On the difference in ionization properties between planar interfaces and linear polyelectrolytes.

Ionizable planar interfaces and linear polyelectrolytes show markedly different proton-binding behavior. Planar interfaces protonate in a single broad step, whereas polyelectrolytes mostly undergo a two-step protonation. Such contrasting behavior is explained using a discrete-charge Ising model. This model is based on an approximation of the ionizable groups by point charges that are treated within a linearized Poisson-Boltzmann approximation. The underlying reason as to why planar interfaces exhibit mean-field-like behavior, whereas linear polyelectrolytes usually do not, is related to the range of the site-site interaction potential. For a planar interface, this interaction potential is much more long ranged if compared with that of the cylindrical geometry as appropriate to a linear polyelectrolyte. The model results are in semi-quantitative agreement with experimental data for fatty-acid monolayers, water-oxide interfaces, and various linear polyelectrolytes.