Impedance of EC Reaction at a Rotating Disk Electrode

Controls: each slider changes the quantity of each parameter

Theoretical description [1]:

The redox reaction E of one electron transfer between two ionic species is often preceded and/or followed by a chemical reaction in the electrolyte solution. For example, ferrous or ferric ions in aqueous solution in the presence of chloride ions are complexed by these ions, and the electron transfer is preceded/followed by decomplexation or complexation steps.

Consider the following mechanism:

(1)

(2)

which consists of a redox reaction and a first-order chemical reaction between the oxidizing agent and an "electroinactive" species , that is, one that does not react at the electrolyte|electrode interface, present in the electrolyte solution.

We have: and , and with the perfect gas constant and the Faraday constant, the electrode potential and the standard redox potential of the considered redox couple. and are the forward and backward chemical reaction rates, respectively.

The first step is an electron transfer step that takes place at the electrode|electrolyte interface. The second step is a chemical step, that is, without electron transfer, which takes place in the electrolyte and not at the electrode|electrolyte interface. This second step is a reaction consecutive to electron transfer in the oxidation direction and prior to electron transfer in the reduction direction. This mechanism is then called EC since the reaction is written to be proceeding a priori in this direction. As the two steps can take place in the direct or reverse direction, the result of this study also concerns the reaction CE. The species is produced by a chemical reaction, that is, with no electron transfer in the electrolytic solution. It does not take part in the electrochemical interfacial reaction.

The kinetics of the electrochemical reaction are Butler–Volmer kinetics under steady-state Nernst or convection-diffusion conditions [1], that is to say at a rotating disk electrode (RDE). The following assumptions and simplifications were made:

,

,

,

,

.

In steady state, all the time-dependent terms are equal to 0; we can then write the interfacial concentrations

(3)

and

. (4)

The steady-state Faradaic current density writes:

(5)

with the bulk concentration of species , where and are the bulk concentrations of species and , respectively; the meaning of the other symbols is described elsewhere [2–5].

The Faradaic impedance writes

(6)

with the charge transfer resistance, and and the concentration impedances of the species and , respectively. Their expressions are described elsewhere.

The polarization resistance can be expressed as

. (7)

Finally, the electrode impedance is calculated by plugging a capacitor in parallel to the Faradaic impedance:

. (8)

Description of the controls:

The top-left graph shows the Faradaic current as a function of the electrode potential relative to the standard redox potential. The black dot represents the operating voltage value at which the various impedance graphs are calculated (bottom left and bottom right). The various factors affecting the Faradaic current are shown in Eq. (5): .

The top-right graph shows the nondimensional interfacial concentrations of species and O expressed by Eqs. (3) and (4). The black dot represents the operating voltage value at which the various impedance graphs are calculated (bottom left and bottom right). The various factors affecting the interfacial concentrations are the same as for the Faradaic current.

The bottom-left graph shows the concentration impedance of the species and , divided by the polarization resistance , expressed by Eq. (7). Effectively, all the control parameters affect the normalized concentration impedances but these affect them more importantly: . The black dot represents a frequency value on the graph.

The bottom-right graph shows the Faradaic impedance , expressed by Eq. (6), and the electrode impedance , expressed by Eq. (8), both divided by the polarization resistance .

The red dot represents the characteristic radial frequency , related to the presence of a double-layer capacitor in parallel to the Faradaic impedance .

The blue dot represents the characteristic radial frequency associated to the bounded diffusion (or diffusion-convection) impedance.

The green dot represents the characteristic radial frequency related to the bounded diffusion and reaction (Gerischer) impedance.

References

[1] J.-P. Diard, B. Le Gorrec and C. Montella, Cinétique Electrochimique, Paris: Hermann, 1996.

[2] H. Gerischer, "Wechselstrompolarisation von Elektroden mit einem potentialbestimmenden Schritt beim Gleichgewichtspotential I.," Zeitschrift für Physikalische Chemie, 198(1), 1951 pp. 286–313. doi:10.1515/zpch-1951-19824.

[3] E. Levart and D. Schuhmann, "Sur la détermination générale de l’impédance de concentration (diffusion convective et réaction chimique) pour une électrode à disque tournant," Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 53(1), 1974 pp. 77–94. doi:10.1016/0022-0728(74)80005-7.

[4] J.-P. Diard, B. Le Gorrec and C. Montella, Étude de Réactions Électrochimiques par Spectroscopie d'Impédance, Reactions EC/CE. doi:10.13140/RG.2.2.34169.54888.

[5] J.-P. Diard, B. Le Gorrec and C. Montella, Handbook of Electrochemical Impedance Spectroscopy. Diffusion Impedances. doi:10.13140/RG.2.2.27472.33288.