Skip to main content
SpringerLink
Log in

Modeling the response of polymer–ionic liquid electromechanical actuators

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A model is derived for the electromechanical response of a porous membrane swollen with an ionic liquid and sandwiched between two nanoscale-thin electrodes under DC current. Bending of the membrane is induced by pressure in pores arising due to diffusion of ions through a network of nanochannels. Transport of ions is governed by the applied electric field and redox reactions at the surfaces of electrodes. Constitutive equations for the mechanical response of a porous medium and diffusion of ions are derived by means of the free energy imbalance inequality under an arbitrary deformation with finite strains. Under the assumption regarding small strains, but finite changes in concentrations of ions and the electrostatic potential, an explicit expression is developed for the curvature of the membrane. A steady-state solution to the Poisson–Nernst–Planck equations is obtained by means of the method of matched asymptotic expansions. Results of numerical analysis demonstrate the ability of the constitutive equations to describe observations. In particular, the model provides an explanation for bending to the anode and to the cathode and predicts qualitatively the effects of applied voltage, concentration of ionic liquid, and thickness of a membrane on its curvature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shahinpoor M., Kim K.J.: Ionic polymer–metal composites: I. Fundamentals. Smart Mater. Struct. 10, 819–833 (2001)

    Article  Google Scholar 

  2. Kim K.J., Shahinpoor M.: Ionic polymer–metal composites: II. Manufacturing techniques. Smart Mater. Struct. 12, 65–79 (2003)

    Article  Google Scholar 

  3. Shahinpoor M., Kim K.J.: Ionic polymer–metal composites: III. Modeling and simulation as biomimetic sensors, actuators, transducers, and artificial muscles. Smart Mater. Struct. 13, 1362–1388 (2004)

    Article  Google Scholar 

  4. Tiwari R., Garcia E.: The state of understanding of ionic polymer metal composite architecture: a review. Smart Mater. Struct. 20, 083001 (2011)

    Article  Google Scholar 

  5. Jo C., Pugal D., Oh I.-K., Kim K.J., Asaka K.: Recent advances in ionic polymer–metal composite actuators and their modeling and applications. Prog. Polym. Sci. 38, 1037–1066 (2013)

    Article  Google Scholar 

  6. Green M.D., Wang D., Hempc S.T., Choi J.-H., Winey K.I., Heflin J.R., Long T.E.: Synthesis of imidazolium ABA triblock copolymers for electromechanical transducers. Polymer 53, 3677–3686 (2012)

    Article  Google Scholar 

  7. Imaizumi S., Kokubo H., Watanabe M.: Polymer actuators using ion-gel electrolytes prepared by self-assembly of ABA-triblock copolymers. Macromolecules 45, 401–409 (2012)

    Article  Google Scholar 

  8. Wu T., Wang D., Zhang M., Heflin J.R., Moore R.B., Long T.E.: RAFT synthesis of ABA triblock copolymers as ionic liquid-containing electroactive membranes. ACS Appl. Mater. Interfaces 4, 6552–6559 (2012)

    Article  Google Scholar 

  9. Lee J.-W., Yu S., Hong S.M., Koo C.M.: High-strain air-working soft transducers produced from nanostructured block copolymer ionomer/silicate/ionic liquid nanocomposite membranes. J. Mater. Chem. C 1, 3784–3793 (2013)

    Article  Google Scholar 

  10. Jangu C., Wang J.-H.H., Wang D., Sharick S., Heflin J.R., Winey K.I., Colby R.H., Long T.E.: Well-defined imidazolium ABA triblock copolymers as ionic-liquid-containing electroactive membranes. Macromol. Chem. Phys. 215, 1319–1331 (2014)

    Article  Google Scholar 

  11. Bennett M.D., Leo D.J.: Ionic liquids as stable solvents for ionic polymer transducers. Sens. Actuators A 115, 79–90 (2004)

    Article  Google Scholar 

  12. Green M.D., Long T.E.: Designing imidazole-based ionic liquids and ionic liquid monomers for emerging technologies. Polym. Rev. 49, 291–314 (2009)

    Article  Google Scholar 

  13. Bideau, J.Le, Viau, L., Vioux, A.: Ionogels, ionic liquid based hybrid materials. Chem. Soc. Rev. 40, 907–925 (2011)

  14. Kikuchi K., Tsuchitani S.: Nafion-based polymer actuators with ionic liquids as solvent incorporated at room temperature. J. Appl. Phys. 106, 053519 (2009)

