Modeling the effects of pH and ionic strength on swelling of polyelectrolyte gels

A model is developed for the elastic response of a polyelectrolyte gel under unconstrained and constrained swelling in a water bath with an arbitrary pH, where a monovalent salt is dissolved. A gel is treated as a three-phase medium consisting of an equivalent 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 and fixed ions and accompanied by chemical reactions (self-ionization of water molecules, dissociation of functional groups attached to polymer chains, and formation of ion pairs between bound charges and mobile counter-ions). Constitutive equations are derived by means of the free energy imbalance inequality for an arbitrary three-dimensional deformation with finite strains. Adjustable parameters in the governing relations are found by fitting equilibrium swelling diagrams on several hydrogels. The effects of pH, ionic strength of solution, and constraints on equilibrium water uptake are studied numerically.