A Scaling Theory for Polyelectrolyte Brushes: Insights from Intermonomer Electrostatic Interactions

We develop a scaling theory for polyelectrolyte (PE) brushes using a cell model that incorporates intermonomer electrostatic interactions. A new scaling regime is identified, where the brush height H scales with salt concentration ns as H ∝ ns–1/5. This arises from nonoverlapping electric double layers (EDLs) between charged monomers at high salt concentrations, in contrast to the classical salted brush regime H ∝ ns–1/3, where EDLs overlap. We also identify a critical charge fraction φc and find that the classical salted brush H ∝ ns–1/3 holds only for weakly charged (φ < φc) and loosely grafted brushes. In comparison, a weaker salt dependence of brush height is often observed, which can be categorized as the newly identified scaling law H ∝ ns–1/5, or a transition to the neutral brush regime, as confirmed by our molecular dynamics simulations. We anticipate that this scaling analysis will be helpful to guide the design of PE systems with tailored swelling–shrinking behavior.