    Article  Google Scholar 

  15. Lin J., Liu Y., Zhang Q.M.: Charge dynamics and bending actuation in Aquivion membrane swelled with ionic liquids. Polymer 52, 540–546 (2011)

    Article  Google Scholar 

  16. Kim D., Kim K.J., Nam J.-d., Palmre V.: Electro-chemical operation of ionic polymer–metal composites. Sens. Actuators B 155, 106–113 (2011)

    Article  Google Scholar 

  17. Liu Y., Ghaffari M., Zhao R., Lin J.-H., Lin M., Zhang Q.M.: Enhanced electromechanical response of ionic polymer actuators by improving mechanical coupling between ions and polymer matrix. Macromolecules 45, 5128–5133 (2012)

    Article  Google Scholar 

  18. Zhu Z., Chang L., Asaka K., Wang Y., Chen H., Zhao H., Li D.: Comparative experimental investigation on the actuation mechanisms of ionic polymer–metal composites with different backbones and water contents. J. Appl. Phys. 115, 124903 (2014)

    Article  Google Scholar 

  19. Nemat-Nasser S., Zamani S., Tor Y.: Effect of solvents on the chemical and physical properties of ionic polymer–metal composites. J. Appl. Phys. 99, 104902 (2006)

    Article  Google Scholar 

  20. Liu Y., Liu S., Lin J., Wang D., Jain V., Montazami R., Heflin J.R., Li J., Madsen L., Zhang Q.M.: Ion transport and storage of ionic liquids in ionic polymer conductor network composites. Appl. Phys. Lett. 96, 223503 (2010)

    Article  Google Scholar 

  21. Akle B.J., Leo D.J.: Characterization and modeling of extensional and bending actuation in ionomeric polymer transducers. Smart Mater. Struct. 16, 1348–1360 (2007)

    Article  Google Scholar 

  22. Akle B.J., Habchi W., Wallmersperger T., Akle E.J., Leo D.J.: High surface area electrodes in ionic polymer transducers: numerical and experimental investigations of the electro-chemical behavior. J. Appl. Phys. 109, 074509 (2011)

    Article  Google Scholar 

  23. Nemat-Nasser S., Wu Y.: Tailoring the actuation of ionic polymer–metal composites. Smart Mater. Struct. 15, 909–923 (2006)

    Article  Google Scholar 

  24. Lee J.-W., Yoo Y.-T.: Anion effects in imidazolium ionic liquids on the performance of IPMCs. Sens. Actuators B 137, 539–546 (2009)

    Article  Google Scholar 

  25. Okuzaki H., Takagi S., Hishiki F., Tanigawa R.: Ionic liquid/polyurethane/PEDOT:PSS composites for electro-active polymer actuators. Sens. Actuators B 194, 59–63 (2014)

    Article  Google Scholar 

  26. Nemat-Nasser S., Li J.Y.: Electromechanical response of ionic polymer–metal composites. J. Appl. Phys. 87, 3321–3331 (2000)

    Article  Google Scholar 

  27. Naji L., Chudek J.A., Abel E.W., Baker R.T.: Electromechanical behaviour of Nafion-based soft actuators. J. Mater. Chem. B 1, 2502–2514 (2013)

    Article  Google Scholar 

  28. Festina N., Plesse C., Pirim P., Chevrot C., Vidal F.: Electro-active interpenetrating polymer networks actuators and strain sensors: fabrication, position control and sensing properties. Sens. Actuators B 193, 82–88 (2014)

    Article  Google Scholar 

  29. Imaizumi S., Kato Y., Kokubo H., Watanabe M.: Driving mechanisms of ionic polymer actuators having electric double layer capacitor structures. J. Phys. Chem. B 116, 5080–5089 (2012)

    Article  Google Scholar 

  30. Bennett M.D., Leo D.J., Wilkes G.L., Beyer F.L., Pechar T.W.: A model of charge transport and electromechanical transduction in ionic liquid–swollen Nafion membranes. Polymer 47, 6782–6796 (2006)

    Article  Google Scholar 

  31. Kwon K.-S., Ng T.N.: Improving electroactive polymer actuator by tuning ionic liquid concentration. Org. Electron. 15, 294–298 (2014)

    Article  Google Scholar 

  32. Hong W., Almomani A., Montazami R.: Influence of ionic liquid concentration on the electromechanical performance of ionic electroactive polymer actuators. Org. Electron. 15, 2982–2987 (2014)

