# Mechanism of Rejuvenation in Aged SBS-Modified Asphalt by Density Functional Theory
## 4 Results and Discussion
### Charge Transfer Number (\(Q_{\text{transfer}}\))  
\(Q_{\text{transfer}}\) was used to characterize the interaction between molecules, which not only reflected the intensity of molecular interaction, but also indicated whether the chemical interaction occurred. Generally, there were no chemical bonds between molecules, and no chemical interactions occurred when \(Q_{\text{transfer}}\) was less than 0.5 e. The chemical interactions were more likely to occur when \(Q_{\text{transfer}}\) was more than 0.5 e [38; 39; 40]. The calculation formula for \(Q_{\text{transfer}}\) is shown in Equation (2). \[Q_{\text{transfer}}=Q_{\text{AB}}-Q_{\text{A}} \tag{2}\]  
where, \(Q_{\text{transfer}}\) is the charge transfer number between A and B; \(Q_{\text{AB}}\) is the total charge number of A and B; \(Q_{\text{A}}\) is the charge number of A. \(Q_{\text{transfer}}\) between aromatic molecules in rejuvenator and components molecules in aged asphalt are presented in Tables 9 and 10. \(Q_{\text{transfer}}\) between saturate molecules in rejuvenator and components molecules in aged asphalt are presented in Tables 11 and 12. From Tables 9 and 10, it is found that in short-term aged asphalt, the absolute values of \(Q_{\text{transfer}}\) between rejuvenator aromatic molecules with asphaltene-phenol(S), asphaltene-pyyrrole (S), and asphaltene-thiophene (S) molecules are 0.0937 e, 0.0389 e, and 0.0623 e. However, in long-term aged asphalt, \(Q_{\text{transfer}}\) turns into 0.0811 e, 0.1171 e, and 0.0519 e, respectively. This indicates that the closeness of the interaction between asphaltene molecules in asphalt and aromatic molecules in rejuvenator could not be affected by asphalt aging level. Combined with the \(E_{\text{binding}}\) conclusion, it could be inferred that there was no direct correlation between the interaction potential and closeness of molecular interactions. \begin{table}
\begin{tabular}{c c} \hline
**Properties** & \(E_{\text{binding}}\)**/Ha** \\ \hline Aromatic—SBS & 0.136 \\ Aromatic—SBS molecular aging product 1 & 0.111 \\ Aromatic—SBS molecular aging product 2 & \(-\)0.056 \\ Saturate—SBS & 0.023 \\ Saturate—SBS molecular aging product 1 & \(-\)0.075 \\ Saturate—SBS molecular aging product 2 & 0.075 \\ \hline \end{tabular}
\end{table} 
Table 8: \(E_{\text{binding}}\) between light components in rejuvenator and SBS molecule with its aging products. \begin{table}
\begin{tabular}{c c} \hline
**Properties** & \(Q_{\text{transfer}}\)**/e** \\ \hline Aromatic—Pyridinohopane (S) & 0.1477 \\ Aromatic—Asphaltene-phenol (S) & 0.0937 \\ Aromatic—Quinolinolnopane (S) & 0.0864 \\ Aromatic—Benzobisbenzothiophene (S) & \(-\)0.0762 \\ Aromatic—Thioisorenieratane (S) & 0.0688 \\ Aromatic—Trimethylbenzeneoxane (S) & 0.0682 \\ Aromatic—Asphaltene-thiophene (S) & 0.0623 \\ Aromatic—Asphaltene-pyrrole (S) & 0.0389 \\ \hline \end{tabular}
\end{table} 
Table 9: \(Q_{\text{transfer}}\) between aromatic components in rejuvenator and heavy components in short-term aged asphalt. Similarly, from Tables 11 and 12, it can be observed that \(Q_{\text{transfer}}\) between saturate molecules in rejuvenator and component molecules in aged asphalt are all less than 0.5 e, which indicates that there is no chemical interaction between rejuvenator and aged asphalt. Table 13 presents \(Q_{\text{transfer}}\) between aromatic and saturate components in rejuvenator with SBS and its aging products. The conclusion could be summarized as \(Q_{\text{transfer}}\) between SBS and its aging products molecules with aromatic molecules in rejuvenator were positive, while those with saturate molecules were negative. It could be related to the molecular structure. Aromatic molecules had a stable structure with benzene rings, which could be considered as electron donors. Saturate molecules and SBS molecules both had long-chain structures, which were unstable and prone to accept electrons.