Electrostatic interactions in the presence of surface charge regulation: exact results

We study the problem of charge regulation and its effects on electrostatic interactions between dissociable charge groups immersed in a univalent electrolyte, within a family of one dimensional exactly solvable models. We consider the case of both charge regulated plates, but also the interaction of pairs of finite size dielectric "particles". Using the transfer matrix formalism we are able to determine the disjoining pressure as well as the correlations between the charge and the dipole moments of the objects as a function of their separation and electrolyte concentration