## 2 Surface Free Energy Theory  
A method for the determination of the surface energy of bitumen and its components is discussed. According to the analysis by [PERSON] et al., the surface energy of a substance (\(\gamma\)) is mainly composed of a polar component (\(\gamma^{p}\)) and a dispersion component (\(\gamma^{d}\)); the polar component includes a Lewis acid (\(\gamma^{+}\)) and a Lewis base (\(\gamma^{-}\)). The relationship is as shown in Equation (1):  
\[\gamma=\gamma^{d}+\gamma^{p}=\gamma^{d}+2\sqrt{\gamma^{+}\gamma^{-}} \tag{1}\]  
During the mixing process, the asphalt will wrap and adhere to the aggregate surface. According to the surface physicochemical theory, the surface energy change of the asphalt and aggregate system can be expressed by Equation (2):  
\[W_{as}=\gamma_{a}+\gamma_{s}-\gamma_{as} \tag{2}\]  
Among them, \(W_{as}\) is asphalt-aggregate adhesion work, \(\gamma_{a}\) is asphalt surface energy, \(\gamma_{s}\) is aggregate surface energy, \(\gamma_{as}\) is interface energy on the interface between asphalt and aggregate. According to the description in the literature [30], the free energy of the interface between asphalt and aggregate can be expressed by Equation (3):  
\[\gamma_{as}=\gamma_{a}+\gamma_{s}-2\sqrt{\gamma_{a}^{d}\gamma_{s}^{d}}-2\sqrt {\gamma_{a}^{p}\gamma_{s}^{p}} \tag{3}\]  
\(\gamma_{a}^{d}\) and \(\gamma_{s}^{d}\) are the dispersion components of asphalt and aggregate, but \(\gamma_{a}^{p}\) and \(\gamma_{s}^{p}\) are the polar components of asphalt and aggregate, respectively. In addition, according to [PERSON]'s equation, the relationship between the contact angle of asphalt and stone surface and its SFE and interface energy satisfies the relationship shown in Equation (4):  
\[\gamma_{a}\cos\theta=\gamma_{s}-\gamma_{as} \tag{4}\]  
Combining Equations (1) to (4), we can obtain Equation (5) as follows:  
\[W_{as}=\gamma_{a}(1+\cos\theta)=2\sqrt{\gamma_{a}^{d}\gamma_{s}^{d}}+2\sqrt{ \gamma_{a}^{+}\gamma_{a}^{-}}+2\sqrt{\gamma_{a}^{-}\gamma_{s}^{+}} \tag{5}\]  
In fact, Equation (5) is the classic Young-Dupre formula. Notably, this formula has two effects in this study. In the mixing process of asphalt mixture, the asphalt is Newtonian fluid. Then, the SFE of asphalt and aggregate and its component can be substituted into Equation (5), and the adhesion work of the asphalt-aggregate system can be obtained. At normal temperature, the asphalt is solid. If the contact angles of the three liquids with known surface energy parameters and the surface of the solid asphalt are respectively measured,the equation can be established according to Equation (5) to obtain the SFE component value of the asphalt. Substituting it into Equation (1), we can calculate the SFE of asphalt. Asphalt cohesion calculation. The water damage of asphalt mixture mainly includes two aspects: the cohesion failure of asphalt cracking and the adhesion failure of asphalt from the surface of aggregate. The SFE of asphalt and its component value are not the final indicators required for research. As described above, from a thermodynamic point of view, the energy required to produce a new surface per unit area of a material under vacuum is the surface energy of the material. For asphalt, the cohesion failure per unit area can produce two new asphalt surfaces, and it is known that the cohesion work (\(W_{\textit{cohesion}}\)) is numerically equal to 2 times the surface energy value, as shown in Equation (6):  
\[W_{\textit{cohesion}}=2\gamma_{a} \tag{6}\]  
Asphalt-aggregate adhesion work calculation. As described above, the adhesion work of the asphalt aggregate can be calculated by Equation (5). Peeling work calculation. The adhesion work of asphalt-aggregate characterizes the adhesion ability of asphalt and aggregate under anhydrous conditions. In actual engineering, water must participate in the asphalt mixture.