Generalized stern models of the electric double layer considering the spatial variation of permittvity and finite size of ions in saturation regime

The interaction between a charged metal implant surface and a surrounding body fluid (electrolyte solution) leads to ion redistribution and thus to formation of an electrical double layer (EDL). The physical properties of the EDL contribute essentially to the formation of the complex implant-biosystem interface. Study of the EDL began in 1879 by Hermann von Helmholtz and still today remains a scientific challenge. The present mini review is focused on introducing the generalized Stern theory of an EDL, which takes into account the orientational ordering of water molecules. To ascertain the plausibility of the generalized Stern models described, we follow the classical model of Stern and introduce two Langevin models for spatial variation of the relative permittivity for point-like and finite sized ions. We attempt to uncover the subtle interplay between water ordering and finite sized ions and their impact on the electric potential near the charged implant surface. Two complementary effects appear to account for the spatial dependency of the relative permittivity near the charged implant surface — the dipole moment vectors of water molecules are predominantly oriented towards the surface and water molecules are depleted due to the accumulation of counterions. At the end the expressions for relative permittivity in both Langevin models were generalized by also taking into account the cavity and reaction field.