Derivation of finite element formulation for electrochemical governing equations of ionic polymer actuators

Ionic polymer actuators have recently attracted a great deal of interest as electroactive materials with potentials as soft actuators, sensors, artificial muscles, robotics, and microelectromechanical systems because of their numerous advantages, including low voltage requirement, high compliance, lightness, and flexibility. The platinum-plated Nafion, a perfluorosulfonic acid membrane made by Dupont, is commonly used as a polyelectrolyte in actuator applications. The bending of the ionic polymer actuators in an electric field is dominated by the electro-osmosis of hydrated ions and slow diffusion of free water molecules. The changes in hydration cause a local volumetric strain resulting in bending deformation, such as expansion and contraction. In this study, a two-dimensional finite element (FE) formulation based on the Galerkin method is derived for the governing equations describing these electrochemical responses. In addition, a three-dimensional FE deformation analysis is conducted on the bending behaviors of the platinum-plated ionic polymer actuators. Several numerical studies for ionic polymer actuators, such as plates with various electrode arrangements and disk models in electric field, are performed to confirm the validity of the proposed formulation.