On Contemporary Tafel Analysis

Tafel slope analysis has been the cornerstone of mechanistic interpretation in multi-step electrochemical reactions for nearly a century, underpinning our understanding of reactions from hydrogen evolution to carbon dioxide reduction. Here we demonstrate that the IUPAC-endorsed framework, universally adopted for relating Tafel slopes to rate-determining step identity and position, is mathematically erroneous, a consequence of omitting the chain rule in its original derivation. Instead, it is only valid in the low coverage limit where the electrode remains dominated by empty sites, or when the number of electrons transferred before the rate-determining step is only counted from the step consuming the most abundant surface species. We resolve this inconsistency by introducing a corrected analytical framework for both bound and unbound adsorption models, the latter expressed in closed matrix form amenable to machinelearning-assisted mechanism discovery. Applied to the hydrogen evolution and oxidation reactions, the corrected framework reveals that small Tafel slopes are indicative of a reversible Volmer step with low surface coverage, irrespective of reaction path and adsorption type, while mechanistic discrimination only emerges at high Tafel slopes. Experimentally, we observe Tafel slopes of 140mV dec−1-190mV dec−1 on polycrystalline Pt in alkaline media, values not captured by the classical framework but naturally described by the corrected one. Furthermore, by providing a continuous analytical solution that spans from these interaction-dominated asymptotes down to the rigorous 0mV dec−1 reversible limit, our framework eliminates the need to heuristically define Tafel regions.