Modelling and simulation of time dependent ion migration process and bending of ion-doped rubber films using a minimal set of physically estimated parameters

Abstract Films of soft polymers, i.e. above their glass transition temperature, when doped with ionic electric charges, exhibit mechanical deformations such as bending when subjected to an electric field. Previous studies have shown the drift of positive and negative ions, generating a current in the film, is responsible for such deformations due to differences in their diffusion coefficients.In this study, a numerical model is developed to reproduce both the current density and bending behavior of electroactive polymers and to clarify the underlying mechanism. The proposed model consists of two steps. First, the Poisson-Nernst-Planck equations are solved to obtain ion concentration distributions caused by drift and diffusion. From these, the electrostatic energy density distribution is calculated, which induces Maxwell stress within the film. Second, the resulting bending deformation is calculated based on this stress. The simulation results show good agreement with experimental data for both current density and bending behavior. Upon field application, ions migrate in opposite directions, forming electric double layers near the electrodes and ion depletion layers adjacent to the electric double layers. The bending behavior is governed by the imbalance in electrostatic energy density around ion depletion layers between the left-and right-hand side originating from differences in ion diffusion coefficients. Furthermore, simulations of specific electric field sequences reveal that incomplete ion diffusion during electric field interruptions cause a "memory effect", wherein current density and bending profiles resume from the point where the electric field was interrupted.