Structure and Phase Behavior of the Confined Water in Graphene

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C: Physical Processes in Nanomaterials and Nanostructures

The Structure and Phase Behavior of the Confined Water in Graphene Nanocapillaries Studied by an ABEEM## Polarizable Force Field Lan-Lan He, Yan Li, Dong-Xia Zhao, Ling Yu, Chong-Li Zhao, Li-Nan Lu, Cui Liu, and Zhong-Zhi Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09840 • Publication Date (Web): 13 Feb 2019 Downloaded from http://pubs.acs.org on February 18, 2019

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The Journal of Physical Chemistry

The Structure and Phase Behavior of the Confined Water in Graphene Nanocapillaries Studied by an ABEEMσπ Polarizable Force Field Lan-Lan He†, Yan Li†, Dong-Xia Zhao*,†, Ling Yu†,‡, Chong-Li Zhao†, Li-Nan Lu†, Cui Liu*,†, Zhong- Zhi Yang*,† †School

of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, 116029, People’s Republic of China

‡Liaoning

Panjin Fine Chemical Industrial Park Administrative Committee, Panjin 124000, China Corresponding authors E-mail address: [email protected] (Zhong-Zhi Yang); [email protected] (Dong-Xia Zhao) [email protected] (Cui Liu) Tel: +86 411-82159607

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Abstract: Since the two-dimensional (2D) square ice in graphene nanocapillaries was observed by transmission electron microscopy (TEM), a variety of theoretical methods have been applied to explore this phenomenon. However, a satisfactory model has not yet been described. Here, we investigate the structural properties and phase behavior of the confined water in graphene nanocapillaries by using the ABEEMσπ polarizable force field (PFF) with the ABEEM-7P water model and ABEEMσπ graphene model. The ordered AB stacked bilayer and ABA stacked trilayer square ice samples are acquired in 8.0 and 10.2 Å graphene nanocapillaries, respectively, at 298 K at a constant volume. Furthermore, bilayer and trilayer ices demonstrate rhombus-square-triangular ice as the graphene nanocapillary changes from 7.8 to 8.6 Å and 10.0 to 11.0 Å, respectively. The results yielded by using a fixed charge force field (FCFF) with SPC/E water model are different from those obtained by ABEEMσπ PFF. By changing the constant pressure from 0.5 to 1.5 GPa, the monolayer (bilayer) triangular ice is transformed to bilayer (trilayer) square ice in a 6.5 (9.0) Å graphene nanocapillary system. Additionally, the van der Waals interactions, density of the confined water, confinement width, polarization effects and pressure all play decisive roles in the distribution of the confined water. Our study provides some clues for clarifying the experimental consequences of TEM.

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Introduction Water confined in a nanometer-sized interface, particularly for hydrophobic surfaces such as graphene and carbon nanotubes (CNTs), has been a hot point of scientific research1-31 because of nanotechnological and biological applications. Since the square ice in graphene nanocapillaries was observed by transmission electron microscopy (TEM) in 2015 guided by Algara-Siller et al.,32 a scientific upsurge of investigating the confined water33-45 in graphene nanocapillaries has occurred. They reported that the nanoconfined water forms ‘square ice’ at 298 K with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites with AA stacking. They discussed that the adhesion between the encapsulating graphene sheets imposes pressure on the confined water and estimated that the pressure is roughly equivalent to 1 GPa. Furthermore, they carried out molecular dynamic (MD) simulations with the SPC/E water model to support TEM observations. However, only monolayer imperfect square ice was found, which was slightly similar to rhombic ice. Following this, a great deal of theoretical investigations33, 36-37, 39-40, 43-45 dedicated to exploring the structural and dynamics properties of the confined water in graphene nanocapillaries were carried out in order to explain the experimental phenomenon. To search the monolayer, bilayer and trilayer ice, Mario et al.33 used the reactive force field (ReaxFF) to implement an annealing MD simulation with the temperature starting at 400 K and ending at 0 K. They supported that monolayer confined water formed rhombic-square ice, not AA stacked square ice for bilayer ice, and the conformation of trilayer ice was similar to that of monolayer ice. In 2016, Chen et al.37 employed a first principle method to study confined 2D ice as a function of pressure. They reported that the hexagonal and pentagonal structures became the

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most stable at ambient pressure and persisted up to ~2 GPa, where the square ice and rhombic ice were stable. Zhu et al.39 performed MD simulations with the TIP5P water model and showed the hydrogen bonding network of 2D interlocked pentagonal bilayer ice (IPBI) in graphene nanocapillaries. They argued that the hydrogen bonding network can serve as a generic guide to understand the rich phase behaviors of nanoconfined water. Later, Chakeaborty et al.40 studied the structure and thermodynamics of the confined water in graphene slit pores and CNTs. They found that the effect of pressure was to enhance the water structure and push water molecules toward the plates. Pestana et al.45 held that the structural properties as well as phase behavior of mono-, bi- and trilayer confined water were affected by whether the graphene surface was flexible or rigid. Moreover, the phase coexistence of the confined water was captured in the presence of flexible graphene sheets. To figure out the effect of the pressure, Sataifard et al.44 carried out MD simulations with applying high lateral pressure (0.7~6.0 GPa) on the confined water. They observed the transformations from monolayer ice to AB stacked bilayer ice and AB stacked bilayer ice to ABC stacked trilayer ice with the distances between the two graphene slabs of 6.0-7.0 Å and 8.0-9.0 Å, respectively, and reported lattice constants of 2.5-2.6 Å of the confined ice, which were less than that of Algara-Siller et al. (2.83±0.03 Å). In addition, they observed that monolayer and bilayer rhombus ice samples and trilayer ABC-hexagonal ice were different from the square ice obtained by TEM. Walet et al.43 applied a density function approach to study water confined between graphene layers with a potential model for the interaction between water and graphene. They showed the configurations of the strongest confinement, which suggested that a rhombic unit cell liked a perfect equilateral triangular crystal at the lowest energy

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states, and the square crystal state was relatively insensitive to the details of the confining potential. Recently, Zhu et al.46 exhibited square-like bilayer ice between two parallel hydrophobic walls guided by MD simulation with the TIP4P/2005 water model, but the realistic structure of the bilayer square-like ice was the ordered ABstacking of two hexagonal monolayers of ice, each exhibiting an elongated hexagonal structure. Furthermore, the two bilayer hexagonal ices with ordered AA and AB stacking can be transformed either directly from one to another or indirectly through a liquid phase via changing the width of the slit pores. Up until now, the bilayer and trilayer square ices reported by Algara-Siller et al.32 have not been reasonably interpreted by theoretical simulations. Our purpose is to investigate the structural properties and phase behavior of the confined water between two graphene sheets by using ABEEMσπ PFF with the ABEEM-7P water model and ABEEM graphene model. The electrostatic interactions between the graphene and the confined water have been considered. Water on a solid-liquid interface has also been studied by various force fields5, 17, 23, 28, 47-49.

