Table 1.
The most representative cases of studies investigated by ECs for a correct EIS profiles/data evaluation.
| Original Metal Samples | Equivalent Circuit (ECs) and Electrical Elements | Real Case of Study: Original Metal Coatings/Layers | References |
|---|---|---|---|
| Clean metals | Randles circuit with Re that is the electrolyte resistance; CPEdl is the double-layer capacitance; Rct is the charge transfer resistance, and finally W is the Warburg impedance for copper ions, during their diffusion through the oxide film | The Randles circuit was analytically standardize and validated, by using the standard corrosion events of copper in slightly mineralized neutral aqueous solutions (such as tap water, as conventional working medium) | [60,61] |
| Clean metals | A variation of the previous Randles circuit consists of the charge transfer resistances of cathodic and anodic processes, are in parallel in different branches of the circuit | The EIS spectra, acquired with the modified Randles circuit, was applied to recorded EIS profiles for artistic bronze coupons in artificial rain | [60] |
| Clean metals | Other authors have applied a simple two nested (R-CPE) couple circuit, but fitting results showing the exponent of the second CPE close to 0.5, suggesting a diffusion impedance, both in copper and brass | Copper and brass surfaces for application of the two nested (R-CPE) couple of electrochemical circuits | [62,63,64] |
| Metals with patinaCopper and alloys | The first EC (where the pair CPEdl-Rct is not considered to be electrical equivalent element) represents the double-layer patina morphology, quite similar to the anodized layers in aluminum model, which consist of a thin barrier layer covered by a porous outer layer | This equivalent circuit describes the outdoor copper and bronze patinas, exhibiting a double-layer structure. In particular, the inner layer contains cuprous oxide materials and an outer layer, appears more porous for the presence of different cupric compounds, depending on the environment to which the object is exposed and located | [65] |
| Metals with patina Copper and alloys | The second EC with two nested (R-CPE) couple circuit, represents the impedance of the inner and outer patina layer. Considering an exponent value of 0.5 for the CPE in the inner layer, a Warburg/W impedance, could replace the CPE final circuit. | The same EC was applied to study the response of bronze roman coins and natural copper patinas, formed during 1–3 years in Chile in different environments, with different thickness and porosity depending on their location | [66] |
| Metals with patina Copper and alloys | Three nested (R-CPE) circuits were reported in the literature, to explain the electrochemical output signals regarding artificial patinas, putting in Na2SO4-NaHCO3, as working electrolytes. The first (R-CPE) pair represents the resistance and capacitance of the patina, the second (R-CPE), at intermediate frequencies, represents the corrosion process on the metal surface, while third (R-CPE) couple that corresponds to the low-frequency loop is explained as a result of oxidation–reduction processes of the corrosion products taking place at the electrode surface | A first example of this three nested (R-CPE) circuits is the EIS spectrum profiles of samples, collected by a brass object, excavated from the archaeological area of Tharros, in 0.1 M NaCl (as working electrolyte). Another example concerns archaeological bronze coins, working with NaCl 0.3 M-5% agar electrolyte and mineral water. This EC is depicted in a different order (Re[(Rct-CPEdl)(Rpl-CPEpl)]) that is mathematically. Equivalent as EC and which best represents the original sample |
[67,68,69,70,71] |
| Metals with patina Iron and steel | Two-cell EC have been applied to describe the impedance of the two interfaces: metal/rust layer and rust layer/electrolyte, respectively. A third time constant seems to be present at low frequencies, applying the R(RC(C[RW])) model and performing measurements in the G-PE cell | Regarding the Two-cell EC circuits electrochemical studies were carried out on weathering steel sculptures from Adriana Veyrat; Politecnico di Torino performed EIS measurements on historic iron surface/coating belonging to the Notre-Dame Cathedral of Amiens and the Metz Cathedral, in France | [72] |
| Evaluation of coatings | A metal-coating system is a capacitor and a resistance in parallel, according to the capacitance (Ccoat) and resistance (Rcoat) of the metal coating in series with the resistance of the working electrolyte, (Re). In highly protective coatings, Rcoat is very high and the system becomes Ccoat in series with Re (no current crosses the resistance). When the coating deteriorates the circuit, changes and the main electric components/elements are Cdl (the double-layer capacitance and Rct (the charge transfer resistance) of the corrosion process that occurs at the metal-electrolyte interface. This circuit was applied to the characterization of organic coatings, including varnishes and waxes for bronze and historic steel artwork objects | Not reported cases of studies on original samples | [73,74,75] |
| Evaluation of inhibitors | The EC circuits are the same of the clean surfaces, only differing in the values of different parameters | Not reported cases of studies on original samples | [76,77] |