Current Distribution on a Rotating Disk Electrode below the Mass‐Transfer‐Limited Current: Correction for Finite Schmidt Number and Determination of Surface Charge Distribution

Abstract

The two-dimensional model for the current distribution on a rotating disk below the mass-transfer-limited current developed by Newman is extended here to account for the influence of a finite Schmidt number and to provide the charge distribution in the diffuse part of the double layer. A polynomial expansion in terms of Sc' is developed for the dimensionless concentration derivative at the electrode surface. The charge distribution is estimated under the assumption that specific adsorption can be neglected. This approach requires introduction of only one additional parameter corresponding to the distance between the metal surface and the plane of closest approach f or solvated ions. Zero-frequency asymptotes for the local impedance values, determined from the steady-state calculations, are used to establish the need for a two-dimensional model for the impedance response of a disk electrode.

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

“…29. The development that follows is valid under the assumptions of either a binary electrolyte or an excess of supporting electrolyte.…”

“…Evaluation of the impedance response requires the derivative of ⌿ ϳ m with respect to at the electrode surface, which is given by [28] or, in terms of ϳ m [29] The remaining development is given in terms of…”

“…where B Under the assumption of a steady state, the current density was related to the normal component of the potential gradient at the electrode surface 29 The total current density is given by [47] where i ϳ C is given by Eq. 36 and the total potential is given by [48] where V ϳ is the perturbation in potential applied to the system.…”

Re-examination of the diffusion–convection impedance for a uniformly accessible rotating disk. Computation and accuracy

“…In contrast, Newman [22], Durbha and Orazem [23], Verbrugge [24] and Dong et al [25] investigated the influence of radial position on the disk electrode, at steady state, under 2-D mass transport conditions. Durbha et al [26] presented the mathematical formalism for frequencydomain techniques.…”

“…From the theoretical predictions in Refs. [22][23][24][25][26], it is known that current distribution on the electrode surface is highly uniform in the case of low Ohmic drop and slow electron-transfer kinetics. The present article focuses on such conditions and, therefore, on 1-D diffusion-convection processes.…”