Abstract
Ion transport problem related to controlled potential experiments in electrochemistry is studied. The problem is assumed to be superposition of diffusion and migration under the influence of an electric field. The comparative analysis are presented for three well-known models—pure diffusive (Cottrell’s), linear diffusion-migration, and nonlinear diffusion-migration (Cohn’s) models. The nonlinear model is derived by the identification problem for a nonlinear parabolic equation with nonlocal additional condition. This problem reduced to an initial-boundary value problem for nonlinear parabolic equation. The nonlinear finite difference approximation of this problem, with an appropriate iteration algorithm is derived. The comparative numerical analysis for all three models shows an influence of the nonlinear migration term, the valences of oxidized and reduced oxidized species, also diffusivity to the value of the total charge. The obtained results permits one to estimate bounds of linear and nonlinear ion transport models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ciszkowska M., Stojek Z. (1999). J. Electroanal. Chem. 466: 129
Kucza W., Danielewski M., Lewenstam A. (2002). Electrochem. Commun. 8: 416
Bard A.J., Faulkner L.R. (1980) Electrochemical Methods. Wiley, New York
Cottrell F.G. (1903). Z. Phys. Chem. 42: 385
Lange R., Doblhofer K. (1987). J. Electroanal. Chem. 237: 13
Myland J.C., Oldham K.B. (1999). Electrochem. Commun. 1: 467
Bieniasz L.K. (2002). Electrochem. Commun. 4: 917
A. Hasanov, Şafak Hasanoglu, Math. Chem. 10 (2007) (to appear)
A. Hasanov, Şafak Hasanoglu, Math. Chem. (2008) (to appear)
Cohn S., Pfabe K., Redepenning J. (1999). Math. Mod. Meth. Appl. Sci. 9: 455
Hasanov A. (1998). Math. Meth. Appl. Sci. 21: 1195
Hasanov A., Mueller J.L., Cohn S., Redepenning J. (2000). Comput. Math. Appl. 39: 225
Pfabe K., Shores T.S. (2000). Appl. Numer. Math. 32: 175
Şafak Hasanoglu, Arzu Erdem, Math. Chem. 10 (2008) (to appear)
Liberti L., Helffrich F.G. (1987) Mass Transfer and the Kinetics of Ion Exchange (NATO ASI Series). Martinus Mijhoff, Boston
Samarskii A.A. (2001) The Theory of Difference Schemes. Marcel Dekker, New York
Buck R.P., Madaras M.B., Mäckel R. (1994) Diffusion-migration capacitance in homogeneous membranes, modified electrodes and thin-layer cells. J. Electroanal. Chem. 366: 55–68
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hasanov, A., Hasanoglu, Ş. Comparative analysis of linear and nonlinear models for ion transport problem in chronoamperometry. J Math Chem 44, 731–742 (2008). https://doi.org/10.1007/s10910-008-9350-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-008-9350-2