Lateral Structure Formation in Polyelectrolyte Brushes Induced by Multivalent Ions

We provide a theoretical model for the collapse of polyelectrolyte brushes in the presence of multivalent ions, focusing on the formation of lateral inhomogeneties in the collapsed state. Polyelectrolyte brushes are important in a variety of applications, including stabilizing colloidal particles and lubricating surfaces. Many uses rely on the extension of the densely grafted polymer chains from the surface in the extended brush morphology. In the presence of multivalent ions, brushes are significantly shorter than in monovalent ionic solutions, which greatly affects their properties. We base our theoretical analysis on an analogous collapse of polyelectrolyte brushes in a poor solvent, providing an energy balance representation for pinned micelles and cylindrical bundles. The equilibrium brush heights predicted for these structures are of a similar magnitude to those measured experimentally. The formation of lateral structures can open new avenues for stimuli-responsive applications that rely on nanoscale pattern formation on surfaces.