    Article  Google Scholar 

  33. Montazami R., Liu S., Liu Y., Wang D., Zhang Q., Heflin J.R.: Thickness dependence of curvature, strain, and response time in ionic electroactive polymer actuators fabricated via layer-by-layer assembly. J. Appl. Phys. 109, 104301 (2011)

    Article  Google Scholar 

  34. Hatipoglu G., Liu Y., Zhao R., Yoonessi M., Tigelaar D.M., Tadigadapa S., Zhang Q.M.: A highly aromatic and sulfonated ionomer for high elastic modulus ionic polymer membrane micro-actuators. Smart Mater. Struct. 21, 055015 (2012)

    Article  Google Scholar 

  35. Gong Y., Fan J., Tang C.-y., Tsui C.-p.: Numerical simulation of dynamic electro-mechanical response of ionic polymer–metal composites. J. Bionic Eng. 8, 263–272 (2011)

    Article  Google Scholar 

  36. de Gennes, P.G., Okumura, K., Shahinpoor, M., Kim, K.J.: Mechanoelectric effects in ionic gels. Europhys. Lett. 50, 513–518 (2000)

  37. Yamaue T., Mukai H., Asaka K., Doi M.: Electrostress diffusion coupling model for polyelectrolyte gels. Macromolecules 38, 1349–1356 (2005)

    Article  Google Scholar 

  38. Doi M., Takahashi K., Yonemoto T., Yamaue T.: Electro-mechanical coupling in ionic gels. React. Funct. Polym. 73, 891–893 (2013)

    Article  Google Scholar 

  39. Farinholt K., Leo D.J.: Modelling of electromechanical charge sensing in ionic polymer transducers. Mech. Mater. 36, 421–433 (2004)

    Article  Google Scholar 

  40. Nemat-Nasser S., Zamani S.: Modeling of electromechanical response of ionic polymer–metal composites with various solvents. J. Appl. Phys. 100, 064310 (2006)

    Article  Google Scholar 

  41. Wallmersperger T., Leo D.J., Kothera C.S.: Transport modeling in ionomeric polymer transducers and its relationship to electromechanical coupling. J. Appl. Phys. 101, 024912 (2007)

    Article  Google Scholar 

  42. Bufalo G.D., Placidi L., Porfiri M.: A mixture theory framework for modeling the mechanical actuation for ionic polymer metal composites. Smart Mater. Struct. 17, 045010 (2008)

    Article  Google Scholar 

  43. Wallmersperger T., Horstmann A., Kroplin B., Leo D.J.: Thermodynamical modeling of the electromechanical behavior of ionic polymer metal composites. J. Intell. Mater. Syst. Struct. 20, 741–750 (2009)

    Article  Google Scholar 

  44. Nardinocchi P., Pezzulla M., Placidi L.: Thermodynamically based multiphysic modeling of ionic polymer metal composites. J. Intell. Mater. Syst. Struct. 22, 1887–1897 (2011)

    Article  Google Scholar 

  45. Nardinocchi P., Pezzulla M.: Curled actuated shapes of ionic polymer metal composites strips. J. Appl. Phys. 113, 224906 (2013)

    Article  Google Scholar 

  46. Schicker D., Wallmersperger T.: Modeling and simulation of the chemo-electro-mechanical behavior of ionic polymer–metal composites. J. Appl. Phys. 114, 163709 (2013)

    Article  Google Scholar 

  47. Aureli M., Porfiri M.: Nonlinear sensing of ionic polymer metal composites. Contin. Mech. Thermodyn. 25, 273–310 (2013)

    Article  MathSciNet  Google Scholar 

  48. Caponetto R., De Luca V., Graziani S., Sapuppo F.: An optimized frequency-dependent multiphysics model for an ionic polymer–metal composite actuator with ethylene glycol as the solvent. Smart Mater. Struct. 22, 125016 (2013)

    Article  Google Scholar 

  49. Cha Y., Porfiri M.: Mechanics and electrochemistry of ionic polymer metal composites. J. Mech. Phys. Solids 71, 156–178 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  50. Attaran A., Brummund J., Wallmersperger T.: Modeling and simulation of the bending behavior of electrically-stimulated cantilevered hydrogels. Smart Mater. Struct. 24, 035021 (2015)

    Article  Google Scholar 

  51. Marekha B.A., Kalugin O.N., Bria M., Buchner R., Idrissi A.: Translational diffusion in mixtures of imidazolium ILs with polar aprotic molecular solvents. J. Phys. Chem. B 118, 5509–5517 (2014)

