## 3 Results and Discussion
### Analysis of Interaction Energy  
The bonding performance of the C-S-H/SiO\({}_{2}\) systems is typically assessed through the interaction energy between the C-S-H and the aggregate [13]. The interaction energy detailed formulae are as follows:  
\[E_{CSH-aggregate}=E_{aggregate}+E_{CSH}-E_{aggregate+CSH} \tag{2}\]  
Figure 5: Radial distribution functions (RDFs) of the different ionic pairs for different C-S-H/SiO\({}_{2}\) interfacial models: (**a**) Ca\({}_{\text{h}}\)-Si\({}_{\text{CSH}}\); (**b**) Si\({}_{\text{CSH}}\)-OC\({}_{\text{SH}}\). where \(E_{aggregate+CSH}\) represents the C-S-H/aggregate system total energy at balance; \(E_{aggregate}\) represents the aggregate energy; and \(E_{CSH}\) represents the C-S-H energy. The positive interaction energy represents repulsion, while the negative interaction energy represents attraction. As the positive value increases, the interface becomes more unstable. The interface adhesion improves as the absolute value of the negative value increases. In previous experimental studies, the energy ratio (ER) has frequently served as a metric to assess the ramifications of the water content on the adhesive characteristics of asphalt, in relation to the aggregate [32]. This approach derived its underpinnings from the supposition that the water susceptibility is positively correlated to the dry adhesion work, and negatively correlated to the debonding work. On this basis, [PERSON] et al. [33] and [PERSON] et al. [13] evaluated the bonding performance among C-S-Hs with the aggregate, demonstrating the effectiveness of this method on the microscopic scale. The ER can be computed by Equation (3), the adhesion work among C-S-H with the aggregate is computed with Equation (4), and the work of debonding due to the addition of water to it can be calculated according to Equation (5). The detailed formulae are as follows:  
\[ER=\left|W_{adhesion}/W_{debonding-water}\right| \tag{3}\]  
\[W_{adhesion}=\Delta E_{CSH\_aggregate}/A \tag{4}\]  
\[W_{debonding-water}=\left(\Delta E_{aggregate-water}+\Delta E_{CSH-water} \right)/A-\Delta E_{CSH-aggregate}/A \tag{5}\]  
where \(W_{adhesion}\) represents the adhesion work among C-S-H structures with the aggregate structure; \(W_{debonding-water}\) represents the work required to debond the two structures when water is present in the interface region; \(\Delta E_{CSH-water}\) represents the interaction energy of the C-S-H with water; \(\Delta E_{aggregate-water}\) represents the interaction energy among the aggregate with water; \(\Delta E_{CSH-aggregate}\) refers the interaction energy between the C-S-H and the aggregate; and \(A\) refers the area of the interface contact region. Figure 6 displays the computed interaction energy and energy ratio (ER) of C-S-H/SiO\({}_{2}\) in varying moisture contents. From Figure 6a, it can be seen that the interaction energy of the C-S-H/SiO\({}_{2}\) progressively became larger as the interfacial water-layer thickened. The occurrence of water at the interface weakened the interfacial interactions, and reduced the bonding capacity. There was a tendency for the interfacial interactions to become weaker as 1 A-thick interfacial water molecules were introduced, and the interaction energy rose from \(-\)532.8849 kcal/mol to \(-\)487.7079 kcal/mol. This phenomenon arose because the O atom in the interface water bonded easily with the Ca\({}^{2+}\) ions [28; 34], resulting in the bond created between the Ca\({}^{2+}\) ions in C-S-H and the O in SiO\({}_{2}\) being destroyed (as shown in Figure 7). As more Ca\({}^{2+}\) ions entered the water layer, the movement ability of Ca\({}^{2+}\) ions was enhanced, and it was easier to bond with the O atoms of water. Therefore, as the water layer thickened further (growing to 5 A), the interfacial interactions became observably weaker, and the energy increased from \(-\)487.7079 kcal/mol to \(-\)181.4997 kcal/mol. This result coincides with the Ca\({}^{2+}\) ion distribution law in Figure 4c,d.