Algebraic Form and New Approximation of Butler–Volmer Equation to Calculate the Activation Overpotential

The Butler–Volmer equation has been widely used to analyze the electron transfer for electrochemical simulation. Although it has been broadly employed with numerous successful applications, the Butler–Volmer equation needs to be solved numerically to find the activation overpotential, which results in the increase of the calculation difficulties. There are also some parameters in Butler–Volmer equation such as exchange current density and symmetry factor that are not always known parameters. In order to avoid the latest mentioned limitation and the numerical calculation which is time consuming and for simplification, there are some approximation equations such as Tafel, linear low polarization, and hyperbolic sine approximation. However, all these equations are only applicable in a specific range of current density or definite condition. The aim of this paper is to present a new form of Butler–Volmer equation using algebraic operation to calculate activation overpotential. The devised equation should be accurate, have a wide application range, able to remove any numerical calculation, and be useful to find exchange current density. In this research, a new form of Butler–Volmer equation and a new approximation equation (called K–J equation) have been successfully derived. The comparison result shows that the new derived form is exactly equal to the Butler–Volmer equation to calculate the activation overpotential, and it removed the necessity of numerical calculation to find the activation overpotential. In addition, the K–J approximation has a good agreement with Butler–Volmer equation over a wide range of current density and is applicable to predict the activation loss.