Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 4, 2008, Pages

  Kuksenok, Olga ^a   Yashin, Victor V ^a   Balazs, Anna C ^a  

^a University of Pittsburgh   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABS RESINS; BOUNDARY VALUE PROBLEMS; COLLOIDS; FINITE ELEMENT METHOD; GELATION; GELS; MOTION ESTIMATION; POLYMERS; TWO DIMENSIONAL;

CHEMICAL OSCILLATIONS; COMPUTATIONAL MODELS; COMPUTATIONAL STUDIES; CRITICAL VALUES; DYNAMICAL BEHAVIORS; EFFECTIVE TOOLS; FINITE DIFFERENCES; FINITE ELEMENT TECHNIQUES; FINITE RANGES; LARGE SAMPLES; LATTICE SPRING MODELS; POLYMER GELS; REACTION PARAMETERS; SIZE AND SHAPES; THREE-DIMENSIONAL MODELS; TRANSITION POINTS;

THREE DIMENSIONAL;

EID: 55149107437     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.041406     Document Type: Article

References (39)

1. Nonlinear Dynamics in Polymeric Systems, edited by, J. A. Pojman, and, Q. Tran-Cong-Miyata, ACS Symposia Series No. 869 (ACS, Washington, D.C., 2004).
2. M. Shibayama and T. Tanaka, Adv. Polym. Sci. 109, 1 (1993).
3. A. P. Dhanarajan, G. P. Misra, and R. A. Siegel, J. Phys. Chem. A 10.1021/jp026086v 106, 8835 (2002).
4. T. G. Szanto and G. Rabai, J. Phys. Chem. A 10.1021/jp050833h 109, 5398 (2005).
5. K. Kurin-Csorgei, I. R. Epstein, and M. Orban, Nature (London) 10.1038/nature03214 433, 139 (2005).
6. A. Ryan, Nano Lett. 10.1021/nl0520617 6, 73 (2006).
7. J. Boissonade, Phys. Rev. Lett. 10.1103/PhysRevLett.90.188302 90, 188302 (2003).
8. Reflexive Polymers and Hydrogels: Understanding and Designing Fast Responsive Polymeric Systems, edited by, N. Yui, R. Mrsny, and, K. Park, (CRC Press, Boca Raton, FL, 2004).
9. J. Boissonade, Chaos 10.1063/1.1880592 15, 023703 (2005).
10. V. V. Yashin and A. C. Balazs, Macromolecules 10.1021/ma052622g 39, 2024 (2006).
11. V. V. Yashin and A. C. Balazs, Science 10.1126/science.1132412 314, 798 (2006).
12. V. V. Yashin and A. C. Balazs, J. Chem. Phys. 10.1063/1.2672951 126, 124707 (2007).
13. B. P. Belousov, Collection of Short Papers on Radiation Medicine (Medgiz, Moscow, 1959);
14. A. N. Zaikin and A. M. Zhabotinsky, Nature (London) 10.1038/225535b0 225, 535 (1970).
15. T. Yamaguchi, L. Kuhnert, Zs. Nagy-Unvarai, S. C. Muller, and B. Hess, J. Phys. Chem. 10.1021/j100168a024 95, 5831 (1991).
16. R. Yoshida, T. Takahashi, T. Yamaguchi, and H. Ichijo, J. Am. Chem. Soc. 10.1021/ja9602511 118, 5134 (1996).
17. R. Yoshida, E. Kokufuta, and T. Yamaguchi, Chaos 10.1063/1.166402 9, 260 (1999).
18. R. Yoshida, Curr. Org. Chem. 10.2174/138527205774610949 9, 1617 (2005).
19. R. Yoshida, J. Phys. Chem. A 10.1021/jp0011600 104, 7549 (2000).
20. T. Sakai and R. Yoshida, Langmuir 10.1021/la035833s 20, 1036 (2004).
21. R. Yoshida, J. Phys. Chem. A 10.1021/jp992027e 103, 8573 (1999).
22. O. Kuksenok, V. V. Yashin, and A. C. Balazs, Soft Matter 10.1039/b707393c 3, 1138 (2007).
23. V. Labrot, P. De Kepper, J. Boissonade, I. Szalai, and F. Gauffre, J. Phys. Chem. B 10.1021/jp055095b 109, 21476 (2005).
24. D. M. Holloway and L. G. Harrison, Ann. Bot. (London) 101, 361 (2008).
25. S. K. Scott, Oscillations, Waves, and Chaos in Chemical Kinetics (Oxford University Press, New York, 1994).
26. J. J. Tyson and P. C. Fife, J. Chem. Phys. 10.1063/1.440418 73, 2224 (1980).
27. B. Barriere and L. Leibler, J. Polym. Sci., Part B: Polym. Phys. 10.1002/polb.10341 41, 166 (2003).
28. R. J. Atkin and N. Fox, An Introduction to The Theory Of Elasticity (Longman, New York, 1980).
29. S. Hirotsu, J. Chem. Phys. 10.1063/1.460672 94, 3949 (1991).
30. T. Amemiya, T. Ohmori, and T. Yamaguchi, J. Phys. Chem. A 10.1021/jp9929317 104, 336 (2000).
31. S. Sasaki, S. Koga, R. Yoshida, and T. Yamaguchi, Langmuir 10.1021/la0270035 19, 5595 (2003).
32. I. M. Smith and D. V. Griffiths, Programming the Finite Element Method (Wiley, Chichester, England, 2004).
33. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method (Butterworth-Heinemann, Oxford, England, 2000), Vol. 1.
34. We note that the linear hexahedral element was chosen for the simplicity. Any other element could be chosen, but all of the forces and integrals should be recalculated according to a procedure similar to the one described above. There is, however, no need to choose a more complex element since the model is robust with the above choice.
35. We note that the actual run time for the simulation results shown in Fig. 3 (from t=0 until t=2000 with the time steps specified at the end of the model section) took 26 min on a single processor Intel Northwood 3.2 GHz.
36. In the simulations presented in Fig. 3, as well as in the simulations presented below, we chose the standard deviation to be equal 0.05; we note, however, that any other choice of the standard deviation leads to identical results in terms of regular periodic oscillations at late times. More specifically, we compared the evolution of the same system for the cases when we start with the much smaller or larger initial fluctuation (taking the standard deviations within the range from 0.0001 to 0.9) and confirmed that the late-time oscillations always were identical to the ones shown in Fig. 3.
37. The vertical lines in Fig. 7 between the data points at f= fL* and data points corresponding to regular oscillations (marked with blue, dark blue and green colors online for L=2, 6, and 12, respectively) simply serve as a guide for the eye; there are no simulation data points along these vertical lines.
38. R. Aihara and K. Yoshikawa, J. Phys. Chem. A 10.1021/jp010908r 105, 8445 (2001).
39. S. Maeda, Y. Hara, R. Yoshida, and S. Hashimoto, Adv. Mater. Res. 19, 3480 (2007).