Ion Adsorption Enhances Apparent Nonelectrostatic Attraction between Monomers in Polyelectrolyte Brushes

Polyelectrolyte brushes are responsive to salt in the environment, and this has found broad applications in antifouling, biolubrication, and drug delivery. Salt primarily influences the conformation of the polyelectrolytes through ion adsorption. While ion adsorption is typically associated with electrostatic interactions, our research reveals that in multivalent ion solutions, it also enhances nonelectrostatic interactions by bringing distant polyelectrolyte segments closer together. The finding is based on a comparative study between theoretical, simulation, and experimental data for monovalent, divalent, and trivalent cation solutions of sodium poly(styrenesulfonate) (PSS) and potassium poly(3-sulfopropyl methacrylate) (PSPMA) brushes. By incorporating an apparent Flory-Huggins parameter that is linearly dependent on the extent of ion adsorption, we developed a theoretical model for polyelectrolyte brushes that predicts brush heights in good agreement with experimental and simulation data. This work provides three major contributions to our understanding of polyelectrolyte brushes. (a) The theoretical framework reveals that while electrostatic interactions primarily drive the contraction of short-chain brushes (approximately 50 monomers), nonelectrostatic interactions arising from ion adsorption induce the collapse of long-chain brushes (approximately 500 monomers) in multivalent ion solutions. (b) Traditional scaling theory is applied only to long polymer chains in monovalent cation systems. Our modified framework broadens the scope to include both short and long chains in both monovalent and multivalent systems, while most of the traditional scaling theory can only be applied to long-chain systems. (c) We provided a comprehensive quantitative examination of the inter- and intrachain cross-links.