Unambiguous characterization of in-plane dielectric response in nanoconfined liquids: water as a case study

Abstract

The in-plane dielectric constant of nanoconfined water has attracted growing interest over the last years. Nevertheless, this magnitude is not well-defined at the nanoscale due to its dependence on the arbitrary choice of water width. We propose the in-plane 2D polarizability, $α_{\parallel}$, as an unambiguous characterization of the in-plane dielectric response under 2D confinement, in analogy to what has been recently done for the perpendicular response. Using classical molecular dynamics simulations, we compute $α_{\parallel}$ via two independent and consistent methods: based on fluctuation--dissipation theory, and from the induced dipole moment when water is placed in a capacitor. Our results provide the framework to quantify the in-plane dielectric response of polar liquids across simulations and experiments.

Figures (6)

• Figure 1: Schematic representation of the capacitor set-up. Single-atom-thick Au electrodes of area $A=L_x\times L_z$ are located at $y=0$ and $y=l_{\mathrm{p}}$, which fix a potential difference $\Delta V$ (battery symbol). The water slab (blue) is confined by two Lennard-Jones 9-3 potentials (grey).
• Figure 2: In-plane 2D polarizability $\alpha_{\parallel}$ computed from dipole-moment fluctuations as a function of the lateral supercell size under PBC. The horizontal dashed line indicates the converged value $\alpha_{\parallel}^{\mathrm{PBC}_y}\sim 620$ Å. Inset: cumulative running average of $\alpha_{\parallel}$ for $L_{\parallel}=37.5$ Å.
• Figure 3: Capacitor-based estimates of the in-plane 2D polarizability, $\alpha_{\parallel}^{\mathrm{cap}}$, as a function of the plate separation $l_{\mathrm{p}}$: fluctuation estimates at $\Delta V=0$ (blue circles), and field-response estimates at $\Delta V=0.5$ V obtained from the induced 2D polarization of the full water slab (green squares) and of its central $100$ Å slice (orange diamonds), together with an estimate inferred from the induced electrode charge (red triangles). Dashed lines are fits to Eq. (\ref{['eq:3']}). The horizontal dashed black line shows the PBC$_y$ reference value $\alpha_{\parallel}^{\mathrm{PBC_{y},fluc}}=620$ Å.
• Figure 4: Induced charge on the gold atom rows of the positive electrode, $Q_{\mathrm{ind}}$, as a function of the $z$ coordinate for $l_{\mathrm{p}}=950$ Å (blue line with circles). The background snapshot shows the electrode rows (gold spheres) and the confined water slab, with oxygen atoms in red and hydrogen atoms in white.
• Figure 5: In-plane relative permittivity $\varepsilon_{\parallel}$ computed from $\alpha_{\parallel}=620$ Å as a function of the chosen film width $w$ (blue solid line). Vertical dashed lines indicate three choices of $w$ used in the literature (see main text). The inset reports the relative difference $\delta_{\varepsilon_{\parallel}}$ (see main text) as a function of $w_1$.