## 3 Results and Discussion
### Electrochemical Impedance Spectroscopy (EIS)  
Figure 2 shows the Nyquist plots of the carbon steel electrode in 1 M HCl solutions with different contents of TSCA at 298 K. The addition of TSCA does not change the shape of the Nyquist plot, indicating that the electrochemical reaction mechanism of carbon steel remains unchanged. However, the radius of the plot increases with increasing TSCA concentration from 0 to 40 mg/L. This reveals that the corrosion process of carbon steel is significantly inhibited by TSCA. All the Nyquist plots are similarly depressed semicircle-shaped in the frequency range from \(10^{5}\) to 0 Hz, demonstrating that the corrosion reaction process of carbon steel is mainly determined by the charge transfer rate [36; 37]. The capacitive arcs are flattened due to the coarse exposed surface of carbon steel adsorbing TSCA molecules, ions, and corrosion products [38; 39]. In addition, inductive loops arise in the Nyquist plots in the frequency range from 0 to \(10^{-2}\) Hz. This is caused by the adsorption and desorption behavior of TSCA [40]. Thus, the obtained EIS experimental data was fitted by the equivalent circuit model, as illustrated in Figure 3. In the model, \(R_{\mathrm{s}}\), \(R_{\mathrm{ct}}\), and \(R_{\mathrm{L}}\) represent the resistance of the corrosion solution, charge transfer, and inductive, respectively. \(L\) and \(CPE\) represent the inductive and constant phase elements, respectively. The derived inhibition efficiency from EIS measurement (\(\eta_{\mathrm{E}}\)) is shown in the following equation:  
\[\eta_{\mathrm{E}}=\frac{R_{\mathrm{ct}}^{1}-R_{\mathrm{ct}}^{0}}{R_{\mathrm{ct }}^{1}}\times 100\% \tag{2}\]  
where \(R_{\mathrm{ct}}^{0}\) and \(R_{\mathrm{ct}}^{1}\) are the fitted charge transfer resistances in the presence and absence of TSCA inhibitor, respectively. The fitted impedance parameters and the corresponding inhibition efficiency for carbon steel immersed in 1 M HCl solutions with different contents of TSCA are given in Table 2. The charge transfer resistance of carbon steel and the corresponding inhibition efficiency increase with increasing TSCA concentration, and the highest inhibition efficiency of 96.3% can be obtained at 40 mg/L. This is in accordance with the weight loss result. The double-layer capacitance (\(C_{\mathrm{dl}}\)) and deviation parameter (\(n\)) are derived from the following equation [41]:  
\[C_{\mathrm{CPE}}=\frac{C_{\mathrm{dl}}}{\left(2\pi f_{\mathrm{max}}\right)^{n -1}} \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \(C_{\mathrm{TSCA}}\) **(mg\(\cdot\) L\({}^{-1}\))** & \(W\) **(g\(\cdot\)m\({}^{-2}\).h\({}^{-1}\))** & \(\eta_{W}\) **(\%)** \\ \hline
0 & 19.08 & - \\
1 & 6.68 & 65.0 \\
10 & 2.96 & 84.5 \\
20 & 1.62 & 91.5 \\
40 & 0.76 & 96.0 \\ \hline \end{tabular}
\end{table} 
Table 1: Corrosion rate of carbon steel and inhibition efficiency of TSCA at various concentrations for carbon steel in 1 M HCl at 298 K.  
where \(C_{\rm CPE}\) represents the capacitance of the \(CPE\), and \(f_{\rm max}\) represents the corresponding frequency of the maximum -\(Z^{\prime}\) value in the Nyquist plot. As shown in the table, the double-layer capacitance decreases with increasing TSCA concentration. This is caused by the change in thickness of the film (\(d\)) and local dielectric constant (\(\epsilon\)), which can be calculated by the following equation [42]:  
\[C_{\rm dl}=\frac{\epsilon^{0}\epsilon A}{d} \tag{4}\]  
where \(\epsilon^{0}\) is the permittivity of air, and \(A\) is the exposed surface area. On the carbon steel/solution interface, the TSCA molecules replace the water molecules, thickening the film and decreasing the local dielectric constant in the replacement process due to the larger particle size and lower electrical conductivity of the TSCA molecule than the water molecule [43]. Thus, the double-layer capacitance decreases in the presence of TSCA molecules, which is good for protecting the carbon steel. In addition, the deviation parameter value is controlled by the inhomogeneity of the carbon steel surface.