Charge State of Weak Polyelectrolyte Brushes Determines Salt-Dependent Swelling and Hysteretic Behavior

We investigate the combined effects of ionizable monomer fraction f, pH, and monovalent salt concentration C_s on the swelling of weak polyelectrolyte brushes (PEBs) by using in situ ellipsometry. Our system consists of random copolymers of basic (2-(dimethylamino)ethyl acrylate, DMAEA) and neutral (2-hydroxyethyl acrylate, HEA) monomers at varying fractions of ionizable monomer. Swelling of the brushes qualitatively follows the trends predicted by scaling laws for PEBs under different charge states but quantitatively deviates at specific ionic strengths and pH values. We posit these deviations stem from the lack of excluded volume effects and assumptions of strong chain stretching in current theoretical models. Most notably, we uncover a salt-dependent, nonmonotonic hysteretic behavior as weak PEB brushes are cycled from protonated to deprotonated and back. The nonmonotonic trend of hysteresis with salt can be explained by an interplay between the protonation facilitating effects of salt in the osmotic regime and the charge screening effects in the salted regime, which make charge distribution along weak PEBs more uniform. Our results provide insight into the mechanisms that determine whether polyelectrolytes exhibit weak versus strong polyelectrolyte behavior in various environmental conditions.