# Structure and Dynamics of Water at Carbon-Based Interfaces

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Liquid Water on Carbon-Based Interfaces

#### 2.1. Thermodynamic Stability

^{2}, corresponding to ≈ 905 and 790 water molecules around each CNT, respectively, and ≈ 7.4 × 10

^{−8}g/cm

^{2}> 3 × 10

^{−8}g/cm

^{2}of the bulk at volumic density is $\rho =1$ g/cm

^{3}. This finding implies that a stable layer of liquid water adsorbs on top of the (9,9) and (5,5) CNTs under the simulated conditions.

^{2}and 5 Å

^{2}. Furthermore, for the considered range of densities, F has a concave shape, corresponding to thermodynamically unstable states. The fact that F must be, for thermodynamic consistency, convex over a large-enough range of densities, implies that there must be two coexisting stable phases, one at higher density and another at lower density than those explored, but that they are inaccessible under the study conditions. As a consequence, in the considered range of T and ρ, there is no stable layer of liquid water adsorbed on top of the (12,12) CNT or the graphene sheet. This result is consistent with the findings of Werder et al. [53].

#### 2.2. Structure and Hydrogen Bonding

#### 2.3. Diffusion Coefficients

#### 2.3.1. Water inside CNTs

#### 2.3.2. Water outside CNTs and on Flat Rigid Graphene

^{−5}cm

^{2}/s [75]. Assuming this drawback of the force field employed in the present work, one can observe from Table 3 that diffusion coefficients of water computed alongside z-axis are about 20% lower than that of the bulk unconstrained system. Therefore, the interaction of water with the CNT leads to a decrease of water diffusion parallel to the surface.

#### 2.3.3. Water on Corrugated Graphene

^{−5}cm

^{2}/s, 28% smaller than that indicated above (4.6 × 10

^{−5}cm

^{2}/s).

^{−5}–2.8 × 10

^{−5}cm

^{2}/s in good agreement with the results reported previously [64] for narrow slit pores. This value is about 20% smaller than near a flat graphene sheet, independent on the kind of corrugation. Therefore, the interface roughness reduces water diffusion, possibly due to the hindrance caused along the surface.

^{−5}–2.3 × 10

^{−5}cm

^{2}/s, very close to the water self-diffusion coefficient for the same model in bulk [81], i.e., 2.5 × 10

^{−5}cm

^{2}/s.

## 3. Results

#### 3.1. Crystallization of Water by Confinement between Graphene Plates

#### Dynamics of Confined Water

^{2}/ns characterizes the diffusion of liquid water for 6.5 Å $<d<8.5$ Å and $d>10$ Å. The value of the diffusion coefficient in these regions is close to the value obtained for bulk water at $T=275$ K for the TIP4P/2005 water model [88]. For plate separations 8.5 Å $<d<10$ Å, the diffusion coefficient drops dramatically reaching zero, evidencing a dynamical arrest of water molecules. An inspection of the typical simulation snapshots for $d=9$ Å clearly shows that under these conditions the confined water forms hexagonal ice (Figure 6). In the next section we will see clearly that the ice has a bilayer structure.

#### 3.2. Structure of Confined Water

## 4. Computational Methods

#### 4.1. Water Adsorbed at the Outside of Rigid CNTs and on Flat Graphene

^{3}for water-(5,5)CNT system, 100.0 × 100.0 × 64.3 Å

^{3}for the water-(9,9)CNT, 150.0 × 150.0 × 83.35 Å

^{3}for water-(12,12)CNT, and 31.929 × 34.032 × 40 Å

^{3}for water-graphene, with periodicity along all three spatial directions. All carbon atoms were explicitly taken into account in the calculation and were considered to be rigid, i.e., the carbon atoms were not allowed to move in the simulation runs. This approximation was investigated in detail in a previous study [78], which concluded that the mobility of carbons does not induce any noticeable change in the structure and dynamics of interfacial water. Nevertheless, a set of simulations with flexible armchair CNTs and flexible graphene have been conducted to verify the rigid-carbon approximation and to compute vibrational spectra of carbons.

