Modeling the response of polymer–ionic liquid electromechanical actuators

A model is derived for the electromechanical response of a porous membrane swollen with an ionic liquid and sandwiched between two nanoscale-thin electrodes under DC current. Bending of the membrane is induced by pressure in pores arising due to diffusion of ions through a network of nanochannels. Transport of ions is governed by the applied electric field and redox reactions at the surfaces of electrodes. Constitutive equations for the mechanical response of a porous medium and diffusion of ions are derived by means of the free energy imbalance inequality under an arbitrary deformation with finite strains. Under the assumption regarding small strains, but finite changes in concentrations of ions and the electrostatic potential, an explicit expression is developed for the curvature of the membrane. A steady-state solution to the Poisson–Nernst–Planck equations is obtained by means of the method of matched asymptotic expansions. Results of numerical analysis demonstrate the ability of the constitutive equations to describe observations. In particular, the model provides an explanation for bending to the anode and to the cathode and predicts qualitatively the effects of applied voltage, concentration of ionic liquid, and thickness of a membrane on its curvature.