Ice Nanoribbons Confined in Uniaxially Distorted Carbon Nanotubes

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Cite This: J. Phys. Chem. C 2018, 122, 18493−18500

Ice Nanoribbons Confined in Uniaxially Distorted Carbon Nanotubes Haruka Kyakuno,*,†,‡ Hiroto Ogura,† Kazuyuki Matsuda,‡ and Yutaka Maniwa*,† †

Department of Physics, Graduate School of Science and Engineering, Tokyo Metropolitan University, Hachioji 192-0397, Japan Institute of Physics, Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan

‡

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S Supporting Information *

ABSTRACT: Water confined inside nanopores exhibits unusual static and dynamic properties that depend on the pore size, pore topology, and hydrophobicity and roughness of the pore walls. The properties also depend on the geometrical shape of the pore cross sections. Here, we investigated water inside distorted single-wall carbon nanotubes (SWCNTs) by means of classical molecular dynamics calculations, over a temperature range of 100−350 K. SWCNTs, which provide ideal one-dimensional cylindrical pores with atomically smooth nonpolar walls, were uniaxially compressed in a direction perpendicular to the SWCNT axes with a deformation ratio γ up to 60%, where γ represents the ratio of deformation amount to the initial SWCNT diameter D. With increasing γ in an SWCNT with D = 1.24 nm, a hexagonal ice nanotube was converted to the liquid state with high water mobility down to 200 K and then to a new form of ice, ice nanoribbon, consisting of four ferroelectric water chains. In an SWCNT with D = 1.51 nm, on the other hand, the water was converted to an ice nanoribbon with five ferroelectric water chains from the liquid state. It was demonstrated that the application of uniaxial pressure is a useful technique to control water properties, such as dielectricity, mobilities, and structures.

1. INTRODUCTION Water in confining geometries exists everywhere on earth and inside living bodies. Since it plays important roles in various fields, from functions of proteins to development of new nanodevices,1−9 establishing fundamental understanding of its unusual static, dynamic, and thermodynamic properties is critical. Confined water has been studied both theoretically and experimentally using various nanostructured materials, such as silica pores,10,11 zeolites,12,13 slit nanopores,14−16 and carbon nanotubes.17−23 The properties substantially depend on the nature of the confinement systems provided by the nanomaterials, i.e., sizes and dimensionality of confining spaces, as well as hydrophobicity and roughness of pore walls.24−28 The pore geometry is also expected to have significant effects on the properties of confined water, but systematic studies have been rather limited. Here, we investigated the properties of water confined in noncylindrical pores that are systematically generated by compressing single-wall carbon nanotubes (SWCNTs). SWCNTs29,30 provide atomically smooth cylindrical onedimensional (1D) pores with a hydrophobic or nonpolar wall that confines water. It has been shown that the water inside SWCNTs exhibits a variety of phases depending on the diameter D and temperature T. For thin SWCNTs (D < ca. 1.45 nm), the confined water exhibits a liquid−solid transition with decreasing temperature and forms tubule ice with a 1D periodicity, referred to as ice nanotubes (ice-NTs).17−23,31−33 For thick SWCNTs (D > ca. 1.45 nm), on the other hand, the water undergoes a dynamical/structural transition at Tc ≈ 200−220 K from a mobile liquid state to a disordered solid (or amorphous) state,33−35 instead of ordered ice. In contrast, © 2018 American Chemical Society

Mobil Composition of Matter (MCM)-41 systems provide hydrophilic 1D pores that confine water. Comparisons between MCM-41 and SWCNT systems clarified the roles of the hydrophobicity of the pore wall on water properties such as liquid−solid transitions and water dynamics.35 Here, effects of pore geometry on water properties inside SWCNTs were investigated by means of classical molecular dynamics (MD) simulations. SWCNTs were uniaxially compressed in the direction perpendicular to SWCNT axes with the deformation ratio γ up to 60%, where γ represents the ratio of deformation amount to the initial SWCNT diameter. Previous simulation studies36−38 of empty and water-filled SWCNTs and the present simulations have estimated that the pressure required for uniaxial deformations is on the order of a few gigapascals, which can easily be achieved experimentally.

