Orthogonal Collocation Simulation of the Rotating Ring Disk Electrode: Mass Transfer with Homogeneous Reaction

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Abstract
The partial differential equations describing the mass transfer to a rotating ring disk electrode where the intermediate generated at the disk electrode is decomposed by chemical reaction in the solution have been solved by the orthogonal collocation technique. The two spatial dimensions (normal and radial) are discretized leaving a continuous dependence in time. The space in the normal direction is discretized by exponentially weighted polynomials, whereas the “shifted” Jacobi polynomials are used in the radial direction. Results are presented for an electron transfer at the disk and ring together with decomposition of the intermediate generated at the disk by first or second order kinetics. Two different boundary conditions at the disk are investigated, namely, a constant potential in the limiting current region and a constant applied current. The transient and steady‐state currents at the disk and the ring electrodes, as well as the simulated collection efficiency, are in excellent agreement with previous theoretical treatments. This algorithm, however, is much more accurate and takes much less computer time as compared to other techniques. The working curves provided allow the determination of rate constants of homogeneous reactions from ring current‐rotation rate data obtained from a rotating ring disk electrode.

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