# Mechanism of Rejuvenation in Aged SBS-Modified Asphalt by Density Functional Theory
## 4 Results and Discussion  
### Single-Point Energy (E\({}_{single}\)) and Binding Energy (E\({}_{binding}\))  
Electric potential plays a crucial role in physics research. It is defined as the electric field interaction potential caused by the charge density distribution in a space where no electric current is occurring. Therefore, it is used to represent the distribution of charge density in a system. From Figure 6, it can be observed that there are significant differences in the charge density at different positions in molecular structure of SBS-modified asphalt components. The negative charge is primarily distributed in the aromatic ring region. This is because there are a large number of \(\pi\) electrons within the aromatic ring, resulting in a negative charge distribution. Therefore, the positive charge is distributed in the outer region of the aromatic ring and on branched-chain near the aromatic ring. Table 3 exhibits \(E_{\text{single}}\) of asphalt components and SBS with its aging products. In general, the higher the energy of a molecule, the more unstable it tends to be. And the greater the energy difference between two molecules, the better the compatibility between them [37]. Figure 6: Electron density of SBS-modified asphalt components. From Table 3, it can be observed that \(E_{\text{single}}\) of SBS molecules is significantly higher than that of asphalt components. Therefore, compared to the molecules of asphalt components, SBS molecules were less stable and prone to fracture. The energy difference between SBS molecules and DOCHN is the largest, while the difference between SBS molecules and asphaltene-pyrrole is the smallest, indicating that SBS polymer has the best compatibility with aromatic components and the poorest compatibility with asphaltene components. Analysis of the \(E_{\text{single}}\) of asphalt components reveals that asphaltene-pyrrole > asphaltene-thiophene > thioisorenieratane > asphaltene-phenol > quinolinohopane > benzobisbenzothiophene > pyridinohopane > hopane > PHPN > trimethylbenzeneoxane > squalane > DOCHN. The conclusion could be summarized that \(E_{\text{single}}\) of a molecule is related to the size. The larger the molecule, the greater the \(E_{\text{single}}\), leading to greater instability. \(E_{\text{binding}}\) is a commonly used microscopic characterization that quantifies the strength of interactions between two molecules. A negative value indicates mutual attraction, while a positive value indicates mutual repulsion. The absolute value of \(E_{\text{binding}}\) indicates the interaction potential strength of the interactions between molecules. And the calculation formula for \(E_{\text{binding}}\) is shown in Equation (1). \[E_{\text{binding}}=E_{\text{AB}}-(E_{\text{A}}+E_{\text{B}}) \tag{1}\]  
where \(E_{\text{AB}}\) is the single-point energy of the combination of A and B; \(E_{\text{A}}\), \(E_{\text{B}}\) are the single-point energy of A and B, respectively. Since rejuvenation is the light components entered into the aged asphalt to reduce the high proportion of heavy components, only the interaction between light components in rejuvenator and heavy components in aged asphalt was studied [30]. The calculated results of \(E_{\text{binding}}\) between aromatic molecules in rejuvenator and the components molecules in aged asphalt are presented in Tables 4 and 5. And \(E_{\text{Binding}}\) between saturate molecules in rejuvenator and the components molecules in aged asphalt are presented in Tables 6 and 7. From Tables 4-7, it is found that the absolute values of \(E_{\text{binding}}\) between asphaltene molecules in short-term aged asphalt and aromatic molecules in rejuvenator are higher than those between asphaltene molecules in long-term aged asphalt and aromatic molecules in rejuvenator. This could be explained as during the short-term aging process, there was a rapid increase in the content of asphaltene components in asphalt, which also attracted a large number of aromatic molecules to be adsorbed on its surface.