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Polyelectrolyte Gels

Basics, Modelling and Simulation
  • Thomas Wallmersperger
  • Bernd Kröplin
  • Rainer W. Gülch
Part of the International Centre for Mechanical Sciences book series (CISM, volume 462)

Abstract

The increasing precision of shapes and displacements required by structures in both, aerospace and precision mechanics, as well as the desire of health monitoring of damaged components, lead to the concept of structures with actuatoric and sensoric capabilities. The basis for the adaptive structures are multi-functional materials.

A very promising representative of these materials are electroactive polymers (EAP). In the first section of this paper we give a short overview on this group of materials. In the following we focus our interest on polyelectrolyte gels which is one key material of EAP. These gels - consisting of a polymer network with fixed ionizable groups and a liquid phase with mobile ions - are distinguished by enormous swelling capabilities under the influence of external physical or chemical stimuli. These properties make them very attractive for a new generation of “pseudomuscular” actuators.

In the present work we investigate chemically and electrically stimulated polymer gels. At first we give a model based on the theory of “swelling of network structures” by Flory (1953). In the third section we present a coupled chemo-electro-mechanical multi-field formulation which is capable to describe the phenomena occurring in the different fields. Then, an overview over the space-time finite element discretization method is given. These unconditionally stable finite elements give the possibility to treat the phenomena in space and time equally.

In the last section, chemical as well as electrical stimulation is considered. The numerical simulation is computed for all the fields involved. The numerical results of the electric potential show a promising correlation with experiments in which the Donnan potential has been registered in PAAm/PAA gels with a new microelectrode technique. For anionic gels, in both theory and experiment “hyperpolarisation”, i.e. increased negativity, can be found on the anode-side of the gel and “depolarisation” on the cathode-side. These changes in the electric potential, which are supposed to affect swelling or deswelling of polyelectrolyte gels, lead to bending deformations of the gel.