2. METHODS MD simulations were performed using SCIGRESS ME 2.3 (Fujitsu, Ltd.) to generate distorted SWCNTs and to examine structures and dynamics of water inside the SWCNTs, as in previous studies.33−35 Two SWCNTs of length 13.5 nm and chiralities (10, 8) and (11, 11) were used as the default SWCNTs, whose diameters were 1.24 and 1.51 nm, respectively. To generate distorted SWCNTs, ideal SWCNTs were sandwiched between two graphene sheets. One of the Received: May 5, 2018 Revised: July 16, 2018 Published: July 27, 2018 18493

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

Article

The Journal of Physical Chemistry C graphene sheets was fixed in the simulation cell, and the SWCNTs were compressed in a direction perpendicular to the tube axis by an external force F, as shown in Figure 1a. The

step of 1.0 fs. The velocity-scaling method was used to control the system temperature at every time step. After initially equilibrating the system at 350 or 300 K, where water molecules were highly mobile, the temperature was gradually decreased to 100 K. To check the effect of cooling/heating rates on the water behavior, the ramp rates of 12.5, 5.0, and 2.0 K/ns were applied to simulations of the same setups (see Figure S3). Because the results were essentially the same among these cooling/heating rates, the results for 2.0 K/ns are presented in the following sections. The calculations were performed in NVT ensembles, and no periodic boundary condition was applied. At lower temperatures, ca. below 200 K, where the correlation time becomes longer than the simulation times, the water systems could not be equilibrated. From the MD results, snapshot structures at each temperature were extracted and they were equilibrated for more than 3 ns to calculate mean-square displacements and to obtain the self-diffusion coefficient. Since the inner cavities of SWCNTs are quasi-1D, we focused on mean-square displacements along the SWCNT axis (z axis), MSDz = zi(t) − zi(0)2, where zi(t) is the axial coordination of the ith water molecule at time t along the z direction. The self-diffusion coefficient, Dz, is related to MSDz with the Einstein relation

Figure 1. Setup for MD simulations. (a) Top views of a default SWCNT (left) and the compressed SWCNT sandwiched between two graphene sheets (right). For the compression, a uniaxial external force, F, was applied to one of the graphene sheets, while the other sheet was fixed in space. (b) Schematic setup of a water−SWCNT system. The red and blue spheres represent oxygen and hydrogen in water molecules, respectively, and the gray framework represents the SWCNT. Two flat walls made of artificial atoms (light blue spheres) are fixed at 0.3 nm from both open ends of the SWCNTs to prevent water molecules from escaping from the inside of the SWCNT.

⟨MSDz ⟩ = 2Dz t

3. RESULTS AND DISCUSSION 3.1. Water Structures. Figures 2a and S4 show examples of snapshot structures of the confined water at 300 and 100 K in the 1.24 nm SWCNTs with deformation γ. While the confined water was liquidlike at 300 K irrespective of γ (lefthand-side figures), the low-T structures varied significantly depending on γ (middle and right-hand-side figures). For γ < 24%, the water at 100 K was a distorted tubule structure (“distorted ice-NT”), while for γ > 24%, monolayer ribbon structures (“ice nanoribbons”) appeared. The result for γ = 0% is consistent with the previous study for the SPC/E water model.31 The total potential energies of water molecules inside the 1.24 nm SWCNTs for various γ’s are displayed in Figure 2b as a function of temperature. The total energy is the sum of contributions from the water−water intermolecular interactions and the water−SWCNT interactions. The potential curves exhibited abrupt changes with temperature, accompanying hysteresis between cooling and heating processes except for γ ≈ 24%. This behavior suggests a first-order liquid−solid structural transition. In Figure 2b, the potential curves for γ = 52 and 56% deviate significantly from the others. This is due to a substantial increase in the Lenard-Jones interaction potential between SPC/E water and carbon atoms in the SWCNTs, which is caused by the shortened carbon−water distance. The d for γ = 56%, for example, is ∼0.55 nm, which is much shorter than 2σOC ∼ 0.66 nm. The results for the 1.51 nm SWCNTs are shown in Figures 3 and S5. All of the high-T structures were liquidlike irrespective of the deformation γ (left-hand-side figures in Figure 3a), similar to the case of the 1.24 nm SWCNTs and consistent with previous reports for γ = 0%.33,34 However, with increasing γ, the low-T structures changed from a disordered structure to ribbon structures for γ = 46 and 54% through a fused-tubule structure (“fused ice-NT”) for γ = 18%. The total potential energy is shown in Figure 3b. The observed abrupt

