Volume phase transition in thermo-responsive hydrogels: constitutive modeling and structure–property relations

A model is developed for the elastic response of a thermo-responsive hydrogel subjected to swelling under an arbitrary deformation with finite strains. The constitutive equations involve the stress–strain relation, the nonlinear diffusion equation for water molecules, the heat conduction equation, and the Allen–Cahn equation for a scalar order parameter (proportional to the concentration of hydrophilic segments in polymer chains). Material constants are found by fitting equilibrium mass uptake diagrams for macro- and microgels under unconstrained and constrained swelling in the vicinity of the volume phase transition temperature. Quantitative agreement is demonstrated between the experimental data and the results of simulation. The effect of composition of hydrogels (concentrations of monomers and cross-linker) on adjustable parameters is analyzed numerically.