Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions

S. Pavithra; L. Rajendran; Sunil Kumar

doi:doi:10.11648/j.acm.20170602.13

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Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions

S. Pavithra, L. Rajendran, Sunil Kumar

Published in Applied and Computational Mathematics (Volume 6, Issue 2)

Received: 23 February 2017 Accepted: 14 March 2017 Published: 27 March 2017

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Abstract

Cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present analytical relation between the concentration at the electrode surface and the current for quasi-reversible reaction.A new semi analytic description ofquasi-reversible cyclic voltammetry at a electrode is obtained, assuming equal diffusion coefficients. It provides rigorous and complete expression for the voltamettric current, in the form of the integral or the integral equation.This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

Published in	Applied and Computational Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.acm.20170602.13
Page(s)	83-87
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mathematical Modeling, Boundary Value Problems, Non Linear Equations, Quasi-Reversible

References

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[5]	R. S. Nicholson and Irving Shain, “Theory of stationary electrode polarography. single scan and cyclic methods applied to reversible, irreversible, and kinetic systems,” Anal. Chem. Analytical Chemistry 36(4), 706-723 (1964).
[6]	Allen J. Bard and Larry R. Faulkner, Electrochemical methods : Fundamentals and Applications (Wiley, New York, 2001).
[7]	L. Bortels, B. Van Den Bossche, and J. Deconinck, “Analytical solution for the steady-state and migration. Application to the identification of Butler-Volmer electrode reaction parameters,” Journal of electroanalytical chemistry 422(1/2), 161-167 (1997).
[8]	A. Molina, E. Torralba, C. Serna, and J. A. Ortuno, “Analytical solution for the facilitated ion transfer at the interface between two immiscible electrolyte solutions via successive complexation reactions in any voltammetric technique: Application to square wave voltammetry and cyclic voltammetry,” Electrochim Acta Electrochimica Acta 106, 244-257 (2013).
[9]	TalivaldisBerzins and Paul Delahay, “Oscillographicpolarographic waves for the reversible deposition of metals on solid electrodes,” Journal of the American Chemical Society 75(3), 555-559 (1953).
[10]	Jan C. Myland and Keith B. Oldham, “Quasireversible cyclic voltammetry of a surface confined redox system: a mathematical treatment,” Electrochemistry Communications 7(3), 282-287 (2005).
[11]	Keith B. Oldham and Jan C. Myland, “Modelling cyclic voltammetry without digital simulation,” Electrochimica Acta Electrochimica Acta 56(28), 10612-10625 (2011).
[12]	A. Eswari and L. Rajendran, “Mathematical modeling of cyclic voltammetry for EC reaction,” Russian Journal of Electrochemistry 47(2), 181-190 (2011).
[13]	A. Eswari and L. Rajendran, “Mathematical modeling of cyclic voltammetry for EC2 reaction,” Russian Journal of Electrochemistry 47(2), 191-199 (2011).
[14]	Adib J. Samin, and Jinsuo Zhang, “Analytical solutions of the plannar cyclic voltammetry process for two soluable species with equal diffusivities and fast electron transfer using the method of eigen function expansion”, AIP Advances, 5 087141,(2015).
[15]	Tanja R. Vidakovic-Koch,Vladimir V. Panic, Milan AndriMenkaPetkovska, Kai Sundmacher, “Nonlinear frequency response analysis of the ferrocyanideoxidation kinetics. part i. a theoretical analysis”, J. Phys. Chem. C 2011, 115, 17341–17351.
[16]	G. Moutiers, M. Cassir, J. Devynck, “A thermodynamic, voltammetric and convolution potential sweep characterization”, J. Electronal. Chem. 324(1992) 175-189.

