An electromechanical model for sensing and actuation of ionic polymer metalcomposites

Abstract

Ionic polymer metal composites (IPMCs) are active materials that exhibit a bidirectionalelectromechanical coupling. An IPMC is an electrolytic polymer membrane thatis plated by two metallic electrodes. A voltage difference across the electrodesgenerates structural deformations; and, conversely, a mechanical deformation yields avoltage difference across the electrodes. In this paper, we develop a physics-basedmodel for the sensing and actuation of IPMCs undergoing small deformations.The model describes a variety of phenomena taking place in an IPMC, includingcounterions, solvent, and polymer motions; electric dipole generation; osmoticeffects; boundary layer formation; polymer swelling; and local charge imbalances.We specialize the model to the analysis of linear static deformations of a thinand flat IPMC, for which we derive a plate-like model. The reduced-order linearplate-like model is derived by using the principle of virtual work and a parallel-plateapproximation for the electrostatic field inside the IPMC. The proposed plate-likemodel is equivalent to traditional plate models for moderately thin piezoelectricbimorph plates. The constitutive parameters of the plate-like model are expressed interms of fundamental IPMC physical quantities, such as polymer hydration level,IPMC dielectric constant, polymer and electrode dimensions and elastic properties,and solute concentration. We validate the reduced-order model by comparingits predictions with available experimental data on mechanical stiffness, electriccapacitance, and sensing and actuation capacity of water-hydrated Nafion inNa+ form. The model predictions are in close agreement with experimental findings. The modelprovides new insights into the design and optimization of IPMCs and into the role of theIPMC electric capacitance on electromechanical performance. More specifically, we showthat the IPMC capacitance is largely independent of the IPMC thickness andhighly correlated to the thickness of the boundary layers formed by the counterionspecies in the vicinity of the electrodes. Further, we analytically show that thecapacitance strongly influences the sensing and actuation effectiveness of IPMCs.