# Mechanism of Rejuvenation in Aged SBS-Modified Asphalt by Density Functional Theory
## 4 Results and Discussion
### Analysis of Quantum Mechanical Simulations  
[PERSON] and [PERSON] [27] calculated the molar mass and proportions of each molecule in the AAA-1 model, as shown in Table 14.  
To further analyze the correlation between simulation results and experiment results, the \(E_{\text{binding}}\) of each molecule was recalculated based on the proportions of molar mass. And the weighting calculation is showed in Figure 9a,b, which shows \(E_{\text{binding}}\) between the light components in rejuvenator and heavy components in SBS-modified asphalt. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Asphalt Components** & **Molar Mass/g \(\times\) mol\({}^{-1}\)** & **Numbers** & **Mass/\%** \\ \hline Asphaltene-phenol & 575.8 & 3 & 9.11 \\ Asphaltene-pyrrole & 888.5 & 2 & 14.08 \\ Asphaltene-thiophene & 707.2 & 3 & 11.21 \\ Benzobisbenzodiiophene & 290.4 & 15 & 4.60 \\ Pyridinobpane & 530.9 & 4 & 8.41 \\ Quinolinohopane & 554.0 & 4 & 8.78 \\ Thioisoriereiratane & 573.1 & 4 & 9.08 \\ Trimethylbenzeneoxane & 414.8 & 5 & 6.57 \\ DOCHN & 406.8 & 13 & 6.44 \\ PHPN & 464.8 & 11 & 7.36 \\ Hopane & 483.0 & 4 & 7.65 \\ Squalane & 422.9 & 4 & 6.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Molar mass of each molecule and their respective proportions in AAA-1 model [27]. Figure 8: (**a**) Effect of temperature on runtime factor; (**b**) effect of temperature on fatigue factor. Figure 9: \(E_{\text{binding}}\) between light components in rejuvenator and heavy components in aged SBS-modified asphalt. From Figure 9a, on one hand, there is a significant difference between light components in rejuvenator and heavy components in the original asphalt. \(E_{\text{binding}}\) between aromatic components and asphaltene was very low, which indicated that the combination was very unstable. It could be explained that due to the influence of oxidative aging, aromatic components were most prone to transform to be resins, and further to be asphaltene. On the other hand, \(E_{\text{binding}}\) between asphaltene in the original asphalt with saturate components in rejuvenator was three times higher than those with aromatic components of rejuvenator. This indicated that saturate components had a stable combination with asphaltene, which was not easily affected by oxidative aging to be transformed. These results verified the conclusion that saturate components have a stable and inactive nature. From Figure 9b, it can be found that in virgin asphalt and short-term aged asphalt, the interaction between resin with saturate components is more stable than that with aromatic components, while in long-term aged asphalt, the conclusion is reversed. Since the oxidative aging process of asphalt did not cause the transformation of saturate components, the combination between saturate components and asphaltene, as well as resins, remained in a stable state throughout. \(E_{\text{binding}}\) between saturate components and asphaltenes increased with the increasing level of asphalt aging. Therefore, it could be used as an evaluation parameter for the rejuvenation effect of rejuvenator in aged SBS-modified asphalt. And this conclusion was validated by examining the changes in complex shear modulus \(G^{*}\). In order to facilitate analysis, the concept of elastic transformation rate is defined as follows. \[P_{\text{rej}}=\frac{|G^{*\prime}-G^{*}|}{G^{*}}\times 100\% \tag{3}\]  
where \(P_{\text{rej}}\) is the elastic transformation rate; \(G^{*\prime}\) is the complex shear modulus of aged SBS-modified asphalt after rejuvenator was added; \(G^{*}\) is the complex shear modulus of SBS-modified asphalt before aging. Results of elastic transformation rate \(P_{\text{rej}}\) for SBS-modified asphalt at different aging levels are shown in Figure 10. It presented that the more severe the asphalt aging level, the greater the elastic transformation rate \(P_{\text{rej}}\). In the same temperature, the \(P_{\text{rej}}\) in long-term aged asphalt was almost double that in short-term aged asphalt.