Abstract
The system of coupled nonlinear diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of mediator and substrate are presented using Homotopy perturbation method. A simple expression of electrochemical rate constant K +ME is also obtained for all values of reaction parameters. The available limiting case results are compared with our results and are found to be in good agreement.
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References
Lakshmanan, M., Nonlinear Dynamics, Springer, 2003.
Murray, R.W., Chemically Modified Electrodes, Electroanal. Chem., Vol. 13, Bard A.J, ed., New York: Marcel Dekker Inc., 1984.
Murray, J.D., Mathematical Biology, Springer Verlag, 1989, p. 109.
Murray, R.W., Ewing, A.G., and Durst, R.A., Anal. Chem., Ser. A, 1987, vol. 59, p. 379.
Murray, R.W., Molecular Design of Electrode Surfaces, Murray, R.W., ed., in Techniques of Chemistry, New York: John Wiley and Sons, 1992.
Andrieux, C.P., Dumas-Bouchiat, J.M., and Saveant, J.M., J. Electroanal. Chem., 1982, vol. 131, p. 1.
Lyons, M.E.G. and Barlett, P.N., J. Electronal. Chem., 1991, vol. 316, pp. 1–22.
Lyons, M.E.G., McCormark, D.E., and Barlett, P.N., J. Electronal. Chem., 1989, vol. 261, p. 1.
Albery, W.J. and Hillman, A.R., J. Electronal. Chem., 1984, vol. 170, pp. 27–49.
Albery, W.J. and Hillman, A.R., Roy. Soc. Chem. Ann. Rep., Ser. C, 1981, vol. 377, p. 78.
Andrieux, C.P., Dumas-Bouchiat, J.M., and Saveant, J.M., J. Electronal. Chem., 1984, vol. 169, p. 9.
Coely, A., et al., Backlund and Darboux Transformation, American Mathematical Society, Providence, RI, 2001.
Wadati, M., Sanuki, H., Konno, K., Prog. Ther. Phys., 1975, vol. 53, p. 419.
Gardener, C.S., Green, J.M., Kruskal, M.D., and Miura, R.M., Phys. Rev. Lett., 1967, vol. 19, p. 1095.
Hirota, R., Phys. Rev. Lett., 1971, vol. 27, p. 1192.
Malfliet, W., Am. J. Phys., 1992, vol. 60, p. 650.
He, J.H., Comput. Methods Appl. Mech. Engrg., 1998, vol. 167, no. 1–2, p. 57.
He, J.H., Appl. Math. Comput., 2005, vol. 26, no. 3, pp. 695–700.
He, J.H., Phys. Lett., Ser. A, 2006, vol. 350, no. 1–2, pp. 87–88.
He, J.H., Appl. Math. Comput., 2003, vol. 140, pp. 217–222.
Ganji, D.D. and Rafei, M., Phys. Lett., Ser. A, 2006, vol. 356, no. 2, pp. 131–137.
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Published in Russian in Elektrokhimiya, 2011, Vol. 47, No. 2, pp. 159–167.
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Meena, A., Rajendran, L. Analytical solution of nonlinear diffusion processes in modified electrode. Russ J Electrochem 47, 147–155 (2011). https://doi.org/10.1134/S1023193511020133
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DOI: https://doi.org/10.1134/S1023193511020133