Asymptotic analysis of compression sensing in ionic polymer metal composites: the role of interphase regions with variable properties

Valentina Volpini and Lorenzo Bardella

Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Via Branze, 4325123, Brescia, Italy

Abstract

Ionic Polymer Metal Composites (IPMCs) consist of two noble metal electrodes plating an electroactive polymeric membrane, referred to as ionomer, which is electroneutralised by a solvent including mobile ions. The IPMC manufacturing leads to thin interphase regions next to the electrodes, the so-called Composite Layers (CLs), in which metal atoms occupy interstitial sites within the ionomer. In this work we extend previous efforts of our group on IPMC compression sensing to include the important effect of CLs, where large variations of the electrochemical properties occur. In IPMC compression sensing the application of a through-the-thickness displacement leads to a short-circuit electric response, here assumed to be governed by a linearised modified Poisson-Nernst-Planck (PNP) system of partial differential equations (PDEs), to be solved for the time-evolving electric potential and mobile ions concentration as functions of the displacement field evaluated through the linear momentum balance. The variation of material properties in the CLs requires the simultaneous integration of the governing system of PDEs in three regions: the membrane and the two CLs. To this purpose, we resort to the perturbative method of matched asymptotic expansions. Except for a numerical inverse Laplace transform, this allows us to obtain an analytical solution through which we establish an equivalent circuit model elucidating the main features of the IPMC sensing behaviour. We validate and discuss the analytical solution through comparison with finite element analyses, whereby we also numerically solve the nonlinear modified PNP systems fully coupled with the linear momentum balance accounting for the electrochemical stresses. We finally provide an insight into the role of CLs in the IPMC sensing behaviour, by assessing its sensitivity to some key parameters. We expect the obtained results to aid the design of optimised IPMC sensors.

Author Keywords: Ionic polymer metal composite; composite layer; Sensing; Electrochemomechanics; Poisson-Nernst-Planck system; Boundary layer; Perturbative problem; Matched asymptotic expansion; Finite element method