Science China Technological Sciences

, Volume 53, Issue 7, pp 1862–1868 | Cite as

Nonlinear dynamics of self-oscillating polymer gels

  • PengFei Wang
  • JinXiong Zhou
  • MeiE Li
  • Feng Xu
  • TianJian Lu
Article
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Abstract

Self-oscillating polymer gels driven by Belousov-Zhabotinsky (BZ) chemical reaction are a new class of functional gels that have a wide range of potential applications (e.g., autonomously functioning membranes, actuate artificial muscles). However, the precise control of these gels has been an issue due to limited investigations of the influences of key system parameters on the characteristics of BZ gels. To address this deficiency, we studied the self-oscillating behavior of BZ gels using the nonlinear dynamics theory and an Oregonator-like model, with focus placed upon the influences of various system parameters. The analysis of the oscillation phase indicated that the dynamic response of BZ gels represents the classical limit cycle oscillation. We then investigated the characteristics of the limit cycle oscillation and quantified the influences of key parameters (i.e., initial reactant concentration, oxidation and reduction rate of catalyst, and response coefficient) on the self-oscillating behavior of BZ gels. The results demonstrated that sustained limit cycle oscillation of BZ gels can be achieved only when these key parameters meet certain requirements, and that the pattern, period and amplitude of the oscillation are significantly influenced by these parameters. The results obtained in this study could enable the controlled self-oscillation of BZ gels system. This has several potential applications such as controlled drug delivery, miniature peristaltic pumps and microactuators.

Keywords

Belousov-Zhabotinsky reaction self-oscillating gels numerical simulation limit cycle parameter analysis 
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References