The water model usually adopts a simple point charge model (SPC), SPC/E,32

TIP3P,40 TIP4P45 or TIP5P39 with a fixed bond length, bond angle and charge on water without considering the polarization effect. Although the classical MD simulation with those models can simulate a large-sized system of water molecules confined between graphene surfaces or in CNTs, the central carbon atoms are uncharged in most common force fields. Thus, they did not deal with the polarization effects of the central carbon atoms of graphene and the water molecules. That is, the central carbon atoms of graphene have no contribution to the electrostatic interactions of the system, which is obviously not accurate.5

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Based on the electronegativity equalization method (EEM) and density functional theory (DFT), Yang et al.50-60 developed a polarizable force field (PFF) called ABEEMσπ PFF. In this force field, the electrostatic interaction is the important characteristic. The ABEEMσπ model divides the charge distribution of the system into atom regions, σ and π bond regions and lone-pair electron regions. The charge in each region can fluctuate simultaneously with the changing geometry and surroundings. ABEEMσπ PFF has succeeded in modeling various systems including water clusters,54,

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liquid water,53 ammonia clusters,62 liquid ammonia,63 ionic

solutions,55-56, 64 amino acids,65 base pairs66 and biological macromolecular systems.59, 67-69

In this paper, MD simulations are implemented by means of ABEEMσπ PFF to study confined water in graphene nanocapillaries. In section II, we shed light on the ABEEMσπ model and methodology as well as simulation standards. In Section III, a general analysis is given for our results. Following this, diffusion coefficients, structural properties, and charge distributions are depicted in detail. Section IV gives our conclusion.

Model and Methodology ABEEM-7P water model and ABEEM graphene model We make use of the ABEEM-7P water model and ABEEMσπ graphene model outlined in Figure 1 and Figure 2 to carry out MD simulation via ABEEMσπ PFF. The ABEEM-7P water model53 adopts a slightly complicated tetrahedral geometry, which introduces seven interaction sites, including two hydrogen atoms, one oxygen atom, two O-H bonds, and two lone pair electrons to describe the charge in more

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detail. All of the charges of the seven sites are fluctuating with the surrounding structure. In addition, unlike the fixed water model, the ABEEM-7P model has molecular flexibility, i.e., with the geometry and surrounding environment changing, the vibrations of bond lengths and angles are free to adjust to adapt to the intramolecular interactions. Such improvements have been desirable to develop models with increasing accuracy, and the ABEEM-7P water model can reproduce the properties of several gas-phase water clusters (H2O)n (n = 1-6),54, 58, 61 liquid water53 and ion-water solutions55-57, 64, 70 that are in reasonable agreement with those measured using available experiments and ab initio calculations.

Figure 1. A diagram of the ABEEM-7P water molecule sites, including one oxygen atomic region, two hydrogen atomic regions, two O-H σ bond regions and two lone pair regions.

Figure 2. A diagram of ABEEMσπ naphthalene sites, including ten carbon atomic regions, eight hydrogen atomic regions, eleven C-C σ bond regions, eight C-H σ bond regions and twenty π electron regions.

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Every graphene carbon atom connecting with the nearby three atoms is sp2 hybridized to form three σ bonds with one p electron participating in forming the large π-π conjugate structure. In our graphene model, the interior carbon atom of graphene connects with three carbon atoms, and the marginal carbon atom connects with two carbon atoms and one hydrogen atom, which is similar to the ABEEMσπ benzene model71 and naphthalene model. The diagram of ABEEMσπ naphthalence model including ten carbon atomic regions, eight hydrogen atomic regions, eleven carboncarbon σ bond regions, eight carbon-hydrogen σ bond regions and twenty π electron regions up and down the carbon plane is displayed in Figure 2. The atomic site is located at the center of the atom, the σ bond site is located in the middle of the covalent radius of the two atoms, which forms a bond, and the π electron sites are located up and down the corresponding carbon atom at 0.74 Å. In ABEEMσπ PFF, we obtain the charge distribution of the graphene based on the standard of Mulliken charge50,

52, 56, 70

under the appropriate basis set, and the electrons, which are

symmetrical to the carbon atmospherically, are located in the region of the carbon atom. That is, most of electrons of graphene distribute in the region of the atoms. Since the nuclear charge number of the carbon atom is six, the charge distributions of carbon atomic regions are +0.16 ~ +0.23 e in ABEEMσπ PFF. However, only a small amount of electrons is distributed in the region of the carbon-carbon σ bond and the π bond region, which are -0.14 ~ -0.16 e and -0.0075 ~ -0.0085 e, respectively. The charge distribution of the ABEEMσπ graphene model is dramatically smaller than those of other force fields. For example, Heinz et al.72 developed graphitic materials and π conjugated molecules, and gave +1.0 e on each aromatic carbon atom as well as -0.5 e on the two corresponding virtual electron clouds above and below the atomic

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plane. Its charge distribution is rough, which will produce overwhelming electrostatic interaction. Obviously, the electrostatic interactions between π electrons of graphene and hydrogen atoms of water molecules computed by ABEEMσπ PFF are more moderate. Furthermore, we introduce two weak hydrogen bonding interactions. One is between the π electron regions of C atoms and H atomic regions of water molecules, and the other is between a lone pair of one water molecule and a hydrogen atom of another. The functions kHB(RlpO,H)53 and kHB(RπC,H) of the two hydrogen bonds are written in the supporting information (SI) Eqs. S(1) and S(2).

Methodology We applied ABEEMσπ PFF50-56, 60, 68 to simulate the confined water in the graphene slit pores. The ABEEMσπ molecular mechanic (ABEEMσπ/MM) potential energy function is expressed in Eq. S(3). The total energy of the ABEEMσπ model is depicted in Eq. S(4). It is able to obtain the partial charge on each atom, each bond, each lone-pair electron and each π electron for water and graphene molecules through electronegativity equalization equations associated with the charge conservation equations. The effective electronegativity equations of atom a, bond a–b, lone-pair electron lp and π bonds have been given in (Eqs. S(5–8)). The electronegativity equalization principle demands Eqs. S(9-11). Therefore, Eqs. S(9-10) and Eq. S(11) apply to the local conservation and the whole conservation serving for charge transfer, respectively. The local conservation means that the total charge of every molecule is zero, and each site of charge is allowed to transfer among its own molecule during the

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recalculating of the charge distribution of the simulated system. For the whole conservation, the total charge of the whole simulated system is zero, and each site of charge is allowed to transfer among the whole system during the recalculating of the charge distribution. Both the local and whole conservations serving for charge transfer are implemented for ABEEMσπ PFF MD simulations.

Simulation standards All of the structures of simulation systems are constructed by Packmol software. The simulation systems consist of two parallel graphene surfaces with terminal C connecting with H, and the confined water between them is shown in Figure 3. All of the MD simulations are performed by using ABEEMσπ PFF with the two graphene slabs fixed. The three-dimensional periodic boundary conditions are employed, and the box lengths are 22.5 Å, 19.0 Å and 50.0 Å respectively. The Berendsen thermostats73 are utilized to keep the temperature a constant over all of the simulations. The relaxation times of temperature and pressure are set to 0.01 and 0.1 ps, respectively. The cut-off radius is 9.5 Å for the nonbonded interactions. Each MD simulation time is 1 ns, and the time step size is set to 1.0 fs. The charge distributions of atoms, σ and π bonds and lone-pair electrons of the simulated systems are recalculated every 100 steps. The nonbonding interactions are truncated by using force shifting. Therefore, the computed force and energy are smoothly shifted to zero at the cut-off position. The charge and force field parameters of ABEEMσπ PFF are listed in Table S1 and S2, respectively. To investigate the monolayer, bilayer and trilayer crystallites, the MD simulation are launched at 298 K in a canonical ensemble NVT (constant number of molecules,

