ANALYTICAL EXPRESSIONS FOR THE CONCENTRATION AND CURRENT IN THE REDUCTION OF HYDROGEN PEROXIDE AT A METAL-DISPERSED CONDUCTING POLYMER FILM

A mathematical model describing the reduction of Hydrogen peroxide (H2O2) to water in a metal dispersed conducting polymer film is discussed. The model is based on a system of reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. The approximate analytical expressions corresponding to the concentration of substrate and product for steady and non-steady state conditions have been obtained using a new approach to homotopy perturbation method (HPM). Approximate analytical expressions of the electrochemical oxidation current are also presented for steady and non-steady state conditions. The numerical simulation (Matlab program) response for concentration profiles was carried out and compared with the analytical results of this work and are found to be in good agreement. The influence of initial substrate concentration, the thickness of the film as well as the diffusion layer and kinetic parameters on the current response were investigated. A graphical procedure for estimating the kinetic parameters from the expression of the current response is also proposed.

本文讨论了一种用于描述金属分散型导电聚合物膜内过氧化氢（Hydrogen peroxide, H₂O₂）还原生成水的数学模型。该模型基于反应扩散方程组构建，方程组包含与酶促反应米氏动力学（Michaelis-Menten kinetics）相关的非线性项。本文采用同伦扰动法（Homotopy perturbation method, HPM）的一种新求解策略，得到了稳态与非稳态条件下底物与产物浓度对应的近似解析表达式。同时给出了稳态与非稳态条件下电化学氧化电流的近似解析表达式。通过Matlab程序开展了浓度分布的数值模拟，并将模拟结果与本文所得解析结果进行对比，二者吻合度良好。研究了初始底物浓度、膜厚度、扩散层厚度以及动力学参数对电流响应的影响。此外还提出了一种基于电流响应表达式估算动力学参数的图解方法。