PadéTafelSystem

PadéTafelSystem is a computational framework for modeling electrochemical kinetics by integrating Padé approximants with Tafel analysis. It represents the current–potential relationship with a Padé approximant, a rational function P_m(E)/Q_n(E), enabling simultaneous accommodation of Tafel-like exponential growth at high overpotentials and the smoother behavior near equilibrium. The approach can be applied to either current versus potential data or to the log of current versus potential, depending on the chosen formulation.

Methodology within PadéTafelSystem involves selecting the degrees m and n of the Padé approximant, fitting the rational function to experimental data using nonlinear least squares or robust fitting techniques, and optionally enforcing known Tafel constraints in the high-overpotential limit. From the resulting fitted function, kinetic parameters such as the Tafel slope, exchange current density, and related transfer coefficients can be inferred. The framework also supports extrapolation beyond the measured range with controlled asymptotic behavior, providing a continuous, smooth model across different electrochemical regimes.

Advantages of the approach include improved fit quality across a wide potential range, better extrapolation to unmeasured conditions, and a natural incorporation of asymptotic behavior without relying on piecewise models or high-degree polynomials. It is particularly useful in electrochemical kinetics studies, corrosion science, fuel cells, batteries, and related areas where accurate interpretation of current–potential data is essential.

Limitations include sensitivity to the choice of m and n, potential identifiability issues between parameters, and dependence on data quality. Careful validation and uncertainty assessment are recommended when applying PadéTafelSystem to experimental datasets.