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volume and temperature) when widths of graphene nanocapillaries are set to 5.0-7.0 Å, 7.8-8.6 Å and 10.0-12.0 Å, respectively. For the sake of studying the effect of the temperature on the structure and phase behavior of the confined water, a set of different temperature simulations including 0, 100, 200, 273, 298, 373, 473 and 673 K is implemented in a canonical ensemble NVT when the widths of graphene slit pores are 8.0 Å and 10.2 Å. However, we found little change in the conformation of the confined water at different temperatures, as discussed in the SI. To clarify the distribution of the confined water under different densities, a set of MD simulations is implemented with water densities of 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.25 and 1.5 g·cm3

when the width of the graphene slit pore is 10.2 Å in a canonical ensemble NVT at

the temperature of 298 K. The results suggest that the density of the confined water plays an important role in the conformation of the confined water as analyzed in the SI. To study the effect of pressure on the structure of the confined water in graphene nanocapillaries, we perform a serious of MD simulations at constant pressures of 0.5, 1.0, 1.5 and 2.0 GPa at 298 K in the NPT (constant number of molecules, pressure and temperature) ensemble with various widths of graphene nanocapillaries from 5.9 to 11.0 Å. The specific analysis is described in section III. The results yielded by the simulations at a constant volume and constant pressure are marked as CV and CP, respectively.

Figure 3. A graphic of our MD simulation system

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Results and Discussion First, we present a general description of our results. We performed a series of MD simulations to study the confined water in 5.9, 6.5, 7.8, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries at constant volume (CV) and in 6.5, 7.0, 8.0, 9.0 and 10.0 Å graphene nanocapillaries at constant pressures (CP) of 0.5, 1.0, 1.5 and 2.0 GPa. To determine the phase behavior of the confined water, we first analyze the diffusion coefficients of the confined water under different MD simulation conditions. The diffusion coefficient of the confined water yielded by ABEEMσπ PFF is in accordance with the experimental value of ice.74 Following this, to check the structure of the confined ice, the conformation of the confined water, radial distribution function (RDF), number density, O-O-O angle distribution in each layer, orientation distribution and hydrogen bonding distribution are analyzed in detail. By observing the conformation of the confined water at CV, we found ordered monolayer confined ice in 5.9 and 6.5 Å graphene nanocapillaries, bilayer ice in 7.8, 8.0 and 8.6 Å graphene nanocapillaries, and trilayer ice in 10.0, 10.2 and 11.0 Å graphene nanocapillaries. Compared with the conformation of the confined water obtained from FCFF with the SPC/E water model, we have never obtained the ordered bilayer and trilayer confined water. The RDF and number density of the confined water support the formation of the monolayer, bilayer and trilayer confined ice in 5.96.5 Å, 7.8-8.6 Å and 10.0-11.0 Å graphene nanocapillaries, respectively. Furthermore, we found the transition of rhombus-square-triangular for bilayer and trilayer ice samples in 7.8-8.6 Å and 10.0-11.0 Å graphene nanocapillaries. This is corroborated by the analysis of the O-O-O angle distribution. To describe the distribution of the confined water in more detail, we compute the orientation distribution (ψ, φ) of the confined water, which not only suggests the distribution of hydrogen and oxygen 12


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atoms but also shows the AB stacking bilayer and ABA stacking trilayer structures. To gain further insight into the distribution of the confined water, we discuss the hydrogen bonding distribution of the confined ice. We come to a decision that the hydrogen bonding distribution can influence the distribution of the confined water directly. However, the hydrogen bonding interactions are affected by the electrostatic interactions. Hence, we analyze the charge distributions of atom sites of the simulation systems with and without considering the charge transfer between graphene and water molecules, which suggests that the electrostatic interaction between water and graphene in ABEEMσπ PFF is more moderate than those of other force fields. In addition, by checking the conformations of the confined water in 6.5, 7.0, 8.0, 9.0 and 10.0 Å graphene nanocapillaries at CP, it has been found that the ordered monolayer (bilayer) triangular ice can transform to bilayer (trilayer) square ice in a 6.5 Å (9.0 Å) graphene nanocapillary when the pressure is changed from 0.5 to 1.5 GPa. This result of ABEEMσπ PFF is similar to that of Satarifard et al.44 The number density and O-O-O angle distribution analysis can testify to the conformation of the confined water. 1. Dynamic properties 1.1 Diffusion Coefficients Table 1. The diffusion coefficients of the confined water obtained by ABEEMσπ PFF at CV in various graphene slit pores at 298 K. 5.9 Å 8.90*10-14

Diffusion coefficients (m2/s) 6.5 Å 8.0 Å 8.6 Å 10.2 Å 2.58*10-13

1.81*10-12

1.91*10-13

1.01*10-13

11.0 Å 2.39*10-13

As we all know, bulk water belongs to the liquid phase at 298 K. However, what is the phase behavior of the confined water at 298 K? It can be examined by the

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diffusion property. Table 1 lists the lateral diffusion coefficients (without the Z-axial direction) of the confined water computed by using Einstein’s relation (shown in Eq. S(13)) at CV at 298 K, and the results of CP are listed in Table S3. Table 1 gives that the lateral diffusion coefficients for the 5.9, 6.5, 8.0, 8.6, 10.2 and 11.0 Å graphene slit pore systems are 8.90×10-14, 2.58×10-13, 1.81×10-13, 1.91×10-13, 1.01×10-13 and 2.39×10-13 m2/s respectively, which are in line with experimental values found by Xray analysis.74 The lateral diffusion coefficients of the confined water computed by ABEEMσπ PFF at CP are on the magnitude order of 10-13-10-10 m2/s, as listed in Table S3. Trout et al.75 found the diffusion coefficient of hexagonal ice to be 2.3*10-13 m2/s by MD simulation. Koga et al.2 suggested that the diffusion coefficient (along the axial direction) of ice in carbon nanotubes was on the 10-14 m2/s order of magnitude by MD simulation. Hirunsit et al.26 reported that the diffusion coefficient of ice in graphene slit pores was on the 10-13 m2/s order of magnitude, as obtained from MD simulation with the SPC/E water model. Diffusion coefficients of the confined water samples obtained by ABEEMσπ PFF simulations are in accordance with those of ice produced by others.2,

26, 74-75

This has confirmed that the phase

transition of the confined water occurs in ABEEMσπ PFF simulation.

