# 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

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**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