Catalysis of electrochemical reactions at redox polymer electrodes: Kinetic model for stationary voltammetric techniques

A kinetic model describing the catalytic activity of redox polymer film electrodes is presented and discussed for reaction schemes in which the primary reaction between the active form of the catalyst and the substrate is the rate-determining step. The derivations are given for stationary techniques, such as rotating disc electrode voltammetry. Besides the diffusion of the substrate from the bulk of the solution to the film—solution interface, three kinetic factors determine the magnitude of the catalytic current: “diffusion” of electrons from the electrode surface to the film—solution interface; diffusion of the substrate in the opposite direction; rate of the rate-determining step of the catalytic reaction. Correspondingly, the kinetics of the diffusion—reaction process can be entirely described by only three dimensionless parameters expressing the relative rates of the rate-controlling processes. Provision is made for the partition coefficient of the substrate between the film and the solution to be different from unity. A finite-difference resolution of the kinetics is developed, but attention is mainly focused on the search of characteristic behaviors depending upon a lesser number of parameters and expressed by simple closed-form equations which are particularly convenient to use in the processing of experimental data. These are essentially of four types.

• 1.(1) The electron and substrate diffusion of the film are so fast that the rate-controlling phenomenon in the film is the catalytic reaction.
• 2.(2) The cataytic reaction is so fast that the kinetics is controlled jointly by the two diffusion process.
• 3.(3) When “diffusion” of electron is faster than diffusion of substrate in the film a pure kinetic situation may arise by mutual compensation of the latter process and the catalytic reaction.
• 4.(4) In the opposite case a pure kinetic situation may again arise resulting this time from mutual compensation of electron “diffusion” and catalytic reaction.

The kinetics observed in intermediary situations is also described, as well as the variations of the parameters that are required to pass from one limiting behavior to the other. It is shown that, according to the kinetic situation prevailing in the film, a second wave way appear which features the direct reduction of the substrate at the electrode surface after it has diffused through the film. Diagnostic criteria of the various limiting situation are presented, being based on the variations of the height of the catalytic wave with the rotation speed and the solution concentration of the substrate, as well as on the existence and height of the second wave. The electron “diffusion” through the film can be characterized independently by means of experiments involving the oxido-reduction of the film in the absence of substrate. Conversely, the substrate diffusion in the film can be characterized using analogous system in wich catalysis is absent. With the help of these data, the catalytic reaction occuring in the film can be quantitatively characterized. It is shown that this does not require exact knowledge of the film thickness. Such application of the kinetic model to actual experimental systems are illustrated by the discussion of experimental data from the literature.