2. Structural properties 2.1 The conformations of the confined water samples 2.1.1 The conformations of the confined water samples (CV) After a series of MD simulations by using ABEEMσπ PFF at CV with the confined water in different sizes of graphene nanocapillaries, the ordered structures of the confined water samples, including mono-, bi- and trilayer solid ices are observed, and the transition points of the rhombus-square-triangular ice have been found, as shown 14


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in Figure 4(a-p), which have never been reported previously. The monolayer ice behaves as an ordered triangle in 6.0-7.0 Å graphene nanocapillaries. The conformation of the confined water in a 6.5 Å graphene nanocapillary is displayed in Figure 4(c-d), which is different from the results of FCFF MD simulation with the SPC/E model32 and the results of MD simulation using ReaxFF.33 The conformation of the confined water between the graphene slit pores optimized by Walet et al.43 using a first principle with the DFT method demonstrated a perfect equilateral triangle at the lowest energy structures. This is in agreement with our results. Meanwhile, when the size of the graphene nanocapillary is smaller than 6.0 Å, a few square ice crystals appear (see Figure 4(a-b)). To investigate monolayer square ice, additional simulations are carried out with the size of the graphene nanocapillaries ranging from 5.0 to 6.0 Å and the area density of the confined water changing from 5.0 to 6.0 Å-2. However, it fails. Surprisingly, bilayer square ice exists in an orderly manner with AB stacking in an 8.0 Å graphene nanocapillary, while the density of the confined water is 1.25 g·cm-3. Based on this, we alter the size of the graphene slit pore from 7.8 to 8.6 Å with every 0.1 Å interval to figure out the formation process of AB stacked square ice. It has been found that when the slit pore is 7.8 Å, the two layers of ice are very close to each other, and most confined water samples form a parallelogram, which may be called a rhombus, in their own layer with little square conformation, as shown in Figure 4(e-f). Two-layer ordered square ice occurs with AB stacking in the 8.0 Å graphene nanocapillary (see Figure 4(g-h)). As the graphene nanocapillary continues to increase, the square conformation of the confined water starts to distort. When the graphene

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nanocapillary is 8.6 Å, two-layer AB stacked triangular ice is perfectly presented, as shown in Figure 4(i-j). To check the conformation of the trilayer ice obtained by ABEEMσπ PFF, the size of the graphene slit pore ranged from 10.0 to 11.0 Å with a 0.2 Å interval. It has been found that the trilayer square ice displays ABA stacking in a 10.2 Å graphene nanocapillary (see Figure 4(m-n)) with 1.56 g·cm-3 confined water. The formation process of trilayer square ice is similar to that of bilayer square ice. In the slit pore of 10.0 Å, the conformation of the confined water in each layer shows a parallelogram, which is close to a rhombus, as displayed in Figure 4(k-l). While the graphene slit pore is greater than 10.2 Å, the square ice tends to distort. When the width of the graphene slit pore is 11.0 Å, perfect triangular ice appears, as shown in Figure 4(o-p). From the above results, it is concluded that the formation of the square ice is closely related to the density of the confined water and the size of the graphene nanocapillary. The reason for the formation of monolayer, bilayer and trilayer square ice samples in graphene nanocapillaries found by TEM guided by Algara-Siller et al.32 is likely due to that the confined water is squeezed into a small volume with a certain moderate pressure, which is very difficult to measure. In ABEEMσπ PFF, the moderate pressure mainly depends on the van der Waals and electrostatic interactions between the two graphene slabs and the confined water.

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Figure 4(a-p). Snapshots of water molecules confined between two graphene slabs with various sizes: (a-b) 5.9 Å; (c-d) 6.5 Å; (e-f) 7.8 Å; (g-h) 8.0 Å; (i-j) 8.6 Å; (k-l) 10.0 Å; (m-n) 10.2 Å; and (o-p) 11.0 Å. (a, c, e, g, i, k, m, o) are pictures of the whole systems. (b, d, f, h, j, l, n, p) are the oxygen atomic distributions of the monolayer confined water for the corresponding systems.

As a reference, the FCFF and SPC/E water models are utilized to simulate the confined water in 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries. The microstructures of the equilibrium systems without and with considering the electrostatic interactions of graphene slabs are shown in Figure 5(a-h) and Figure 6(a-h), respectively. Like the results of ABEEMσπ PFF, monolayer confined water is located in 5.9 and 6.5 Å graphene slit pores, bilayer water is found in 7.8, 8.0 and 8.6 Å graphene slit pores, and trilayer water is found in 10.0, 10.2 and 11.0 Å slit pores. For FCFF MD simulations with considering the electronstatic interaction between graphene slabs and the confined water, the charge distributions of carbon atoms and marginal hydrogen atoms of graphene are derived from the corresponding average charges of ABEEMσπ PFF. However, compared with the results of ABEEMσπ PFF, the conformation of the confined water for the SPC/E model is not very orderly except for the conformation of the confined water in 5.9 and 17



6.5 Å graphene slit pores. In 5.9 and 6.5 Å graphene slit pores, with and without considering electrostatic interactions between the graphene and water molecules, the structures displayed in Figure 5(a, b) and Figure 6(a, b) show rhombus ice, which is similar to the results of Algara-Siller et al.32 When the width of the graphene slit pore is 7.8 Å, the ordered structures of the confined water samples have never been obtained, as shown in Figures 5(c) and 6(c). In graphene slit pores of 8.0 Å, the confined water has never presented square ice (see Figures 5(d) and 6(d)), which is different from that of ABEEMσπ PFF. Furthermore, there is no triangular ice in 8.6 Å graphene slit pores, as shown in Figures 5(e) and 6(e). For the three layers in confined water systems, the confined water samples present disordered conformations in 10.0 and 10.2 Å graphene slit pores, as shown in Figures 5(f, g) and 6(f, g). When the graphene slit pore reaches 11.0 Å, no ordered trilayer ice has been found (see Figure 5(h) and 6(h)), which is also different from the results of ABEEMσπ PFF. Therefore, it may be said that the polarization effect plays a significant role in the distribution of the confined water conformations in graphene slit pores.

Figure 5(a-h). Snapshots of water molecules confined between two graphene slabs of various sizes without considering the electrostatic interactions between the graphene and water molecules: (a) 5.9 Å; (b) 6.5 Å; (c) 7.8 Å; (d) 8.0 Å; (e) 8.6 Å; (f) 10.0 Å; (g) 10.2 Å; and (h) 11.0 Å. 18


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Figure 6(a-h). Snapshots of water molecules confined between two graphene slabs of various sizes with considering the electrostatic interactions between the graphene and water molecules: (a) 5.9 Å; (b) 6.5 Å; (c) 7.8 Å; (d) 8.0 Å; (e) 8.6 Å; (f) 10.0 Å; (g) 10.2 Å; and (h) 11.0 Å.

2.1.2 The conformations of the confined water samples (CP) To explore the structure of the confined water at a constant pressure, the MD simulations have been performed by using ABEEMσπ PFF at 0.5, 1.0, 1.5 and 2.0 GPa with various widths of graphene nanocapillaries. Figure 7(a-t) exhibits the conformations of the confined water in 6.5, 7.0, 8.0, 9.0 and 10.0 Å graphene nanocapillaries, respectively. We obtained an interesting result that the monolayer (bilayer) triangular ice is transformed to bilayer (trilayer) square ice. The details are described below. The monolayer confined water forms an ordered triangle when the width of the graphene nanocapillary is 6.5 Å at the pressure of 0.5 GPa, as outlined in Figure 7(a). When pressure increases to 1 GPa, the confined water starts a trend to be layered but still keeps the triangular conformation, as shown in Figure 7(b). The ordered AB stacked bilayer square ice appears at 1.5 and 2.0 GPa, as shown in Figure 7(c, d). This suggests the confined water experiences monolayer to bilayer transformations at different pressures, which significantly influences the conformation. 19



The confined water samples in 7.0 and 8.0 Å graphene nanocapillaries at pressures of 0.5, 1.0, 1.5, and 2.0 GPa show ordered AB stacked bilayer ices (see Figure 7(e-l)), but the ice is square for the 7.0 Å graphene nanocapillary at 0.5-1.5 GPa and distorted square at 2.0 GPa, and triangular for the 8.0 Å graphene nanocapillary. In the 9.0 Å graphene nanocapillary, the ordered AB stacked bilayer triangular ice is observed at 0.5 GPa, as shown in Figure 7(m). However, a trend exists for layering the confined water at a pressure of 1.0 GPa, as shown in Figure 7(n). When pressures are 1.5 and 2.0 GPa, the obvious ABA stacked three-layer square ices are formed, as shown in Figure 7(o-p). When the water is confined in a 10.0 Å graphene nanocapillary, the conformation of the confined water presents an ABA stacking triangle. It proves that the width of the graphene nanocapillary affects the conformation of the confined water tremendously.

