Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The LangevinPoissonBoltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general LangevinBikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the PoissonBoltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.