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

Valentina Volpini; Lorenzo Bardella; Valentina Volpini; Lorenzo Bardella

doi:10.3934/mine.2021014

Mathematics in Engineering

2021, Volume 3, Issue 2: 1-31. doi: 10.3934/mine.2021014

Previous Article Next Article

Research article

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

Valentina Volpini ,
Lorenzo Bardella ^,

Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, via Branze, 43, 25123 Brescia, Italy

Received: 27 November 2019 Accepted: 06 April 2020 Published: 18 June 2020

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 shortcircuit 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 some 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.
- ionic polymer metal composite,
- composite layer,
- sensing,
- electrochemomechanics,
- Poisson-Nernst-Planck system,
- boundary layer,
- perturbative problem,
- matched asymptotic expansion,
- finite element method
Citation: Valentina Volpini, Lorenzo Bardella. Asymptotic analysis of compression sensing in ionic polymer metal composites: The role of interphase regions with variable properties[J]. Mathematics in Engineering, 2021, 3(2): 1-31. doi: 10.3934/mine.2021014

Related Papers:

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 shortcircuit 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 some 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.

References

[1]	Shahinpoor M, Kim KJ (2001) Ionic polymer-metal composites: I. Fundamentals. Smart Mater Struct 10: 819-833.
[2]	Oguro K, Takenaka H, Kawam Y (1993) Actuator element. US Patent 5268082.
[3]	Kim KJ, Shahinpoor M (2003) Ionic polymer-metal composites: II. Manufacturing techniques. Smart Mater Struct 12: 65-79.
[4]	Cha Y, Porfiri M (2014) Mechanics and electrochemistry of ionic polymer metal composites. J Mech Phys Solids 71: 156-178.
[5]	Wallmersperger T, Akle BJ, Leo DJ, et al. (2008) Electrochemical response in ionic polymer transducers: An experimental and theoretical study. Compos Sci Technol 68: 1173-1180.
[6]	Porfiri M (2008) Charge dynamics in ionic polymer metal composites. J Appl Phys 104: 104915.
[7]	Nemat-Nasser S, Li JY (2000) Electromechanical response of ionic polymer-metal composites. J Appl Phys 87: 3321-3331.
[8]	Aureli M, Porfiri M (2013) Nonlinear sensing of ionic polymer metal composites. Continuum Mech Therm 25: 273-310.
[9]	Leronni A, Bardella L (2019) Influence of shear on sensing of ionic polymer metal composites. Eur J Mech A-Solid 77: 103750.
[10]	Porfiri M (2019) Sensing mechanical deformation via ionic polymer metal composites: A primer. IEEE Instru Meas Mag 22: 8868271.
[11]	Nemat-Nasser S (2002) Micromechanics of actuation of ionic polymer-metal composites. J Appl Phys 92: 2899-2915.
[12]	Carrico JD, Tyler T, Leang KK (2017) A comprehensive review of select smart polymeric and gel actuators for soft mechatronics and robotics applications: fundamentals, freeform fabrication, and motion control. Int J Smart Nano Mater 8: 144-213.
[13]	Porfiri M, Leronni A, Bardella L (2017) An alternative explanation of back-relaxation in ionic polymer metal composites. Extreme Mech Lett 13: 78-83.
[14]	Boldini A, Porfiri M (2020) Multiaxial deformations of ionic polymer metal composites. Int J Eng Sci 149: 103227.
[15]	Tiwari R, Kim KJ (2010) Effect of metal diffusion on mechanoelectric property of ionic polymermetal composite. Appl Phys Lett 97: 244104.
[16]	Cha Y, Aureli M, Porfiri M (2012) A physics-based model of the electrical impedance of ionic polymer metal composites. J Appl Phys 111: 124901.
[17]	Cha Y, Porfiri M (2013) Bias-dependent model of the electrical impedance of ionic polymer metal composites. Phys Rev E 87: 022403.
[18]	Borukhov I, Andelman D, Orland H (1997) Steric effects in electrolytes: A modified poissonboltzmann equation. Phys Rev Lett 79: 435-438.
[19]	Kilic MS, Bazant MZ, Ajdari A (2007) Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging. Phys Rev E 75: 021502.
[20]	Kilic MS, Bazant MZ, Ajdari A (2007) Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations. Phys Rev E 75: 021503.
[21]	Porfiri M (2009) Influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites. Phys Rev E 79: 041503.
[22]	Aureli M, Porfiri M (2012) Effect of electrode surface roughness on the electrical impedance of ionic polymer-metal composites. Smart Mater Struct 21: 105030.
[23]	Volpini V, Bardella L, Rodella A, et al. (2017) Modelling compression sensing in ionic polymer metal composites. Smart Mater Struct 2: 035030.
[24]	Kocer BY (2014) Experimental study of ionic polymer metal transducers: characterization of transient response in sensing, PhD thesis of Swanson School of Engineering, University of Pittsburgh.
[25]	Porfiri M, Sharghi H, Zhang P (2018) Modeling back-relaxation in ionic polymer metal composites: The role of steric effects and composite layers. J Appl Phys 123: 014901.
[26]	Verhulst F (2005) Methods and Applications of Singular Perturbations, Springer.
[27]	Cheng DK, (1983) Field and Wave Electromagnetics, Addison-Wesley Publishing Company.
[28]	Wallmersperger T, Akle BJ, Leo DJ, et al. (2004) Coupled chemo-electro-mechanical formulation for ionic polymer gels-numerical and experimental investigations. Mech Mater 36: 411-420.
[29]	Crank J, (1975) The Mathematics of Diffusion, Oxford University Press.
[30]	Wolfram S (2011) Wolfram Mathematica — Release 8.0.1.0, Champaign, IL, USA.
[31]	Bard AJ, Faulkner LR (2001) Electrochemical Methods. Fundamentals and Applications, John Wiley & Sons.
[32]	Borukhov I, Andelman D, Orland H (2000) Adsorption of large ions from an electrolyte solution: A modified Poisson-Boltzmann equation. Electrochim Acta 46: 221-229.
[33]	Carrico JD, Traeden NW, Aureli M, et al. (2015) Fused filament 3D printing of ionic polymer-metal composites (IPMCs). Smart Mater Struct 24: 125021.
[34]	Stalbaum T, Trabia S, Hwang T, et al. (2018) Guidelines for making ionic polymer-metal composite (IPMC) materials as artificial muscles by advanced manufacturing methods, In: Bar-Cohen, Y., Advances in Manufacturing and Processing of Materials and Structures, CRC Press, 379-395.

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)