Figure 7(a-t). The conformation of the confined water in 6.5 Å (a-d), 7.0 Å (e-h), 8.0 Å (i-l), 9.0 Å (m-p) and 10.0 Å (q-t) graphene nanocapillaries at the pressures of 0.5 GPa (a, e, i, m, q), 1.0 GPa (b, f, j, n, r), 1.5 GPa (c, g, k, o, s), and 2.0 GPa (d, h, l, p, t), respectively.

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2.2 Radial distribution function (CV) The radial distribution function can reflect the distribution of the confined water in the graphene nanocapillary. Figure 8 and Figure 9 (a-h) show the RDFs of gOO(r), gCO(r) and gCH(r) obtained from the systems of 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries. In the snapshot of the RDF gOO(r), the positions of the first peaks for the above systems are at 2.95, 2.88, 2.87, 2.90, 2.97, 2.85, 2.84 and 2.97 Å, as shown in Figure 8, respectively, which are close to the TEM experimental data (2.83±0.03 Å) guided by Algara-Siller et al.32 Observing the RDFs of gCO(r), there is one obvious wide peak for the 5.9 and 6.5 Å graphene nanocapillary systems as shown in Figure 9(a-b), two almost parallel peaks with a flag shape for the 7.8, 8.0 and 8.6 Å graphene nanocapillary systems as shown in Figure 9(c-e), and three parallel peaks for the 10.0, 10.2 and 11.0 Å graphene nanocapillary systems as shown in Figure 9(f-h), respectively, with the corresponding positions of the peaks at 3.33 and 3.03 Å for the 5.9 and 6.5 Å graphene nanocapillary systems, 3.11 and 5.09 Å for the 7.8 Å graphene nanocapillary system; 3.28 and 5.03 Å for the 8.0 Å graphene nanocapillary system; 3.32 and 5.91 Å for the 8.6 Å graphene nanocapillary system; 3.28, 5.26 and 7.15 Å for the 10.0 Å graphene nanocapillary system; 2.99, 6.05 and 7.79 Å for the 10.2 Å graphene nanocapillary system; and 3.29, 5.74 and 8.03 Å for the 11.0 Å graphene nanocapillary system. This suggests that there have been monolayer, bilayer and trilayer ordered structures in the 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries, respectively, which is in agreement with the conformation analysis. In 6.5 Å graphene slit pores, the H and O atoms of the confined water are 2.38 and 3.03 Å away from the graphene surface, which suggests that most of the H atoms of

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the water molecules point toward the graphene surface. Although the positions of first peaks of gCH(r)s are closer than those of gCO(r)s for all other systems, the positions of the first peaks of gCO(r) and gCH(r) are very close. This is mainly because the confined water does not have enough room to rotate slightly. Thus, the H and O atoms of the confined water are almost in the same plane, which may be the reason why square ice forms.

Figure 8. The radial distribution function of the gOO(r) for 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillary systems.

Figure 9(a-h). The radial distribution functions of gCO(r) and gCH(r): (a) 5.9 Å, (b) 6.5 Å, (c) 7.8 Å, (d) 8.0 Å, (e) 8.6 Å, (f) 10.0 Å, (g) 10.2 Å, and (h) 11.0 Å.

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2.3 The number density of the confined water 2.3.1 The number density of the confined water (CV) The number densities of the confined water in the Z-axial direction of 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillary systems are plotted in Figure 10. In Figure 10, we can observe that one, two and three peaks are symmetrical between the two graphene slabs derived from the systems of 5.9 and 6.5 Å; 7.8, 8.0 and 8.6 Å; and 10.0, 10.2 and 11.0 Å graphene slit pores, respectively. This indicates that the confined water forms the solid-like snapshot layer by layer, i.e., monolayer in 5.9 and 6.5 Å graphene slit pores; bilayer for 7.8, 8.0 and 8.6 Å graphene slit pores; and trilayer for 10.0, 10.2 and 11.0 Å, which is in line with the results of the conformation and RDFs of the confined water guided by ABEEMσπ PFF. It is found that when the widths of the graphene slit pores are 7.8, 8.0 and 8.6 Å, the corresponding distances between the layers of the confined water are 0.7, 1.0 and 1.6 Å. For 10.0, 10.2 and 11.0 Å graphene nanocapillary systems, the corresponding distances between the layers of the confined water are 0.9, 1.0 and 1.7 Å. Additionally, the distances between the graphene surface and the first layer of confined water for the systems of 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries are 2.60, 2.75, 2.95, 2.95, 3.00 and 3.05 Å, respectively. Those indicate that as the width of the graphene slit pore increases, the confined water can move slightly apart.

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Figure 10. The snapshots of the number density of the confined water in 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillaries.

2.3.2 The number density of the confined water (CP) To gain further insight into the effect of pressure, we present the number density of the confined water in 6.5, 7.0, 8.0, 9.0 and 10.0 Å graphene nanocapillary systems at constant pressures of 0.5, 1.0, 1.5 and 2.0 GPa, as outlined in Figure 11(a-d′). It has been observed that the number density of the confined water in a 6.5 Å graphene nanocapillary at 0.5 GPa shows a single peak, as displayed in Figure 11(a), which indicates the formation of monolayer confined water. When the pressure begins to increase, the number density of the confined water in a 6.5 Å graphene nanocapillary shows two peaks, as shown in Figure 11 (b-d), and the spacing of the two peaks at 1.5 and 2.0 GPa is wider than that at 1.0 GPa, which is in agreement with the conformation analysis of the confined water at CP. This indicates that the monolayer confined water tends to split into two layers at 1.0 GPa, and the two layers of the confined water get away from each other with the pressure increase. It verifies that pressure plays a significant role in the distribution of the confined water, which is consistent with the conformation analysis. When the widths of graphene nanocapillaries are 7.0 and 8.0 Å, there are still two peaks in the number density chart, as shown in Figure 11(a-d′). In a 9.0 Å graphene nanocapillary, two peaks appear at 0.5 and 1.0 GPa (see Figure 11(a′, b′)), which demonstrates bilayer confined water. However, there are three peaks at 1.5 and 2.0 GPa (see Figure 11(c′, d′)). This suggests that the confined water is organized into three layers at 1.5 and 2.0 GPa, which verifies the influence of pressure on the distribution of the confined water. In a 10.0 Å graphene nanocapillary, there are three layers of confined water appearing at each pressure, which suggests that the widths of

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graphene nanocapillaries also influence the distribution of the confined water, which is in agreement with the conformation analysis.