#### 4.2. Corrugated Graphene

#### 4.3. Water Confined between Graphene Plates

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Gileadi, E.; Kirowa-Eisner, E.; Penciner, J. Interfacial Electrochemistry; Addison-Wesley: Reading, MA, USA, 1975. [Google Scholar]
- Thiel, P.A.; Madey, T.E. The interaction of water with solid surfaces: fundamental aspects. Surf. Sci. Rep.
**1987**, 7, 211–385. [Google Scholar] [CrossRef] - Butler, G.; Ison, H.C.K. Corrosion and Its Prevention in Waters; Reinhold: New York, NY, USA, 1966. [Google Scholar]
- Bartón, K. Protection against Atmosferic Corrosion: Theories and Methods; Wiley: London, UK, 1976. [Google Scholar]
- Turner, J.E.; Hendewerk, M.; Somorjai, G.A. The photodissociation of water by doped iron oxides: The unbiased p/n assembly. Chem. Phys. Lett.
**1984**, 105, 581–585. [Google Scholar] [CrossRef] - Xue, G.; Xu, Y.; Ding, T.; Li, J.; Yin, J.; Fei, W.; Cao, Y.; Yu, J.; Yuan, L.; Gong, L.; et al. Water-evaporation-induced electricity with nanostructured carbon materials. Nat. Nano
**2017**. [Google Scholar] [CrossRef] [PubMed] - Pruppacher, H.R.; Klett, J.D. Microphysics of Clouds and Precipitation; Springer: Dordrecht, The Netherlands, 1978; pp. 257–268. [Google Scholar]
- Kim, J.; Lu, W.; Qiu, W.; Wang, L.; Caffey, M.; Zhong, D. Ultrafast hydration dynamics in the lipidic cubic phase: Discrete water structures in nanochannels. J. Phys. Chem. B
**2006**, 110, 21994–22000. [Google Scholar] [CrossRef] [PubMed] - Tong, J.; Briggs, M.M.; McIntosh, T.J. Water permeability of aquaporin-4 channel depends on bilayer composition, thickness, and elasticity. Biophys. J.
**2012**, 103, 1899–1908. [Google Scholar] [CrossRef] [PubMed] - Russo, C.J.; Passmore, L.A. Progress towards an optimal specimen support for electron cryomicroscopy. Curr. Opin. Struct. Biol.
**2016**, 37, 81–89. [Google Scholar] [CrossRef] [PubMed] - Gelb, L.D.; Gubbins, K.E.; Radhakrishnan, R.; Sliwinska-Bartowiak, M. Phase separation in confined systems. Rep. Prog. Phys.
**1999**, 62, 1573–1660. [Google Scholar] [CrossRef] - Evans, R.; Marini Bettolo Marconi, U.; Tarazona, P. Fluids in narrow pores: Adsorption, capillary condensation, and critical points. J. Chem. Phys.
**1986**, 84, 2376–2399. [Google Scholar] [CrossRef] - Bal, P.C.; Evans, R. Temperature dependence of gas adsorption on a mesoporous solid: Capillary criticality and hysteresis. Langmuir
**1989**, 5, 714–723. [Google Scholar] [CrossRef] - Zangi, R.; Mark, A.E. Monolayer Ice. Phys. Rev. Lett.
**2003**, 91, 025502. [Google Scholar] [CrossRef] [PubMed] - Zangi, R. Water confined to a slab geometry: A review of recent computer simulation studies. J. Phys. Condens. Matter
**2004**, 16, S5371–S5388. [Google Scholar] [CrossRef] - Kumar, P.; Buldyrev, S.V.; Starr, F.W.; Giovambattista, N.; Stanley, H.E. Thermodynamics, structure, and dynamics of water confined between hydrophobic plates. Phys. Rev. E
**2005**, 72, 051503. [Google Scholar] [CrossRef] [PubMed] - Vilanova, O.; Franzese, G. Structural and dynamical properties of nanoconfined supercooled water. arXiv, 2011; arXiv:1102.2864. [Google Scholar]
- Chen, J.; Schusteritsch, G.; Pickard, C.J.; Salzmann, C.G.; Michaelides, A. Two Dimensional Ice from First Principles: Structures and Phase Transitions. Phys. Rev. Lett.
**2016**, 116, 025501. [Google Scholar] [CrossRef] - Corsetti, F.; Matthews, P.; Artacho, E. Structural and configurational properties of nanoconfined monolayer ice from first principles. Sci. Rep.
**2016**, 6, 18651. [Google Scholar] [CrossRef] [PubMed] - Lee, C.Y.; McCammon, J.A.; Rossky, P.J. The structure of liquid water at an extended hydrophobic surface. J. Chem. Phys.
**1984**, 80, 4448–4455. [Google Scholar] [CrossRef] - Zhu, S.-B.; Robinson, G.W. Structure and dynamics of liquid water between plates. J. Chem. Phys.
**1990**, 94, 1403–1410. [Google Scholar] [CrossRef] - Mamatkulov, S.I.; Khabibullaev, P.K.; Netz, R.R. Water at hydrophobic substrates: curvature, pressure, and temperature effects. Langmuir
**2004**, 20, 4756–4763. [Google Scholar] [CrossRef] [PubMed] - Choudhury, N.; Pettitt, B.M. On the mechanism of hydrophobic association of nanoscopic solutes. J. Am. Chem. Soc.
