Swelling of pH-responsive cationic gels: Constitutive modeling and structure–property relations

A constitutive model is developed for the elastic response of pH-sensitive cationic gels under swelling. A polyelectrolyte gel is treated as a three-phase medium that consists of an equivalent polymer network, solvent, and solute (mobile ions). Transport of solvent and solute is modeled as their diffusion through the network accelerated by an electric field formed by mobile and bound ions and accompanied by chemical reactions (self-ionization of water molecules and protonation of functional groups attached to polymer chains). Constitutive equations are derived by means of the free energy imbalance inequality for an arbitrary three-dimensional deformation with finite strains. These relations are applied to the analysis of equilibrium swelling diagrams on chemically cross-linked chitosan, poly(vinylimidazole), and poly(diethylaminoethyl methacrylate-g-ethylene glycol) gels with various concentrations of monomers and cross-linker. Good agreement is demonstrated between the experimental data and results of simulation.