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

An ionic polymer metal composite (IPMC) is a porous charged polymer saturated with an electrolytic solvent and plated by two metallic electrodes. A voltage difference across the electrodes generates structural deformations; similarly, a mechanical deformation yields a voltage difference across the electrodes. The electrolytic solvent comprises a mobile ionic species and an uncharged solvent. Interactions between mobile ions and the solvent and between the solvent and the backbone polymer are responsible for sensing and actuation. We present a mixture theory framework for mechanical modeling of IPMCs and of species interactions occurring therein. The model consists of three coupled linear partial differential equations, and it is applicable to a large variety of IPMC geometries and microstructures. The framework allows for a thorough description of actuation mechanisms, including osmotic pressure, hydraulic pressure, and electrostatic forces. The model describes the presence of boundary layers of mobile ions and solvent concentrations in the vicinity of the electrodes. We particularize the general three-dimensional model to a slender IPMC, and we derive a one-dimensional distributed model using the Euler-Bernoulli beam theory and a parallel-plate approximation. We validate our theoretical findings through a set of experiments conducted on Nafion-based IPMCs.