Proton binding characteristics of branched polyelectrolytes

Acid-base properties of branched, weak polyelectrolytes are analyzed theoretically by means of Ising models with short-range interactions. Assuming that the structure of the branched polyelectrolyte can be approximated by the topology of a tree (no closed loops), the Ising model with nearest neighbor pair interactions can be solved with exact recursion relations. We demonstrate that the branching structure has important implications for the protonation behavior of weak polyelectrolytes. For instance, the protonation a dendritic and a comblike polyelectrolyte proceed rather differently. Within this framework, the titration behavior of branched poly(ethylene imine) can be explained quantitatively.