Keywords

Applied Electric Field Electroactive Polymer Intrinsic Time Scale Prescribe Strain Time Slab 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. Banks, H. T., Smith, R. C., Wang, Y., 1996. Smart Material Structures: Modeling, Estimation and Control. John Wiley and Sons Ltd, Ch. Smart Materials Technology and Control Application.Google Scholar
  2. Bar-Cohen, Y., 2001. Electroactive Polymer (EAP) Actuators as Artificial Muscles–Reality, Potential, and Challenges. Vol. PM 98. SPIE Press, Bellingham, WA, USA, Ch. EAP History, Current Status, and Infrastructure, pp. 4–44.Google Scholar
  3. Bar-Cohen, Y., Leary, S., Yavrouian, A., Oguro, K., Tadokoro, S., Harrison, J., Smith, J., Su, J., 2000. Challenges to the application of IPMC as actuators of planetary mechanisms. In: Bar-Cohen, Y. (Ed.), 7th International Symposium on Smart Structures and Materials. Electroactive Polymer Actuators and Devices. SPIE, pp. 140–146, newport Beach, 2000.Google Scholar
  4. Barth, T. J., Sethian, J. A., 1997. Numerical schemes for the Hamilton-Jacobi and level set equa- tions on triangulated domains. NAS report NAS-97–022, NASA Ames Research Center.Google Scholar
  5. Brock, D., Lee, W., Segalman, D., Witkowski, W., 1994. A dynamic model of a linear actuator based on polymer hydrogel. J. Intelligent Material Systems and Structures 5, 764–771.CrossRefGoogle Scholar
  6. Chiarelli, P., Basser, P. J., Rossi, D. D., Goldstein, S., 1992. The dynamics of a hydrogel strip. Biorheology, 383–398.Google Scholar
  7. deGennes, P. G., Okumura, K., Shahinpoor, M., Kim, K. J., 2000. Mechanoelectric effects in ionic gels. Europhysics Letters 50 (4), 513–518.CrossRefGoogle Scholar
  8. Doi, M., Matsumoto, M., Hirose, Y., 1992. Deformation of ionic polymer gels by electric fields. Macromolecules 25, 5504–5511.CrossRefGoogle Scholar
  9. Finkelmann, H., Kock, H. J., Rehage, G., 1981. Investigations on liquid crystalline silozanes: 3.liquid crystalline elastomer - a new type of liquid crystalline material. Makromolecular Chemistry 2, 317.Google Scholar
  10. Flory, P. J., 1953. Principles of Polymer Chemistry. Cornell University Press, Ithaca, NY.Google Scholar
  11. Grimshaw, P. E., Nussbaum, J. H., Grodzinsky, A. J., Yarmush, M. L., 1990. Kinetics of electrically and chemically induced swelling in polyelectrolyte gels. J. Chem. Phys. 93 (6), 4462–4472.CrossRefGoogle Scholar
  12. Grohmann, B., Konstanzer, P., Lay, A., Wallmersperger, T., Kröplin, B., 11.-12. November 1998. On the principle of adaptive structure systems. In: NAFEMS Seminar “FEM-Anwendungen für adaptive Struktursysteme”. NAFEMS, Magdeburg.Google Scholar
  13. Grohmann, B. A., 2002. Stabilized space-time finite elements for transonic aeroelasticity. Ph.D. thesis, ISD, Universität Stuttgart, shaker Verlag, Aachen.Google Scholar
  14. Gulch, R. W., Holdenried, J., Weible, A., Wallmersperger, T., Kröplin, B., 2000. Polyelectrolyte gels in electric fields: A theoretical and experimental approach. In: Bar-Cohen, Y. (Ed.), 7th International Symposium on Smart Structures and Materials. Vol. 3987 of Electroactive Polymer Actuators and Devices. SPIE, pp. 193–202, newport Beach, 2000.Google Scholar
  15. Hughes, T. J. R., 1987. The Finite Element Method - Linear Static and Dynamic Finite Element Analysis. Prentice-Hall.Google Scholar
  16. Hughes, T. J. R., Franca, L. P., Hulbert, G. M., 1989. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 75, 173–189.Google Scholar
  17. Hughes, T. J. R., Hauke, G., Jansen, K., Johan, Z., 1994. Stabilized finite element methods in fluids: Inspirations, origins, status and recent developments. In: Hughes, T. J. R., Onate, E., Zienkiewicz, O. C. (Eds.), Recent Developments in Finite Element Analysis - A Book dedicated to Robert L. Taylor. CIMNE, Barcelona.Google Scholar
  18. Hughes, T. J. R., Hulbert, G. M., 1988. Space-time finite element methods for elastodynamics: formulations and error estimates. Comput. Methods Appl. Mech. Engrg. 66, 339–363.Google Scholar
  19. Hulbert, G. M., 1989. Space-Time Finite Element Methods for Second-Order Hyperbolic Equations. Ph.D. thesis, Stanford University.Google Scholar
  20. Hulbert, G. M., 1992. Time finite element methods for structural dynamics. Int. J. Nu-mer. Meth. Eng. 33, 307–331.Google Scholar
  21. Hulbert, G. M., 1994. A unified set of single-step asymptotic annihilation algorithms for structural dynamics. Comput. Methods Appl. Mech. Engrg. 113, 1–9.Google Scholar
  22. Johnson, C., 1985. Finite Elements in Fluids. John Wiley Sons.Google Scholar
  23. Johnson, C., 1993. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Comput. Methods Appl. Mech. Engrg. 107, 117–129.Google Scholar
  24. Kim, J., Kim, J.-Y., Choe, S. J., 2000. Electro-active papers: its possibility as actuators. In: Bar-Cohen, Y. (Ed.), 7th International Symposium on Smart Structures and Materials. Vol. 3987 of Electroactive Polymer Actuators and Devices. SPIE, newport Beach, 2000.Google Scholar
