Validation of a model for an ionic electro-active polymer in the static case

IPMCs consist of a Nafion${}^{\circledR }$ ionic polymer film coated on both sides with a thin layer of metallic electrodes. The polymer completely dissociates when it is saturated with water, releasing small cations while anions remain bound to the polymer chains. When this strip is subject to an orthogonal electric field, the cations migrate towards the negative electrode, carrying water away by osmosis. This leads to the bending of the strip. We have previously published a modelling of this system based on the thermodynamics of irreversible processes. In this paper, we use this model to simulate numerically the bending of a strip. Since the amplitude of the deflection is large, we use a beam model in large displacements. In addition, the material permittivity may increase with ion concentration. We therefore test three permittivity models. We plot the profiles of the cations concentration, pressure, electric potential and induction, and we study the influence of the strip geometry on the tip displacement and on the blocking force. The results we obtain are in good agreement with the experimental data published in the literature. The variation of these quantities with the imposed electric potential allow us to discriminate between the three models. (paper)