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Multi-scan cyclic voltammetry of a solution containing mixed valence states

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Abstract

When both members of a redox pair are present in a voltammetric cell, the applied signal must start at the null potential if pure cyclic voltammetry is to be conducted. Here the current from a limitless number of repetitive cyclic scans is predicted mathematically for any initial reductant to oxidant ratio. The predictions were prompted by, and are compared with, published experiments. Some simplifying conditions are imposed: the reaction is reversible; the redox pair share the same diffusivity; the reversal potentials are symmetrically disposed with respect to the halfwave potential.

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Notes

  1. Five such voltammograms, with mole fractions of 0, 0.25, 0.50, 0.75, and 1.00 are reported as Figure 5 in [1].

  2. Figure 5 of [1]

  3. I(Emin) is invariably negative

  4. As evident in Figure 6 of [1]. Note that the abscissa, the molar fraction, is mislabeled “molar ratio”.

  5. A potential removed from the halfwave potential by 200 mV or more is adequate in practice.

  6. In theory, the current spike would be of infinite height if the electrode reaction were reversible, though extraneous resistance and capacitance would impose a limit.

  7. The subscripted Ds in 2:1 represent the diffusivities of their subscripts; other symbols are defined in Table 1.

  8. This assumption is adopted only for notational economy. To cater to unequal diffusivities, one may simply replace each \( {c}_{\mathrm{R}}\;\mathrm{by}\ {c}_{\mathrm{R}}\sqrt{D_{\mathrm{R}}/D} \) and each \( {c}_{\mathrm{O}}\;\mathrm{by}\ {c}_{\mathrm{O}}\sqrt{D_{\mathrm{O}}/D} \) throughout the development.

  9. This fraction would be ½ for an equimolar analyte mixture. In our example, the fraction is 1/3, less than a moiety because our example has the bulk concentration of O exceeding that of R threefold.

  10. With help from Eq. 1:4, Eq. 2:1, and the Table 1 definitions of P and ξ.

  11. These modifying functions [11, chap. 8] split a number into an integer and a positive residuum; for example, Int{π} = 3 and frac{π}=0.1416.

  12. Operations of the fractional calculus require a specified lower limit. Throughout this document, all references to semiintegration and semidifferentiation imply a lower limit of zero.

  13. The withdrawal of (−)Int{κ} from within the hyperbolic tangent’s argument is legitimized by that function’s oddness [11, chap. 30].

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  1. Department of Chemistry, Trent University, Peterborough, Ontario, Canada

    Keith B Oldham & Jan C Myland

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  1. Keith B Oldham
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  2. Jan C Myland
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Correspondence to Keith B Oldham.

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Oldham, K.B., Myland, J.C. Multi-scan cyclic voltammetry of a solution containing mixed valence states. J Solid State Electrochem 23, 3355–3361 (2019). https://doi.org/10.1007/s10008-019-04431-1

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  • DOI: https://doi.org/10.1007/s10008-019-04431-1

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