# Effect of Aggregate Crystalline Surface Anisotropy on
## 3 Results and Discussion  
### Distribution of Asphalt Compositions on Aggregate Surface  
The spatial distribution characteristics of asphalt component molecules significantly influence the microcolloid structures of asphalt-aggregate systems. The \(RDF\) is considered a crucial parameter in characterizing the spatial distribution of molecules. The position of one molecule relative to the distance from other molecules is assessed, providing insights into the orderliness and internal correlation of the substance. The \(RDF\) also reflects the degree of molecular aggregation during movement [31]. The effect of aggregate crystalline surface anisotropy on the spatial distribution characteristics of asphalt components was investigated by calculating and analyzing the \(RDF\) between the asphalt components and the aggregate at different crystalline surfaces. The \(RDF\) is represented as the probability of finding a particle at a distance \(r\) from a reference point. It is used to describe the distribution of molecules within the internal structure of a material. Changes in density and morphological structure are reflected in the \(RDF\) curve, which can predict variations in the mechanical properties. The \(RDF\) value, typically denoted as \(g(r)\), is shown as in Equation (1):  
\[g(r)=\frac{dN}{\rho 4\pi r^{2}dr} \tag{1}\]  
where \(g(r)\) is the \(RDF\); \(r\) is the radial distance; \(dN\) is the number of specified particles at a distance \(r\) to \(r+dr\) from the reference particle; \(\rho\) is the average density of the interfacial  
Figure 7: Model of asphalt–aggregate interface: (**a**) SiO\({}_{2}\) of (0 0 1) surface; (**b**) SiO\({}_{2}\) of (1 0 0) surface; (**c**) SiO\({}_{2}\) of (1 0 1) surface; (**d**) CaCO\({}_{3}\) of (1 0 4) surface; (**e**) CaCO\({}_{3}\) of (0 1 8) surface; (**f**) CaCO\({}_{3}\) of (2 1 4) surface. system; \(4\pi r^{2}\) is the volume between the reference particle \(r\) and \(r+dr\); \(r\) is the spacing between the asphalt molecules. In this study, the optimized equilibrium model was selected to calculate the \(RDF\) values of each asphalt component in each interfacial model using the _Forcite_ module. The \(RDF\)s of the molecules of each asphalt component in the asphalt-SiO\({}_{2}\) and asphalt-CaCO\({}_{3}\) molecular systems are shown in Figure 8.  
As shown in Figure 8, as the distance \(r\) from the aggregate surface increased, the RDF gradually increased and then stabilized. The distribution pattern of the four components on the aggregate surface was observed as follows: near the aggregate surface, the aromatic fraction exhibited the highest degree of aggregation, showing the steepest \(RDF\) curve, followed by the resin and finally the saturate and asphaltene. As the distance from the aggregate surface increased, the aromatic fraction was the first to reach equilibrium near 25 A and leveled off. The distribution of the saturate rapidly increased, exceeding that of the resin in the range of 25 to 30 A, eventually surpassing the aromatic fraction between 30 and 35 A, peaking, and then declining between 35 and 40 A. The resin and asphaltene fractions were gradually raised and slowed down as they approached the farthest point. The distribution pattern of the asphalt components on the surfaces of different aggregate types and different crystalline aggregates was essentially the same. This implies that the type of aggregate and crystalline anisotropy did not cause significant attraction or repulsion in any specific component, thereby avoiding uncertainty in the distribution pattern of the asphalt components. The magnitude of the \(RDF\) varies with different crystalline surfaces of aggregates. In the asphalt-SiO\({}_{2}\) interfacial model, the largest \(RDF\) value of the asphalt components was observed on the (1 0 1) face, as shown in (a).