A Mathematical Model for the Radially Dependent Impedance of a Rotating Disk Electrode

TLDR: In this article, an analytic model for the impedance response of a rotating disk electrode was presented. But the model was only valid for an infinite Schmidt number and was used as part of a model for radially dependent convective diffusion on impedance response.

Abstract: Frequency-domain techniques are commonly employed in the study of electrode kinetics and mass transfer in electrolytic solutions. While the information obtained is similar to that from transient techniques, better resolution of physical processes can be achieved because the noise level in frequency-domain measurements can be made extremely small. 1-3 A second advantage of the frequency domain techniques over transient techniques is that the KramersKronig relations can be used to identify instrumental artifacts or changes in baseline properties. 4-7 The uniform accessibility of the rotating disk at the mass-transfer-limited current makes it an attractive tool for frequency-domain techniques. Significant effort has been expended on developing analytic formulae for the impedance response of a rotating disk electrode. 8-19 A comparative study of the application of these models to interpretation of impedance spectra has been presented by Orazem et al. 20 A one-dimensional numerical model for the impedance response of a rotating disk electrode which accounted for the influence of a finite Schmidt number was presented by Tribollet and Newman. 21 This model accounts for effects associated with kinetics, mass-transport, and ohmic potential drop within the bulk of the solution under the assumption that the disk can be treated as being uniform. The first two terms in the Cochran 22 expansion for the axial component of fluid velocity were included in the convective diffusion equation. Tribollet et al. 18 reported that the errors in the calculated Schmidt numbers caused by assuming an infinite Schmidt number, i.e., by neglecting the second and higher terms in the axial velocity expansion, could be as high as 24% for a Schmidt number of 1000. This result was confirmed by regression of various masstransfer models to impedance data. 20 Mathematical models have been developed which account for frequency dispersion associated with the nonuniform potential distribution on the disk electrode, 23-26 but to date, no comparable model has been developed for the influence of nonuniform mass transfer on the impedance response. Appel and Newman 27 provided a preliminary mathematical development, valid for an infinite Schmidt number, that could be used as part of a model for the influence of radially dependent convective diffusion on the impedance response. Appel used this approach to calculate the radial distribution of impedance, but results were presented only for a single dimensionless frequency due to numerical difficulties associated with implementation of the model. 28