Structural and dynamical fingerprints of the anomalous dielectric properties of water under confinement

There is a long-standing question about the molecular configuration of interfacial water molecules in the proximity of solid surfaces, particularly carbon atoms, which plays a crucial role in electrochemistry and biology. In this study, the dielectric, structural, and dynamical properties of confined water placed between two parallel graphene walls at different interdistances from the angstrom scale to a few tens of nanometer have been investigated using molecular dynamics. For the dielectric properties of water, we show that the dielectric constant of the perpendicular component of water drastically decreases under sub-2-nm spatial confinement. The dielectric constant data obtained through linear response and fluctuation-dissipation theory are consistent with recent reported experimental results [L. Fumagalli et al., Science 360, 1339 (2018)]. By determining the charge density as well as fluctuations in the number of atoms, we provide a molecular rationale for the behavior of the perpendicular dielectric response function. We also interpret the behavior of the dielectric response in terms of the presence of dangling O-H bonds of water. By examining the residence time and lateral diffusion constant of water under confinement, we reveal that the water molecules tend to keep their hydrogen bond networks at the interface of water-graphene. We also found consistency between lateral diffusion and the $z$-component of variance in the center of mass of the system as a function of confinement.

Figure 1

Water molecules under two-dimensional slits and graphene walls. Gray balls represent carbon atoms, red balls denote oxygen, and white balls denote hydrogen. This figure is not scaled in the $x$ and $y$ directions according to real system cell parameters.

Figure 2

Inverse of the perpendicular component of the dielectric constant for different wall distances as a function of height $z$. Gray and blue vertical dashed lines indicate the surfaces of graphene and water, respectively. Different thicknesses of water slabs are (a) $L_z=7.5\AA$, (b) $L_z=8.5\AA$, (c) $L_z=14.4\AA$, and (d) $L_z=24.8\AA$.

Figure 3

Computational (blue data) and experimental (red data) perpendicular component of the dielectric constant for different distances of graphene walls. Corresponding dashed lines indicate the bulk values of the SPC/E water model $(\sim 71)$ and pure water. The error bars of computational data are small, staying inside of each data circle.

Figure 4

(a) The time-averaged $z$ component of dipole moments of water molecules as a function of height $z$. Regions $A$ and $B$ correspond to the first and second layer estimated by the density of particles (blue curve), respectively. Additionally, the green curve presents the number of H-bonds. The slab thickness is $L_z=24.8\AA$. The particle density and number of hydrogen bonds have been multiplied by 0.0003 and $\frac{1}{50}$, respectively, as a rescaling for a better display. (b) The fluctuations in the number of hydrogen and oxygen per atom of each type as a function of height $z$ for thickness $L_z=24.8\AA$. The diagrams of $\mathrm{\Delta }{\mathcal{N}}_{\perp }\left(H\right)$, $\mathrm{\Delta }{\mathcal{N}}_{\perp }\left(O\right)$, and density of particles have been multiplied by 20, 20, and $\frac{1}{2500}$.

Figure 5

Schematic figure for a few layers of water near the interface of water-graphene.

Figure 6

(a) The purple marker and ${\varepsilon }_{\perp }^{-1}$ maximum determine the restriction of water molecules in order to rotate out of the $x\text{−}y$ plane, causing a very low dielectric constant. The red area is compatible with the low-density region between the first and second layer of the water molecules. The orange zone shows the presence of dangling OH bonds, leading to higher values for ${\varepsilon }_{\perp }$. The slab thickness is $L_z=24.8\AA$. (b) Inverse of the perpendicular component of the dielectric constant vs the density of charges as well as the density of particles. Region $A$ shows the opposite behavior of ${\varepsilon }_{\perp }^{-1}$ and the density of charges $\left({\rho }_e\right)$. Region $B$ indicates the consonant trend between ${\varepsilon }_{\perp }^{-1}$ and ${\rho }_e$. The water thickness is $L_z=12.5\AA$. The diagrams for ${\rho }_e$ and ${\rho }_m$ have been scaled up via dividing the values by 20 and 2500, respectively.

Figure 7

Residence time correlation function of water molecules between graphene walls for $L_z=24.8\AA$. The residence time is obtained for early layers of each system, indicating that the first layer (green line) has the longest residence time, and then the second layer (purple line) is the layer with the highest survival time. The third layer (blue line) and the bulk segments (orange dashed line) of the confined channel have mostly the same residence time with pure SPC/E water (black dashed-dotted lines) without confinement.

Figure 8

(a) The lateral diffusivity (blue data) and variance in the $z$ component of the center of mass (red data) of confined systems as a function of the thickness of the water slab. These two diagrams are shown together to compare the trends. This shows that the effect of commensurability and the hopping of water molecules between early layers of water are two factors determining the lateral diffusivity. The black dashed line shows the bulk value of the lateral diffusion constant for bulk water without confinement with graphene walls. (b) The behavior of residence time for the first layer and ${\sigma }_z^2$ as defined in the main text. As can be seen from the diagram, ${\tau }_1$ and ${\sigma }_{z,\text{com}}^2$ have opposite trends, demonstrating that as the number of hopping increases (higher ${\sigma }_{z,\text{com}}^2$), the residence time ${\tau }_1$ decreases.

Figure 9

Molecular (left) and charge (right) densities of confined water in channels with different heights. Dashed lines in gray and blue indicate the position of graphene and water, respectively. The particle density indicates the layered structure of water under confinement, and it also indicates a dense layer in the first layer of water closest to graphene surfaces. Extreme reduction in the density of particles after the first maximum on both sides of the diagrams shows the low-density region with a thickness of $\sim 2\AA$ between the first and the second layers of water. The diagrams for the density of charges reveal more tendency of hydrogen atoms to be near graphene sheets. This demonstrates that the total charges in the low-density region between the first and the second layer of water are positive, following the presence of dangling O-H bonds in these regions. The water slabs in the figure are (a) $L_z=7.5\AA$, (b) $L_z=8.5\AA$, and (c) $L_z=16.4\AA$.

Figure 10

Four different choices of $dz$ in order to show that the changes in the perpendicular component of the dielectric constant are independent of bin size $dz$.