated Water under Pressure. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics 1999, 60, 6757-6768. 38. Picaud, S.; Collignon, B.; Hoang, P. N. M.; Rayez, J. C., Adsorption of Water Molecules on Partially Oxidized Graphite Surfaces: A Molecular Dynamics Study of the Competition Between OH and COOH Sites. Physical Chemistry Chemical Physics 2008, 10 (46), 6998-7009. 39. Hamad, S.; And, J. A. M.; Lago, S.; And, S. P.; Hoang, P. N. M., Theoretical Study of the Adsorption of Water on a Model Soot Surface: I. Quantum Chemical Calculations. Journal of Physical Chemistry B 2004, 108 (17), 5405-5409. 40. Tarasevich, Y. I.; Aksenenko, E. V., Interaction of Water, Methanol and Benzene Molecules with Hydrophilic Centres at A Partially Oxidised Model Graphite Surface. Colloids & Surfaces A Physicochemical & Engineering Aspects 2003, 215 (1), 285-291.



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Figure 1. Structures (Å) and charge distributions (e) of the (a) G-COOH, (b) G-OH and (c) G-H nanosheets.


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Figure 2. Illustration of the layer-by-layer matrix of GO membranes. Placement of G-COOH, G-OH or G-H nanosheets (grey cross-linked beads) in water box (white-red lines) with same gap width and same interlayer distance according to the layouts of the matrixes. The hub space, inter-layer channel and inter-edge gap are shown in dark red, blue and light red squares, respectively. After equilibrium, all redundant atoms external to the space bounded by the dashed lines in the x-axis and all water molecules outside the nanosheet matrix in the y-axis were removed. Periodic boundary condition was then applied to build a GO membrane. Finally, an impermeable sheet was put at the top of the system, which functioned to induce the pressure to push water molecules through the GO membrane.



Figure 3. Characteristics of water molecules in GO membranes with different edge functional groups at diffusion equilibrium in the absence of external pressure. (a) Illustration of the layer-by-layer structure of GO membrane in the MD simulation. GO nanosheets are represented by grey squares. (b-g) Geometric and simplified structures of G-COOH, G-OH and G-H nanosheets. (h) Simplified illustration of ‘plate’ steric structure of the G-H nanosheet. (i) Simplified illustration of ‘pot’ structure of the G-COOH and G-OH nanosheets. (j) Water diffusion coefficients around the inter-edge gap in a constant water box thickness at 14 Å in the z-axis. (k) Water density of the 7 × 7 G-OH membrane corresponding to the region enclosed by the dashed black line in (a). (l) Water density of the 7 × 7 hubs along the z-axis corresponding to the region enclosed by the solid red line in (k). (m) Water density profile of the 7 × 14 G-OH membrane corresponding to the region enclosed by the dashed black line in (a). (n) Water density profile of the 7 × 14 hubs along the z-axis corresponding to the region enclosed by the solid red line in (m). Water densities of the G-COOH and G-H membranes are shown in Figure S4.


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Figure 4. Radial distribution functions of G-COOH, G-OH and G-H nanosheets including (a) C atoms, (b) O atoms and (c) H atoms. HW is H atom of water molecule. OW is O atom of water molecule. C1COOH is the C atom of GO nanosheet linked with COOH group. C2COOH is the C atom of COOH functional group linked with GO nanosheet. COH is the C atom of GO nanosheet linked with OH group. CH is the C atom of GO nanosheet linked with H atom. O1COOH is the O atom of COOH edge functional group linked with C2COOH with double bonds. O2COOH is the O atom of COOH edge functional group linked with both C1COOH and HCOOH. OOH is the O atom of OH edge functional group. HCOOH is the H atom of COOH edge functional group linked with O1COOH atom. HOH is the H atom of OH edge functional group linked with OOH. HH is the edge H atom of H edge functional group linked with CH.



Figure 5. Water transport within the 7 × 14 membranes at 2,500 bar. (a) Illustration of the 7 × 14 membrane system. (b) Water permeance. (c-h) Water distributions within the (c, d) G-COOH, (e, f) G-OH and (g, h) G-H membranes corresponding to the region enclosed by the dashed line in (a). These dark blue areas in (c) (e) (g) show the effective boundaries of the GO nanosheets. The vertical dashed lines in (c-h) show the geometric sizes of the middle layer nanosheets and the inter-edge gaps that are illustrated by the grey and red squares in (a), respectively. (d) (f) (h) Water distributions averaged from the region whose thickness at 4 Å along the x-axis, which corresponding to the middle nanosheet layer as bounded by the horizontal dashed lines in (c) (e) (g), respectively.


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Figure 6. Water transport within the 7 × 7 membranes at 2,500 bar. (a) Illustration of the 7 × 7 membrane system. (b) Water permeance. (c-k) Water distributions within the (c, d, e) G-COOH, (f, g, h) G-OH and (i, j, k) G-H membranes corresponding to the region enclosed by the dashed line in (a). The dark blue areas in (c) (f) (i) show the effective boundary of the GO nanosheets. The vertical dashed lines in (c-k) illustrate the geometric sizes of the middle layer nanosheets and the inter-edge gaps as illustrated in grey and red squares in (a), respectively. (d) (g) (j) Water distribution averaged from the region whose thickness at 4 Å in the z-axis along the x-axis, which corresponding to the middle layer (the inter-edge gaps) as illustrated in red squares in (a). (e) (h) (k) Water distribution averaged from the region whose thickness at 3 Å in the zaxis along the x axis, which corresponding to the region between the entrance and middle, and middle and exit layers of membranes (locations are shown in Figure 2) as illustrated in purple squares in (a). The red arrows in (e) and (h) highlight the positions with low water densities.



Figure 7. Water transport within the 23 × 7 membranes at 2,500 bar. (a) Illustration of the 23 × 7 membrane system. The white and yellow arrows mark the positions of the hub entrances and exits, respectively. (b) Water permeance. (c-h) Water distributions within the (c, d) G-COOH, (e, f) G-OH and (g, h) G-H membranes corresponding to the region enclosed by the dashed line in (a). These dark blue areas in (c) (e) (g) show the effective boundaries of the GO nanosheets. The vertical dashed lines in (c-h) show the geometric sizes of the nanosheets as illustrated in grey squares in (a). (d) (f) (h) Water distribution averaged from the region whose thickness at 3 Å in the z-axis along the x-axis, which corresponding to the region between the entrance and middle, and middle and exit layers of membranes (locations are shown in Figure 2) as illustrated in purple squares in (a). The red arrows in (d) and (f) highlight the low water densities corresponding to the positions of the hub entrances/exits.


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Figure 8. Summary of the individual influences of the three kinds of edge functional groups on water transport under different geometric membrane structures. (a) Illustration of the membrane system. Geometric structures of the membranes are (b-d) 7 × 14, (e-g) 23 × 7, and (h-j) 7 × 7. While their edge functional groups are (b) (e) (h) COOH, (c) (f) (i) OH and (d) (g) (j) H. Green, orange, red and white parts of arrows illustrate the promoted, neutral, restricted and not obvious influences from the edge functional groups, respectively.


The Effects of Edge Functional Groups on Water Transport in

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