Figure 11(a-d′). The snapshots of the number density of the confined water at constant pressures of 0.5, 1.0, 1.5 and 2.0 GPa in 6.5, 7.0, 8.0, 9.0 and 10.0 Å graphene nanocapillaries.

2.4 The probability distribution of the O-O-O angle 2.4.1 The probability distribution of the O-O-O angle (CV) To gain further insight into the conformation of the confined water in the same layer in a graphene nanocapillary, the probability distributions of the O-O-O angle in each single layer in 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene slit pores are plotted in Figure 12(a-h). For the confined water in a 5.9 Å graphene nanocapillary, three main peaks appear at 60, 120 and 180°, with a small peak emerging at approximately 90°, as shown in Figure (a), suggesting the existence of mostly triangular ice as well as a little square ice, which is in agreement with the conformation acquired by ABEEMσπ PFF simulation. However, in the 6.5 Å graphene nanocapillary, three smoother peaks are found at 60, 120 and 180°, as shown in Figure (b), which demonstrates that the conformation of the confined water 25



is ordered triangular. A slightly wider distribution of the O-O-O angle is exhibited in the 7.8 Å graphene nanocapillary (see Figure 12(c)), and the continuous distribution at 70-110° suggests the coexistence of many parallelograms and a few square ice crystals. The distribution of the O-O-O angle in the 8.0 Å graphene slit pore takes on two perfect peaks at 90 and 180°, as shown in Figure 12(d). It manifests that the confined water in each layer forms ordered square ice, which verifies the conformation yielded by the ABEEMσπ PFF simulation. As the width of the graphene slit pore gradually increases, square ice becomes deformed. In the 8.6 Å graphene slit pore, three peaks appear perfectly at 60, 120 and 180°, as shown in Figure 12(e), which corroborates the formation of triangular ice. The above analysis also demonstrates the formation process of bilayer square ice. In 10.0, 10.2 and 11.0 Å graphene nanocapillaries, the confined water forms trilayer orderly ice. When the graphene slit pore is 10.0 Å, the probability distribution of the O-O-O angle mainly emerges at 90 and 180°, as shown in Figure 12(f), but a few small peaks are located at approximately 60 and 130°, which suggests that most confined water forms square ice with some distorted square ice. When the slit pore is 10.2 Å, the O-O-O angle distribution peaks appear at 90 and 180°, as shown in Figure 12(g). A three-layer square ice is examined reliably. As the width of the slit pores continues to increase, square ice gradually loses its shape, and the O-O-O angle in each layer ultimately presents as triangular. For example, in 11.0 Å graphene slit pores, the probability distribution of the O-O-O angle exhibits peaks located at 60, 120 and 180°, as shown in 12(h), which supports the formation of perfect triangular ice. The above discussion is the formation process of the ABA stacked square ice. Our MD simulations show that the triangular ice is the most stable conformation for the

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confined water in graphene nanocapillaries at CV. The formation of square ice demands a certain range of values for the slit pores and the density of the confined water.

Figure 12(a-h). The probability distributions of the O-O-O angle in each layer for different graphene nanocapillaries: (a) 5.9 Å; (b) 6.5 Å; (c) 7.8; (d) 8.0 Å; (e) 8.6 Å; (f) 10.0 Å; (g) 10.2 Å; and (h) 11.0 Å.

2.4.1 The probability distribution of the O-O-O angle (CP) To corroborate the conformation of the confined water in each layer at constant pressure, we checked the probability distribution of the O-O-O angle in each layer at 0.5, 1.0, 1.5 and 2.0 GPa when the graphene nanocapillaries are 6.5 and 9.0 Å (see Figure 13(a-h)) as well as 7.0, 8.0 and 10.0 Å (see Figure S3). In a 6.5 Å graphene nanocapillary, the probability distributions of the O-O-O angle at pressures of 0.5, 1.0, 1.5 and 2.0 GPa are obviously different. When the pressure is 0.5 GPa, the probability distribution of the O-O-O angle shows three peaks at 60, 120 and 180° (see Figure 13(a)), which suggests the formation of triangular ice. When the pressure is 1.0 GPa, the short and flat third peak experiences a wide range from 120 to 180°, as shown in Figure 13(c). This suggests that the conformation of water molecules is still triangular, but a few water molecules trend to form the middle layer. Thus, the triangle is a little distorted. When the pressures are 1.5 and 2.0 GPa, bilayer ice forms, as shown in 27



Figure 13(e, g), and the positions of the peaks are located at 90 and 180°, which suggests the formation of bilayer square ice. This verifies that the monolayer triangular ice is transformed into bilayer square ice. In a 9.0 Å graphene nanocapillary, the probability distributions of the O-O-O angle at 0.5, 1.0, 1.5 and 2.0 GPa are exhibited in Figure 13(b, d, f, h). When the pressures are 0.5 and 1 GPa, two-layer ice appears. Three peaks are found in Figure 13(b, d) at 60, 120 and 180°, respectively, which suggests the formation of triangular ice. However, the third peak at 1 GPa is wider and flatter than that at 0.5 GPa, which suggests that a few water molecules form the third layer. When the pressures are 1.5 and 2.0 GPa, three layers of the confined ice form in Figure 13(f, h). Additionally, the positions of the two peaks appear at 90 and 180°. This corroborates the transition from bilayer triangular ice to trilayer square ice. The above analysis clearly indicates the conformation of the confined water. In addition, it suggests that pressure plays a vital role in the distribution of the confined water.

Figure 13(a-h). The probability distributions of the O-O-O angle in each layer for different graphene nanocapillaries at 0.5, 1.0, 1.5 and 2.0 GPa. 28


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2.5 Orientation distribution (CV) The positions of hydrogen atoms of the confined water can be hardly deciphered by means of experiments. The orientation analysis can exhibit the direction of hydrogen atoms of the confined water. Therefore, we check the orientation angles (ψ and φ) of the confined water in 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene slit pores, as shown in Figure 14(a-h′). The defined angle ψ is between the dipole direction of one water molecule and the normal vector of the graphene surface, and φ is between an OH bond of one water molecule and the normal vector of the graphene surface. Figures 14(a) and 14(b) demonstrate that the ψ angles approximately range from 60 to 120° and the positions of peaks emerge at approximately 90°. This indicates that the dipole orientations of most of the confined water molecules are parallel to the graphene surface in 5.9 and 6.5 Å graphene slit pore systems. Figures 14(a′) and 14(b′) show significance differences. In Figure 14(a′), the probability distribution of the φ angle for monolayer confined water in a 5.9 Å graphene nanocapillary appears at 90°. This indicates that the direction of the OH bonds of the confined water is parallel to the graphene surface. That is, the whole confined water is parallel to the graphene surface. However, Figure 14(b′) shows that the probability distribution peaks of the φ angle for monolayer confined water in a 6.5 Å graphene nanocapillary appear at 50 and 130°. This indicates that the angles between OH bonds and the graphene surface are 130 and 50°, which are complementary. The ψ and φ angles together testify that the confined water is symmetrical between the two graphene slabs, with two hydrogen atoms pointing toward them, respectively. Due to the small width difference, the probability distributions of ψ and φ angles in the 7.8 and 8.0 Å graphene slit pores present peaks at approximately 80 and 100°, as 29



shown in Figure 14(c, c′, d, d′). This suggests that the dipole and OH bond directions of two-layer confined water are in the same plane, and both directions deviate slightly from the graphene surface. In an 8.6 Å graphene nanocapillary, the positions of the peaks of the ψ and φ angles appear at 60 and 120°, as shown in Figure (e, e′). This suggests that the two-layer confined water is tilted toward the graphene surface. For three-layer confined water in 10.0, 10.2 and 11.0 Å graphene nanocapillaries, the distributions of the orientation angles ψ and φ are wider than above, as shown in Figure (f, f′, g, g′, h, h′). The orientation angles of the confined water with regards to the nearby graphene surfaces show the same shape. The orientation distribution of the middle layer of confined water ranges from 0 to 180°. Thus, it also confirms the formation of ABA stacked ice.

