Inhomogeneous swelling of pH-responsive gels

A model is developed for the mechanical response of pH-sensitive gels under an arbitrary three-dimensional deformation accompanied by swelling. A polyelectrolyte gel is treated as a three-phase medium consisting of a polymer network, solvent (water), and solute (mobile ions). Transport of solvent and solute is thought of as their diffusion through the network accelerated by an electric field formed by mobile ions and bound charges and accompanied by chemical reactions. Constitutive equations are derived by means of the free energy imbalance inequality with reference to the principle of electro-mechanical equivalence. An analog of the Donnan equilibrium conditions is developed where self-ionization of water molecules is taken into account. Material constants are found by matching swelling diagrams under unconstrained water uptake by covalently cross-linked poly(acrylic acid) and poly(aspartic acid) gels. The effect of pH on distribution of water molecules and ions in core-shell microgel particles is studied numerically.