Modeling of the pH-sensitive behavior of an ionic gel in the presence of diffusion

In this paper, we develop a model for swelling of an ionic gel in a solvent of varying pH and diffusion of the solvent through the swollen gel by applying a variational method originally presented by Baek and Srinivasa (Int. J. Nonlinear Mech. 39 (2004) 201). The approach presented here, based on the balance laws of a single continuum with mass diffusion and ionic chemical reactions, delivers system equations and boundary conditions by assuming two constitutive scalar functions for the free energy of the system and the rate of dissipation, instead of assuming osmotic pressure, electrostatic repulsive force, etc. In the equilibrium case, the model describes pH-dependent behavior and the effect of other counterions on the swelling of ionic gels. In the non-equilibrium case, it accounts for the pH-dependent mass flux through ionic gels. Moreover, the model shows that the mass flux can be induced by the gradient of chemical potential, the concentration of the mobile species and ionic charges. This model is applied to a typical carboxylated copolymer gel, and compared with an experiment for equilibrium swelling, and predicts the pH-dependence for a pressure-induced mass flux.