# Effect of Aggregate Crystalline Surface Anisotropy on
## 3 Results and Discussion
### Adhesion of Asphalt with Aggregates  
The adhesion property between asphalt and aggregates is a crucial factor in determining the durability of asphalt mixtures. MD simulations provide a better evaluation of the differences in the adhesion properties across asphalt-aggregate interfaces under various conditions. In this section, the variation in the adhesion properties between asphalt and the crystallographically anisotropic acidic aggregate SiO\({}_{2}\) and basic aggregate CaCO\({}_{3}\) is investigated using the interaction energy and adhesion energy as evaluation indexes. Interaction energy refers to the energy required for components within a system to combine. It is an important indicator of the strength of the interaction between two substances. A negative interaction energy value indicates attraction, and the larger the absolute value, the stronger the force. The interaction energy is calculated as shown in Equation (4):  
\[E_{int}=E_{total}-E_{A}-E_{B} \tag{4}\]  
where \(E_{int}\) is the interaction energy between the parts; \(E_{total}\) is the total energy of the equilibrium of the blending system; \(E_{A}\) is the total energy after the equilibrium of part \(A\) of the blending system; \(E_{B}\) is the total energy after the equilibrium of part \(B\) of the blending system. The adhesion energy is the work performed per unit area when the interface between two separated phases generates two free surfaces. It is closely related to the fracture damage resistance and the durability of the blend. This calculation method has been proven effective in assessing the bonding strength of the interfacial model by many researchers. The adhesion energy is calculated as shown in Equation (5) [32]. \[W_{adhesion}=\frac{\Delta E}{A}\times K=\frac{-E_{int}}{A}\times K \tag{5}\]  
where \(W_{adhesion}\) is the adhesion energy at the interface; \(\Delta E\) is the binding energy between the two materials, i.e., the negative value of the interaction energy; \(A\) is the cross-sectional area of the interface; and the unit of conversion factor is \(K\) = 695. When the interface area is the same, higher adhesion energy is exhibited by systems with higher interaction energy, as shown in Figure 11. The interaction energy is composed of van der Waals energy and electrostatic energy. Van der Waals energy is defined as the non-electric short-range force energy produced by external forces acting on an object, while electrostatic energy is defined as the electric long-range force energy generated by interactions between electrons [33]. Negative interaction energy indicates that an attractive force exists between the two. Thus, adhesion work is essentially represented as the work performed by the attractive force per unit interface area; a higher value indicates better adhesion performance. The adhesion energy of the six asphalt-aggregate interface models calculated in this study is consistent with the experimental results (60-150 mJ/m\({}^{2}\)) of related studies [34; 35]. The average adhesion energy of asphalt on the three surfaces of alkaline aggregates is 22.9% greater than that on the three surfaces of quartz, as shown in Figure 12. The interaction energy in the asphalt-SiO\({}_{2}\) system is primarily dominated by van der Waals energy, whereas, in the asphalt-CaCO\({}_{3}\) system, both van der Waals and electrostatic energy play significant roles. Comparing the three interface models of asphalt-SiO\({}_{2}\) and asphalt-CaCO\({}_{3}\), the interaction energy of the asphalt-SiO\({}_{2}\) system is dominated by van der Waals energy. In contrast, both van der Waals energy and electrostatic energy significantly influence the interaction energy of the asphalt-CaCO\({}_{3}\) system, resulting in larger interaction energy than that of the asphalt-SiO\({}_{2}\) system.