Effects of Ion Valency on Polyelectrolyte Brushes: A Unified Theory

Ion valency has strong effects on the conformation of polyelectrolyte brushes, which is important for designing the adhesive and lubrication properties of the surface. But a unified theory applicable to both monovalent and multivalent ions is still lacking. Using a consistent description of ion adsorption, we demonstrate the significant effect of ion valency on the brush conformation and the distribution of ions in the system. Our theoretical predictions are consistent with experimental and simulation results. When the system involves only monovalent ions in the solution, our theory predicts that the brush height vs added salt concentration undergoes osmotic and salted brush regimes, consistent with the previous studies. Interestingly, when multivalent ions are present in the solution, the brush height undergoes an adsorption regime-which has not been reported before-in addition to the osmotic and salted regimes. Furthermore, at low salt concentrations, the ion valency of added ions can cause a phase transition in the brush. Our study provides a unified theory for the effects of ions on polyelectrolyte brushes. It reveals that the collapse behavior of the multivalent cation system is mainly caused by adsorption, which originates from the strong electrostatic interaction between monomers and multivalent cations under specific adsorption configurations.