Modeling of electric-stimulus-responsive hydrogels immersed in different bathing solutions

By reformulation of the fixed charge density and consideration of finite deformation, a previous model simulating the pH-sensitive hydrogels is refined in this paper for extension to simulating the electric-sensitive hydrogels, which is termed the refined multi-effect-coupling electric-stimulus (rMECe) model. The rMECe model is based on the assumptions: (a) the hydrogel is isotropic and macroscopically homogeneous, (b) all the three phases are incompressible, including the polymeric solid matrix, interstitial water and mobile ions, (c) the effect of electro-osmosis is neglected, (d) bath solution is ideal so that the variation of the activity coefficients with ionic strength can be negligible, i.e., its effect on the concentration profiles is negligible, (e) the smart hydrogel is immersed in an unstirred solution in vibration-free experimental device; the bulk flow of fluid or hydrodynamic velocity can thus be eliminated and subsequently the convective flux is neglected, and (f) the pore of the present hydrogel is narrow enough so that the diffusion dominates the transmission of flux. The model consists of nonlinear coupled partial differential governing equations with the coupling effects of chemo-electro-mechanical multi-energy domains and the fixed charge density with the effect of externally applied electric-field. By comparing the simulating results with experimental data extracted from literature, a very good agreement is achieved and thus this validates the computing accuracy and stability of model. The present rMECe model shows the capability of efficiently predicting the ionic transport and the performance of the hydrogels when they are immersed in a bath solution subject to externally applied electric voltage. The model is used for quantitative analysis of the electric-sensitive hydrogels and for discussion of the influences of several physical parameters on the response of the hydrogels, including the externally applied electric voltage, the initially fixed charge density, and the ionic strength and valence of surrounding solution.