As carbon nanotube (CNT) fabrication techniques improving,many potential applications of CNTs are proposed,e.g.,nanoscale devices,sensors,and machines^{[1, 2, 3, 4]}. The most outstanding nature of CNTs is their quasi-one-dimensional and hollow structure,especially for single-walled carbon nanotubes (SWCNTs). In addition,since SWCNTs have similar properties to biological water channels in both size and hydrophobic characteristics,they are widely accepted as a simple model for complicated structure of biological water channels^{[5, 6]}. Therefore,the properties of water both inside and outside CNTs have attracted more and more attention,especially the behaviors of water confined in CNTs^{[7, 8, 9, 10, 11, 12, 13, 14]}.

Due to the intrinsic difficulties in experimental characterization of water structure in nano- scale,computational techniques,such as molecular dynamics (MD) simulations,are used exten- sively to predict nanoscale properties of water/CNT systems^{[14, 15]}. Results from MD simula- tions indicated that the behaviors of water inside and outside of SWCNTs could be influenced by many factors. At atmospheric pressure and room temperature,if the diameter of SWCNTs is comparable to the scale of water molecule,a one-dimensional chain of ordered water molecules is formed inside the SWCNTs^[7]. In comparison,a typical layered structure can be observed instead of a single file inside SWCNTs with larger radii^[11]. However,the behavior of the outside water molecules remains independent of the SWCNT diameter^[13]. As the pressure increases or the temperature decreases,liquid-to-solid phase transition or even ice structure might be observed inside the SWCNT^{[9, 16]}. Furthermore,several other strategies have been proposed to control the flow and structures of water inside and outside SWCNTs,such as adjusting the SWCNT structure^[17],adding charges to the carbon atoms of SWCNTs^[18],positioning a single charge or charge group near SWCNTs^{[6, 19]},and anchoring functional groups on the wall or the open end of SWCNTs^{[20, 21]}.

Electric field has been widely applied to water/CNT systems^{[22, 23, 24, 25, 26]}. By evaluating the grand- canonical partition function,Vaitheeswaran et al.^[22] showed that water molecules from bulk phase favor filling into empty SWCNTs in the presence of electric field parallel with the SWCNT axis. Xu et al.^[23] found that the electric field along the SWCNT axis would reduce the effective hydrophobicity,and the behavior was asymmetric with respect to the direction of the electric field. Fu et al.^[24] investigated the effects of electric field along the tube axis on the phase behavior of water inside SWCNTs at atmospheric pressure. They found that liquid water can freeze continuously into either pentagonal or helical ice nanotube,depending on the strength of the electric field. Additionally,Su and Guo^[25] indicated that a controllable net water flow through a (6,6) SWCNT can be achieved by applying an electric field along the nanotube axis.

However,there are fewer works on the effects of electric field perpendicular to the tube axis on the behaviors of water inside and outside SWCNTs. Vaitheeswaran et al.^[27] and England et al.^[28] found that the depletion of water between two closely spaced flat plates immersed in a water reservoir occurred when an electric field was applied perpendicular to the plates. Figueras and Faraudo^[26] showed that the hydrogen bond (H-bond) structure of the one-dimensional water chain inside (6,6) SWCNTs would be disrupted,and the water flow would be blocked by the perpendicular electric field. Nevertheless,they did not illustrate the detailed changes of the water structure inside (6,6) SWCNTs and what would happen inside the wider SWCNTs. In addition,the behavior of water structure outside the SWCNTs under a perpendicular electric field is also worth being investigated. In the present work,by using extensive MD simulations, the structures of water inside and outside (6,6),(8,8),and (10,10) SWCNTs under the electric field perpendicular to the SWCNT axes are investigated. The effects of the changes in the SWCNT diameters and the strength of the electric field are discussed. The rest of the paper is organized as follows. Section 2 introduces the physical model and numerical methods. Section 3 analyzes the simulated results in detail. Finally,some concluding remarks are made in Section 4.