**2005**, 127, 3556–3567. [Google Scholar] [CrossRef] [PubMed] - Choudhury, N.; Pettitt, B.M. Dynamics of water trapped between hydrophobic solutes. J. Phys. Chem. B
**2005**, 109, 6422–6429. [Google Scholar] [CrossRef] [PubMed] - Gallo, P.; Rovere, M. Anomalous dynamics of confined water at low hydration. J. Phys. Condens. Matter
**2003**, 15, 7625–7633. [Google Scholar] [CrossRef] - Rovere, M.; Ricci, M.A.; Vellati, D.; Bruni, F. A molecular dynamics simulation of water confined in a cylindrical SiO2 pore. J. Chem. Phys.
**1998**, 108, 9859–9867. [Google Scholar] [CrossRef] - Spohr, E. Computer simulation of the water/platinum interface. Dynamical results. Chem. Phys.
**1990**, 141, 87–94. [Google Scholar] [CrossRef] - Rustad, J.R.; Felmy, A.R.; Bylaska, E.J. Molecular simulation of the magnetite-water interface. Geochim. Cosmochim. Acta
**2003**, 67, 1001–1016. [Google Scholar] [CrossRef] - Martins, L.R.; Skaf, M.S.; Ladanyi, B.M. Solvation dynamics at the water/zirconia interface: Molecular dynamics simulations. J. Phys. Chem. B
**2004**, 108, 19687–19697. [Google Scholar] [CrossRef] - Gordillo, M.C.; Martí, J. Molecular dynamics description of a layer of water molecules on a hydrophobic surface. J. Chem. Phys.
**2002**, 117, 3425–3430. [Google Scholar] [CrossRef] - Striolo, A.; Chialvo, A.; Cummings, P.T.; Gubbins, K.E. Water adsorption in carbon-slit nanopores. Langmuir
**2003**, 19, 8583–8591. [Google Scholar] [CrossRef] - Cabrera Sanfelix, P.; Holloway, S.; Kolasinski, K.W.; Darling, G.R. The structure of water on the (0001) surface of graphite. Surf. Sci.
**2003**, 532–535, 166–172. [Google Scholar] [CrossRef] - Pertsin, A.; Grunze, M. Water-graphite interaction and behavior of water near the graphite surface. J. Phys. Chem. B
**2004**, 108, 1357–1364. [Google Scholar] [CrossRef] - Gordillo, M.C.; Nagy, G.; Martí, J. Structure of water nanoconfined between hydrophobic surfaces. J. Chem. Phys.
**2005**, 123, 054707. [Google Scholar] [CrossRef] [PubMed] - Hummer, G.; Rasaiah, J.C.; Noworyta, J.P. Water conduction through the hydrophobic channel of a carbon nanotube. Nature
**2001**, 414, 188–190. [Google Scholar] [CrossRef] [PubMed] - Gordillo, M.C.; Martí, J. Water on the outside of carbon nanotube bundles. Phys. Rev. B.
**2003**, 67, 205425. [Google Scholar] [CrossRef] - Striolo, A.; Chialvo, A.; Cummings, P.T.; Gubbins, K.E. Simulated water adsorption in chemically heterogeneous carbon nanotubes. J. Chem. Phys.
**2006**, 124, 074710. [Google Scholar] [CrossRef] [PubMed] - Nagy, G. Water structure at the graphite (0001) surface by STM measurements. J. Electroanal. Chem.
**1996**, 409, 19–23. [Google Scholar] [CrossRef] - Daio, T.; Bayer, T.; Ikuta, T.; Nishiyama, T.; Takahashi, K.; Takata, Y.; Sasaki, K.; Matthew Lyth, S. In-Situ ESEM and EELS Observation of Water Uptake and Ice Formation in Multilayer Graphene Oxide. Sci. Rep.
**2015**, 5, 11807. [Google Scholar] [CrossRef] [PubMed] - Scodinu, A.; Fourkas, J.T. Comparison of the orientational dynamics of water confined in hydrophobic and hydrophilic nanopores. J. Phys. Chem. B
**2002**, 106, 10292–10295. [Google Scholar] [CrossRef] - Teschke, O.; de Souza, E.F. Water molecular arrangement at air/water interfaces probed by atomic force microscopy. Chem. Phys. Lett.
**2005**, 403, 95–101. [Google Scholar] [CrossRef] - Tombari, E.; Salvetti, G.; Ferrari, C.; Johari, G.P. Thermodynamic functions of water and ice confined to 2 nm radius pores. J. Chem. Phys.
**2005**, 122, 104712. [Google Scholar] [CrossRef] [PubMed] - Ricci, M.A.; Bruni, F.; Gallo, P.; Rovere, M.; Soper, A.K. Water in confined geometries: experiments and simulations. J. Phys. Condens. Matter
**2000**, 12, A345–A350. [Google Scholar] [CrossRef] - Janiak, C.; Scharmann, T.G.; Mason, S.A. Two-dimensional water and ice layers: Neutron diffraction studies at 278, 263, and 20 K. J. Am. Chem. Soc.
