4.1. Single-Point Energy (Esingle) and Binding Energy (Ebinding)
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 π 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
Esingle 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].
From
Table 3, it can be observed that
Esingle 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
Esingle 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
Esingle of a molecule is related to the size. The larger the molecule, the greater the
Esingle, leading to greater instability.
Ebinding 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
Ebinding indicates the interaction potential strength of the interactions between molecules. And the calculation formula for
Ebinding is shown in Equation (1).
where
EAB is the single-point energy of the combination of A and B;
EA,
EB 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
Ebinding between aromatic molecules in rejuvenator and the components molecules in aged asphalt are presented in
Table 4 and
Table 5. And
Ebinding between saturate molecules in rejuvenator and the components molecules in aged asphalt are presented in
Table 6 and
Table 7.
From
Table 4,
Table 5,
Table 6 and
Table 7, it is found that the absolute values of
Ebinding 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. The interaction between asphaltene and aromatic components was stable. In the long-term aging process, the content of aromatic components and resins was insufficient to promote the aggregation of asphaltene, which tend to combine with each other. More aromatic components started to interact with resins, and the interaction potential between aromatic components and asphaltene decreased.
It was also found that asphalt aging level affected the interaction between aromatic components in rejuvenator and asphaltene in aged asphalt. The interaction potential between aromatic components in rejuvenator and asphaltene in short-term aged asphalt in descending order were: asphaltene-thiophene (0.096 Ha) > asphaltene-phenol (0.091 Ha) > asphaltene-pyrrole (0.079 Ha). However, as for long-term aged asphalt, the order changed to: asphaltene-pyrrole (0.046 Ha) > asphaltene-phenol (0.030 Ha) > asphaltene-thiophene (0.027 Ha).
Table 8 presents
Ebinding between aromatic and saturate components in rejuvenator with SBS and its aging products. The conclusion can be summarized that compared with most asphalt components, SBS had better interaction potential with aromatic components of rejuvenator. So, some aromatic components would react with SBS first, after rejuvenator was added into aged and SBS-modified asphalt. To a certain extent, it could weaken the rejuvenation of aged asphalt.
4.2. Charge Transfer Number (Qtransfer)
Qtransfer 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
Qtransfer was less than 0.5 e. The chemical interactions were more likely to occur when
Qtransfer was more than 0.5 e [
38,
39,
40]. The calculation formula for
Qtransfer is shown in Equation (2).
where,
Qtransfer is the charge transfer number between A and B;
QAB is the total charge number of A and B;
QA is the charge number of A.
Qtransfer between aromatic molecules in rejuvenator and components molecules in aged asphalt are presented in
Table 9 and
Table 10.
Qtransfer between saturate molecules in rejuvenator and components molecules in aged asphalt are presented in
Table 11 and
Table 12.
From
Table 9 and
Table 10, it is found that in short-term aged asphalt, the absolute values of
Qtransfer between rejuvenator aromatic molecules with asphaltene-phenol(S), asphaltene-pyrrole (S), and asphaltene-thiophene (S) molecules are 0.0937 e, 0.0389 e, and 0.0623 e. However, in long-term aged asphalt,
Qtransfer 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
Ebinding conclusion, it could be inferred that there was no direct correlation between the interaction potential and closeness of molecular interactions.
Similarly, from
Table 11 and
Table 12, it can be observed that
Qtransfer 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
Qtransfer between aromatic and saturate components in rejuvenator with SBS and its aging products. The conclusion could be summarized as
Qtransfer 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.
4.3. Dynamic Shear Rheological Test (DSR)
As a viscoelastic material, the viscosity and elasticity of asphalt changed significantly after aging. Generally, DSR was used to study these changes.
Temperature scanning tests were performed on asphalt samples with different aging levels. The test temperature was set to 52–76 °C. And the temperature gradient was set to 6 °C. The temperature equilibrium time was 9 s. The test strain was 1.25%. And the angular frequency was 10 rad/s. The test results are shown in
Figure 7a,b.
