On Maxwell stress and its relationship with the dielectric constant in the actuation of ionic metal

Ionic polymer metal composites (IPMCs) are unique electroactive polymers that show promise as actuators in soft robotics and biomedical applications. The modeling and numerical simulation of the behavior of these materials are significantly complicated by the nature of the underlying electrochemical phenomena, which occur in nanometer-thick layers in the proximity of the electrodes. Hence, the dielectric constant of IPMCs is often rescaled to help numerically resolve the electric double layers. However, the effect of such a rescaling on IPMC actuation has never been systematically assessed. Motivated by recent efforts on the effect of the rescaling on Maxwell stress, we put forward a physically based analysis of the role of dielectric constant on IPMC actuation. We demonstrate that an increase of the dielectric constant decreases the magnitude of the electric field during actuation, due to the widening of the electric double layers. The decrease in the electric field intensity perfectly balances the increase of the dielectric constant scaling Maxwell stress, such that Maxwell stress is independent of the IPMC dielectric constant. The bending moment generated by Maxwell stress increases with the dielectric constant, since the thickness of the electric double layers where Maxwell stress is relevant is larger. However, the same scaling is common to all the bending moments associated with the electrochemistry, so that the relative importance of each term on IPMC actuation does not depend on the dielectric constant. This study contributes an important analysis that can support feasible and faithful numerical implementations of theories on IPMC mechanics and electrochemistry.