Figure 14(a-f). Orientation angle (φ, ψ) distributions of the confined water. For 5.9 Å graphene slit pores (a) ψ and (a′) φ; for 6.5 Å graphene slit pores (b) ψ and (b′) φ; for 7.8 Å graphene slit pores (c) ψ and (c′) φ; for 8.0 Å graphene slit pores (d) ψ and (d′) φ; for 8.6 Å graphene slit pores (e) ψ and (e′) φ; for 10.0 Å graphene slit pores (f) ψ and (f′) φ; for 10.2 Å graphene slit pores (g) ψ and (g′) φ; and for 11.0 Å graphene slit pores (h) ψ and (h′) φ.

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2.6 Hydrogen bonding analysis (CV) The hydrogen bonding networks play a crucial role in the distribution of the confined water. The so-called bulk ice rule is that every water serves as a double donor and a double acceptor of hydrogen bonds with the distance of the two oxygen atoms shorter than 3.4 Å and the O…H-O angle larger than 135°. Under nanoscale confinements, some hydrogen bonds cannot meet this condition. For example, Algara-Siller et al.32 reported square ice with a 90° hydrogen bonding angle both within and between the layers. In this paper, on account of the formation of ices with different conformations, we define the conditions for the formation of hydrogen bonds as a LP (lone-pair)…HO hydrogen bond angle larger than 120° and a distance between the two oxygen atoms of less than 3.4 Å. For showing the hydrogen bonding distribution of monolayer, bilayer and trilayer confined water systems, we take 6.5, 8.0, 8.6 and 10.2 Å graphene nanocapillary systems as examples. The hydrogen bonding distributions of 5.9, 7.8, 10.0 and 11.0 Å graphene nanocapillaries are shown in Figure S4. The distributions of hydrogen bonds between different graphene slit pores yielded by ABEEMσπ PFF simulations are shown in Figure 15(a-f). As a reference, Figure 15(a′c′) shows the distributions of the hydrogen bonds obtained from the FCFF simulation with the SPC/E water model. The SPC/E water model is a three point rigid body water model, and thus, no lone pair electron is displayed in the distribution of the hydrogen bonds. The distance between the two oxygen atoms and the LP…H-O angle are labeled clearly. Figure 15(a) shows us the hydrogen bonding distribution of monolayer triangular ice with the distance between the two oxygen atoms less than 3.0 Å and the LP…H-O angle larger than 120°. Each confined water has six surrounding water

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molecules but only forms four hydrogen bonds with four adjacent water molecules. For the confined water in the same layer, it has been found that the lone pair in one water molecule points toward the hydrogen atom of the neighboring water molecule. Compared with the hydrogen bonding information of monolayer ice in a 6.5 Å graphene nanocapillary obtained from the FCFF with SPC/E water model, each water molecule has four water molecules around it to form four hydrogen bonds in the same plane due to the formation of distorted square ice, as shown in Figure 15(a′). The conformation of the confined water is closely related to the formation of hydrogen bonds. In the ABEEMσπ PFF simulation, each confined water interacts with the six surrounding water molecules. However, in the FCFF simulation, each confined water interacts directly with four surrounding water molecules. Moreover, the ABEEM-7P water model in ABEEMσπ PFF is different from the SPC/E water model in FCFF. The electrostatic polarization between water molecules, which form hydrogen bonds in ABEEMσπ PFF, is stronger than that of PCFF. Thus, ABEEMσπ PFF MD simulations reach equilibrium in a shorter period of simulation time. For AB stacking bilayer square ice yielded by the ABEEMσπ PFF simulation, the hydrogen bonding distribution is shown in Figure 15(b), and the side view is outlined in Figure 15(c). The three atoms of one water molecule are nearly in the XY plane with two lone pairs up and down the plane, respectively. Each water forms four hydrogen bonds in its own layer, with two hydrogen atoms pointing to the near lone pairs, one lone pair pointing to two hydrogen atoms of different water molecules and the other lone pair pointing to the center of the square in the opposite layer. It displays clearly that the distance between the two oxygen atoms is less than 3.05 Å and the LP…H-O angle is larger than 135°. Nevertheless, it is found that few hydrogen bonds

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form between the layers. However, for FCFF simulation, we do not receive the ordered structure, and thus, the hydrogen bonding information cannot be acquired regularly. Figure 15(b′) shows a part of the ordered structure and the hydrogen bonding information. One water molecule forms three or four hydrogen bonds, among which one water molecule forms two hydrogen bonds in the same line with the front and back water molecules, and another one or two hydrogen bonds exist between the confined water layers. The distribution of hydrogen bonds between layers is charted in Figure 15(c′). Thus, the hydrogen bonding information obtained by the ABEEMσπ PFF simulation is in greater order than that of FCFF with the SPC/E water model. For AB stacking triangular ice (see Figure 15(d)), the oxygen atom of the bottom layer confined water is labeled with O. Each confined water forms four hydrogen bonds with three hydrogen bonds in the same layer and one between two layers. In each confined water layer, there are six water molecules around one water molecule, which is similar to that of monolayer triangular ice. Once one lone pair of the confined water in the top layer inclines downwards toward the bottom layer, and one hydrogen atom in the bottom layer inclines invariably upwards to form one hydrogen bond with it. The side view shows many ordered hydrogen bonds between layers in Figure 15(e). However, for FCFF simulation, we do not receive the ordered structure, and thus, the hydrogen bonding information cannot be shown regularly. Figure 15(f) outlines the ABA stacked square ice and triangular ice. Each confined water in the top and bottom layers forms four hydrogen bonds, including three hydrogen bonds in the same layer and one between layers. Thus, most water molecules in the middle layer produce two hydrogen bonds in that layer and another two between layers, respectively. For FCFF simulations, we obtained a three-layered

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structure, but there is not much order in each layer. Thus, the hydrogen bonding information cannot be shown. From the above analysis, it is concluded that the hydrogen bonding information obtained from the ABEEMσπ PFF simulation is in more order and compacted than that obtained from the PCFF with SPC/E water model.

Figure 15(a-f). The hydrogen bonding distribution graphs of the confined water in different graphene slit pores. For (a, a′) 6.5 Å graphene slit pore; (b, b′, c, c′) 8.0 Å; (d, e) 8.6 Å; and (f) 10.2 Å. (a, b, c, d, e, f) stand for the hydrogen bond distributions obtained from ABEEMσπ PFF; (a′, b′, c′) stand for the hydrogen bond distributions obtained from FCFF.