A sketch of the physical model is displayed in Fig. 1(a),where an open-ended armchair SWCNT is immersed in a water cubic box. Three different types of armchair SWCNTs are considered: (6,6),(8,8),and (10,10) with the radii of 0.407nm,0.543 nm,and 0.678 nm,respec-tively. The length of the SWCNTs is chosen as 4.30 nm,which is long enough to remove the end effects^[11]. The simulated box has a dimension of L_x = 6 nm,L_y = 6 nm,and L_z = 6 nm. The SWCNTs are located at the centers of the cubic boxes and their axes are along the z-direction.

The simulations are performed at a constant temperature 300K with the large scale MD package GROMACS 4.0.7^[29]. The extended simple point charge (SPC/E) model is utilized for water molecules,which is reasonable when the external electric field strength is below 10 V/nm^[30]. The van der Waals (vdW) interactions of the carbon atoms of SWCNTs are modeled as uncharged Lennard-Jones (LJ) particles with the parameter of σ_cc = 0.34 nm and ǫ_cc = 0.36 kJ/mol. The harmonic potentials are used to maintain the bond length of 0.14 nm and the bond angle of 120^◦ with the energy constants 393 960 kJ/mol and 527 kJ·mol−1·rad−2, respectively. Meanwhile,the bonds of CNTs are represented by weak proper dihedral angle potentials. The CNT-water interaction is considered by a carbon-oxygen LJ potential with the parameters of σ_cc = 0.33 nm and ǫ_cc = 0.48 kJ/mol. All these parameters employed here have been widely used in previous researches^{[6, 7, 11]}.

A uniform external electric field in the range from E = 0V/nm to E = 3V/nm in the x-direction (see Fig. 1(b)) is applied perpendicular to the SWCNT axis (z-direction). The LJ interactions are truncated at the cut-off distance r₀ = 1.2 nm,and the particle mesh Ewald (PME) method^[31] with a real-space cut-off of 1 nm is utilized to treat the long-range electro- static interactions. Periodic boundary conditions are imposed in all directions. The time step in all simulations is set to be 1 fs.

Fig. 1 Snapshot of simulation system

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All carbon atoms are frozen during the simulations. Previous investigations showed that this only has little influence on the dynamics of the adjacent water molecules^[12]. Initially, water molecules with the density 998 kg/m³ are filled in the space outside of the SWCNT. Minimization of energy is performed with the steepest descent method on the initial system. The system is simulated for 5 ns in the absence of electric field. During the process,the SWCNTs are rapidly filled up with water molecules from the surrounding reservoir. Then,the simulations continue for another 5 ns in the presence of electric field perpendicular to the tube axis with different strength. In all cases,statistics are collected during the last 4 ns and samples are taken every 0.2 ps.

When the water molecules are confined inside SWCNTs,some special structures will be formed. For example,inside the (6,6) and (8,8) SWCNTs,a single-file structure and a typi- cal layered structure of water are found,respectively. While inside the (10,10) SWCNT,the combination of the single-file and layered structure is formed. When an electric field is applied perpendicular to the tube axis,those structures change dramatically or even are destroyed. A significant phenomenon caused by electric field is the reorientation of the water molecular dipole moment. An angle ψ is defined for the angle between the dipole moment of water molecule and the z-axis,as shown in Fig. 1(a). The probability distributions of the angle ψ with different field intensities for (6,6),(8,8),and (10,10) SWCNTs are plotted in Figs. 2(a),2(b),and 2(c),respec- tively. In the absence of electric field,there are two peaks of probability distribution around ψ = 35^◦ and ψ = 145^◦ for all the three types of SWCNTs. The confinement effect of the SWCNT wall can be clearly observed. There are no molecules oriented around ψ = 90^◦ for the (6,6) SWCNT, whereas water molecules are able to be oriented to ψ = 90^◦ for wider SWCNTs. The previous result showed that the average duration time of the states around ψ = 35^◦ or ψ = 145^◦ inside the (6,6) SWCNT was about 14 ns^[32]. We need longer simulation time (100 ns) to obtain the symmetric probability distribution of the (6,6) SWCNT when E = 0V/nm,but symmetric distribution in wider SWCNTs is obtained by 4 ns simulation. When the perpendicular electric field is applied,due to the polarity of the water molecules,the dipole orientations tend to be parallel to the field direction. As shown in Fig. 2,for the SWCNTs of the same diameter,the stronger the field intensity is,the more water molecules align their dipole direction in the field direction. For the (6,6) SWCNT,the distributions around ψ = 90^◦ are found when the field intensity is higher than 2.0V/nm,but most of the molecules are still oriented around ψ = 35^◦ and ψ = 145^◦ due to the confinement effect. For wider (8,8) and (10,10) SWCNTs,the two peaks of the distribution converge to one peak at ψ = 90^◦ in the presence of stronger field. Therefore,when the electric field is strong enough,the wall confinement effect will be overcome to certain extent.

