Coupled Thermal–Chemical Stimuli in Hydrogel Swelling: A Multifield Kinetic Model for Dual-Responsive Hydrogel

Stimuli-responsive hydrogels are intelligent soft materials capable of large volume changes under environmental stimuli. To capture their complex coupled behavior under temperature and pH variations, a fully coupled thermo-chemo-electro-mechanical (TCEM) kinetic model is developed, which can be used to predict both equilibrium and kinetic gel swelling, especially incorporating the gel modulus evolution under different temperatures and gel fractions. The model integrates ionic transport, Poisson electrostatics, mechanical equilibrium, and Flory–Rehner-based polymer swelling thermodynamics. The numerical implementation is validated against experimental data across various pH and temperature conditions, demonstrating strong agreement. A systematic sensitivity analysis is conducted to evaluate the influence of fixed-charge density, dissociation constant, buffer ion concentration, ion diffusion coefficients, and dry-state modulus. The results highlight key parameters governing the deformation kinetics and equilibrium morphology of the smart hydrogels. This work establishes a robust mechanistic model for predicting equilibrium and transient swelling, offering insights into the rational design of hydrogel-based systems for biomedical, soft robotic, and environmental applications.