Modelling compression sensing in ionic polymer metal composites

Valentina Volpini, Lorenzo Bardella, Andrea Rodella

DICATAM, Faculty of Engineering, University of Brescia, Via Branze, 4325123, Brescia, Italy

Youngsu Cha

Korea Institute of Science and Technology, Center for Robotics Research, 5, Hwarang-ro 14-gil, Seongbuk-gu, Seoul, 02792, Republic of Korea

Maurizio Porfiri

Department of Mechanical and Aerospace Engineering, Tandon School of Engineering Polytechnic Institute of New York University, Six MetroTech Center, Brooklyn, NY 11201, USA

Abstract

Ionic Polymer Metal Composites (IPMCs) consist of an ionomeric membrane, including mobile counterions, sandwiched between two thin noble metal electrodes. IPMCs find application as sensors and actuators, where an imposed mechanical loading generates a voltage across the electrodes, and, vice versa, an imposed electric field causes deformation. Here, we present a predictive modelling approach to elucidate the dynamic sensing response of IPMCs subject to a time-varying through-the-thickness compression ("compression sensing"). The model relies on the continuum theory recently developed by Porfiri and co-workers, which couples finite deformations to the modified Poisson-Nernst-Planck (PNP) system governing the IPMC electrochemistry. For the "compression sensing" problem we establish a perturbative closed-form solution along with a Finite Element (FE) solution. The systematic comparison between these two solutions is a central contribution of this study, offering insight on accuracy and mathematical complexity. The method of matched asymptotic expansions is employed to find the analytical solution. To this end, we uncouple the force balance from the modified PNP system and separately linearise the PNP equations in the ionomer bulk and in the boundary layers at the ionomer-electrode interfaces. Comparison with FE results for the fully coupled nonlinear system demonstrates the accuracy of the analytical solution to describe IPMC sensing for moderate deformation levels. We finally demonstrate the potential of the modelling scheme to accurately reproduce experimental results from the literature. The proposed model is expected to aid in the design of IPMC sensors, contribute to an improved understanding of IPMC electrochemomechanical response, and offer insight into the role of nonlinear phenomena across mechanics and electrochemistry.

Author Keywords: Ionic polymer metal composites; sensing; finite deformations; electrochemistry; matched asymptotic expansions; finite element method