Is there any correlation between impedance shapes and electrocatalytic activity?

Though electrochemical impedance spectroscopy (EIS) has been widely used in mechanistic investigations of electrocatalytic reactions, the correlation between the shape of an EIS diagram and electrocatalytic activity is largely unclear; the rich complexity of electrocatalytic reactions casts an air of pessimism over the existence and stability of such a correlation. Understanding the correlation can help select reaction mechanisms and electrical circuit models in data analysis, use EIS shape as a descriptor of electrocatalytic activity, and detect side reactions. Herein, the problem is tackled by a systematic mathematical analysis of firstly single-adsorbate reactions and then more complicated reactions. A complete regime diagram of all possible EIS shapes of single-adsorbate reactions is provided, navigating the analysis in the multi-dimensional parametric space. For single-adsorbate reactions involving two steps with identical transfer coefficients of 0.5 in the absence of lateral adsorbate interactions, several rigorous corollaries are derived. Most of them fail miserably when different transfer coefficients and lateral interactions are considered. Nevertheless, several trends in EIS shapes are robust against complexities of reaction mechanisms and variations in reaction parameters, which also receive experimental evidence collected from the literature.