Modeling and simulation of the chemo-electro-mechanical behavior of ionic polymer-metal composites

Ionic polymer-metal composites (IPMCs) consist of a thin ionomer plated with metal electrodes. IPMCs exhibit large bending deformations when a small voltage is applied between its electrodes. This bending process is the result of variations in the cation and solvent distribution inside the IPMC. The bending behavior differs for different types of IPMCs, and so a numerical prediction of the behavior needs to be formulated based on various physical phenomena. The bending for several IMPCs can consist of two phases: (1) a fast bending towards the anode and (2) a slow reverse bending. As the physical reasons for reverse bending, i.e., back relaxation of Nafion-based IPMCs is not completely understood, a comprehensive physics-based model of the bending process is still a demanding task. In this paper a numerical model describing the actuation behavior of an IPMC is formulated based on a multi-field approach considering chemical, electrical, and mechanical field equations. This model is based on the cluster model developed by Nemat-Nasser and Li [J. Appl. Phys. 87(7), 3321–3331 (2000)] and Nemat-Nasser [J. Appl. Phys. 92(5), 2899–2915 (2002)] and the chemo-electro-mechanical model given by Wallmersperger et al. [Mech. Mater. 36(5-6), 411–412 (2004); J. Appl. Phys. 101, 024912 (2007)]. The cluster model is a model being able to describe the bending behavior of different IPMCs with and without back relaxation. In the present research the chemical, electrical, and mechanical field equations are discretized using finite differences and solved by a full coupling using the Newton-Raphson technique. By this nonlinear process a detailed representation of the cation and solvent distribution as well as the resulting forces inside the IPMCs are obtained in space and time. Finally a comparison with experimental data published by Nemat-Nasser and Wu [J. Appl. Phys. 93(9), 5255–5267 (2003)] is given for a Nafion-based IPMC with distinctive back relaxation.