## 3 Results and Discussion
### Electrochemical Studies
Regarding the systems including both Na\({}_{2}\)HPO\({}_{4}\)-MBT or only Na\({}_{2}\)HPO\({}_{4}\) in either WSS or 3.5 wt % NaCl (_Steel-WSS-Na\({}_{2}\)HPO\({}_{4}\)_, _Steel-WSS-Na\({}_{2}\)HPO\({}_{4}\)-MBT_, _Steel-NaCl-Na\({}_{2}\)HPO\({}_{4}\)-MBT_), the relative equivalent circuit consists of five components and corresponds to an EIS spectra of two relaxation times. More specifically, it includes the resistance of the solution (\(R_{\text{sol}}\)), the pore resistance, and the CPE of the inhibitor layer (\(R_{\text{inh}}\)-\(\text{CPE}_{\text{inh}}\)) in parallel connection, which are attributed to the response of the electrolyte inside the pores of the layer, and finally, the charge transfer resistance and the double-layer CPE (\(R_{\text{ct}}\)-\(\text{CPE}_{\text{dl}}\)) that are due to the presence of the corrosion process. Taking into account the aforementioned Equation (4), the \(C_{\text{inh}}\), \(C_{\text{int}}\), and \(C_{\text{dl}}\) parameters were calculated. In principal, the \(C_{\text{dl}}\) value is influenced by the roughness of the metal surface [38; 39]. The determined values of the EIS fitting parameters for the WSS and 3.5 wt % NaCl electrolytic solutions are tabulated in Tables S2 and S3, respectively. However, taking into account the \(\text{CPE}_{\text{inh}}\)-P values [\(\text{CPE}_{\text{inh}}\)-P represents the \(n\) which is the CPE exponent in Equations (3) and (4)] calculated for the _Steel-WSS-Na\({}_{2}\)HPO\({}_{4}\)-MBT_ (0.50334) and _Steel-WSS-Na\({}_{2}\)HPO\({}_{4}\)_ (0.50486) samples after exposure to WSS solution for 96 h, it can be mentioned that these elements cannot be associated to a non-ideal capacitor (Table S2) [84]. Similar assessments can be reported for the \(\text{CPE}_{\text{inh}}\)-P values determined for the _Steel-NaCl-Na\({}_{2}\)HPO\({}_{4}\)-MBT_ sample after exposure to 3.5 wt % NaCl solution for 24 h (0.5009), 48 h (0.50201), 72 h (0.50471), and 96 h (0.50474), as well as for the _Steel-NaCl-Na\({}_{2}\)HPO\({}_{4}\)_ sample after exposure to 3.5 wt % NaCl solution for 96 h (0.50913) (Table S3). Nevertheless, it should be mentioned that the introduction of a Warburg impedance component did not improve the numerical fitting of the EIS results. Moreover, it should be taken into consideration that Tables S2 and S3 do not demonstrate the mean values of the EIS fitting parameters. Finally, considering the obtained \(R_{\text{p}}\) and \(R_{\text{ct}}\) values of Table 4 and Tables S2 and S3, it can be stated that both LPR and EIS methods confirm that the systems including both \(Na_{2}\)HPO\({}_{4}\) and \(MBT\) inhibitors exhibit the best anticorrosive behavior after 96 h of exposure to either WSS or 3.5 wt % NaCl electrolytic solutions. The evolution of the mean values together with the corresponding error bars of the EIS fitting parameters \(R_{\text{ct}}\), \(C_{\text{dl}}\) of the mild steel panels after their exposure to WSS solution for 96 h in the presence or absence of corrosion inhibitors is depicted in Figure 22. Concerning the determined values, it can be mentioned that the system including both the inhibitors Na\({}_{2}\)HPO\({}_{4}\) and MBT exhibits the highest \(R_{\text{ct}}\) values for all the exposure time intervals. It is important to notice that high \(R_{\text{ct}}\) values indicate enhanced resistance to the corrosion process [87]. On the other hand, the lowest low \(C_{\text{dl}}\) values are observed for the  
Figure 21: Electrochemical impedance spectroscopy (EIS) equivalent circuits used for numerical simulation of the EIS data obtained for the mild steel panels after submission in the electrolytic solutions in the absence or presence of corrosion inhibitors: (**a**) equivalent circuit with three elements, (**b**) equivalent circuit with five elements. system containing the inhibitors Na2 HPO4, revealing a low corrosion reaction area [87]. Furthermore, small variations are discerned in the \(C_{\rm dl}\) of this system, indicating that the corrosion reaction area does not undergo changes.