**2002**, 124, 14010–14011. [Google Scholar] [CrossRef] [PubMed] - Kolesnikov, A.I.; Zanotti, J.-M.; Loong, C.-K.; Thiyagarajan, P.; Moravsky, A.P.; Loufty, R.O.; Burnham, C.J. Anomalously soft dynamics of water in a nanotube: a revelation of nanoscale confinement. Phys. Rev. Lett.
**2004**, 93, 035503. [Google Scholar] [CrossRef] [PubMed] - Sliwinska-Bartkoviak, M.; Jazdzewska, M.; Huan, L.L.; Gubbins, K.E. Melting behavior of water in cylindrical pores: Carbon nanotubes and silica glasses. Phys. Chem. Chem. Phys.
**2008**, 10, 4909–4919. [Google Scholar] [CrossRef] [PubMed] - Mouterde, T.; Lehoucq, G.; Xavier, S.; Checco, A.; Black, C.T.; Rahman, A.; Midavaine, T.; Clanet, C.; Quere, D. Antifogging abilities of model nanotextures. Nat. Mater.
**2017**. [Google Scholar] [CrossRef] [PubMed] - Abraham, J.; Vasu, K.S.; Williams, C.D.; Gopinadhan, K.; Su, Y.; Cherian, C.; Dix, J.; Prestat, E.; Haigh, S.J.; Grigorieva, I.V.; et al. Tuneable Sieving of Ions Using Graphene Oxide Membranes. arXiv, 2017; arXiv:1701.05519. [Google Scholar]
- Gordillo, M.C.; Martí, J. Structure of water adsorbed on a single graphene sheet. Phys. Rev. B.
**2008**, 78, 075432. [Google Scholar] [CrossRef] - Iijima, S. Helical microtubules of graphitic carbon. Nature
**1991**, 354, 56–58. [Google Scholar] [CrossRef] - Saito, R.; Dresselhaus, G.; Dresselhaus, M.S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, UK, 1998. [Google Scholar]
- Calero, C.; Gordillo, M.C.; Martí, J. Size effects on water adsorbed on hydrophobic probes at the nanometric scale. J. Chem. Phys.
**2013**, 138, 214702. [Google Scholar] [CrossRef] [PubMed][Green Version] - Werder, T.; Walther, J.H.; Jaffe, R.L.; Halicioglu, T.; Koumoutsakos, P. On the water-carbon interaction for use in molecular dynamics simulations of graphite and carbon nanotubes. J. Phys. Chem. B
**2003**, 107, 1345–1352. [Google Scholar] [CrossRef] - Martí, J. Dynamic properties of hydrogen-bonded networks in supercritical water. Phys. Rev. E
**2000**, 61, 449–456. [Google Scholar] [CrossRef] - Boero, M.; Terakura, K.; Ikeshoji, T.; Liew, C.C.; Parrinello, M. Hydrogen bonding and dipole moment of water at supercritical conditions: A first-principles molecular dynamics study. Phys. Rev. Lett.
**2000**, 85, 3245–3248. [Google Scholar] [CrossRef] [PubMed] - Matubayasi, N.; Wakai, C.; Nakahara, M. Structural study of supercritical water. I. Nuclear magnetic resonance spectroscopy. J. Chem. Phys.
**1997**, 107, 9133–9140. [Google Scholar] [CrossRef] - Martí, J.; Nagy, G.; Gordillo, M.C.; Guàrdia, E. Molecular simulation of liquid water confined inside graphite channels: Thermodynamics and structural properties. J. Chem. Phys.
**2006**, 124, 094703. [Google Scholar] [CrossRef] [PubMed] - Nagy, G.; Gordillo, M.C.; Guàrdia, E.; Martí, J. Liquid water confined in carbon nanochannels at high temperatures. J. Phys. Chem. B
**2007**, 111, 12524–12530. [Google Scholar] [CrossRef] [PubMed] - Cicero, G.; Grossman, J.K.; Schwegler, E.; Gygi, F.; Galli, G. Water confined in nanotubes and between graphene sheets: A first principle study. J. Am. Chem. Soc.
**2008**, 130, 1871–1878. [Google Scholar] [CrossRef] [PubMed] - Choudhury, N. On the Manifestation of Hydrophobicity at the Nanoscale. J. Phys. Chem. B
**2008**, 112, 6296–6300. [Google Scholar] [CrossRef] [PubMed] - Madden, P.; Kivelson, D. A consistent molecular treatment of dielectric phenomena. Adv. Chem. Phys.
**1984**, 56, 467–566. [Google Scholar] - Gilijamse, J.J.; Lock, A.J.; Bakker, H.J. Dynamics of confined water molecules. Proc. Natl. Acad. Sci. USA
**2005**, 102, 3202–3207. [Google Scholar] [CrossRef] [PubMed] - Tummala, N.R.; Striolo, A. Hydrogen-Bond Dynamics for Water Confined in Carbon Tetrachloride-Acetone Mixtures. J. Phys. Chem. B
**2008**, 112, 10675–10683. [Google Scholar] [CrossRef] [PubMed] - Martí, J.; Nagy, G.; Gordillo, M.C.; Guàrdia, E. Molecular dynamics simulation of liquid water confined inside graphite channels: Dielectric and dynamical properties. J. Phys. Chem. B
**2006**, 110, 23987–23994. [Google Scholar] [CrossRef] [PubMed] - Martí, J.; Gordillo, M.C. Temperature effects on the static and dynamic properties of liquid water inside nanotubes. Phys. Rev. E
**2001**, 64, 021504. [Google Scholar] [CrossRef] [PubMed] - Ye, H.; Zhang, H.; Zheng, Y.; Zhang, Z. Nanoconfinement induced anomalous water diffusion inside carbon nanotubes. Microfluid. Nanofluid.
