## 4 Molecular Dynamics Simulation
### Kinetics at the Adsorption Interface  
The corrosion of the ECC by the sulfate solution can be understood in two aspects. First, there is the corrosion caused by water molecules, and second, there is the corrosion induced by SO\({}_{4}\)\({}^{2-}\). RDF analysis indicates that the CN can be adsorbed between C-S-H, water, and SO\({}_{4}\)\({}^{2-}\). These adsorptions will cause changes in the properties at the interface. It can be seen that the CN's enhancement mechanism of sulfate corrosion resistance can be understood by analyzing the kinetic characteristics of water molecules and SO\({}_{4}\)\({}^{2-}\) at the interface. Figure 12: The dipole moment of solution. Figure 13a illustrates the RDF results between the Na\({}_{2}\)SO\({}_{4}\) solution (without the CN) and C-S-H. A pronounced peak between Na\({}^{+}\) and O\({}_{\rm C}\) indicates a strong interaction between Na\({}^{+}\) and O\({}_{\rm C}\), suggesting significant adsorption of Na\({}^{+}\) on the C-S-H surface. Additionally, a robust interaction between O\({}_{\rm S}\) and Ca\({}_{\rm C}\) is observed, implying that SO\({}_{4}\)\({}^{2-}\) reacts with C-S-H to form expansive products. Furthermore, coordination interactions between O\({}_{\rm H}\)-H\({}_{\rm C}\), O\({}_{\rm H}\)-Ca\({}_{\rm C}\), and H\({}_{\rm O}\)-O\({}_{\rm C}\) suggest that water molecules also interact with C-S-H, leading to the dissolution of hydration products and the degradation of C-S-H's internal structure. Figure 13b presents the RDF results for the CN solution, where a decrease in the peak value for O\({}_{\rm S}\)-Ca\({}_{\rm C}\) is evident. This suggests that the presence of CN reduces the spatial correlation between Na\({}_{2}\)SO\({}_{4}\) and C-S-H, lowers the coordination number between atomic pairs, and mitigates the corrosive effect of SO\({}_{4}\)\({}^{2-}\) on the matrix. Additionally, the decrease in the peaks corresponding to O\({}_{\rm H}\)-H\({}_{\rm C}\), O\({}_{\rm H}\)-Ca\({}_{\rm C}\), and H\({}_{\rm O}\)-O\({}_{\rm C}\) coordination indicates that the adsorption between C-S-H and water molecules is weakened, and CN alleviates the erosion of C-S-H by water. Under the interaction of O\({}_{\rm CN}\)-H\({}_{\rm C}\), O\({}_{\rm CN}\)-Ca\({}_{\rm C}\), and H\({}_{\rm CN}\)-O\({}_{\rm C}\) atom pairs (Figure 11), the CN adsorbs onto the surface of C-S-H, forming a protective layer that mitigates the corrosion of C-S-H by SO\({}_{4}\)\({}^{2-}\) and water molecules. Additionally, the adsorption of the CN by SO\({}_{4}\)\({}^{2-}\) reduces the amount of SO\({}_{4}\)\({}^{2-}\) adsorbed by C-S-H, thereby inhibiting the formation of expansive products. The adsorption of water molecules by the CN further diminishes the number of water molecules involved in C-S-H adsorption, alleviating the erosion of C-S-H by water. In summary, the surface coating protection provided by the CN and its ability to absorb both SO\({}_{4}\)\({}^{2-}\) and water molecules are critical factors in significantly enhancing the sulfate corrosion resistance of the ECC. The density distribution of water molecules along the CN adsorption direction (Z-axis) is shown in Figure 14a. The water molecule density reaches a maximum of approximately 1.4 g/cm\({}^{3}\) at 1.8 A from the adsorption interface, indicating the strong hydrophilicity of C-S-H. The presence of the CN slightly decreases the maximum density of water molecules from 1.40 g/cm\({}^{3}\) to 1.39 g/cm\({}^{3}\), likely due to the hydrophilic CN adsorbing some water molecules and preventing them from approaching the C-S-H surface. Furthermore, the presence of the CN significantly reduces the density of water molecules at distances of 3-5 A from the interface, as the CN occupies the positions previously held by water molecules after adsorbing onto the C-S-H surface. Figure 13: RDF results between sodium sulfate solution and C-S-H. (**a**) Without CN; (**b**) with CN. The density distribution of SO4\({}^{2-}\) in Figure 14b exhibits a trend similar to that of water molecules.