  25. Lee, W., 1996. Polymer gel based actuator: Dynamic model of gel for real time control. Ph.D. thesis, Massachusetts Institute of Technology, Boston, USA.Google Scholar
  26. Nemat-Nasser, S., Li, J. Y., 2000. Electromechanical response of ionic polymer-metal composites. Journal of Applied Physics 87 (7), 3321–3331.CrossRefGoogle Scholar
  27. Neubrand, W., 1999. Modellbildung and Simulation von Elektromembranverfahren. Ph.D. thesis, Universität Stuttgart.Google Scholar
  28. Oguro, K., Kawami, Y., Takenaka, H., 1992. Bending of an ion-conducting polymer film-electrode composite by an electric stimulus at low voltage. Trans. Journal of Micromachine Society 5, 27–30.Google Scholar
  29. Ohmine, I., Tanaka, T., 1982. Salt effects on the phase transition of ionic gels. Journal of Chemical Physics 77 (11), 5725–5729.CrossRefGoogle Scholar
  30. Pelrine, R., Kornbluh, R., Pei, Q., Joseph, J., 2000. High speed electrically actuated elastomers with strain greater than 100%. Science 287, 836–839.CrossRefGoogle Scholar
  31. Ricka, J., Tanaka, T., 1984. Swelling of ionic gels: Quantitative performance of the donnan theory. Macromolecules 17, 2917–2921.Google Scholar
  32. Schröder, U., Oppermann, W., 1996. Physical Properties of Polymeric Gels. John Wiley and Sons, Ch. Properties of Polyelectrolyte Gels, pp. 19–38.Google Scholar
  33. Schröder, U. P., 1994. Experimentelle and theoretische Untersuchungen an hochgequollenen hydrogelen. Ph.D. thesis, Institut für Textil and Faserchemie der Universität Stuttgart.Google Scholar
  34. Shahinpoor, M., 1995. Micro-electro-mechanics of ionic polymeric gels as electrically controllable artificial muscles. J. Intelligent Material Systems and Structures 6, 307–314.CrossRefGoogle Scholar
  35. Shahinpoor, M., 2000. Elastically-activated artificial muscles made with liquid crystal elastomers. In: Bar-Cohen, Y. (Ed.), 7th International Symposium on Smart Structures and Materials. Vol. 3987 of Electroactive Polymer Actuators and Devices. SPIE, pp. 187–192, newport Beach, 2000.Google Scholar
  36. Shakib, F., 1988. Finite element analysis of the compressible euler and navier-stokes equations. Ph.D. thesis, Stanford University.Google Scholar
  37. Shibayama, M., Tanaka, T., 1993. Volume phase transition and related phenomena of polymer gels. In: Responsive Gels: Volume Transitions I. Vol. 109 of Advances in Polymer Science. Springer-Verlag, pp. 1–62.Google Scholar
  38. Shiga, T., Kurauchi, T., 1990. Deformation of polyelectrolyte gels under the influence of electric field. J. of Applied Polymer Science 39, 2305–2320.CrossRefGoogle Scholar
  39. Soulaimani, A., Fortin, M., 1994. Finite element solution of compressible viscous flow using conservative variables. Comput. Methods Appl. Mech. Engrg. 118, 319–350.Google Scholar
  40. Tezduyar, T. E., Behr, M., 1992. A new strategy for finite element computations involving moving boundaries and interfaces — The deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput. Methods Appl. Mech. Engrg. 94,339— 351.Google Scholar
  41. Thompson, L. L., Sept. 1995. A multi-field space-time finite element method for structural acoustics. In: Design Engineering Technical Conferences. Vol. 3 — Part B. ASME, Boston, pp. 49–64.Google Scholar
  42. Treloar, L. R. G., 1958. The Physics of Rubber Elasticity. Oxford University Press.Google Scholar
  43. Turrin, S., 2003. Protein-based polymers as pseudo-muscular actuators. Master’s thesis, Institut für Statik und Dynamik der Luft-und Raumfahrtkonstruktionen ( ISD ), Universität Stuttgart.Google Scholar
  44. Wallmersperger, T., 2003. Modellierung und Simulation stimulierbarer polyelektrolytischer Gele. Ph.D. thesis, ISD, Universität Stuttgart, Fortschritt-Berichte VDI Reihe 5, VDI-Verlag, Düsseldorf.Google Scholar
  45. Wallmersperger, T., Grohmann, B., Kröplin, B., 1999. Time-discontinuous stabilized space-time finite elements for PDEs of first-and second-order in time. In: European Conference on Computational Mechanics ECCM ‘89. GACM, München, Germany.Google Scholar
  46. Wallmersperger, T., Kröplin, B., Gulch, R. W., 2001. Electroactive Polymer (EAP) Actuators as Artificial Muscles–Reality, Potential, and Challenges. Vol. PM 98. SPIE Press, Bellingham, WA, USA, Ch. Modelling and Analysis of Chemistry and Electromechanics, pp. 285–308.Google Scholar

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Thomas Wallmersperger
    • 1
  • Bernd Kröplin
    • 1
  • Rainer W. Gülch
    • 2
  1. 1.Institut für Statik und Dynamik der Luft- und RaumfahrtkonstruktionenUniversität StuttgartStuttgartGermany
  2. 2.Physiologisches Institut IIUniversität TübingenTübingenGermany

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