Modeling of Nonlinear Reaction–diffusion Processes of Amperometric Polymer-Modified Electrodes

A mathematical model of amperometric response for a polymer-modified electrode system has been developed. The model is based on nonstationary diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. 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. The analytical solutions for substrate concentration and transient current for both steady and nonsteady-state are obtained using Danckwerts' relation and variable and separable method. An excellent agreement with the previous analytical results are noted. The combined analytical set of solution of steady-state current in all the nearest sites is also described in a case diagram. A general simple analytical approximate solution for steady-state current for all values of α is also given. A two-point Padé approximation is also derived for the nonsteady-state current for all values of saturation parameter α. Limiting case results (α ≪ 1 and α ≫ 1) are compared with Padé approximation results and are found to be in good agreement.