Electrostatic free energy of interacting ionizable double layers

The electrostatic contribution to the interaction free energy of charge-regulating materials, similar as well as dissimilar, contains electric work as well as chemical work and can be obtained from an integration over the diffuse part of the double layer together with a summation of the surface contribution to the free energy over the two surfaces. Examples for the surface contribution are given for acid, base, zwitterionic, and amphoteric (1-pK and 2-pK) materials for a diffuse double layer and for the Stern-Gouy-Chapman model, with and without ion adsorption. For charge-regulating materials, the electrostatic contribution to the interaction free energy at contact (adhesion force of curved surfaces, or particles) is always finite and can be obtained from a simple calculation