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APA Style

S. Pavithra, L. Rajendran, Sunil Kumar. (2017). Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Applied and Computational Mathematics, 6(2), 83-87. https://doi.org/10.11648/j.acm.20170602.13

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ACS Style

S. Pavithra; L. Rajendran; Sunil Kumar. Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Appl. Comput. Math. 2017, 6(2), 83-87. doi: 10.11648/j.acm.20170602.13

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AMA Style

S. Pavithra, L. Rajendran, Sunil Kumar. Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Appl Comput Math. 2017;6(2):83-87. doi: 10.11648/j.acm.20170602.13

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@article{10.11648/j.acm.20170602.13,
  author = {S. Pavithra and L. Rajendran and Sunil Kumar},
  title = {Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {83-87},
  doi = {10.11648/j.acm.20170602.13},
  url = {https://doi.org/10.11648/j.acm.20170602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.13},
  abstract = {Cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present analytical relation between the concentration at the electrode surface and the current for quasi-reversible reaction.A new semi analytic description ofquasi-reversible cyclic voltammetry at a electrode is obtained, assuming equal diffusion coefficients. It provides rigorous and complete expression for the voltamettric current, in the form of the integral or the integral equation.This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.},
 year = {2017}
}

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TY  - JOUR
T1  - Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions
AU  - S. Pavithra
AU  - L. Rajendran
AU  - Sunil Kumar
Y1  - 2017/03/27
PY  - 2017
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DO  - 10.11648/j.acm.20170602.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - Cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present analytical relation between the concentration at the electrode surface and the current for quasi-reversible reaction.A new semi analytic description ofquasi-reversible cyclic voltammetry at a electrode is obtained, assuming equal diffusion coefficients. It provides rigorous and complete expression for the voltamettric current, in the form of the integral or the integral equation.This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
VL  - 6
IS  - 2
ER  -

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Author Information

S. Pavithra

Department of Mathematics, SethuInistitute of Technology, Kariapatti, India
L. Rajendran

Department of Mathematics, SethuInistitute of Technology, Kariapatti, India
Sunil Kumar

Department of Mathematics, National Institute of Technology, Jamshedpur, India

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APA Style

S. Pavithra, L. Rajendran, Sunil Kumar. (2017). Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Applied and Computational Mathematics, 6(2), 83-87. https://doi.org/10.11648/j.acm.20170602.13

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ACS Style

S. Pavithra; L. Rajendran; Sunil Kumar. Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Appl. Comput. Math. 2017, 6(2), 83-87. doi: 10.11648/j.acm.20170602.13

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AMA Style

S. Pavithra, L. Rajendran, Sunil Kumar. Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions. Appl Comput Math. 2017;6(2):83-87. doi: 10.11648/j.acm.20170602.13

Copy | Download

@article{10.11648/j.acm.20170602.13,
  author = {S. Pavithra and L. Rajendran and Sunil Kumar},
  title = {Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {83-87},
  doi = {10.11648/j.acm.20170602.13},
  url = {https://doi.org/10.11648/j.acm.20170602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.13},
  abstract = {Cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present analytical relation between the concentration at the electrode surface and the current for quasi-reversible reaction.A new semi analytic description ofquasi-reversible cyclic voltammetry at a electrode is obtained, assuming equal diffusion coefficients. It provides rigorous and complete expression for the voltamettric current, in the form of the integral or the integral equation.This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Analytical Relation Between the Concentration of Species at the Electrode Surface and Current for Quasi-Reversible Reactions
AU  - S. Pavithra
AU  - L. Rajendran
AU  - Sunil Kumar
Y1  - 2017/03/27
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170602.13
DO  - 10.11648/j.acm.20170602.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 83
EP  - 87
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170602.13
AB  - Cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present analytical relation between the concentration at the electrode surface and the current for quasi-reversible reaction.A new semi analytic description ofquasi-reversible cyclic voltammetry at a electrode is obtained, assuming equal diffusion coefficients. It provides rigorous and complete expression for the voltamettric current, in the form of the integral or the integral equation.This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
VL  - 6
IS  - 2
ER  -

Copy | Download