The effects of pH and ionic strength on equilibrium swelling of polyampholyte gels

A model is developed for the elastic response of a charge-balanced polyampholyte gel subjected to swelling in an aqueous solution of a monovalent salt with arbitrary pH. A gel is treated as a three-phase continuum composed of a solid phase (polymer network formed by chains with acidic and basic functional groups), 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 (self-ionization of water, ionization of functional groups, formation of ion pairs between bound charges and mobile counter-ions, and formation of physical cross-links between fixed ions with opposite charges). Constitutive equations are derived by means of the free energy imbalance inequality for three-dimensional deformation with finite strains. The governing equations are applied to study equilibrium water uptake by polyampholyte and polyelectrolyte gels. Numerical analysis demonstrates that the model reproduces all characteristic features of swelling diagrams qualitatively. The ability of the model to describe swelling curves quantitatively is confirmed by comparison of results of simulation with experimental data on three polyampholyte gels.