Size Effect of Multivalent Counterions on Polyelectrolyte Brushes in Different Polar Solvents

Ion specificity of multivalent counterions plays an important role in determining the structures and functionalities of the polyelectrolyte brushes. Herein, using molecular dynamics simulations, we systematically study the ion specificity represented by the size effect of the multivalent counterions. Our results clearly show the strong counterion-size-specific effects on brush morphologies and brush heights beyond the traditional bridging effect of multivalent counterions. Specifically, at low grafting density, with increasing multivalent counterionic size in solvents of given polarity, brush morphology undergoes a sequence of transitions: from lateral homogeneous collapsed brush to heterogeneous pinned-micelle, vertical phase separated double-layered structure, and vertically stretched brush. Along with this structure transition sequence, brush height manifests a nonmonotonic variation with the increase of counterionic size. Effects of grafting density and chain polydispersity are also addressed carefully. These ion-specific behaviors are attributed to the competition between two important factors when the multivalent counterion interacts with the polyelectrolyte brush, namely, the electrostatic correlation effect manifested as ion bridging and the excluded volume effect between counterions. Our results here provide a clear guide to future studies of ion-specificity effects in polyelectrolyte systems in the presence of multivalent counterions for both theoretical and experimental investigations.