graphene sheets were treated as a rigid body. The intramolecular interactions among carbon atoms in the SWCNTs were expressed by an optimized Tersoff potential.39 The intermolecular carbon−carbon interactions were given by universal force fields.40 The deformation, γ, of the SWCNT was defined as (D − d)/D, where D is the initial diameter of the SWCNT and d is the shortened diameter after the compression, as shown in Figure 1a. A typical force F needed to compress an empty 1.24 nm SWCNT of length 1 m to γ ≈ 50% was 2.7 N, consistent with a previous report.37,38 After the compression, the carbon atoms making up the SWCNT were fixed in the simulation cell, and water molecules, described by the extended simple point charge (SPC/E) water model,41 were encapsulated in the SWCNT (Figure 1b). The SPC/E water model has been successfully used to study water structures and dynamics inside SWCNTs in previous works.31,34,35 The water encapsulated in each SWCNT did not completely fill the SWCNT pore at the lowest temperature, as exemplified in Figure 1b. The effect of the system size was examined in 1.24 nm SWCNTs (see Figures S1 and S2). The interaction between SPC/E water and carbon atoms in the SWCNT is given by the 12-6 LenardJones potential with εOC/kB = 46.88 K and σOC = 0.3285 nm, where kB is the Boltzmann constant.34 The Coulomb interaction potential between point charges in different SPC/ E molecules is given by the formula, V ijCoulomb =

1 qiqj , 4πε0 rij

(1)

where

rij is the distance between point charges qi and qj in an SPC/E molecule pair and ε0 is the dielectric constant of vacuum. The cutoff length of Lennard-Jones potential and Coulomb interaction potential was set to 2.0 nm. The equation of motion was integrated using the Gear algorithm with a time 18494

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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The Journal of Physical Chemistry C

Figure 2. Snapshot structures and total potential energy of water inside the D = 1.24 nm SWCNTs with deformation γ. The system temperatures decreased and increased at a ramp rate of 2.0 K/ns. (a) Snapshot structures of the confined water. Left-hand-side panels show the snapshots at 300 K, and middle and right-hand-side panels are those at 100 K (top views with SWCNT and side views without SWCNT, respectively). The small blue spheres and the large red spheres represent hydrogen atoms and oxygen atoms in water molecules, respectively, and the gray frameworks represent SWCNTs. (b) T-dependence of the total potential energy per water molecule. The potentials for 0 ≤ γ ≤ 24% are displayed in the lefthand-side panel, while those for γ ≥ 24% are in the right-hand-side panel. The potential for γ = 24% is shown in both panels for ease of comparison. In the intermediate-temperature region, hysteresis behaviors were observed between cooling and heating processes, as shown by arrows. The inset in the left-hand-side panel schematically shows the definition of ΔTm.

changes for γ = 18, 27, 43, 46, and 54% indicate a liquid−solid structural phase transition. The transition temperature Tm extracted from the Tdependence of total potential energy in Figures 2b and 3b are summarized in Figure 4a,b as T−γ (or T−d) phase diagrams. Here, Tm is defined from the potential curves as follows. For the potential curves accompanied by a hysteresis, Tm − ΔTm/2 and Tm + ΔTm/2 are the temperatures at which the freezing and melting transitions are completed in the cooling and heating processes, respectively, and ΔT m represents the extent of the hysteresis. For the gradual changes, Tm is defined as the temperature at which the potential energy curve changes its slope without hysteresis.