3. Charge distribution analysis (CV) Table 2. The average charge of carbon, oxygen, hydrogen atomic sites produced by ABEEMσπ PFF as well as the charge of SPC/E water. ABEEM charge Ca CHb HCc Od He Of Hg

6.5 Å -0.0040 -0.0317 0.0673 -0.3880 0.1940

6.5 Åt -0.0042 -0.0303 0.0684 -0.3893 0.1928

8.0 Å -0.0036 -0.0325 0.0676 -0.3919 0.1958

8.0 Åt -0.0029 -0.0307 0.0699 -0.3891 0.1918

Bulk ice O H

-0.6448 0.3224

Bulk water O H

SPC/E water model O -0.8476

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10.2 Å -0.0041 -0.0307 0.0661 -0.3929 0.1965 -0.3916 0.1953 -0.5400 0.2700

10.2 Åt -0.0011 -0.0316 0.0645 -0.3921 0.1895 -0.3666 0.2102

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H 0.4288 interior carbon atoms; bdenotes marginal carbon atoms; cdenotes terminal hydrogen atoms; doxygen atoms in the first adsorbed layer; ehydrogen atoms in the first adsorbed layer; foxygen atoms in the second adsorbed layer; and ghydrogen atoms in the second adsorbed layer. tstands for the results from the MD simulation with the charge transfer between graphene and the confined waters.

adenotes

The average charges of interior carbon atoms, marginal carbon atoms, terminal hydrogen atoms of the graphene surface, and oxygen and hydrogen atoms of the confined water in the first and second adsorbed layers are found by ABEEMσπ PFF MD simulation with the local and whole charge conservations, and the oxygen and hydrogen atoms of bulk ice and water are listed in Table 2. Moreover, the oxygen and hydrogen atom charges of the SPC/E water model are listed in Table 2. We only list the charge distribution of 6.5, 8.0 and 10.2 Å graphene nanocapillary systems as an example for monolayer, bilayer and trilayer confined water systems. The charge distributions of 5.9, 7.8, 8.6, 10.0 and 11.0 Å graphene nanocapillary systems are listed in Table S4. Moreover, we obtained the same rule for the charge distribution of 5.9, 6.5, 7.8, 8.0, 8.6, 10.0, 10.2 and 11.0 Å graphene nanocapillary systems. When the charge transfer is allowed in one molecule, it suggests that the average negative charges of surface carbon atoms are less than those of marginal carbon atoms by one order. Surprisingly, it has been found that the absolute values of the average negative charges of oxygen atoms in the first and second adsorbed layers are much less than those of oxygen atoms in bulk water or ice, and the average positive charges for hydrogen atoms in the first and second adsorbed layers are less than those of hydrogen atoms in bulk water or ice. Referring to the Raman experiment guided by Geiger et al.,76 we can come to the conclusion that graphene indeed plays a highly significant role in screening charge. For the results of the charge transfer allowed in the whole system, the whole graphene molecule presents a little positive charge, and

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the overall charge of the confined waters is slightly negative, which demonstrates that few π electrons transfer from the graphene surface to oxygen atoms of the first layer confined waters via hydrogen atoms. This should be due to that the electronegativity of oxygen atoms is greater than that of the π bonds. At the same time, we can estimate the electrostatic interactions between graphene and the confined water for different force fields. Taking the graphene model of Heinz et al.72 as an example, they distribute +1.0 e on carbon atoms of graphene and -0.5 e on π electrons up and down carbon atoms. The charge distributions of O and H atoms of the SPC/E water model are -0.8476 and 0.4288 e, respectively. If the SPC/E water model is applied, the electrostatic interaction between this graphene model and the SPC/E water model is largely overestimated. In ABEEMσπ PFF, the carbon atomic charge is 0.003 ~ 0.004 e, and the oxygen and hydrogen atom charges of the confined water are approximately -0.4 e and 0.2 e, respectively. The electrostatic interaction between graphene and the confined water in ABEEMσπ PFF is overwhelmingly smaller than that of Heinz et al72. The electrostatic interaction is moderate in ABEEMσπ PFF, which agrees well with the formation of the confined water conformation. Conclusions We implemented MD simulations to study the confined water in graphene slit pores through ABEEMσπ PFF at 298 K in both the NVT and NPT ensembles. The applied ABEEM-7P water model and ABEEMσπ graphene model have more detailed charge distribution than other force fields. At constant volume, we have observed that the conformations of mono-, bi- and trilayer ices are clearly different from the previous results. The ordered AB stacked bilayer and ABA stacked trilayer square ices appear in 8.0 and 10.2 Å graphene nanocapillary systems, respectively. Furthermore, bilayer

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and trilayer ices present rhombus-square-triangular ices by changing graphene slit pore from 7.8 to 8.6 Å and 10.0 to 11.0 Å every 0.1 Å spacing, respectively. Taking a series of FCFF MD simulations with the SPC/E water model as a reference, we only obtain the slightly distorted monolayer square-like ice, which is actually rhombic, and no ordered bilayer or trilayer ice. The hydrogen bond analysis manifests that each confined water forms four hydrogen bonds by ABEEMσπ PFF simulation. However, sometimes one lone pair or hydrogen atom participates in forming two hydrogen bonds. There is little hydrogen bonding between the two layers of AB stacked square ice but much for AB stacked triangular ice. For the trilayer ice, the hydrogen bonds exist consistently between two adjacent layers. As a reference, the distribution of hydrogen bonds obtained from FCFF simulation shows no ordered structure except for monolayer triangular ice. In general, the distribution of hydrogen bonds in ABEEMσπ PFF presents more order than that in FCFF, which may be due to the special electrostatic interaction in HBIR. The charge distribution analysis suggests that the electrostatic interaction between graphene and the confined water in ABEEMσπ PFF is more moderate than that in other force fields. At constant pressure, we found that the monolayer triangular ice can transforms to AB stacked bilayer square ice in a 6.5 Å graphene nanocapillary by changing the pressure from 0.5 to 1.5 GPa or at 0.5 to 1.0 GPa by changing the width of the graphene nanocapillary from 6.5 to 7.0 Å. Furthermore, we also observed that the ordered AB stacked bilayer triangular ice transforms to ABA stacked trilayer square ice when the graphene nanocapillary is 9.0 Å by changing the pressure from 0.5 to 1.5 GPa. In addition to the van der Waals interactions between graphene slabs and water, the size of the slits pore, density of the confined water, polarization effects and pressure of the simulation

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systems play a vital role in the distribution of the confined water in graphene slit pores. These results may provide significant information on the structure and phase behavior of the confined water in graphene slabs.

Associated content Supporting information The Supporting Information is available free of charge on the ACS Publications website. Hydrogen

bonding

fitting

function;

the

ABEEMσπ

molecular

mechanic

(ABEEMσπ/MM) potential energy function; the total energy of the ABEEMσπ model and effective electronegativity equations; parameters for molecular dynamics simulation; the diffusion coefficient computed by using Einstein’s relation; diffusion coefficients at constant pressure; the distribution of confined water at different densities; the probability distribution of the O-O-O angle for each layer of confined water at different temperatures; the probability distribution of the O-O-O angle for each layer of confined water for odd simulation systems (CP); the hydrogen analysis for the complementary data systems (CV); charge distribution for the complementary data (CV); and references.

Acknowledgements We greatly thank Professor Jay William Ponder for providing the Tinker programs. This work was supported by the National Natural Science Foundation of China [No.21473083, 21603091 and 21133005].

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Structure and Phase Behavior of the Confined Water in Graphene

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