Reaction/diffusion with Michaelis–Menten kinetics in electroactive polymer films. Part 1. The steady-state amperometric response

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Abstract
The theoretical analysis of the steady-state amperometric response for a polymer-modified electrode system whcih exhibits Michaelis–Menten kinetics is discussed. In particular, the interplay between substrate diffusion within the polymer matrix and substrate reaction at the catalytic polymer sites is examined. A non-linear reaction/diffusion equation describing the substrate transport and reaction kinetics within the film is formulated and approximate analytical solutions for the substrate concentration profiles and corresponding current responses are developed. Four distinct limiting cases are developed and are represented schematically in a kinetic case diagram. The theoretical analysis is extended to consider the complicating situation of substrate diffusion in the Nernst diffusion layer adjacent to the polymer film. The allied problem of the response of a potentiometric sensor exhibiting Michaelis–Menten kinetics is also examined. The theoretical model developed in the paper is validated by examining the electro-oxidation of dopamine, adrenaline and noradrenaline at surfactant-doped polypyrrole-modified electrodes. Good agreement between the amperometric current response predicted from the theoretical model and the current response obtained experimentally from batch amperometry is obtained. Non-linear least-squares analysis of the batch amperometric data in tandem with the theoretical expression derived for the steady-state current response produces reasonable values for the Michaelis constant, Km, the catalytic rate constant, Kc, and the substrate diffusion coefficient, Ds, for each of the three catecholamine substrates examined.