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Ultimate cyclic voltammetry: an analytical examination of the reversible case

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Abstract

Multi-scan cyclic voltammetry may lead eventually to a repetitive current-versus-potential graph. Here such “ultimate” cyclic voltammograms are investigated mathematically for reversible electrode reactions. The voltammetric shapes, after an infinite number of cycles, are modelled and their characteristics are documented. It is predicted that the approach to truly repetitive behaviour, within an experimentally realistic length of time, requires that a specific condition—balancing the potential scan range to the initial concentrations—be satisfied.

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Notes

  1. If, for example, \( t=-{\scriptscriptstyle \frac{25}{16}}P,\mathrm{then}\operatorname{Int}\left\{-2t/P\right\}=3\operatorname{and}\mathrm{frac}\left\{-2t/P\right\}={\scriptscriptstyle \frac{1}{8}}. \)

  2. In contradistinction, the lower limit in the companion article [1] is zero.

  3. In a Fourier representation, antisymmetry corresponds to all the coefficients of even harmonic number h equalling zero; that is: a 2 = b 2 = a 4 = b 4 = a 6 = ⋯ = 0.

  4. except, perhaps, for some “this layer” configurations.

  5. Remember that the two diffusivities are here being assumed equal. Otherwise \( \sqrt{D} \) terms must be inserted into equation (30), that will then match equation (9).

  6. also known misleadingly as a “stationary” state

References

  1. Oldham KB (2013) Multi-scan reversible cyclic voltammetry: is the ultimate condition approached and, if so, how fast? J Solid State Electrochem. doi:10.1007/s10008-013-2175-3

  2. Noel M, Vasu KI (1990) Cyclic voltammetry and frontiers of electrochemistry. Aspect, London

    Google Scholar 

  3. Grosser DK (1993) Cyclic voltammetry: simulation and analysis of reaction mechanisms. VCH, New York

    Google Scholar 

  4. Compton RG, Banks CE (2007) Understanding voltammetry. World Scientific, Singapore

    Book  Google Scholar 

  5. Marken F, Neudeck A, Bond AM (2012) In: Scholz F (ed) Electrochemical methods, 2nd edn. Heidelberg, Springer

    Google Scholar 

  6. Myland JC, Oldham KB (1983) An analytical expression for the current-voltage relationship during reversible cyclic voltammetry. J Electroanal Chem 153:43

    Google Scholar 

  7. Keightley AM, Myland JC, Oldham KB, Symons PG (1992) Reversible cyclic voltammetry in the presence of product. J Electroanal Chem 322:25

    Google Scholar 

  8. Oldham KB, Feldberg SW (1999) The principle of unchanging total concentration and its implications for modeling unsupported transient voltammetry. J Phys Chem B 103:1699

    Google Scholar 

  9. Bard AJ, Inzelt G, Scholz F(eds) (2012) Electrochemical Dictionary 2nd edn. Springer, Berlin, p 362

  10. Oldham KB (1996) Tables of semiintegrals. J Electroanal Chem 430:1

    Google Scholar 

  11. Oldham K, Myland J, Spanier J (2000) An atlas of functions, 2nd edn. Springer, New York, Chap 64

    Google Scholar 

  12. Wolfram S (1999) The Mathematica® Book, 4th edn. Cambridge University Press, Cambridge

    Google Scholar 

  13. Oldham KB, Myland JC, Bond AM (2012) Electrochemical Science and Technology. Wiley, Chichester, equ 16:33

    Google Scholar 

  14. Bard AJ, Faulkner LR (2001) Electrochemical Methods, 2nd edn. Wiley, New York, p 242

    Google Scholar 

  15. Nicholson RS, Shain I (1964) Theory of stationary electrode polarography. Single scan and cyclic methods applied to reversible, irreversible, and kinetic systems. Anal Chem 36:706

    Google Scholar 

  16. Retter U, Lohse H (2012) In: Scholz F (ed) Electrochemical methods, 2nd edn. Heidelberg, Springer

    Google Scholar 

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Acknowledgments

This study was initially supported by the Natural Sciences and Engineering Council of Canada.

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Authors and Affiliations

  1. Trent University, Peterborough, ON, Canada, K9J 7B8

    Keith B. Oldham

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  1. Keith B. Oldham
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Correspondence to Keith B. Oldham.

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Oldham, K.B. Ultimate cyclic voltammetry: an analytical examination of the reversible case. J Solid State Electrochem 17, 2749–2756 (2013). https://doi.org/10.1007/s10008-013-2176-2

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  • DOI: https://doi.org/10.1007/s10008-013-2176-2

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