Fig. 2 Probability distribution of different angles of water molecules inside (6,6),(8,8),and (10,10) SWCNTs for E = 0.0V/nm,1.0V/nm,2.0V/nm,and 3.0V/nm

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The reorientations of the water molecules will affect the relative position between the water molecules,and may destroy the water structure inside. The average number of H-bonds per water molecule hnHBi inside SWCNTs is studied to understand this phenomenon. Herein, the H-bond structure is determined by using a geometrical criterion. Two water molecules are hydrogen bonded if the O-O distance is less than 0.35 nm and simultaneously the angle H-O· · · -O is less than 30^◦. For E = 0V/nm,the values of hnHBi of the (6,6),(8,8),and (10,10) SWCNTs are 1.87,3.00,and 3.04,respectively,which are consistent with the previous results^[10]. When the electric field is applied (see Fig. 3(a)),the significant reduction of hnHBi is found as E increases. For E = 3.0V/nm,hnHBi is found to be as low as 1.65,2.26,and 2.49 for (6,6),(8,8),and (10,10) SWCNTs,respectively.

Fig. 3 Average number of H-bonds per water molecule (nHB) inside SWCNTs and depletion ratio δ = ((N) − (N0))/(N0) as function of E for three types of SWCNTs

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To show the variation of the H-bonds with the presence of electric field,the percentages of water molecules involved in 0-5 H-bonds for all the three types of SWCNTs under different field intensities are displayed in Table 1 For the (6,6) SWCNT,the original single-chain structure can be observed due to the formation of 2 H-bonds. As the field intensity increases,the number of water molecules involving 2 H-bonds decreases sharply and less and less water molecules can form H-bonds with other water molecules. While for both (8,8) and (10,10) SWCNTs,the number of water molecules involved in 3 or 4 H-bonds decreases dramatically. These results indicate that the reorientation caused by electric field is able to destroy the H-bond connection between water molecules,resulting in the damage of the internal structure of water confined in SWCNTs. It can be found that for the SWCNT with smaller diameter,the water structure is much easier to be destroyed. It may be worth mentioning that the behavior of water molecules in the bulk is quite different from that in the confinement. Previous studies indicated that the electric field would increase the H-bond number in the bulk water^[33].

Table 1 Averaged percentages of H-bond populations

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Molecular configurations are presented to show how the perpendicular electric field destroys the water structures in all three types of SWCNTs. In Fig. 4,the snapshots of the structures under different field strength (E = 1.0V/nm,2.0V/nm,3.0V/nm) are displayed. For the (6,6) SWCNT,the whole single-file water chain is broken to two water chains when E = 1.0V/nm, the gap between the two water chains is enlarged when the field intensity increases to 2.0V/nm.An isolated water molecule is found when E = 3.0V/nm. Similar phenomena occur in (8,8) and (10,10) SWCNTs. When E = 1.0V/nm,the layered structures are destroyed at some locations. As the field intensity is increased to 2.0V/nm,a gap appears between two water clusters. When E = 3.0V/nm,the isolated water cluster is observed. These findings are consistent with the variation of H-bonds under the applied fields.

