Reaction/diffusion with Michaelis–Menten kinetics in electroactive polymer filmsPart 2.‡ The transient amperometric response†

Abstract

A theoretical model describing the transient response of an amperometric chemical sensor in which the sensing elements bound in a surface deposited polymer film interact with the substrate via Michaelis–Menten reaction kinetics is outlined. A non-linear time dependent partial differential equation is formulated and solved analytically. In particular the interplay between chemical reaction and substrate diffusion is specifically taken into account. The limiting situations of catalytic site unsaturation and site saturation are considered and analytical solutions for substrate concentration and transient current response are formulated using both the methods of Laplace transformation and finite integral transformation. Both protocols yield similar predictions. The current response predicted under steady state conditions when τ → ∞ is in good accord with that presented in an earlier paper, thus confirming the validity of the mathematical analysis. The time taken to achieve a steady state current response (the sensor response time when operating in the batch amperometric mode ) was found to depend on the balance between substrate diffusion through the polymer matrix and substrate reaction at the immobilised catalytic sites within the polymer film.