Abstract
In this contribution we present a formalism to describe the spatio-temporalevolution of a responsive gel submitted to some autocatalytic chemical reaction. This theory is based on an hydrodynamical multi-diffusional approach of a gel, which is plunged in a chemically active mixture. Emergent volume self-oscillation dynamics of the gel result from the nonlinear coupling of the elastic deformation, the chemical kinetics and the transport phenomenon, that take place in the system. We apply our formalism to the case of the Belouzov-Zhabotinsky oscillatory chemical reaction, for which Yoshida et al. (see in this volume) have obtained many experimental results. In particular we discuss some possible coupling between the gel and the chemical reaction.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Ziaie, A. Baldi, M. Lei, Y. Gu, R. A. Siegel, Adv. Drug Deliv. Revs. 56, 145 (2004).
J. P. Gong, Y. Osada, in Polymer Sensor and Actuators (eds. Y. Osada, D. E. De Rossi, Eds, Springer Verlag, Berlin, 2000).
D. J. Beebe, J. S. Moore, J. M. Bauer, Q. Yu, R. H. Liu, C. Devadoss, B-H. Jo, Nature 404, 588 (2000).
T. Shiga, Adv. Polymer Sci. 134, 131 (1997).
H. Andersson, A. van den Berg, Lab Chip 4, 98 (2004).
R. Siegel in this volume.
T. Tanaka, Phys.Rev. Lett. 40, 820 (1978).
K. Dusek (Ed.), Responsive Gels: Volume Transitions, Adv. Polymer Sci. 109 and 110 (Springer, Berlin, 1993).
M. Bisschops, K. Luyben, L. van der Wielen, Ind. Eng. Chem. Res. 37, 3312 (1998).
S. Wu, H. Li, J. P. Chen, K. Y. Lam, Macromol. Theory Simul 13, 13 (2004).
E. C. Achilleos, K. N. Christodoulou, I. G. Kevrekidis, Comput. Theor. Polym. Sci. 1, 63 (2001).
V. V Yashin, A. C. Balazs, Science 314, 798 (2006).
V. V Yashin, A. C. Balazs, Macromolecules 39, 2024 (2006).
O. Kuksenok, V. V Yashin, A. C. Balazs, Phys. Rev. E 78, 041406 (2008).
M. Doi, 2008, Modeling of Gels (slides for IMA Tutorial). http://www.ima.umn.edu/ matter/fall/t1.html.
K. Sekimoto, J. Phys.II (Fr) 1, 19 (1991).
K. Sekimoto, J. Phys.II (Fr) 2, 1755 (1992).
B. Barrière, L. Leibler, J. Polym. Sci. B, 41, 166 (2003).
R. Yoshida, in this volume.
R. Yoshida, H. Ichijo, T. Hakuta, T. Yamaguchi, Macromol. Rapid. Commun. 16, 305 (1995).
R. Yoshida, T. Yamagushi, H. Ichijo, Material Science and Engineering. 4, 107 (1996).
R. Yoshida, E. Kokufuta, T. Yamagushi, Chaos 9, 260 (1999).
K. Miyakawa, F. Sakamoto, R. Yoshida, E. Kokufuta, T. Yamaguchi, Phys. Rev. E 62, 793 (2000).
R. Yoshida, T. Takahashi, T. Yamaguchi, H. Ichijo, J. Am. Chem. Soc. 118, 5134 (1996).
R. Yoshida, T. Takahashi, T. Yamaguchi, H. Ichijo, Adv. Mater. 9, 175 (1997).
R. Yoshida, T. Sakai, O. Tambata, T. Yamaguchi, Sci. and Tech. Adv. Mat. 3, 95 (2002).
T. Sakai, R. Yoshida, Langmuir 20, 1036 (2004).
R. Yoshida, T. Onodera, T. Yamaguchi, E. Kokufuta, J. Phys. Chem. 103, 8573 (1999).
C. Crook, A. Smith, R. Jones, A. Ryan, Phys. Chem. Chem. Phys. 4, 1367 (2002).
P. Borckmans, G. Dewel, A. De Wit, E. Dulos, J. Boissonade, F. Gauffre, P. De Kepper, Int. J. Bif. and Chaos 12, 2307 (2002).
J. Boissonnade and P. De Kepper, in this volume.
U. P. Schröder, W. Opperman, W. in The physical properties of polymeric gels, ed. J. P. Cohen-Addad, John Wiley and Sons Ltd., (1996).
