Static Dielectric Permittivity Profiles and Coarse-graining Approaches for Water in Graphene Slit Pores

TL;DR

This paper re-derives the Green--Kubo relation for confined fluids, clarifies boundary condition effects on dielectric profiles, and shows water's dielectric response remains bulk-like down to nanometer scales, with implications for experimental interpretation.

Contribution

It provides a rigorous derivation of dielectric response in confined fluids, clarifies misconceptions, and connects microscopic behavior to experimental observables using coarse-graining and effective-medium theory.

Findings

Water retains bulk dielectric response down to ~1 nm confinement.

Effective dielectric response is governed by dielectric interface placement.

Simulated water dielectric properties are consistent across models and setups.

Abstract

The dielectric response of nano-confined fluids is crucial across technologies and biological systems, yet its calculation and interpretation from molecular simulations are often muddled by unclear boundary conditions. We re-derive the Green--Kubo relation for the spatially resolved linear dielectric response of fluids in planar confinement, explicitly accounting for boundary conditions and showing that equilibrium-derived profiles agree with those obtained from external fields. We identify common misconceptions in the literature and outline how microscopic dielectric behavior can be coarse-grained to connect with experimental observables. Simulations show that water retains a bulk-like dielectric response down to $\sim 1\,\mathrm{nm}$ confinement. The reduced \emph{effective} dielectric response that governs capacitance arises from the placement of the dielectric interface. Using effective-medium theory, we demonstrate that long-range reductions reported in experiments and theory are consistent with bulk-like behavior beyond about $1\,\mathrm{nm}$ from the surface. The effective response naturally maps onto an interfacial capacitance, and the dielectric properties of simulated water are robust across simulation setups and water models, reflecting universal polarization correlations.