Understanding the kinetics of catalysed reactions in microheterogeneous thin film electrodes

Abstract In this paper which is dedicated to Professor Richard Compton for his 65th birthday, we examine the problem of describing the transport and kinetics of catalytic reactions in which the catalyst is immobilized within a support matrix such as for example redox enzymes immobilized in a polymer matrix, to form a chemically modified electrode. We examine a mathematical procedure which enables a full analytical solution to the Michaelis-Menten kinetic rate equation when coupled to Ficksian diffusion in thin bounded film. This governing reaction/diffusion equation is non-linear and a full analytical solution has, up until very recently, not been developed. Analytical solutions valid for low and high substrate concentrations have been previously reported. This solution for the amperometric steady state current is accurate whatever the value of substrate concentration. The analysis is applied to diffusion/reaction in a planar slab. General analytical solutions valid for steady state conditions for both the amperometric and potentiometric sensor response are provided. We then extend this useful analysis to consider the effect of concentration polarization in the solution, and to consider the effect of competitive inhibition on the amperometric current response. Finally, the analysis is extended to a polymer modified electrode when a redox mediator is used in the polymer film. General expressions for the current are obtained which were valid for any value of the substrate concentration. Kinetic case diagrams are developed and nine approximate limiting expressions for the amperometric response at steady state when the catalytic matrix is either conducting or insulating are developed.