Physical Interpretation of the Warburg Impedance

Abstract

Abstract The physical origin of the capacitive behavior of the Warburg impedance (ZW) and adsorption pseudocapacitance (Cϕ) is discussed. A simple derivation of ZW, based only on the Nernst diffusion layer thickness (δ = (πDt]1/2), is presented. An alternate equivalent circuit is proposed in which ZW is represented by a series combination of a resistor (the Warburg pseudoresistance [RW]) and a capacitor (the Warburg pseudocapacitance [CW]). The values of these new circuit elements are independent of potential. On the other hand, they are proportional to ω−1/2, leading to the so-called “constant phase element” that is observed experimentally. In contrast, the usual elements employed in equivalent circuit models to describe the voltage-current characteristics of the interphase (e.g., the faradaic resistance [RF], double-layer capacitance [Cdl], and adsorption pseudocapacitance [Cϕ]) are independent of frequency but may change with potential over many orders of magnitude. It is shown that the frequency depen...