MATHEMATICAL MODELING OF THE ELECTRIC POTENTIAL DISTRIBUTION IN THE VOLUME OF AN ELECTROLYTE IN THE PRESENCE OF A CATHODE MODIFIED WITH CARBON NANOTUBES

Abstract

This paper presents a comprehensive mathematical model aimed at analyzing the distribution of electric potential within an electrolyte volume, taking into account the polarization behavior of electrodes. Particular attention is paid to a cathode modified with carbon nanotubes (CNTs), which possess exceptional electrical conductivity and catalytic properties, significantly influencing the electrochemical processes occurring at the electrode–electrolyte interface. The model is based on the Laplace equation, which governs the steady-state distribution of electric potential in a conductive medium. Boundary conditions are formulated to reflect the nonlinear dependence of overpotential on current density, as well as the geometrical and microstructural characteristics of the CNT-modified surface. The finite element method is applied to numerically solve the problem, enabling accurate simulation of complex geometries and electrolyte heterogeneities. The simulation results highlight how nanostructuring of the electrode surface leads to a more uniform current distribution, reduced local overpotentials, and improved electrochemical performance. The findings can be utilized for optimizing electrode design in applications such as electroplating, electrochemical sensors, batteries, and other energy storage or conversion systems. The proposed model is adaptable for studying other types of nanostructured electrode modifications, thus expanding its applicability to a wide range of electrochemical technologies.