Electrostatic Correlation Induced Charge Inversion and Nonmonotonic Conformational Change of Polyelectrolyte Brushes

Polyelectrolyte brushes are widely used to regulate transport of ions and molecules, control wettability, adhesion, and lubrication of surfaces. The conformation of brushes is of particular importance which can respond to external stimulus such as salt ions. In the presence of multivalent ions, there are many phenomena observed in experiments and simulations, such as the nonmonotonic dependence of brush height on salt concentration and diminish of the lubricity, cannot even be qualitatively explained by existing theories. Here, we develop a new theory which incorporates the Gaussian renormalized fluctuation theory for charged systems into the self-consistent field theory for polymers. Particularly, the correlation between charged segments and mobile ions are fully accounted for. The coupling between chain conformation and electrostatic effects is also captured self-consistently. For monovalent salt ion, we find that the height of brushes decreases monotonically as salt concentration increases, consistent with the mean-field prediction. However, for divalent salt ion, brushes collapse at low salt concentrations but re-expand as the salt concentration further increases due to electrostatic correlation. Furthermore, for trivalent salt ion, besides the re-expansion of brush height, both the density profile of polymers and the distribution of salt ion exhibits an oscillating behavior, which indicates stronger correlation. We reveal that the re-expansion of the brush is accompanied by the phenomenon of charge inversion where multivalent counterions overcompensate the total charge carried by the polyelectrolyte chains.