Charge State\nof Weak Polyelectrolyte Brushes Determines\nSalt-Dependent Swelling and Hysteretic Behavior

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