    Article  Google Scholar 

  52. Zhu Z., Asaka K., Chang L., Takagi K., Chen H.: Multiphysics of ionic polymer–metal composite actuator. J. Appl. Phys. 114, 084902 (2013)

    Article  Google Scholar 

  53. Zhu Z., Asaka K., Chang L., Takagi K., Chen H.: Physical interpretation of deformation evolvement with water content of ionic polymer–metal composite actuator. J. Appl. Phys. 114, 184902 (2013)

    Article  Google Scholar 

  54. Porfiri M.: Influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites. Phys. Rev. E 79, 041503 (2009)

    Article  Google Scholar 

  55. Shen Q., Kim K.J., Wang T.: Electrode of ionic polymer–metal composite sensors: modeling and experimental investigation. J. Appl. Phys. 115, 194902 (2014)

    Article  Google Scholar 

  56. Chang L., Asaka K., Zhu Z., Wang Y., Chen H., Li D.: Effects of surface roughening on the mass transport and mechanical properties of ionic polymer–metal composite. J. Appl. Phys. 115, 244901 (2014)

    Article  Google Scholar 

  57. Lee A.A., Colby R.H., Kornyshev A.A.: Statics and dynamics of electroactuation with single-charge-carrier ionomers. J. Phys. Condens. Matter 25, 082203 (2013)

    Article  Google Scholar 

  58. Lee A.A., Colby R.H., Kornyshev A.A.: Electroactuation with single charge carrier ionomers: the roles of electrostatic pressure and steric strain. Soft Matter 9, 3767–3776 (2013)

    Article  Google Scholar 

  59. Abu-Rjal R., Chinaryan V., Bazant M.Z., Rubinstein I., Zaltzman B.: Effect of concentration polarization on permselectivity. Phys. Rev. E 89, 012302 (2014)

    Article  Google Scholar 

  60. Bazant M.Z., Chu K.T., Bayly B.J.: Current–voltage relations for electrochemical thin films. SIAM J. Appl. Math. 65, 1463–1484 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  61. van Soestbergen, M., Biesheuvel, P.M., Bazant, M.Z.: Diffuse-charge effects on the transient response of electrochemical cells. Phys. Rev. E 81, 021503 (2010)

  62. Kamran, K., van Soestbergen, M., Huinink, H.P., Pel, L.: Inhibition of electrokinetic ion transport in porous materials due to potential drops induced by electrolysis. Electrochim. Acta 78, 229–235 (2012)

  63. Andersen M.B., Rogers D.M., Mai J., Schudel B., Hatch A.V., Rempe S.B., Mani A.: Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes. Langmuir 30, 7902–7912 (2014)

    Article  Google Scholar 

  64. Scherer G.W., Prevost J.H., Wang Z.-H.: Bending of a poroelastic beam with lateral diffusion. Int. J. Solids Struct. 46, 3451–3462 (2009)

    Article  MATH  Google Scholar 

  65. Boutin C.: Behavior of poroelastic isotropic beam derivation by asymptotic expansion method. J. Mech. Phys. Solids 60, 1063–1087 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  66. Bonnefont A., Argoul F., Bazant M.Z.: Analysis of diffuse-layer effects on time-dependent interfacial kinetics. J. Electroanal. Chem. 500, 52–61 (2001)

    Article  Google Scholar 

  67. Barcilon V., Chen D.-P., Eisenberg R.S., Jerome J.W.: Qualitative properties of steady-state Poisson–Nernst–Planck systems: perturbation and simulation study. SIAM J. Appl. Math. 57, 631–648 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  68. Davidson J.Y., Goulbourne N.C.: Nonlinear capacitance and electrochemical response of ionic liquid–ionic polymers. J. Appl. Phys. 109, 084901 (2011)

    Article  Google Scholar 

  69. Bustamante R., Dorfmann A., Ogden R.W.: On electric body forces and Maxwell stresses in nonlinearly electroelastic solids. Int. J. Eng. Sci. 47, 1131 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  70. Paddison S.J., Reagor D.W, Zawodzinski T.A.: High frequency dielectric studies of hydrated Nafion. J. Electroanal. Chem. 459, 91–97 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, Aalborg University, Fibigerstraede 16, Aalborg, 9220, Denmark

    A. D. Drozdov

Authors
  1. A. D. Drozdov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. D. Drozdov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Drozdov, A.D. Modeling the response of polymer–ionic liquid electromechanical actuators. Acta Mech 227, 437–465 (2016). https://doi.org/10.1007/s00707-015-1471-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1471-7

Keywords

Search

Navigation