An Algorithm for the Extraction of Tafel Slopes

The Tafel equation, which serves as a linearized representation of the Butler–Volmer expression, permits the extraction of fundamental parameters of electrochemical systems, such as exchange current densities and Tafel slopes. However, the application of these linear fitting procedures become problematic in the cases of experimental data featuring nonlinearities in the Tafel (log­(J) – V) response. This is especially troubling in low-overpotential regimes, where charge transfer kinetics generally dominate electrode behavior (as opposed to diffusion-limited currents at higher overpotentials) and linearization is expected to be most applicable. As a response to this complication and the ad-hoc forms of fitting that may arise from it, this report outlines a systematic method for the determination of Tafel slopes through a rigorous, quantitative framework. The algorithm’s performance is benchmarked using electrochemical measurements of well-characterized reactions for water splitting, hydrogen evolution, and dioxygen reduction at iridium and platinum electrodes. As a final validation test, we show that the exchange currents extracted through this automated fitting procedure, used in conjunction with the Butler–Volmer model, are capable of reproducing the original electrochemical data in kinetically controlled regimes.塔菲尔方程（Tafel equation）作为巴特勒-沃尔默表达式（Butler–Volmer expression）的线性化形式，可用于提取电化学体系的基础参数，例如交换电流密度与塔菲尔斜率。然而，当实验数据在塔菲尔（log(J) – V）响应中呈现非线性特征时，这类线性拟合方法的应用便会出现问题。这一问题在低过电势区域尤为突出：该区域通常以电荷转移动力学主导电极行为（相较于高过电势下的扩散限制电流），而线性化方法本应在此处最具适用性。针对这一难题以及由此衍生的各类临时拟合方案，本研究提出了一套基于严谨定量框架的塔菲尔斜率测定系统性方法。本算法的性能通过铱与铂电极上水分解、析氢及氧还原等表征充分的反应的电化学测量结果进行了基准测试。作为最终验证实验，我们证明：通过该自动拟合流程提取的交换电流，结合巴特勒-沃尔默模型，能够在动力学控制区域复现原始电化学数据。