Ionization properties of interfaces and linear polyelectrolytes: a discrete charge Ising model

The proton binding characteristics of ionizable interfaces and linear polyelectrolytes are different. While ionizable interfaces protonate in a single broad protonation step, linear polyelectrolytes often show distinct two-step protonation behavior. We explain this phenomenon on the basis of a discrete charge Ising model. The interaction energies between two sites are derived by considering two point charges in a dielectric medium in contact with an electrolyte solution. A semi-infinite dielectric is used to model the planar interface, while a dielectric cylinder mimics the linear polyelectrolyte. For the plane, the inter-charge potential is stronger and much more long ranged than for the cylinder. This results in a mean-field like behavior for the planar system, while for the cylinder the interactions are short ranged and the system behaves in a non-mean-field like fashion. The model is in semi-quantitative agreement with experimental data for fatty-acid monolayers, water–oxide interfaces, and various linear polyelectrolytes.