**2011**, 10, 1359–1364. [Google Scholar] [CrossRef] - Zheng, Y.-G.; Ye, H.-F.; Zhang, Z.-Q.; Zhang, H.-W. Water diffusion inside carbon nanotubes: Mutual effects of surface and confinement. Phys. Chem. Chem. Phys.
**2012**, 14, 964–971. [Google Scholar] [CrossRef] [PubMed] - Bordin, J.R.; de Oliveira, A.B.; Diehl, A.; Barbosa, M.C. Diffusion enhancement in core-softened fluid confined in nanotubes. J. Chem. Phys.
**2012**, 137, 084504. [Google Scholar] [CrossRef] [PubMed] - de los Santos, F.; Franzese, G. Relations between the diffusion anomaly and cooperative rearranging regions in a hydrophobically nanoconfined water monolayer. Phys. Rev. E
**2012**, 85, 010602. [Google Scholar] [CrossRef] [PubMed] - Gordillo, M.C.; Martí, J. Hydrogen bond structure of liquid water confined in nanotubes. Chem. Phys. Lett.
**2000**, 329, 341–345. [Google Scholar] [CrossRef] - Holt, J.K.; Park, H.G.; Wang, Y.; Stadermann, M.; Artyukhin, A.B.; Grigoropoulos, C.P.; Noy, A.; Bakajin, O. Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes. Science
**2006**, 312, 1034–1037. [Google Scholar] [CrossRef] [PubMed] - Martí, J.; Gordillo, M.C. Time-dependent properties of liquid water isotopes adsorbed in carbon nanotubes. J. Chem. Phys.
**2001**, 114, 10486–10492. [Google Scholar] [CrossRef] - Krynicki, K.; Green, C.D.; Sawyer, D.W. Pressure and temperature dependence of self-diffusion in water. Faraday Discuss. Chem. Soc.
**1978**, 66, 199–208. [Google Scholar] [CrossRef] - Jorgensen, W.L.; Chandrasekhar, J.; Madura, J.D.; Impey, R.W.; Klein, M.L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys.
**1983**, 79, 926–935. [Google Scholar] [CrossRef] - Hausser, R.; Maier, G.; Noack, F. Kernmagnetische messungen von selbstdiffusions-koeffizienten in wasser und benzol bis zum kritischen punkt. Z. Naturforsch. A
**1966**, 21, 1410–1415. [Google Scholar] [CrossRef] - Martí, J.; Gordillo, M.C. Structure and dynamics of liquid water adsorbed on the external walls of carbon nanotubes. J. Chem. Phys.
**2003**, 119, 12540–12546. [Google Scholar] [CrossRef] - Martí, J.; Sala, J.; Guàrdia, E. Molecular dynamics simulations of water confined in graphene nanochannels: From ambient to supercritical environments. J. Mol. Liq.
**2009**, 153, 72–78. [Google Scholar] [CrossRef] - Gordillo, M.C.; Martí, J. Effect of surface roughness on the static and dynamic properties of water adsorbed on graphene. J. Phys. Chem. B
**2010**, 114, 4583–4589. [Google Scholar] [CrossRef] [PubMed] - Liu, P.; Harder, E.; Berne, B.J. On the calculation of diffusion coefficients in confined fluids and interfaces with an application to the liquid-vapor interface of water. J. Phys. Chem. B
**2004**, 108, 6595–6602. [Google Scholar] [CrossRef] - Martí, J.; Guàrdia, E.; Padró, J.A. Dielectric properties and infrared spectra of liquid water: Influence of the dynamic cross correlations. J. Chem. Phys.
**1994**, 101, 10883–10891. [Google Scholar] [CrossRef] - Martí, J.; Padró, J.A.; Guàrdia, E. Molecular dynamics simulation of liquid water along the coexistence curve: Hydrogen bonds and vibrational spectra. J. Chem. Phys.
**1996**, 105, 639–649. [Google Scholar] [CrossRef] - Algara-Siller, G.; Lehtinen, O.; Wang, F.C.; Nair, R.R.; Kaiser, U.; Wu, H.A.; Geim, A.K.; Grigorieva, I.V. Square ice in graphene nanocapillaries. Nature
**2015**, 519, 443–445. [Google Scholar] [CrossRef] [PubMed] - Zangi, R.; Mark, E.A. Bilayer ice and alternate liquid phases of confined water. J. Chem. Phys.
**2003**, 119, 1694–1700. [Google Scholar] [CrossRef] - Giovambattista, N.; Rossky, P.J.; Debenedetti, P.G. Phase transitions induced by nanoconfinement in liquid water. Phys. Rev. Lett.
