Electrostatics of a modulated membrane with specific adsorption

Abstract

We present a simple model for the electrostatic properties of a modulated membrane separating two different electrolyte solutions. The model is based on an extension to linear Gouy-Chapman theory. Starting from a Hamiltonian which contains a singular part for the surface contributions, we obtain within the mean-field approach a set of equations which allows us to study the equilibrium between the diffuse and singular parts of the charge carriers. It is shown that the interface modulation leads to a higher potential of zero charge compared to the flat system. The value of this effect depends on the interplay between the height and the characteristic length of the interface modulation and the Debye lengths on both sides, even if the adsorption occurs only on one side of the interface. In the latter case, the side where no adsorption occurs locally exhibits a diffuse charge distribution, which averages to zero, but which makes a contribution to the overall potential drop across the interface. We also calculate the electrostatic contribution to the elastic bending modulus of the membrane and show that specific adsorption of ions can destabilize the flat interface.