In Figure 4a for the 1.24 nm SWCNTs, it is found that two regions are distinguishable with γ. For γ < ∼24%, ice-NTs or distorted ice-NTs form at low temperatures, while for γ > ∼24%, ice nanoribbons appear at low temperatures. Interestingly, the freezing and melting temperatures Tm of both the phases systematically decrease when γ approaches ∼24%, where the water does not freeze down to 200 K. This γ corresponds to d ∼ 0.94 nm. The diagram for the 1.51 nm SWCNTs is shown in Figure 4b. We note that there is no ice-NT even for γ = 0%. Instead, fused ice-NTs (consisting of pentagonal and hexagonal iceNTs) were found at low temperatures for γ ≈ 20−30%. When γ > ∼40% or d < ∼0.91 nm, on the other hand, ice 18495

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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Figure 3. Snapshot structures and total potential energy of water inside the D = 1.51 nm SWCNTs with deformation γ. The system temperatures decreased and increased at a ramp rate of 2.0 K/ns. (a) Snapshot structures of water inside the compressed SWCNTs. Left-hand-side panels show the snapshots at 300 K, and the middle and right-hand-side panels are those at 100 K (top views with SWCNT and side views without SWCNT, respectively). The small blue spheres and the large red spheres represent hydrogen atoms and oxygen atoms in water molecules, respectively, and the gray frameworks represent SWCNTs. (b) T-dependence of the potential energy per water molecule. The potentials for 0 ≤ γ ≤ 40% are displayed in the left-hand-side panel, while those for γ ≥ 40% are in the right-hand-side panel. The potential for γ = 40% is shown in both panels for ease of comparison.

The ice nanoribbons were unstable for d > dc ∼ 0.9 nm both for the 1.24 and 1.51 nm SWCNTs, as shown in Figure 4a,b. This spacing dc is roughly the same as a critical spacing hc ∼ 0.7−0.9 nm of the transition between monolayer structures and bilayer structures in a two-dimensional (2D) water system between two parallel hydrophobic plates.15,16 In the present 1D system, however, the water exhibits a transition from monolayer ribbons to liquid- or ice-NT structures with increasing d, instead of the bilayer structures in 2D systems. The difference may be due to the presence of edge water resulting from the finite width along the y direction in the present 1D systems (see Figure 1). 3.2. Pair Correlation Functions. Oxygen−oxygen (O− O) pair correlation functions goo(r) were calculated to discuss

nanoribbons appeared, whose transition temperature Tm increased with γ. The structural transition was also confirmed by T-dependence of coordination numbers of the water molecules, as shown in Figure S6. It was found that the coordination number exhibits steep change with temperature for γ = 0, 15, and 48% in the 1.24 nm SWCNTs and γ = 18, 46, and 54% in the 1.51 nm SWCNTs. The steep changes indicate the abrupt development of hydrogen-bonding networks in the confined water. The transition temperatures Tm determined from the coordination number, which are also shown in Figure 4a,b, are consistent with those obtained from the potential energy curves. 18496

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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Figure 4. T−γ (or T−d) phase diagram of the confined water for (a) 1.24 nm SWCNTs and (b) 1.51 nm SWCNTs. The shortened diameter d (see Figure 1) is displayed as a secondary (upper) horizontal axis. The closed circles and open squares with error bars show the transition temperature Tm obtained from the potential curves and T-dependence of the coordination numbers (see Figure S6), respectively. Here, the error bar represents the extent of the hysteresis, ΔTm, where Tm − ΔTm/2 and Tm + ΔTm/2 are the temperatures at which the freezing and melting transitions are completed in the cooling and heating processes, respectively. Symbols without error bars represent the temperatures at which the potential energy or the coordination number curves change their slopes without hysteresis. The dashed lines are guide to the eye.

18% indicates the formation of a fused ice-NT having substantial defects at the fused region, as shown in Figure 5e. In γ > ∼40% in 1.51 nm SWCNT, the peaks in goo(r) are ascribed to the ice nanoribbon consisting of five water chains, which is a similar structure to that in the 1.24 nm SWCNTs. With increasing γ, the ribbons change from a rippling structure to a flat structure. For example, the nanoribbon has a zigzag (rippling) structure along the tube direction for γ = 46% and a flat structure for γ = 54% (compare the structures at 100 K in Figure 3a). The ripple direction of the zigzag nanoribbon is different from that of the 1.24 nm SWCNT, i.e., in the y direction for 1.24 nm SWCNT and in the z direction for 1.51 nm SWCNT. The origin of the rippling may be due to cooperation between the space restriction along the ribbon width direction (y direction), bond angle dependence of the water−water potential, and the potential exerted on a water molecule by the SWCNT wall. For example, the water− SWCNT potential profile has a double minimum in the x direction when γ < ∼35% for the 1.24 nm SWCNT. This may enhance the formation of ripple or tubule structures, in conjunction with the bond angle dependence of the water− water potential. In addition, a slightly narrower width of the SWCNT along the y direction, compared to that of the flat ice nanoribbon, serves to stabilize the zigzag structure along the y direction. The ice nanoribbons discovered in the present study are interpreted as 1D ribbons cut out from the 2D monolayer crystalline ice15,16,43−45 of four-coordinated water molecules. Because the present ice nanoribbons have finite widths perpendicular to the tube axis, they are expected to exhibit unusual physical and chemical properties, such as proton conductions and dielectric properties, which arise from their edge water chains. Essentially the same ribbon structures were obtained using TIP3P and TIP4P water models with slightly different transition temperatures. 3.3. Self-Diffusion Coefficients. Self-diffusion coefficients along the tube axis Dz were obtained from mean-square displacements of oxygen atoms in water to examine the water dynamics. The results are shown in Figures 6 and S7. It was

