Approximate Solution of Non-Linear Reaction Diffusion Equations in Homogeneous Processes Coupled to Electrode Reactions for CE Mechanism at a Spherical Electrode

A Eswari,S Usha,L Rajendran

doi:10.4236/ajac.2011.22010

Abstract

A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.

Highlights

Microelectrodes are of great practical interest for quantitative in vivo measurements, e.g. of oxygen tension in living tissues [1,2,3], because electrodes employed in vivo should be smaller than the unit size of the tissue of interest
The model is based on non-stationary diffusion equation containing a non-linear reaction term
This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction

Summary

Introduction

Microelectrodes are of great practical interest for quantitative in vivo measurements, e.g. of oxygen tension in living tissues [1,2,3], because electrodes employed in vivo should be smaller than the unit size of the tissue of interest. Microelectrodes of simple shapes are experimentally preferable because they are more fabricated and generally conformed to simpler voltammetric relationships Those shapes with restricted size in all superficial dimensions are of special interest because many of these reach true steady-state under diffusion control in a semi infinite medium [7]. The use of microelectrodes for kinetic studies has recently been reviewed [11] and the feasibility demonstrated of accessing nano second time scales through the use of fast scan cyclic voltammetry These advantages are earned at the expense of enhanced theoretical difficulties in solving the reaction diffusion equations at these electrodes. Dayton et al [18] derived the spherical response using Neumann’s integral theorem In this literature steady-state limiting current is discussed in [19]

Mathematical Formulation of the Problems

Analytical Expression of Concentrations and Current Using HPM

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