Fig. 4 Side-view of water configurations inside (6,6),(8,8) and (10,10) SWCNTs under E = 1.0V/nm,2.0V/nm,and 3.0V/nm

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The average water occupancy hNi which is defined as the average number of water molecules inside SWCNTs is used to describe the water depletion in the SWCNTs. hN₀i is the value of (N) in the absence of electric field. Then,the depletion ratio δ = ((N) − (N₀))/(N₀) is calculated as a function of different E for all three types of SWCNTs. As shown in Fig. 3(b),the depletion ratio δ decreases monotonously as E increases,indicating that less and less water molecules can stay inside the SWCNTs. This trend is in accord with the reduction of hnHBi inside the SWCNTs as E increases. When the water was confined between two graphite-like plates under a perpendicular electric field,Vaitheeswaran et al.^[27] found that the electric field would reduce the density of water between the plates. In addition,England et al.^[28] obtained the same results by using the mean-field theory.

To describe the dipole moment orientations of water outside SWCNTs,an angle θ between the dipole moment of water and the local radial vector of the SWCNT is defined,which is shown in Fig. 1(b). Walther et al.^[34] indicated that the dipole moment of the water molecules in the closest proximity to the CNT was nearly tangential to the plane of the CNT with θ close to 90^◦ in the absence of electric field. Herein,we focus on the behaviors of the first layer water. We define a counterclockwise rotation angle φ to identify the circumferential location at the SWCNT surface,which is denoted in Fig. 1(b). Then,the variations of the angle θ as a function of the rotation angle φ for (6,6) and (10,10) SWCNTs under different field intensities are illustrated in Figs. 5(a) and 5(b). The two figures are very similar to each other,indicating that the effects of the electric field on the dipole orientations are nearly independent of the SWCNT diameter or surface curvature. In the absence of electric field,θ at all locations are very close to 90^◦,which implies that the molecules prefer to be parallel to the CNT outer surface. When the electric field is applied,the dipole moment of water molecules tends to align in the electric field direction. Consequently,the distribution of the angle θ becomes more and more non-axisymmetric as the field intensity increases. At φ = π/2 and φ = 3π/2,the field direction is tangential to the plane of the SWCNT. Therefore,the values of θ remain approximately 90^◦. At φ = 0 and φ = π,the molecules,originally parallel with the tangential plane of the SWCNT,are forced to reorient to be along the direction of the electric field,which is perpendicular to the solid wall.

Fig. 5 Distribution of angle θ as function of rotation angle φ for (6,6) and (10,10) SWCNTs under different field intensities

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Correspondingly,the average number of the H-bond hnHBi of the first layer water as a func- tion of φ is also calculated under different field intensities for the (10,10) SWCNT (see Fig. 6). The distribution of (nHB) also exhibits non-axisymmetry in the presence of a perpendicular electric field. For example,under the electric field of 3.0V/nm,the average numbers of H- bonds at φ = 0 and φ = π are 2.01 and 1.90,respectively,which are far less than the normal value of 2.82. Meanwhile,at φ = π/2 and φ = 3π/2,the average number of H-bonds can reach as high as 3.28. As an example,we give the distribution of the averaged percentages of water molecules involved 0-5 H-bonds (HB₀₋₅) around the (8,8) SWCNT as a function of φ. The situations of E = 0.0V/nm and 3.0V/nm are presented for comparison. Under E = 0.0V/nm, the distribution is axisymmetrical and the water molecules involved in 4 H-bonds are domi- nant. When E is increased to 3.0V/nm,the distribution becomes non-axisymmetric. From Figs. 7(a) and 7(b),we can see that the changes of hnHBi mainly depend on the changes of the water molecules involved 4 and 5 H-bonds around the SWCNT,indicating that at φ = π/2 and φ = 3π/2,the connection between water molecules becomes stronger; while at φ = 0 and φ = π,the connection between water molecules becomes weaker. The electric field at φ = 0 brings oxygen atoms closer and hydrogens further from the wall,resulting in higher density and more H-bonds than those at φ = π where hydrogen atoms are closer and oxygen atoms are further from the wall. For a perpendicular electric field,Bratko et al.^[35] also revealed a notable increase in the H-bonds at the positively charged wall,where the field brought oxygen atoms closer and hydrogen atoms further from the walls.

