Chemo-Electro-Mechanical Coupled Simulation of pH-Responsive Swelling in Cationic Hydrogels

The tunable swelling of hydrogels underpins applications in drug delivery, soft actuators, and biomedical sensors. Given the complexity of experimentation, computational simulation has become central to elucidating swelling mechanisms. However, prevailing single-phase models assume macroscopic homogeneity and a single continuum, which limits their ability to capture the multicomponent dynamic responses of hydrogels under pH stimulation. This limitation is especially pronounced for cationic hydrogels (e.g., chitosan-based systems), where simulation must account for ion interactions, charge balance, electric field effects, and dynamic protonation, making multiphysics modeling challenging. Here, we propose a chemo-electro-mechanical coupled framework that integrates chemical diffusion, electric field, solid mechanics, and the Arbitrary Lagrangian-Eulerian method to simulate the swelling behavior of cationic hydrogels. The framework quantifies the influence of fixed charge density, Young’s modulus, pKa, and geometric parameters on swelling kinetics and identifies charge density and pKa as dominant regulators of deformation. Empirical equations derived from parameter analyses establish a quantitative relationship between structural parameters and swelling behavior. Experimental validation shows a prediction error of less than 2%. This work deepens understanding of the swelling mechanisms of cationic hydrogels and provides a robust tool for multiphysics analysis of stimulus-responsive polymers, supporting advances in pH-controlled drug delivery, soft robotics, and biomedical sensing.