Comments on “State of Charge-Dependent Polynomial Equivalent Circuit Modeling for Electrochemical Impedance Spectroscopy of Lithium-Ion Batteries”

A recent paper by Wang et al. [ibid., vol. 33, no. 10, pp. 8449–8460, Oct. 2018] proposes a state of a charge-dependent polynomial equivalent circuit model for lithium batteries. The model consists of an inductor, a Warburg element, a constant phase element (CPE), and two resistors. The authors quote the impedance equation of a Warburg element, where τ is the diffusion time constant, ϕ varies between 0 and 1, and RW is the Warburg resistance. This equation is wrong; in a Nyquist plot, the angle in a Warburg element is fixed to 45° at high frequencies, corresponding to ϕ = 0.5. Such behavior is a result of diffusion through a semi-infinite medium. The frequency band where it is observed is called the Warburg region. The correct form of the impedance equation of a Warburg element is provided.