On the Proper Use of a Warburg Impedance

Recent battery papers commonly employ interpretation models for which diffusion impedances are in series with interfacial impedance. The models are fundamentally flawed because the diffusion impedance is inherently part of the interfacial impedance. A derivation for faradaic impedance is presented which shows how the charge-transfer resistance and diffusion resistance are functions of the concentration of reacting species at the electrode surface, and the resulting impedance model incorporates diffusion impedances as part of the interfacial impedance. Conditions are identified under which the two model formulations yield the same results. These conditions do not apply for batteries.