Swelling of thermo-responsive hydrogels

A model is developed for the elastic response and solvent diffusion through a thermo-responsive gel under an arbitrary deformation with finite strains. The constitutive equations involve the stress-strain relation, the nonlinear diffusion equation for solvent molecules, the heat conduction equation, and the Allen-Cahn equation for an order parameter (proportional to the concentration of hydrophilic segments in polymer chains). Material constants are found by fitting swelling diagrams for PNIPA gels under uniaxial tension. Numerical analysis demonstrates good agreement between predictions of the model and observations in tests with stress- and strain-controlled programs.