A modeling study of the effect of environmental ionic valence on the mechanical characteristics of pH–electrosensitive hydrogel

A modeling study is presented to analyze the effect of the ionic valence of the environmental solution on the mechanical behavior of a smart hydrogel responding to the combined stimuli of pH and electric voltage when the hydrogel is immersed in a pH buffer solution subjected to an externally applied electric field. The study is conducted through the multi-effect-coupling pH–electric-stimuli model, which considers chemo-electromechanical coupled effects and incorporates a fixed charge density. The model is composed of nonlinear partial differential governing equations that are capable of predicting the responsive deformation of the hydrogel, the distribution of diffusive ionic species concentrations and the fixed charge density, as well as the electric potential in the whole computational domain covering the hydrogel and surrounding buffer solution. The one-dimensional steady-state simulation is conducted numerically to enable discussion of the influence of the ionic valence of the surrounding buffer solution on the distribution of diffusive ionic species concentrations and the mechanical deformation of the hydrogels subjected to the stimuli of the solution’s pH combined with electric voltage. It is demonstrated that the hydrogel stiffness, fixed charge density and osmotic pressure depend on the equilibrium state of the hydrogel in different pH and ionic environments with monovalent–multivalent ion exchange under AN electric field.