Porous electrodes are prevalent in electrochemical devices. Electrochemical impedance spectroscopy (EIS) is widely used as a noninvasive, in situ characterization tool to investigate multi-phase (electronic, ionic, gaseous) transport and coupling interfacial reactions in porous electrodes. Interpretation of EIS data needs model and fitting which largely determine the type and amount of information that could possibly be obtained, and thereby the efficacy of the EIS method. This review focuses on physics-based models, as such models, compared to electrical circuit models, are more fundamental in our understanding of the porous electrodes, hence more reliable and more informative. Readers can have a glimpse of the long history of porous electrode theory and in particular its impedance variants, acquaint themselves with the celebrated de Levie model and a general theoretical framework, retrace the journey of extending the de Levie model in three directions, namely, incorporating new physico-chemical processes, treating new structural effects, and considering high orders. Afterwards, a wealth of impedance models developed for lithium-ion batteries and polymer electrolyte fuel cells are introduced. Prospects on remaining and emerging issues on impedance modelling of porous electrodes are presented. When introducing theoretical models, we adopt a “hands-on” approach by providing substantial mathematical details and even computation codes in some cases. Such an approach not only enables readers to understand the assumptions and applicability of the models, but also acquaint them with mathematical techniques involved in impedance modelling, which are instructive for developing their own models.

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The low-frequency inductive loop is usually attributed to relaxation of adsorbed intermediates of multistep reactions in electrocatalysis and corrosion. Herein, we report a low-frequency inductive loop for a single-electron reaction when the electrode potential (E M ), the equilibrium potential (E eq ), and the potential of zero charge (E pzc ) are different, namely, under nonequilibrium conditions. Interestingly enough, although both reactions involve only one electron, the metal deposition reaction (M + + e ↔ M) and the redox couple reaction (Fe(CN) 63− + e ↔ Fe(CN) 6 4−) show different impedance shapes. The low-frequency inductive loop is observed only for the M + + e ↔ M reaction in the oxidation direction because its faradaic current has a negative phase angle due to double layer effects. Moreover, we find that the low-frequency inductive loop occurs only when the polarization curve has no diffusion-limiting features.

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Understanding the double layer at the electrode-electrolyte interface is a long-standing challenge in electrochemistry. The orthodox Gouy-Chapman-Stern (GCS) model and its many derivatives invariably picture the double layer as a serial connection of a compact layer and a diffuse layer. We unravel herein that the serial connection tacitly prescribes a zero potential gradient at the solution-side boundary, which is, rigorously speaking, invalid. The bearing of this problematic assumption is pinpointed by comparing the double-layer impedance, which is analytically solved at the potential of zero charge, derived from the original and amended GCS models. Specifically, in the amended GCS model, the capacitance of the compact layer now shows frequency dispersion. The deviation between the original and amended models is greater when the double layer is confined in narrower space.