Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel

Immersed in an ionic solution, a network of polyampholytic polyelectrolyte imbibes the solution and swells, resulting in a polyampholytic pH-sensitive hydrogel, which can respond to changes in the surrounding environmental pH. The presence of fixed charges and mobile ions due to the dissociation of ionizable acidic and basic groups may give rise to a region called the electrical double layer of a thickness scaled by the Debye length. Owing to the existence of the electrical double layer, when the size of a polyampholytic pH-sensitive hydrogels is comparable to, or smaller than, the Debye length, the behavior of the gel may deviate from that of the gel of a large size. To account of the size effects, this paper develops a field theory for polyampholytic pH-sensitive hydrogels by coupling large deformation of the network, the dissociation of the functional groups and the migration of the ions and the solvent. The theory is then applied to explore the influence of pH, salt concentration, geometric constraint and the effects of the electrical double layer on swelling properties by analyzing a thin layer of a polyampholytic pH-sensitive hydrogel immersed in a solution.