**2009**, 102, 050603. [Google Scholar] [CrossRef] [PubMed] - Han, S.; Choi, M.Y.; Kumar, P.; Stanley, H.E. Phase transitions in confined water nanofilms. Nat. Phys.
**2010**, 6, 685–689. [Google Scholar] [CrossRef] - Giovambattista, N.; Rossky, P.J.; Debenedetti, P.G. Effect of pressure on the phase behavior and structure of water confined between nanoscale hydrophobic and hydrophilic plates. Phys. Rev. E
**2006**, 73, 041604. [Google Scholar] [CrossRef] [PubMed] - Abascal, J.L.F.; Vega, C. A general purpose model for the condensed phases of water: TIP4P/2005. J. Chem. Phys.
**2005**, 123, 234505. [Google Scholar] [CrossRef] [PubMed] - Rozmanov, D.; Kusalik, P.G. Transport coefficients in the TIP4P-2005 water model. J. Chem. Phys.
**2012**, 136, 044507. [Google Scholar] [CrossRef] [PubMed] - Vega, C.; Abascal, J.L.F. Relation between the melting temperature and the temperature of maximum density for the most common models of water. J. Chem. Phys.
**2005**, 123, 144504. [Google Scholar] [CrossRef] [PubMed] - Agarwal, M.; Alam, M.P.; Chakravarty, C. Thermodynamic, Diffusional, and Structural Anomalies in Rigid-Body Water Models. J. Phys. Chem. B
**2011**, 115, 6935–6945. [Google Scholar] [CrossRef] [PubMed] - Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Gr.
**1996**, 14, 33–38. [Google Scholar] [CrossRef] - Phillips, J.C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R.D.; Kale, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comp. Chem.
**2005**, 26, 1781–1802. [Google Scholar] [CrossRef] [PubMed] - Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An N · log (N) method for Ewald sums in large systems. J. Chem. Phys.
**1993**, 98, 10089–10092. [Google Scholar] [CrossRef] - Fasolino, A.; Los, J.H.; Katsnelson, M.I. Intrinsic ripples in graphene. Nat. Mat.
**2006**, 6, 858–861. [Google Scholar] [CrossRef] [PubMed][Green Version] - Meyer, J.C.; Geim, A.K.; Katsnelson, M.I.; Novoselov, K.S.; Booth, T.J.; Roth, S. The structure of suspended graphene sheets. Nature
**2007**, 446, 60–63. [Google Scholar] [CrossRef] [PubMed][Green Version] - Abedpour, N.; Neek-Amal, M.; Asgari, R.; Shahbazi, F.; Nafari, N.; Tabar, M.R.R. Roughness of undoped graphene and its short-range induced gauge field. Phys. Rev. B
**2007**, 76, 195407. [Google Scholar] [CrossRef] - Bao, W.; Miao, F.; Chen, Z.; Zhang, H.; Jang, W.; Dames, C.; Lau, C.N. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nat. Nanotechnol.
**2009**, 4, 562–566. [Google Scholar] [CrossRef] [PubMed] - Martí, J.; Padró, J.A.; Guàrdia, E. Molecular dynamics calculation of the infrared spectra in liquid H
_{2}O-D_{2}O mixtures. J. Mol. Liq.**1994**, 62, 17–31. [Google Scholar] [CrossRef] - Toukan, K.; Rahman, A. Molecular-dynamics study of atomic motions in water. Phys. Rev. B
**1985**, 31, 2643–2648. [Google Scholar] [CrossRef] - Martí, J. Analysis of the hydrogen bonding and vibrational spectra of supercritical model water by molecular dynamics simulations. J. Chem. Phys.
**1999**, 110, 6876–6886. [Google Scholar] [CrossRef][Green Version] - Kostov, M.K.; Cheng, H.; Cooper, A.C.; Pez, G.P. Influence of carbon curvature on molecular adsorptions in carbon-based materials: A force field approach. Phys. Rev. Lett.
**2002**, 89, 146105. [Google Scholar] [CrossRef] [PubMed] - Berkowitz, M.L. Ewald summation for systems with slab geometry. J. Chem. Phys.
**1999**, 111, 3155–3162. [Google Scholar] - Spohr, E. Effect of electrostatic boundary conditions and system size on the interfacial properties of water and aqueous solutions. J. Chem. Phys.
**1997**, 107, 6342–6348. [Google Scholar] [CrossRef] - Berendsen, H.J.C.; Postma, J.P.M.; van Gunsteren, W.F.; DiNola, A.; Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys.
**1984**, 81, 3684–3690. [Google Scholar] [CrossRef] - Berendsen, H.J.C.; van der Spoel, D.; van Drunen, R. GROMACS: A message-passing parallel molecular dynamics implementation. Comput. Phys. Commun.
**1995**, 91, 43–56. [Google Scholar] [CrossRef]

