## 2 Background of EIS Corrosion Measurements
such as transmission-line models, provide mechanistic characters for corrosion processes, e.g., pitting corrosion, diffusion processes, and the presence of passive films, and yield a good relation between impedance data and fitting [28]; however, their applications are not straightforward to engineers. Only simplified electrical circuits are reviewed herein. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  
* Ex external counter electrode, 2 In embedded counter electrode in sample, 3 SCE standard calomel electrode, 4 CSE copper copper–sulphate electrode, 5 N.I. No information.  
\end{table} 
Table 1: Experimental setup details using EIS measurements [29]. Figure 2: Equivalent electrical circuits for analysis of steel corrosion in concrete/mortar: R\({}_{c}\), bulk concrete resistance; R\({}_{c}\), resistance of concrete in intermediate frequency; CPE\({}_{c}\), a constant phase element of concrete in intermediate frequency; R\({}_{c}\), resistance in intermediate frequency; CPE\({}_{c}\), a constant phase element in intermediate frequency; R\({}_{c}\), charge transfer resistance or polarization resistance; CPE\({}_{d}\), a constant phase element of double layer; CPE\({}_{d}\), a constant phase element for diffusion process, and W, Warburg impedance [29]. In most electrical equivalent circuits, the response of bulk concrete (R\({}_{\text{c}}\)) is simplified, wherein only a single resistor is used, as shown in Figure 2, for which the high-frequency limit is set up as an origin despite the existence of capacitances and resistances (in the high-frequency arc) together. An analysis error may be induced depending on the high-frequency limit set to determine the concrete's resistance. In addition, the steel-concrete interface is represented by a charge transfer resistance (R\({}_{\text{ct}}\)) in conjunction with a constant phase element (CPE\({}_{\text{dl}}\)) for the double layer. To describe the presence of the low-frequency tail representing the diffusion control of oxygen in the vicinity of the steel surface, a Warburg impedance (W) is introduced in series with the charge transfer resistance, which explains the Faradic process at the interface (A-2, B-2, B-3 in Figure 2). The phenomenon can explain the reason why it is difficult for traditional DC measurements to archive steady states within a prolonged period of time. However, when a Warburg impedance is introduced, it is ambiguous to verify whether the fitting process is proper or not as this tail cannot be always observed, even at lower frequencies [23]. The elements representing the response in the intermediate frequency are mostly introduced in the circuits (R\({}_{\text{if}}\) and CPE\({}_{\text{if}}\) in Series B and C), but the physical meanings proposed by researchers vary. For example, the responses for the intermediate frequency in R-CPE series circuits (Series B) were described by [PERSON] et al. [11] based on the effect on the interfacial layer between mortar and steel; by [PERSON] et al. [22] based on the de-electrical properties of concrete; and by [PERSON] et al. [24] based on the effects of the surface film on steel. Meanwhile, hierarchical R-CPE circuits (Series C) are used to determine an intermediate frequency response. This response is considered with steel's redox transformation [8; 26]; but according to [PERSON] et al. [27], the response (C-3 in Figure 2) is separated into hydration products formed in cement pores around the steel surface (R\({}_{\text{cfi}}\) and CPE\({}_{\text{cif}}\)) and redox transformation (R\({}_{\text{if}}\) and CPE\({}_{\text{if}}\)). The impedance spectrum in the Nyquist plot generally consists of the concrete and steel responses (comprising two semicircles). The electrical circuits are expanded to describe additional semicircles or tails based on a combination of resistors and capacitors, or a Warburg element. However, the roles of some elements used in the circuit are still unclear; therefore, it is necessary to define the role of the element clearly.