Consideration of the charge balances of the ions regarding the behavior of ionic polymer-metal composites (IPMCs): A modeling concept within the framework of the Theory of Porous Media (TPM)

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Ionic polymer-metal composites (IPMCs) are classified as smart materials. These multifunctional materials are made up of a network of polymer fibers with bound anions. The pores are filled with liquid and mobile cations. They can change their properties as a result of external influences and/or active energy supply. The deformations of IPMCs result from the relocation of the cations (diffusion/migration) in the material due to an electric field (actuators). In contrast, mechanical fields (force/displacement) generate an electrical voltage (sensors).Inspired by the behavior of biological systems, the development and production of IPMCs is a subject of international research with regard to new applications in the field of engineering disciplines, materials science and medical technology. An open scientific question is the prediction of the behavior of IPMCs, taking into account the balances of the charges of the ions with source terms (divergence of the electric current). In general, the charge densities of the ions are proportional to the corresponding concentrations (balance of charges are free of sources).The aim of the research project is the extension of a developed thermodynamically consistent model for the description of the coupled electro-chemomechanical behavior of IPMCs. The expansion of the multi-phase model within the framework of the Theory of Porous Media (TPM) refers to the consideration of additional terms with respect to the increments of the electrical energies. This approach is intended to show the dependence of the stresses of the ions on the corresponding electrochemical potentials. Furthermore, the influence of the electric current on the charge densities of the ions and on the electrical potential (Gaussian law) is to be analyzed. With respect to the numerical implementation, it is necessary, in comparison with the existing model, to prepare the weak forms of the balance equations of charges of the ions and the balance law of momentum of the cations (anions are bound to the polymer). The diffusion of the mobile cations and, consequently, the deformation behavior of the IPMCs are strongly influenced by the region of the polymer in close proximity to the electrodes. Thus, it is to be expected that a very fine discretization in space and time is required with regard to the FE-simulation. Therefore, the extended model for the use of ParFEAP (parallel finite element program FEAP) is to be processed in conjunction with the high-performance computing system magnitUDE (HPC system at the University of Duisburg-Essen). Numerical simulations with PARFEAP should show the applicability of the developed model. The results will be validated with available experimental data from the literature.