**Figure 1.**Water energy density E versus the surface density ρ for three of the four systems considered in this work, the (5,5) and (9,9) CNTs and the graphene sheet. In each panel we show simulation results (squares) and least squares fits to Equation (2) (lines) for $T=323$ K (

**a**), $T=310$ K (

**b**) and $T=298$ K (

**c**).

**Figure 2.**Water free energy density F versus the surface per molecule for the (5,5), (9,9) and (12,12) CNTs and the graphene sheet at $T=298$ K, as estimated from Equations (1) and (2) using the fitting parameters calculated in Figure 1. For the thinner (5,5), (9,9) CNTs the free energy minimum is around 4.05 Å

^{2}, while for the (12,12) CNT and the graphene sheet there are no stable minima within the range of densities considered in this work.

**Figure 3.**Number of HBs (lines with symbols, scale on the left) and radial oxygen density profiles (lines without symbols, scale on the right) of water adsorbed at the external volume of CNTs as a function of radial distance from the CNTs axis. The number of hydration HBs is normalized with the bulk HB number. Calculations represented with squares or dashed lines, circles or continuous lines, triangles or dotted lines are for (5,5), (9,9), (12,12) CNTs, respectively.

**Figure 4.**Orientational order of water outside the CNTs as a function of the distance r from the CNTs surface. The two first Legendre polynomial $\langle \mathrm{cos}\theta (r)\rangle $ (

**a**) and $\langle (3\ast \mathrm{cos}{\theta}^{2}-1)(r)\rangle $ (

**b**) characterize water dipolar orientations, being $\theta (r)$ the angle between the instantaneous dipole moment of water and the direction normal to the CNT surface. Symbols and lines are as in Figure 3.

**Figure 5.**Snapshot of MD simulation at $T=275$ K and $P=400$ bar of two fixed parallel graphene plates separated by $d=9.5$ Å and immersed in TIP4P/2005-water (top view). Carbon atoms are in cyan, oxygen in red, hydrogen in white. In our simulations the total number of water molecules, including those outside the confined region, remains constant while the amount of water confined between the graphene sheets depends on the spacing d. Under these conditions the confined water forms a hexagonal ice bilayer.

**Figure 6.**Diffusion coefficient ${D}_{\parallel}$ of confined TIP4P/2005-water at $T=275$ K and $P=400$ bar in a plane parallel to the graphene sheets as a function of inter-plate distance d. The dashed line is a guide to the eyes at ${D}_{\parallel}=0.95$ nm

^{2}/ns, a value close to the bulk diffusion coefficient for this water model under these conditions. ${D}_{\parallel}$ vanishes for 8.5 Å $<d<10$ Å.

