Abstract

The local dielectric permittivity changes abruptly at the water–air interface, from ϵ ≈ 80 in the bulk liquid to ϵ ≈ 1 in the vapor. Previous work has suggested that ϵ(z) should be viewed as a highly structured function of distance z from the surface, changing sign and exhibiting multiple singularities as z approaches zero. Here we present theory and computer simulations that largely reconcile the spatially coarse-grained dielectric response observed at interfaces with bulk material properties. We develop a novel dielectric continuum theory expression that takes the boundary conditions at the interface into account appropriately and predicts how dipole fluctuations in probe volumes are modestly suppressed near the interface. This simple model accurately predicts relative correlations between net polarizations down to probe volumes containing only a few molecules on average, both in bulk and at interfaces. We find that dipole probability distributions from numerical simulations rapidly approach a large deviation form whose non-Gaussian features are chiefly responsible for the finite size effects observed in the linear dielectric response. The success of our simple model in conjunction with the similarities between bulk and interfacial rate functions suggests that water’s dielectric permittivity retains its bulk value essentially up to the water–air interface.