Analytical solution of system of coupled non-linear reaction diffusion equations. Part I: Mediated electron transfer at conducting polymer ultramicroelectrodes

Abstract

An analysis of reaction and diffusion within an electroactive polymer film deposited on an inlaid microdisc electrode is presented. The theoretical analysis of the steady-state amperometric response for a conducting polymer-modified ultramicroelectrodes is re-studied. The coupled processes of chemical reaction, substrate and mediator diffusion are examined. Simple analytical expressions for substrate and mediator concentrations for all values of reaction/diffusion parameters are presented. The variation of current in terms of m (which defines the ratio of the radius of the inlaid microdisc to the thickness of the polymer layer) is also discussed. The model is based on non-stationary system of coupled reaction/diffusion equations containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reactions. He’s Homotopy perturbation method is used to give approximate analytical solutions of coupled non-linear reaction diffusion equations. A good agreement with available limiting case results is noticed.