A mixture theory framework for modeling the mechanical actuation of ionic polymer metalcomposites

Abstract

An ionic polymer metal composite (IPMC) is a porous charged polymer saturated with anelectrolytic solvent and plated by two metallic electrodes. A voltage differenceacross the electrodes generates structural deformations; similarly, a mechanicaldeformation yields a voltage difference across the electrodes. The electrolytic solventcomprises a mobile ionic species and an uncharged solvent. Interactions betweenmobile ions and the solvent and between the solvent and the backbone polymer areresponsible for sensing and actuation. We present a mixture theory framework formechanical modeling of IPMCs and of species interactions occurring therein.The model consists of three coupled linear partial differential equations, and itis applicable to a large variety of IPMC geometries and microstructures. Theframework allows for a thorough description of actuation mechanisms, includingosmotic pressure, hydraulic pressure, and electrostatic forces. The model describesthe presence of boundary layers of mobile ions and solvent concentrations in thevicinity of the electrodes. We particularize the general three-dimensional model toa slender IPMC, and we derive a one-dimensional distributed model using theEuler–Bernoulli beam theory and a parallel-plate approximation. We validate ourtheoretical findings through a set of experiments conducted on Nafion-based IPMCs.