## 4 Molecular Dynamics Simulation
### Adsorption Properties of CN and C-S-H Interfaces  
The prevailing perspective on the enhancement mechanism of nanomaterials in cement-based composites suggests that nanomaterials interact with the matrix by adsorbing at the interface, influencing the behavior of water molecules, ion transport, and other properties, thereby affecting the overall characteristics of cement-based materials [47; 48]. Therefore, it is essential to analyze the adsorption properties at the CN and C-S-H interfaces. Adsorption energy serves as a key parameter for intuitively assessing the adsorption behavior at these interfaces. In this study, the adsorption energy between the CN chain and the C-S-H interface was calculated for CN molecular chains in quantities of 1, 2, 3, and 4, respectively. The results, presented in Figure 9, reveal that the adsorption energy at the CN/C-S-H interface ranges from 900 to 1100 kcal/mol, indicating strong adsorption between the CN and C-S-H. When only one CN chain is present, the adsorption between the CN and C-S-H is optimal. As the number of CN chains increases to four, the adsorption energy between each  
Figure 8: The C-S-H, CN, sodium sulfate solution, and composite adsorption models. Figure 9: Interfacial energy results of CN/C-S-H.  
CN chain and C-S-H decreases from 1060 kcal/mol to 960 kcal/mol. This decrease suggests that an excessive number of CN chains weakens the interface adsorption properties. This effect may be attributed to the high density of hydrophilic groups on the CN surface, which, at higher concentrations, form hydrogen bonds that lead to chain entanglement. As a result, the contact area between the CN and C-S-H decreases, thus reducing the interface adsorption energy. In contrast, when only one CN chain is present, it can maintain a relatively straight conformation, allowing for more effective adsorption on the C-S-H interface. It is known from the experimental results that with the increased addition of the CN, its enhancement effect on ECC performance cannot be continuously increased. The interfacial adsorption energy results also indicate that the larger number of CN chains has a weaker interaction with C-S-H. Obviously, the interfacial adsorption energy results further verified the macroexperimental results. The interface adsorption performance is closely associated with the contact area of the composite interface [49]. Atomic interactions induce shape alterations of the CN chain, thereby influencing the contact area between the CN and C-S-H. The radius of gyration (Rg) serves as a descriptor for the conformation of the model, where a larger Rg indicates a greater molecular surface area [50]. The Rg of the CN throughout the simulation is depicted in Figure 10. The evolution of Rg over time can be divided into three distinct stages: 10.84 in stage 1, 10.79 in stage 2, and stabilizing at 10.77 in stage 3. As the simulation progresses, Rg gradually decreases. During the transition from stage 1 to stages 2 and 3, the CN chain undergoes slight twisting and becomes more curved, though it largely maintains a relatively straight form. The coordination between atoms can be analyzed through the radial distribution function (RDF). The first peak on the X-axis of the RDF curve for an atomic pair reflects the spatial correlation between the atoms [51]. The RDF results for the CN and C-S-H, water, and SO42- are presented in Figure 11. A distinct peak appears at 1.6 A between the O of the CN chain (O\({}_{\text{CN}}\)) and Ca of C-S-H (Ca\({}_{\text{C}}\)). Additionally, notable peaks are observed between O\({}_{\text{CN}}\) and H in C-S-H (H\({}_{\text{C}}\)), as well as between H in the CN chain (H\({}_{\text{C}}\)) and O in C-S-H (O\({}_{\text{C}}\)). This indicates that the CN chain can adsorb to C-S-H through Ca-O and H-O coordination. The RDF curves for H\({}_{\text{CN}}\) and S and O atoms in SO42- (S\({}_{\text{S}}\), O\({}_{\text{S}}\)) also exhibit peaks, suggesting that the CN can adsorb SO42- through hydrogen bonding. Figure 10: The gyration radius results of the CN.