## 3 Results and Discussion  
### Electrochemical Impedance Spectroscopy  
Nyquist diagrams of bronze corrosion recorded after immersion for 1 h in 3.5% NaCl and simulated acid rain (pH = 3.4) solutions, in the absence and in the presence of various concentrations of NAC, are shown in Figure 2. The experimental data, represented by symbols, are displayed together with the fitted spectra depicted as lines with crosses. Figure 1: Molecular structure of N-acetyl cysteine (NAC). Figure 2: Electrochemical impedance spectra of bronze in the form of Nyquist diagrams (**a**,**b**), Bode impedance plots (**a**’,**b**’), and phase-angle plots (**a**’,**b**’**’) recorded after 1 h of exposure to 3.5% NaCl (**a**,**a**’,**a**’) and 0.2 g L\({}^{-1}\) Na\({}_{2}\)SO\({}_{4}\) + 0.2 g L\({}^{-1}\) NaHCO\({}_{3}\) + 0.2 g L\({}^{-1}\) NaHCO\({}_{3}\) (pH = 3.4) (**b**,**b**’,**b**’**,**b**’**’**) solutions, in the absence and in the presence of different concentrations of NAC. As shown in Figure 2, all impedance spectra were characterized by a capacitive behavior with two depressed loops, although their separation was not clearly resolved. A straight line in the low-frequency region could also be noticed for the bronze exposed to both uninhibited corrosive electrolytes, indicating the presence of the Warburg impedance. This suggests that the mechanism of bronze corrosion in the uninhibited solutions was mixed-controlled by the charge transfer and the diffusion of dissolved oxygen towards the electrode [67] or of some soluble metallic species from the surface in the bulk solutions. The significant increase in the capacitive loops in the presence of the drug correlated with the inhibition of the bronze corrosion process in both tested electrolytes. The experimental impedance data were further fitted using the equivalent electrical circuits from Figure 3, in which \(\mathrm{R_{e}}\) is the solution resistance, the high-frequency elements \(\mathrm{R_{ct}}-\mathrm{Q_{dl}}\) are ascribed to the charge transfer process at the bronze/electrolyte interface, the \(\mathrm{R_{F}}-\mathrm{Q_{F}}\) parameters are related to an oxidation-reduction process involving a reaction intermediate (i.e., \(\mathrm{Cu^{+}}\) ions accumulated probably as \(\mathrm{Cu_{2}O}\) during the corrosion process), according to a mechanism previously reported [68], and W stands for the Warburg impedance. The coefficients \(\mathrm{n_{dl}}\) and \(\mathrm{n_{F}}\) were used to reproduce the depressed features of the impedance spectra, as shown in the Nyquist diagrams (Figure 2). In the equivalent circuits shown in Figure 3, the ideal capacitive elements were replaced by constant phase elements (CPEs), represented by the terms Q and n, considering the frequency dispersion effect. The impedance of the CPEs has the following form [69]:  
\[\mathrm{Z_{CPE(\omega)}}=\mathrm{Q}=\left[\mathrm{C(j\omega)^{n}}\right]^{-1} \tag{3}\]  
where Q represents a pre-exponential factor, with the dimensions of \(\mathrm{\Omega^{-1}}\)\(\mathrm{cm^{-2}}\)\(\mathrm{s^{n}}\); \(\omega=2\pi\)f is angular frequency in \(\mathrm{rad\cdot s^{-1}}\) and n is the exponent, which defines the character of frequency dependence (\(-1\leq\mathrm{n}\leq 1\)). The values of n are associated with the non-uniform distribution of current at the solid surface, mainly caused by its roughness, porous layer formation, degree of polycrystallinity, inhibitor adsorption, etc. [70].