The dielectric response of nano-confined fluids is important for a wide range of technologies and biological systems, ranging from the fundamentals of energy storage to the stability of lipid membrane bilayers. Its calculation from molecular simulations has become a viable tool since the 2010s and is often employed to rationalize experimental observations. However, confusion has emerged on the underlying boundary conditions, and correspondingly, the concept of dielectric profiles is often misunderstood in the literature. Here, we re-derive the Green–Kubo relation for the linear dielectric response profile of fluids in planar confinement, while carefully considering the different underlying boundary conditions; if the latter are correctly accounted for, profiles from equilibrium simulations are perfectly in line with results using externally applied fields. We discuss possible pitfalls and address misunderstandings, regarding both the detailed calculation and the general concept of dielectric profiles, as well as procedures to coarse-grain the microscopic dielectric behavior in order to connect to experimental observables. Simulations consistently reveal that the dielectric response of water is bulk-like down to confining scales as small as ∼1 nm. However, the effective dielectric response of confined systems, which determines their capacitance, depends on the precise location of the dielectric interface. Using concepts from effective medium theory, we show that the long-range reduction of the effective dielectric response, reported in both experimental and theoretical studies, is in line with a dielectric response that reaches the bulk value at about 1 nm from the surface. The effective dielectric response can be interpreted in terms of the commonly employed concept of an interfacial capacitance. We find that the dielectric properties of simulated water are independent of the simulation details and the water model employed, thus revealing the universal properties of water polarization correlations.
Stärk et al. (Sun,) studied this question.