Hierarchical Model of Weak Polyelectrolytes with Ionization and Conformation Consistency

Conventional models of weak polyelectrolytes are formulated in terms of either an average degree of ionization or a rigid polymer conformation. While the decoupling of segment-level ionization and polymer structure simplifies the theoretical procedure and is beneficial from a computational perspective, it misses intrachain correlations (i.e., interactions beyond adjacent monomers) that are important for systems at a low polymer concentration with strong electrostatic interactions. In this work, we propose a hierarchical method that incorporates the liquid-state theories with the site-binding model to account for the effects of the local ionic environment on both inter- and intrachain correlations. A wormlike-chain model is introduced to describe the coupling of polymer conformation and monomeric ionization with the long-range electrostatic interactions accounted for by using the Gibbs–Bogoliubov variational principle. Through an extensive comparison of the theoretical predictions with experimental titration curves for poly(acrylic acid) in different alkali chloride solutions, we demonstrate that the hierarchical model is able to quantify the charging behavior of weak polyelectrolytes over a broad range of solution conditions.