P. J. Flory, Statistical Mechanics of Chain Molecules, Wiley-Intersciences (1969).
G. Strobl, The Physics of Polymers, Third Edition, Springer (2007).
M. Rubinstein, R. Colby, Polymer Physics, Oxford University Press (2003).
J. J. Hermanns, J. Poly. Sci., 59, 191 (1962).
W. M. Lai, D. Rubin, E. Krempl, Introduction to Continuum Mechanics, Third Ed., Butterworth Heinemann (1999).
K. Yoshimura, K. Sekimoto, J. Chem. Phys 101, 4407 (1994).
P. C. Parodi, O. Parodi, P. S. Pershan, Phys. Rev. A 6, 2401 (1972).
P. D. Fleming, C. Cohen, Phys. Rev. B 13, 500 (1976).
D. L. Johnson, J. Chem. Phys 77, 1531 (1982).
T. C. Lubensky, R. Mukhopadhyay L. Radzihovsky, X. Xing, Phys. Rev. E 66, 66011702 (2002).
T. Tanaka, J. Filmore, J. Chem. Phys. 70, 1214 (1979).
Y. Li, T. Tanaka, J. Chem. Phys 92, 1365, (1990).
E. Geissler, A. M. Hecht, J. Chem. Phys 77, 1548 (1982).
E. S. Matsuo, T. Tanaka, J. Chem. Phys 90, 5161 (1989).
A. Peters, S. J. Candau, Macromolecules 21, 2278 (1988).
C. J. Durning, K. N. Morman, J. Chem. Phys 98, 4275 (1992).
T. Tomari, M. Doi, Macromolecules 28, 8334 (1995).
T. Tomari, M. Doi, J. Phys. Soc. Japan 63, 2093 (1994).
K. De Sudipto, N. R. Aluru, B. Johnson, W. C. Crone, D. J. Beebe, J. Moore J. of Microelectromechanical Syst. 11, 544 (2002).
G. Rossi, A. Mazich, Phys. Rev. E 48, 1182 (1992).
S. Métens, S. Villain, P. Borckmans to appear in Physica D. doi:10.1016/j.physd. 2009.06.002 (2009).
P. De Kepper, J. Boissonade, I. Szalai, in this volume.
P. Borckmans, S. Métens, in this volume.
P. Gray, S. K. Scott, Chemical oscillations and Instabilities, Clarendon Press — Oxford (1990).
I. R. Epstein, J. Pojman, An introduction to Nonlinear Chemical Dynamics, Oxford University Press, (1998).
Z. Nagy Ungvarai, B. Hess, Physica D 49, 33 (1991).
R. J. Field, E. Körös, R. M. Noyes, J. Am. Chem Soc., 94 8649 (1972).
L. Kuhnert, K. I. Agladze, and V. I. Krinsky, Nature 337, 244 (1989).
J. Tyson, J. Phys. Chem. 86, 3006 (1982).
P. De Kepper, K. Bar Eli, R. Noyes, J. Phys. Chem 87, 480 (1983).
K. Bar Eli, R. Noyes, J. Chem. Phys 86, 1927 (1987).
K. Bar Eli, M. Brons, J. Phys. Chem 94, 7170 (1990).
J. Tyson, J. Chem. Phys 66, 905 (1977).
J. Tyson, J. Chem. Phys 67, 4297 (1977).
P. De Kepper, private communication.
F. Gauffre, V. Labrot, J. Boissonade, and P. De Kepper in Nonlinear Dynamics in Polymeric Systems (J. A. Pojman and Q. Tran-Cong-Miyata, Eds), ACS Symposium Series 869, 80 2003.
V. Labrot, P. De Kepper, J. Boissonade, I. Szalai, and F. Gauffre, J. Phys. Chem. B 109, 21476 (2005).
J. Boissonade, P. De Kepper, F. Gauffre and I. Szalai, Chaos 16, 037110 (2006).
J. Boissonade, Phys. Rev. Lett. 90, 188302 (2003).
J. Boissonade, Chaos 15, 023703 (2005).
M. Tokita, T. Tanaka, J. Chem. Phys. 95, 4613 (1991).
O. Levenspiel, Chemical Reaction Engineering, 3rd Ed. Wiley (1998).
P. Borckmans, K. Benyaich, A. De Wit, G. Dewel in Nonlinear Dynamics in Polymeric Systems ( J. A. Pojman, Qui Tan-Cong-Miyata, Eds), ACS Symposium Series 869, 58 (2003).
Shibayama and Tanaka, Adv. Polymer Sci. 109, 1 (1993).
B. Erman, P. J. Flory, Macromolecules 19, 2342 (1986).
T. A. Orofino, P. J. Flory, J. Chem. Phys. 26, 1067 (1957).
H. Chiu, Y. Lin, Y. Hsu, Biomaterials 23, 1103 (2002).
I. R. Epstein, J. Pojman, An introduction to Nonlinear Chemical Dynamics, Oxford University Press, (1998).
S. Villain, Comportement mécanique de gels soumis ä des réactions auto-catalytiques (in French). Ph.D. Thesis, Université Paris 7 (2007).
J. Horvath, I. Szalai, and P. De Kepper, Science 324, 772 (2009).
J. P. Gong, Y. Katsuyama, T. Kurokawa, Y. Osada, Adv. Mater. 14, 15 (2003).
V. R. Tirumala, T. Tominaga, S. Lee, P. D. Butler, E. K. Lin, J. P. Gong, W-l. Wu, J. Phys. Chem. B 112, 8024 (2008).
T. Tominaga, Y. Osada, and J. P. Gong, in this volume.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V.
About this paper
Cite this paper
Métens, S., Villain, S., Borckmans, P. (2009). Chemomechanical Dynamics of Responsive Gels. In: Borckmans, P., De Kepper, P., Khokhlov, A.R., Métens, S. (eds) Chemomechanical Instabilities in Responsive Materials. NATO Science for Peace and Security Series A: Chemistry and Biology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2993-5_6
Download citation
DOI: https://doi.org/10.1007/978-90-481-2993-5_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2991-1
Online ISBN: 978-90-481-2993-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)