Dielectric response of confined water films from a classical density functional theory perspective

We re-examine the problem of the dielectric response of highly polar liquids such as water in confinement between two walls using simple two-variable density functional theory involving number and polarisation densities. In the longitudinal polarisation case where a perturbing field is applied perpendicularly to the walls, we show that the notion of the local dielectric constant, although ill-defined at a microscopic level, makes sense when coarse-graining over the typical size of a particle is introduced. The approach makes it possible to study the effective dielectric response of thin liquid films of various thicknesses in connection with the recent experiments of Fumagalli et al., [Science, 2018, 360, 1339-1342], and to discuss the notion of the interfacial dielectric constant. We argue that the observed properties as a function of slab dimensions, in particular the very low dielectric constants of the order of 2-3 measured for thin slabs of ∼1 nm thickness do not highlight any special properties of water but can be recovered for a generic polar solvent having similar particle size and the same high dielectric constant. Regarding the transverse polarisation case where the perturbing field is parallel to the walls, the associated effective dielectric constant as a function of slab dimensions reaches bulk-like values at much shorter widths than in the longitudinal case. In both cases, we find an oscillatory behaviour for slab thicknesses in the one nanometer range due to packing effects.