Fig. 6 Average number of H-bond per water molecule of first layer water around (10,10) SWCNT

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Fig. 7 Average percentages of water molecules involved in 0-5 H-bonds around (8,8) SWCNT for E = 0.0V/nm and E = 3.0V/nm

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The reorientation of the water molecules will also affect the structure of the interfacial water. In Fig. 8(a) and Fig. 8(b),the XY -sections of water of the (10,10) SWCNT with E = 0.0V/nm and 3.0V/nm are illustrated,respectively. In the absence of electric field,the distribution of the interfacial water molecules is axisymmetric,and the gaps between the water and the SWCNT walls are almost uniform around the SWCNT. When an electric field is applied,the gap between the SWCNT walls and the water molecules expands around φ = 0 and φ = π,and the local densities in the two areas decrease. The gap at φ = π is wider than that at φ = 0. On the other parts of the liquid-CNT interface,the original water structures remain unchanged.

Fig. 8 XY -sections of water structure of (10,10) SWCNT with E = 0.0V/nm and E = 3.0V/nm

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The azimuthal profiles of density of the first layer water around the (10,10) SWCNT for different E are depicted in Fig. 9. For E = 0V/nm,the distributions are roughly axisym- metric with a wave-like pattern. The wave-like distribution can be attributed to the discrete hexagon arrangement of carbon atoms of the SWCNTs,which was addressed by Huang et al.^[18]. For (6,6),(8,8),and (10,10) SWCNTs,the numbers of wave peaks are 12,16,and 20, respectively. As E increases,the distributions become more non-axisymmetric. The maxima of density appear at φ = π/2 and φ = 3π/2,the minima appear at φ = 0 and φ = π,and the value at φ = 0 is slightly higher than that at φ = π. At φ = π/2 and φ = 3π/2,where the field direction is parallel with the tangential plane of the SWCNT,the water density rises dramatically from 3 000 kg/m³ to 5 000 kg/m³. Meanwhile,at φ = 0 and φ = π,where the tan- gential plane of the SWCNT is perpendicular to the external field,the water density drops down to 800 kg/m³ and 500 kg/m³,respectively. This finding verifies that the loss of H-bonds due to the re-orientation of water dipole results in a profound reduction of liquid density.

Fig. 9 Surrounding density profiles of first layer water around (10,10) SWCNT

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We have investigated the effects of the perpendicular electric field on the structure of water inside and outside (6,6),(8,8),and (10,10) SWCNTs by using MD simulations. The results show that dipole reorientations induced by electric field play a remarkable role on the structures of confined water inside and outside SWCNTs.

When a perpendicular electric field is applied,the dipole moments of the water molecules tend to align in the direction of the electric field. The induced dipole reorientations will affect the relative position between the water molecules,which may destroy the H-bound connection between water molecules,resulting in the damage of the water structure inside or outside SWCNTs.

Inside SWCNTs,the average water occupancy hNi decreases as the electric intensity,the average density of water,and the average number of H-bonds per water molecule hnHBi increase. When the field intensity is sufficiently strong,the initial water structures inside the SWCNTs with the absence of electric field are destroyed and the isolated water clusters can be found.

To show the changes of the H-bonds between water molecules more clearly,the percentages of water molecules involved in 0-5 H-bonds for all the three types of SWCNTs under different field intensities are displayed. The results show that those water molecules involved with most H-bonds are more important to hold the original structures.

The confinement effect of the SWCNT walls is very obvious,especially for (6,6) SWCNTs. It can be found that for the SWCNTs with smaller diameters,the water structure is much easier to be destroyed. The stronger the confinement is,the more obvious the damage caused by the electric field is.

The non-axisymmetric distribution of the density and the H-bond of water outside SWCNTs show the influence of water molecule reorientation caused by electric field. The maxima are located at the region where the electric field direction is parallel with the wall,and the minima are located at the region where the electric field is perpendicular to the wall. In other words, when the electric field direction is parallel with the original preferred orientation,the density and the H-bond connections in water will be increased; when the electric field direction is perpendicular to the original preferred orientation,the density and the H-bond connections in water will be decreased.