## 3 Results and Discussion
### Analysis of Interaction Mechanisms  
The correlation between two particles' spatial positions in a particle system is known as the radial distribution function (RDF) [29]. Its physical meaning lies in the proportion of the atomic density in a system's local area to its average density. The RDF is determined using the following equation:  
\[g(r)=\frac{1}{4r^{2}\tau\rho\delta r}dN(r) \tag{1}\]  
Figure 4: The spatial distribution of Ca\({}^{2+}\) ions at the surface region of the C-S-H. (**a**) 0 Å; (**b**) 1 Å; (**c**) 3 Å; (**d**) 5 Å. (The green spheres represent the position of Ca\({}^{2+}\) ions in the X\(-\)Z planar, and the C-S-H surface positions are indicated by blue dashed lines).  
where \(dN(r)\) represents the number of atoms within a region from r to \(r+\delta r\), \(p\) represents the system's average density, and \(\delta r\) is the regional distance. Differences in system structure can lead to different values and trends of RDF, determining the system state. The RDF of an amorphous system has a wave peak only in the proximity, and tends toward 1 as the radius increases [30]. Given that the ClayFF force field employed different potential energy parameters for the interlayer calcium (Ca\({}_{\text{h}}\)) and intralayer calcium (Ca\({}_{\text{o}}\)) in the C-S-H [31], the Ca\({}_{\text{h}}\) dominated the motion of Ca\({}^{2+}\) ions within the model. Therefore, the RDF was analyzed in this paper by counting the Ca\({}_{\text{h}}\).  
Figure 5 shows the RDF of the different ionic pairs for varying C-S-H/SiO\({}_{2}\) interfacial models. The RDF between the ionic pairs all showed apparent peaks in the near range, and the RDF values gradually tended toward 1, as the atomic spacing increased. This conforms to the short-range ordered and long-range disordered structural characteristics of amorphous matter. The peaks of RDF appeared at the same position, indicating that there was no influence from the interfacial water molecule content on the bond lengths of Ca\({}_{\text{h}}\)-Si\({}_{\text{CSH}}\) and Si\({}_{\text{CSH}}\)-O\({}_{\text{CSH}}\). However, in the C-S-H/SiO\({}_{2}\) model with varying interfacial water molecule contents, there were some variations in the RDF peaks of the different ion pairs.  
When the interfacial water layer thickened (introducing a 1 A thickness), the RDF peak values of Ca\({}_{\text{h}}\)-Si\({}_{\text{CSH}}\) gradually became larger (Figure 5a), indicating that the quantity of Ca\({}_{\text{h}}\) ions around the Si ions increased gradually within C-S-H. The Ca\({}_{\text{h}}\)-Si\({}_{\text{CSH}}\) RDF peak values showed a decreasing law as the water-layer thickness increased from 1 A to 5 A, indicating that the amount of Ca\({}_{\text{h}}\) ions close to the Si ions in C-S-H decreased gradually. This result agrees with the Ca\({}^{2+}\) distribution in the C-S-H surface region observed by the C-S-H/SiO\({}_{2}\) interfacial model for varying thicknesses of the water layer (Figure 4).  
As the interfacial water layer thickened, the RDF peak values of the Si\({}_{\text{CSH}}\)-O\({}_{\text{CSH}}\) increased continuously (Figure 5b). It can be seen that an augmentation of the thickness of the water layer resulted in a higher accumulation of O atoms accumulated by Si atoms in a short range. This result demonstrates that as the water layer became thicker, more water molecules intruded into the C-S-H (Figure 3).