  1. 1.
    Chen F, Ma X Y, Qu X H, et al. Structure and properties of an organic rectorite/poly (methyl methacrylate) nanocomposite gel polymer electrolyte by in situ synthesis. J Appl Polym Sci, 2009, 114: 2632–2638CrossRefGoogle Scholar
  2. 2.
    Colombani O, Ruppel M, Schubert F, et al. Synthesis of poly(n-butyl acrylate)-block-poly(acrylic acid) diblock copolymers by ATRP and their micellization in water. Macromolecules, 2007, 40: 4338–4350CrossRefGoogle Scholar
  3. 3.
    Mather P T. Response materials: Soft answers for hard problems. Nat Mat, 2007, 6: 93–94CrossRefGoogle Scholar
  4. 4.
    Ahn S K, Kasi R M, Kim S C, et al. Stimuli-responsive polymer gels. R Soc Chem, 2007, 4: 1151–1157Google Scholar
  5. 5.
    Baughman R H. Conducting polymer artificial muscles. Synth Met, 1996, 78: 339–353CrossRefGoogle Scholar
  6. 6.
    Qiu Y, Park K. Environment-sensitive hydrogels for drug delivery. Adv Drug Deli Rev, 2001, 53: 321–339CrossRefGoogle Scholar
  7. 7.
    Maeda S, Hara Y, Yoshida R, et al. A chemo-mechanical rotational actuator driven by BZ reaction. In: 2006 1st IEEE RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, 2006. 308–313Google Scholar
  8. 8.
    Yoshida R. Design of functional polymer gels and their application to biomimetic materials. Curr Org Chem, 2005, 9: 1617–1641CrossRefGoogle Scholar
  9. 9.
    Mitsumata T, Abe N. Magnetic-field sensitive gels with wide modulation of dynamic modulus. Chem Lett, 2009, 38: 922–923CrossRefGoogle Scholar
  10. 10.
    Varga I, Szalai I, Meszaros R, et al. Pulsating pH-responsive nanogels. J Phys Chem B, 2006, 110: 20297–20301CrossRefGoogle Scholar
  11. 11.
    Yoshida R, Takahashi T, Yamaguchi T, et al. Self-oscillating gels. Adv Mater, 1997, 9: 175–178CrossRefGoogle Scholar
  12. 12.
    Yoshida R, Takahashi T, Yamaguchi T, et al. Self-oscillating gel. J Am Chem Soc, 1996, 118: 5134–5135CrossRefGoogle Scholar
  13. 13.
    Merkin J H. Travelling waves in the Oregonator model for the BZ reaction. Ima J Appl Math, 2009, 74: 622–643MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Sakai T, Yoshida R. Self-oscillating nanogel particles. Langmuir, 2004, 20: 1036–1038CrossRefGoogle Scholar
  15. 15.
    Yoshida R, Kokufuta E, Yamaguchi T. Beating polymer gels coupled with a nonlinear chemical reaction. Chaos, 1999, 9: 260–266CrossRefGoogle Scholar
  16. 16.
    Yoshida R. Design of self-oscillating gel utilizing oscillating reaction. Electrochem, 2003, 71: 337–341Google Scholar
  17. 17.
    Yoshida R. Self-oscillating soft materials. Membrane, 2006, 31: 307–312Google Scholar
  18. 18.
    Yoshida R, Sakai T, Hara Y, et al. Self-oscillating gel as novel biomimetic materials. J Controlled Release, 2009, 140: 186–193CrossRefGoogle Scholar
  19. 19.
    Yoshida R, Sakai T, Ito S, et al. Self-oscillation of polymer chains with rhythmical soluble-insoluble changes. J Am Chem Soc, 2002, 124: 8095–8098CrossRefGoogle Scholar
  20. 20.
    Hara Y, Yoshida R. Self-oscillation of polymer chains induced by the Belousov-Zhabotinsky reaction under acid-free conditions. J Phys Chem B, 2005, 109: 9451–9454CrossRefGoogle Scholar
  21. 21.
    Shinohara S, Seki T, Sakai T, et al. Chemical and optical control of peristaltic actuator based on self-oscillating porous gel. Chem Commun, 2008, 39: 4735–4737CrossRefGoogle Scholar
  22. 22.
    Maeda S, Hara Y, Yoshida R, et al. Self-oscillating gel actuator for chemical robotics. Adv Robotics, 2008, 22:1329–1342CrossRefGoogle Scholar
  23. 23.
    Sobel S G, Hastings H M, Field R J. Oxidation state of BZ reaction Mixtures. J Phys Chem A, 2006, 110: 5–7CrossRefGoogle Scholar
  24. 24.
    Hegedus L, Forsterling H D, Onel L, et al. Contribution to the chemistry of the Belousov-Zhabotinsky reaction products of the ferriin-bromomalonic acid and the ferriin-malonic acid reactions. J Phys Chem A, 2006, 110: 12839–12844CrossRefGoogle Scholar
  25. 25.
    Yufeng H, Junzhe H, Lei W, et al. Image Processing using BZ Reaction. Proc SPIE, 2001, 4552: 34–39Google Scholar
  26. 26.
    Aliev R R, Yamaguchi T, Kuramoto Y. On the phase dynamics in the BZ reaction. J Phys Chem A, 1997, 101: 7691–7694CrossRefGoogle Scholar
  27. 27.
    Nath M A, Ganaie N B, Rastogi R P, et al. Effect of temperature on oscillatory behaviour of the system containing isomers of hydroxybenzoic acid in batch reactor. E-J Chem, 2008, 5: 832–837Google Scholar
  28. 28.
    Field R J, Noyes R M, Koros E. Oscillations in chemical systems: 2. Thorough analysis of temporal oscillation in bromate-cerium-malonic acid system. J Am Chem Soc, 1972, 94: 8649–8664CrossRefGoogle Scholar
  29. 29.
    Yoshida R, Uesusuki Y. Biomimeic gel exhibiting self-beating motion in ATP solution. Biomacromolecules, 2005, 6: 2923–2926CrossRefGoogle Scholar
  30. 30.
    Boissonade J. Self-oscillations in chemoresponsive gels: A theoretical approach. Chaos, 2005, 15: 9CrossRefGoogle Scholar
  31. 31.
    Yashin V V, Balazs C A. Modeling polymer gels exhibiting selfoscillations due to the Belousov-Zhabotinsky reaction. Macromolecules, 2006, 39: 2024–2026CrossRefGoogle Scholar
  32. 32.
    Yashin V V, Balazs A C. Pattern formation and shape changes in self-oscillating polymer gels. Science, 2006, 314: 798–801CrossRefMathSciNetGoogle Scholar
  33. 33.
    Yamaguchi M, Ono S, Okamoto K. Interdiffusion of dangling chains in weak gel and its application to self-repairing material. Mater Sci Eng B, 2009, 162: 189–194CrossRefGoogle Scholar
  34. 34.
    Kuksenok O, Yashin V V, Balazs A C. Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. Phys Rev E, 2008, 78: 041406CrossRefGoogle Scholar
  35. 35.
    Belousov B. A periodic chemical reaction and its mechanism. Sb Ref Radiats Med Medgiz Moscow, 1959, 145: 145–147Google Scholar
  36. 36.
    Yashin V V, Balazs A C. Theoretical and computational modeling of self-oscillating polymer gels. J Chem Phys, 2007, 126: 124707–124723CrossRefGoogle Scholar
  37. 37.
    Sriram K, Bernard S. Complex dynamics in the Oregonator model with linear delayed feedback. Chaos, 2008, 18: 1–12CrossRefGoogle Scholar
  38. 38.
    Field R J, Noyes R M. Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J Chem Phys, 1974, 60: 2001–2006Google Scholar
  39. 39.
    Field R J, Burger M. Oscillations and Traveling Waves in Chemical Systems. New York: John Wiley&Sons, 1985Google Scholar
  40. 40.
    Liu B Z, Peng J H. Nonlinear Dynamics. BeiJing: Higher Education Press, 2004Google Scholar
  41. 41.
    Yoshida R. Self-oscillating gel as smart materials. Adv Sci Tech, 2009, 57: 1–4CrossRefGoogle Scholar
  42. 42.
    Yashin V V, Van Vliet K J, Balazs A C. Controlling chemical oscillations in heterogeneous Belousov-Zhabotinsky gels via mechanical strain. Phys Rev E, 2009, 79: 046212CrossRefMathSciNetGoogle Scholar
  43. 43.
    Yashin V V, Balazs A C. Chemomechanical synchronization in heterogeneous self-oscillating gels. Phys Rev E, 2008,77: 046210CrossRefGoogle Scholar
  44. 44.
    Tateyama S, Shibuta Y, Yoshida R. Direction control of chemical wave propagation in self-oscillating gel array. J Phys Chem B, 2008, 112: 1777–1782CrossRefGoogle Scholar
  45. 45.
    Hara Y, Yoshida R. A viscosity self-oscillation of polymer solution induced by the Belousov-Zhabotinsky reaction under acid-free condition. J Chem Phys, 2008, 128: 224901–224904CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • PengFei Wang
    • 1
  • JinXiong Zhou
    • 1
  • MeiE Li
    • 2
  • Feng Xu
    • 1
    • 3
  • TianJian Lu
    • 1
  1. 1.Biomedical Engineering and Biomechanics Center, SV LaboratoryXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Materials Science and EngineeringXi’an Jiaotong UniversityXi’anChina
  3. 3.HST Center for Biomedical Engineering, Department of MedicineBrigham and Women’s Hospital, Harvard Medical SchoolBostonUSA

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