Local dielectric permittivity near an interface

– A statistical mechanics expression is derived for the space-dependent dielectric permittivity of a polar solvent near an interface. The asymptotic behaviour of this local per-mittivity is calculated in the low density limit, near a planar interface. The potential of mean force between two ions is shown to agree with the prediction of macroscopic electrostatics for large separations parallel to the interface. Introduction. – An efficient statistical description of complex fluids and biomolecular assemblies generally requires some degree of coarse-graining to be tractable. A good example is the " implicit solvent " description of colloids or biomolecules in aqueous solution where water is replaced by a polarizable continuum. An important, largely unsolved, question that arises is that of inhomogeneous screening of solute ions near interfaces. Can the reduction of the bare Coulomb interactions between charges be described by a spatially varying permittivity ǫ(r), and can one establish a rigorous statistical mechanics foundation of such a local permittivity, similar to Kirkwood's famous expression [1] relating the constant permittivity ǫ of a bulk fluid to dipolar fluctuations? While many phenomenological prescriptions have been put forward for the determination of local permittivities [2], the second question is so far largely unanswered. In a recent paper [3], an attempt was made to calculate the permittivity of a polar fluid near a planar interface by a generalization of Onsager's cavity model [4]. In this letter, we reconsider the problem in a general statistical mechanics framework and a number of exact results are established to assess the validity of the concept of a local permittivity.