## 2 Materials and Methods
### Macroscopic Properties during Sodium Chloride Action
The electrochemical impedance spectroscopy (EIS) curves are exhibited in Figure 9. As demonstrated in Figure 11, the imaginary part (\(-Z_{4}\)) of EIS curves first decreases and then increases with the increasing real part (\(Z_{\text{r}}\)). Meanwhile, the CO\({}_{2}\)-curing time makes the extreme point of the impedance spectrum shift from left to right due to the decreased electrical conduction by CO\({}_{2}\) curing, thus increasing the electrical resistivity [51]. Therefore, the EIS curves shifted from left to right with the increasing CO\({}_{2}\)-curing time. Moreover, specimens with a w/c of 0.3 show the highest real part of the extreme point of impedance spectrum. This is because the free water inside the specimens increases with the w/c, and,  
Figure 8: The variation rate of ultrasonic velocity of specimens during NaCl freeze–thaw cycles. Figure 9: The mass-loss rate of specimens during NaCl freeze–thaw cycles. thus, the free water of specimens with a w/c of 0.3 shows the lowest conduction and the highest electrical resistance. However, the corresponding real part of the extreme point of impedance spectrum of the specimens with a w/c of 0.5 is higher than a w/c of 0.4. This can be attributed to the improved carbonation degree of a higher w/c [52]. Figure 12 depicts the specimens' EIS curves following 300 NaCl freeze-thaw cycles. As illustrated in Figure 12, similar tendencies of the EIS curves to Figure 11 can be observed. Comparing Figure 11 with Figure 12, the corresponding real part of the extreme point of impedance spectrum of the specimens increases with NaCl freeze-thaw cycles, due to the inner cracks generated after freeze-thaw cycles, and thus results in the reduction in electrical conduction of cement mortar [53]. Furthermore, CO\({}_{2}\) curing reduces the rate at which the actual portion increases during NaCl freeze-thaw cycles. This is because CO\({}_{2}\) curing of cement mortar might improve the hydration products' compactness, thereby boosting the resistance to NaCl freeze-thaw cycles [54; 55]. Because of improved compactness and less free water due to a lower water-cement ratio, the actual portion of specimens with a w/c of 0.3 shows the slowest rise. The rise in the real part of specimens with a w/c of 0.5 is lower than that of specimens with a w/c of 0.4, due to the higher carbonation degree. Figure 11: EIS curves of steel bar-reinforced cement mortar before NaCl freeze–thaw cycles. Figure 10: The mass-loss rate of the inner steel bars during NaCl freeze–thaw cycles. To investigate the corrosion degree of steel bars, the equivalent circuit diagram was generated by fitting the experimental curves with Zsimpwin, according to the equivalents of Figures 11 and 12. The equivalent circuits derived from the AC impedance spectrum are shown in Figure 13[56, 57, 58]. As indicated in Figure 13, the corresponding circuits may be separated into four electrical components in series. The first part was the contact electrical resistance between electrodes and specimens. The other three parts were parallel electrical resistance and reactance of pore solution, cement mortar and passive film. The chi square of each specimen was less than or equal to the value of 0.045, indicating that this equivalent circuit model was rational and appropriate to the conductive mechanism. Figure 14 depicts the electrical resistance of the steel bars' passive film, pore solution and cement-mortar matrix calculated using equivalent circuits. Figure 14a shows how the electrical resistance of passive film increases with the number of freeze-thaw cycles and reduces with CO\({}_{2}\)-curing age. This is because the NaCl freeze-thaw process can accelerate the corrosion of the passive film on steel bars, and rust on the surface of steel bars can impede electron transmission, lowering electrical conductivity [59]. A longer CO\({}_{2}\)-curing period, on the other hand, improves the compactness of cement mortar, enhancing corrosion resistance and lowering electrical resistance.