the structures of confined water. The results are shown in Figure 5a,d for the 1.24 and 1.51 nm SWCNTs, respectively. The upper and lower panels in both the figures show the results at 300 and 100 K, respectively. At 300 K, it is found that the O−O correlations of the present systems were much weaker than those of bulk liquid water.42 The distinct first peaks at r ≈ 0.275 nm correspond to the nearest-neighbor O− O distance. For γ ≈ 24% in the 1.24 nm SWCNT and for γ ≈ 40% in the 1.51 nm SWCNT, no apparent peaks were observed in a range r > 0.3 nm. This implies that the present uniaxial compression substantially prevents the formation of hydrogen-bond networks due to geometrical deformation. At 100 K, several new peaks appeared, which can be ascribed to the ordered structures exemplified in Figure 5b,c,e,f. In the 1.24 nm SWCNT, the peaks observed for 0 ≤ γ < ∼24% are derived from the hexagonal ice-NT or distorted ice-NT. The representative peaks in the nondistorted ice-NT at γ = 0% are indicated by arrows labeled a−e in Figure 5a and assigned to those shown in Figure 5b. When the ice-NT distorts, both peaks c and d1 split into two peaks shifted in the smaller and larger r directions, respectively. The long-range correlations along the tube axis of more than 2.0 nm were confirmed for 0 ≤ γ < ∼24% (see Figure S2). This confirms that long-range 1D periodicity of the hexagonal rings or distorted hexagonal rings exists. The peaks labeled f−i in Figure 5a for γ ≈ 48% in 1.24 nm SWCNT are ascribed to distances in the ribbon structure shown in Figure 5c. The ribbon consists of strips of alternating connections of rhombic water rings and approximately square water rings. We note that the ice nanoribbon ripples (with displacements perpendicular to the ribbon surface) when γ = 31 and 35% in 1.24 nm SWCNT (see the snapshot structure for γ = 31% in Figure 2a). As a result, the peak around r ≈ 0.5−0.6 nm shifts in the smaller r direction. For the 1.51 nm SWCNT, examples of the goo(r) at 100 K are shown in the lower panel of Figure 5d. For γ ≈ 18%, blurred but distinct peak structures appeared, which suggest the formation of ordered ices. The snapshot structure for γ ≈ 18497

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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The Journal of Physical Chemistry C

Figure 5. Oxygen−oxygen pair correlation functions goo(r) and representative snapshot structures of the confined water inside the compressed SWCNTs at 300 and 100 K. (a, d) goo(r) of 1.24 and 1.51 nm SWCNTs, respectively; (b, c) ice-NT for γ = 0% and ice nanoribbon for γ = 48%, respectively, at 100 K in the 1.24 nm SWCNT. (e, f) Fused ice-NT for γ = 18% and ice nanoribbon for γ = 46%, respectively, at 100 K in the 1.51 nm SWCNT. The peak positions of goo(r) indicated by arrows in the lower panel of (a) correspond to the distances between oxygen atoms shown by double-headed arrows in (b) and (c). The carbon atoms in SWCNTs are not displayed for clarity. In (f), the snapshot structure captured in the z−x plane is displayed at the bottom.

