Charge regulation of weak polyelectrolytes at low- and high-dielectric-constant substrates

As is well known, the effective charge of weak polyelectrolytes (PEs) decreases with decreasing salt concentration due to the electrostatic repulsion between dissociated charges. Close to dielectric boundaries, image-charge effects influence the dissociation equilibrium. At low-dielectric-constant substrates, one finds a further charge decrease and repulsion from the interface, while at high-dielectric-constant (e.g. metallic) substrates, the effective charge increases and the PE is attracted to the interface.