Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes (Contemporary Mathematics, 2024)
A theoretical analysis is conducted on the electrochemical behaviour of micro disk electrodes coated with thin coatings of electroactive polymers. The main focus of efforts to characterize the planar diffusion chemical reaction within polymer-modified ultra-microelectrodes is the creation of a theoretical model that explicitly takes into account the potential for the polymer film to cover the inlaid micro disc support surface. Approximate formulae for the steady-state amperometric response and formulation of the boundary value problem are given. The impact of substrate concentration, mediator concentration and current responsiveness in the solution besides the polymer film is also investigated. Akbari-Ganji method (AGM) and differential transformation method (DTM), two adequate and widely available analytical methods, were utilized to determine the steady-state non-linear diffusion equation. The approximate analytical solution for the substrate concentration and mediator concentration and the current for the small experimental kinetic values and diffusion coefficients are presented. We additionally determine the problem’s numerical solution using the MATLAB tool. A satisfactory agreement can be seen when the numerical outcomes verify with the analytical findings.
Keywords: Nonlinear Differential Equation, Akbari-Ganji Method and Differential Transformation Method, Modified Polymer Ultra-Microelectrodes