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Abstract A recent experiment by Kim’s group from the University of Nevada, Las Vegas has demonstrated the possibility of actuating ionomer cilia in salt solution. When these actuators are placed between two external electrodes, across which a small voltage is applied, they move toward the cathode. This is in stark contrast with the case of ionic polymer metal composites, where these ionomers are plated by metal electrodes and bending occurs towards the anode. Here, we seek to unravel the factors underlying the motion of ionomer cilia in salt solution through a physically-based model of actuation. In our model, electrochemistry is described through the Poisson-Nernst-Planck system in terms of concentrations of cations and anions and voltage, which is solved through the finite element method. Based on computer simulations, we establish that Maxwell stress is the main driving force for the motion of the cilia. 

Abstract A recent experiment by Kim’s group from the University of Nevada, Las Vegas, has shown the possibility of actuating ionomer cilia in salt solution. When these actuators are placed between two external electrodes, across which a small voltage is applied, they move toward the cathode. This is in stark contrast with ionic polymer metal composites, where the same ionomers are plated by metal electrodes but bending occurs toward the anode. Here, we seek to unravel the factors underlying the motion of ionomer cilia in salt solution through a physically based model of actuation. In our model, electrochemistry is described through the Poisson–Nernst–Planck system in terms of concentrations of cations and anions and voltage. Through finite element analysis, we establish that Maxwell stress is the main driving force for the motion of the cilia. This study constitutes a first effort toward understanding the motion of ionomer cilia in salt solution, which, in turn, may help elucidate the physical underpinnings of actuation in ionic polymer metal composites. 

Ionic polymer metal composites (IPMCs) are soft electroactive materials that are finding increasing use as actuators in several engineering domains, where there is a need of large compliance and low activation voltage. Similar to traditional sandwich structures, an IPMC comprises a hydrated ionomer core that is sandwiched by two stiffer electrodes. The application of a voltage across the electrodes drives charge migration within the ionomer, which, in turn, contributes to the development of an eigenstress, associated with osmotic pressure and Maxwell stress. Critical to IPMC actuation is the variation of the eigenstress through the thickness of the ionomer, which is responsible for strain localization at the ionomer-electrode interfaces. Despite considerable progress in the development of reliable continuum theories and finite element tools, accurate structural theories that could beget physical insight into the inner workings of IPMC actuation are lacking. Here, we seek to bridge this gap by contributing a principled methodology to structural modeling of IPMC actuation. Our approach begins with the study of the IPMC electrochemistry through the method of matched asymptotic expansions, which yields a semi-analytical expression for the eigenstress as a function of the applied voltage. Hence, we establish a total potential energy that accounts for the strain energy of the ionomer, the strain energy of the electrodes, and the work performed by the eigenstress. By projecting the IPMC kinematics on select beam-like representations and imposing the stationarity of the total potential energy, we formulate rigorous structural theories for IPMC actuation. Not only do we examine classical low-order and higher-order beam theories, but we also propose enriched theories that account for strain localization near the electrodes. The accuracy of these theories is assessed through comparison with finite element simulations on a plane-strain problem of non-uniform bending. Our results indicate that an enriched Euler-Bernoulli beam theory, with three independent field variables, is successful in capturing the main features of IPMC actuation at a limited computational cost. 

Ionic polymer metal composites (IPMCs) are a class of soft electroactive polymers. IPMCs comprise a soft ionic polymer core, on which two stiff metal electrodes are plated. These active materials exhibit large bend- ing upon the application of a small driving voltage across their electrodes, in air or in aqueous environments. In a recent work, we presented compelling theoretical and numerical evidence suggesting that ionic polymer membranes exhibit complex multiaxial deformations neglected by reduced-order structural models. Where most beam theories (including Euler-Bernoulli, Timoshenko, and most higher-order shear deformation models) would suggest vanishing through-the-thickness deformation, we discover the onset of localized deformation that rever- berates into axial stretching. Building upon this effort, here we investigate the role of the electrodes and shear on multiaxial deformations of IPMCs. We establish a novel structural theory for IPMCs, based on the Euler- Bernoulli kinematics enriched with the through-the-thickness deformation in the ionic polymer, computed from a Saint-Venant-like problem for uniform bending. While considering boundary conditions that elicit non-uniform bending, we compare the results of this model against classical Euler-Bernoulli beam theory without enrichment and finite element simulations, encapsulating the nonlinear response of the material. We demonstrate that our theory can predict the macroscopic displacement of the IPMC, along with the localized deformation in the ionic polymer at the interface with the electrodes, which are not captured by the classical Euler-Bernoulli beam theory. This work paves the way to the development of more sophisticated structural theories for IPMCs and analogous active materials, affording an accurate description of deformations at a limited computational cost.