3.4. Electric Polarization of Ice Nanoribbons. It is found from the snapshot structures depicted in Figure 5c,f that the ice nanoribbons obtained in the present study consist of four or five 1D chains of water molecules along the SWCNT axis (z axis). Each chain has spontaneous electric moments P along the chain direction due to its proton-ordered structure, as in ice-NTs.8,9 These water chains align antiparallel or antiferroelectrical between the nearest-neighbor chains. Thus, the ice nanoribbons with five (odd number) chains are ferroelectric or ferrielectric with finite spontaneous electric moments along the tube axis, while those with four (even number) chains are antiferroelectric. This implies that the dielectricity of water inside SWCNTs can be controlled by the application of external pressure. For example, Figure 4b suggests that the uniaxial compression converts the confined water from a paraelectric liquid state to a ferroelectric solid

found that water is highly mobile at 300 K in all of the cases studied. On cooling, Dz shows abrupt decreases except for the 1.24 nm SWCNT with γ = 24% and the 1.51 nm SWCNT with γ = 0 and 40%. This is consistent with transitions from the liquid phase to the crystalline solid phase, that is, to ice-NTs, fused ice-NTs, and ice nanoribbons as the lower-T states. The 1/Dz of the noncrystalline water, which was observed in the 1.24 nm SWCNT with γ = 24% and in the 1.51 nm SWCNTs with γ = 0 and 40%, showed non-Arrhenius T-dependence and is better described by a Vogel−Fulcher−Tammann form. It is very similar to the case in large-diameter SWCNTs and in a zeolite-templated carbon with three-dimensional pores.13,35 The possibility of a liquid−liquid transition upon further cooling, as in the large-diameter SWCNTs,35 is left to be examined. 18498

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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The Journal of Physical Chemistry C

Figure 6. Self-diffusion coefficients Dz of confined water in compressed SWCNTs. (a) Dz for 1.24 nm SWCNTs with several γ’s. (b) Dz for 1.51 nm SWCNTs with several γ’s.

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state with polarization along the z axis. For instance, Pz in the 1.51 nm SWCNT with γ > ∼40% was roughly estimated to be ∼1.2 × 10−30 Cm/H2O at 240 K.

Corresponding Authors

*E-mail: [email protected] (H.K.). *E-mail: [email protected] (Y.M.).

4. CONCLUSIONS Confined water inside distorted SWCNTs was systematically studied by MD simulations. It was demonstrated that the liquid−solid transitions, mobilities, and structures at low temperatures can be controlled by uniaxial compression of SWCNTs. In an SWCNT with D = 1.24 nm, with increasing deformation γ, a hexagonal ice-NT observed for γ < 24% was converted to the liquid state with high water mobility down to 200 K and then to a new form of ice, an ice nanoribbon, for γ > 24%. In an SWCNT with D = 1.51 nm, on the other hand, the compression converted a liquid state to an ice nanoribbon for γ > 40%. At the critical spacing dc ∼ 0.9 nm, which corresponds to γ ∼ 24% in the 1.24 nm SWCNT and γ ∼ 40% in the 1.51 nm SWCNT, the liquid states are stable down to 200 K. In the ice nanoribbons found in the present study, the protons of water molecules are ordered, forming four ferroelectric water chains in the distorted 1.24 nm SWCNT and five ferroelectric water chains for the distorted 1.51 nm SWCNT, along the SWCNT axis. Because each ferroelectric chain is antiferroelectrically coupled with the nearest-neighbor chains, the ice nanoribbons with five chains are ferroelectric with a net polarization and those with four chains are antiferroelectric. It was also found that a fused ice-NT is formed in the moderate compression range for the 1.51 nm SWCNT. The present study clearly demonstrated that the shape of the pore cross section plays an important role in controlling the properties of confined water.

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AUTHOR INFORMATION

ORCID

Haruka Kyakuno: 0000-0001-7449-5008 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported in part by Kakenhi Grants-in-Aid (Nos. 15K17738, 26400437, and 25246006) from the Japan Society for the Promotion of Science (JSPS). H.K. acknowledges the financial support from the Foundation Advanced Technology Institute.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b04289. System size dependence of potential energy of water; system size dependence of goo(r); effects of heating/ cooling rates; snapshot structures; temperature dependence of coordination numbers; mean-square displacements of oxygen atoms (Figures S1−S7) (PDF) 18499

DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500

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The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.8b04289 J. Phys. Chem. C 2018, 122, 18493−18500