**Figure 7.**Rotational relaxation time ${\tau}_{1}$ for confined TIP4P/2005-water at $T=275$ K and $P=400$ bar as a function of graphene inter-plate distance d. A large increase of ${\tau}_{1}$, corresponding to a large slowing-down of the rotational dynamics, occurs for 8.5 Å $<d<10$ Å.

**Figure 8.**Density profiles of TIP4P/2005-water at $T=275$ K and $P=400$ bar confined between graphene sheets along the Z-direction perpendicular to the walls at selected inter-plate separations. The occurrence of zeros between the maxima is an evidence of water layering. (

**a**) Two interfacial layers with intermediate liquid water for graphene plates separation $d=17$ Å; (

**b**) two interfacial layers with a slight-deformed intermediate layer for $d=12$Å; (

**c**) two layers for $d=9$ Å; (

**d**) one layer for $d=7$ Å.

**Table 1.**Summary of CNTs used as confining devices in our simulations. We report CNT length (l), CNT diameter (D) and number of water molecules (N

_{w}) considered to set the density of 1 g/cm

^{3}inside the CNT. In the case of graphene, we report the X-Y lengths.

System | l (nm) | D (nm) | N_{w} |
---|---|---|---|

(5,5) CNT | 7.62 (Z-axis) | 0.66 | 835 |

(9,9) CNT | 6.43 (Z-axis) | 1.22 | 935 |

(12,12) CNT | 8.33 (Z-axis) | 1.63 | 4500 |

Graphene | 3.19 × 3.40 | - | 1252 |

Bulk water | - | - | 1000 |

**Table 2.**Self-diffusion coefficients of water inside CNTs at room temperature from MD results for simulations with the potential model described in [72]. All values are given in 10

^{−5}cm

^{2}/s. The experimental value has been taken from [73] for bulk liquid H

_{2}O. ${D}_{\mathrm{total}}$, ${D}_{z-\mathrm{axis}}$ and ${D}_{xy-\mathrm{plane}}$ are the coefficients for overall diffusion, along the CNT axis and within a section of the CNT.

CNT (n,m) | D_{total} | D_{z−axis} | D_{xy−plane} |
---|---|---|---|

(6,6) | 2.5 | 4.3 | 1.6 |

(8,8) | 3.2 | 3.5 | 3.0 |

(10,10) | 3.1 | 3.8 | 2.7 |

H_{2}O (bulk) | 2.6 | - | - |

Experimental | 2.3 | - | - |

**Table 3.**Self-diffusion coefficients along the axial direction of water outside CNTs at room temperature from MD results for simulations with the TIP3P water model [74]. All values are given in 10

^{−5}cm

^{2}/s.

CNT (n,m) | D_{z} |
---|---|

(5,5) | 4.9 |

(9,9) | 4.9 |

(12,12) | 4.6 |

Graphene | 4.6 |

Bulk unconstrained | 5.8 |

**Table 4.**Self-diffusion coefficients of oxygen atoms near corrugated graphene. Water molecules are (i) at the graphene interface if their distance from the closest carbon is < 5 Å; (ii) in the bulk if the distance is > 7 Å and < 12 Å; (iii) at the water-vacuum interface if the distance is > 12 Å. Diffusion coefficients are expressed in 10

^{−5}cm

^{2}/s.

Distortion Amplitude (Å) | Type of Distortion | Water-Graphene | Bulk Region | Water-Vacuum |
---|---|---|---|---|

0 | None | 3.3 | 3.1 | 3.6 |

0.7 | Random | 2.8 | 2.1 | 3.2 |

0.7 | Equation (8) | 2.8 | 2.3 | 3.7 |

0.7 | Equation (9) | 2.8 | 2.1 | 3.6 |

0.7 | Equation (7) | 2.6 | 2.2 | 3.3 |

5 | Equation (8) | 2.6 | 2.2 | 4.3 |

5 | Equation (9) | 2.6 | 2.2 | 4.2 |

5 | Equation (7) | 2.6 | 2.2 | 4.5 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Martí, J.; Calero, C.; Franzese, G. Structure and Dynamics of Water at Carbon-Based Interfaces. *Entropy* **2017**, *19*, 135.
https://doi.org/10.3390/e19030135

**AMA Style**

Martí J, Calero C, Franzese G. Structure and Dynamics of Water at Carbon-Based Interfaces. *Entropy*. 2017; 19(3):135.
https://doi.org/10.3390/e19030135

**Chicago/Turabian Style**

Martí, Jordi, Carles Calero, and Giancarlo Franzese. 2017. "Structure and Dynamics of Water at Carbon-Based Interfaces" *Entropy* 19, no. 3: 135.
https://doi.org/10.3390/e19030135