REACTION DIFFUSION WITH MICHAELIS-MENTEN KINETICS IN ELECTROACTIVE POLYMER-FILMS - PART 2 - THE TRANSIENT AMPEROMETRIC RESPONSE/

A theoretical model describing the transient response of an amperometr ic chemical sensor in which the sensing elements bound in a surface de posited polymer film interact with the substrate via Michaelis-Menten reaction kinetics is outlined. A non-linear time dependent partial dif ferential equation is formulated and solved analytically. In particula r the interplay between chemical reaction and substrate diffusion is s pecifically taken into account. The limiting situations of catalytic s ite unsaturation and site saturation ale considered and analytical sol utions 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. T he current response predicted under steady state conditions when tau-- >infinity is in good accord with that presented in an earlier paper, t hus confirming the validity of the mathematical analysis. The time tak en to achieve a steady state current response (the sensor response tim e when operating in the batch amperometric mode) was found to depend o n the balance between substrate diffusion through the polymer matrix a nd substrate reaction at the immobilised catalytic sites within the po lymer film.