## 3 Results and Discussion
### Corrosion Resistance Performance  
The corrosion protection capabilities of the materials prepared can be effectively evaluated using electrochemical impedance spectroscopy (EIS) tests. The EIS data is graphically represented via Nyquist and Bode plots, as depicted in Figure 3 and the Supplementary Materials. To further scrutinize the electrochemical impedance characteristics, the collected data were processed utilizing CS Studio, specifically employing the Z-view function to extract additional pertinent information. This technique yields two types of visual outputs: Nyquist and Bode plots. These plots depict the behavior of the carbon steel alloy coated with specific weight ratio mixtures of Fe\({}_{3}\)O\({}_{4}\) MNPs and [Poly(aniline-co-o-toluidine)/Fe\({}_{3}\)O\({}_{4}\)] MNPs, combined with alkylcd resin, in a 0.1 mol/L HCl solution. The analysis of the experimental EIS results involves multiple variables, all of which are included in Table 3. These variables include the solution resistance (R\({}_{\text{s}}\)), the polarization resistance of the metal surface (R\({}_{\text{p}}\)), which signifies protective properties, and the constant phase element (CPE) [47]. The phase shift (n) serves as a measure of the metal surface roughness. The double-layer capacitance (C\({}_{\text{dl}}\)) forms a layer due to the coating on the solution's surface, and as calculated using Equation (1) [48; 49; 50; 51]:  
\[\text{C}_{\text{dl}}=1/(2\pi\text{R}_{\text{p}}\text{f}_{\text{max}}) \tag{1}\]  
The efficacy of the prepared coatings can be evaluated from the corrosion protection efficiency (\(\eta\%\)), calculated using Equation (2):  
\[\eta(\%)=\left(\frac{\text{R}_{\text{pinh}}-\text{R}_{\text{p}}}{\text{R}_{ \text{pinh}}}\right)\times 100 \tag{2}\]  
Figure 2: SEM images of (**a**) Fe\({}_{3}\)O\({}_{4}\) MNPs, and (**b**) [Poly(aniline-co-o- toluidine)/Fe\({}_{3}\)O\({}_{4}\)]MNPs. where \(\rm R_{pinh}\) and \(\rm R_{P}\) represent the polarization resistance with and without the presence of particles, respectively. The relaxation time (\(\rm\tau\)) values can be computed using Equation (3) [52]:  
\[\rm\tau=C_{dl}R_{P} \tag{3}\]  
The EIS data depicted in Figure 3a, Figures S1a and S2a (Supplementary Material) show that the Nyquist plots' semicircles of the copolymer[poly(aniline-co-o-toluidine)/Fe\({}_{3}\)O\({}_{4}\)] MNPs combined with alkyl paint at different weight proportions (5-25% \(w\)/\(w\)) are significant, compared to the plots of magnetite (\(\rm Fe_{3}O_{4}\)) and non-magnetized poly(aniline-co-o-toluidine) when mixed with alkyld paint. This signifies an enhanced corrosion protection efficiency for [poly(aniline-co-o-toluidine)/Fe\({}_{3}\)O\({}_{4}\)] MNPs. An increase in polarization resistance implies an increased corrosion protection efficiency. Nyquist plots display only a single capacitive semicircle in the entire frequency range, indicating a singular time constant associated with the charge transfer process [53; 54; 55; 56]. Corresponding Bode plots confirm this one-time constant behavior. The application of the coating on the carbon steel yields an increased value of phase angle, suggesting an excellent anti-corrosion efficiency [57]. The addition of magnetite and [Poly(aniline-co-o-toluidine)/Fe\({}_{3}\)O\({}_{4}\)] MNPs to the alkyl coating at various weight percentages does not alter the corrosion mechanism. Instead, it amplifies the surface coverage, and enhances the coating's efficiency and corrosion protection ability. This improves the coating's barrier properties, and boosts the adhesive force of the coating on the metal surface, hence physically isolating the metal alloy from the corrosive medium [58; 59]. The physical separation signifies the coating's efficiency when  
Figure 3: (**a**) Nyquist plot, and (**b**) Bode plot of [Poly(aniline-co-o-toluidine)/Fe\({}_{3}\)O\({}_{4}\)] MNPs with alkyld paint for carbon steel, in 0.1 mol/L HCl at 298 K.