Mechanics and electrochemistry of ionic polymer metal composites

Ionic polymer metal composites (IPMCs) are electroactive materials composed of a hydrated ionomeric membrane that is sandwiched between noble metal electrodes. Here, we propose a modeling framework to study quasi-static large deformations and electrochemistry of IPMCs. Specifically, IPMC kinematics is described in terms of its mechanical deformation, the concentration of mobile counterions neutralizing the ionomer, and the electric potential. The chemoelectromechanical constitutive behavior is obtained from a Helmholtz free energy density, which accounts for mechanical stretching, ion mixing, and electric polarization. The three-dimensional framework is specialized to plane bending of thin IPMCs. Hence, we propose a structural model, where the moment and the charge stored along the IPMC are computed from the solution of a modified Poisson-Nernst-Planck system, in terms of the through-the-thickness coordinate. For small static deformations, we present a semianalytical solution based on the method of matched asymptotic expansions, which is ultimately used to study IPMC sensing and actuation. We demonstrate that the linearity of IPMC actuation in a broad voltage range could be attributed to the interplay of two competing nonlinear phenomena, associated with Maxwell stress and osmotic pressure. In agreement with experimental observations, our model confirms the possibility of tailoring IPMC actuation by varying the counterion size and the concentration of fixed ions. Finally, the model is successful in predicting the significantly different voltage levels displayed by IPMC sensors and actuators, which are associated with remarkable variations in the ion mixing and polarization energies.