Figure 7a,b displays the impact of temperature on complex shear modulus (
G*) and phase angle (
δ). The conclusion can be summarized that with the increase of asphalt aging level, the
G* value increased and the
δ value decreased. When temperature reached 76 °C, the
G* of virgin SBS-modified asphalt was 1.1 kPa, while those of short-term and long-term aged SBS-modified asphalt were 1.62 kPa and 2.89 kPa, respectively. And
δ of virgin SBS-modified asphalt was 91.5°, while those of short-term and long-term aged SBS-modified asphalt were 87.7° and 78.7°, respectively. Obviously, the aging severity can affect asphalt properties. This is because SBS-modified asphalt is a viscoelastic material. The light components have higher viscosity, while the heavy components have higher elasticity. After the temperature was raised, some light components volatilized, the other light components transformed to heavy components due to oxidation, which cause the proportion of viscous components to decrease while the elastic components increased. So, rejuvenators were added to mitigate this phenomenon.
According to
Figure 8a,b, it can be observed that as the aging level of asphalt becomes more severe, both the rutting factor and fatigue factor increase. This is reflected in the fact that during normal service life, SBS-modified asphalt pavements undergo aging due to environmental and load impact, which ensure high-temperature resistance and rutting performance of the pavement. However, the energy loss under the impact of loads increases, making the pavement susceptible to cracking and damage. After rejuvenator was added, the aged asphalt was provided with sufficient light components. Viscoelastic characteristics of aged asphalt are restored, and mechanical properties are enhanced.
4.4. Analysis of Quantum Mechanical Simulations
Li and Greenfiled [
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
Ebinding of each molecule was recalculated based on the proportions of molar mass. And the weighting calculation is showed in
Figure 9a,b, which shows
Ebinding between the light components in rejuvenator and heavy components in 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.
Ebinding 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,
Ebinding 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 asphaltenes, as well as resins, remained in a stable state throughout.
Ebinding 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.
where
Prej is the elastic transformation rate;
G*′ 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
Prej 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
Prej. In the same temperature, the
Prej in long-term aged asphalt was almost double that in short-term aged asphalt.
Similarly, from
Figure 9a, it can be found that the more severe the asphalt aging level, the greater the
Ebinding between saturate components with asphaltenes. Compared to original asphalt,
Ebinding between saturate components with asphaltenes increased 0.0135 Ha in short-term aged asphalt and increased 0.0269 Ha in long-term aged asphalt. The changes in long-term aged asphalt were almost double those in short-term aged asphalt. To this end, it could be said that
Ebinding between saturate components in rejuvenator with asphaltenes in aged asphalt could be a qualitative evaluation indicator for the rejuvenation of aged asphalt.
Based on the proportions of molar mass from
Table 14,
Qtransfer of each molecule was recalculated. And the weighting calculation is presented in
Figure 11a,b, which shows
Qtransfer between the light components in rejuvenator and heavy components in SBS-modified asphalt.
From
Figure 11a,b,
Qtransfer between heavy components molecules in aged SBS-modified asphalt with saturate components molecules in rejuvenator is more than those with aromatic components molecules. This could be related to molecular structure, which means that long-chain molecules were likely to entangle with each other, making the interactions closer.
However, it is worth noting that Qtransfer between aromatic molecules in rejuvenator with resins molecules in short-term aged asphalt was higher than saturate molecules. This was because in the process of the short-term aging of asphalt, aromatic components turned to resins first, then turned to asphaltenes. The interactions between aromatic components and resins were close, making aromatic components be consumed significantly. When the long-term aging process is coming, the interactions between aromatic components with resins were thin. Since saturate components were not affected by asphalt aging, the interactions between saturate components with asphaltenes and resins could be closer due to the decrease of aromatic components. It could be reflected in Qtransfer that in long-term aged asphalt, Qtransfer between aromatic molecules in rejuvenator with asphaltenes and resins molecules in aged asphalt were lower, at 0.0297 e and 0.0168 e, respectively. Meanwhile, Qtransfer between saturate molecules with asphaltenes and resins molecules were higher, at 0.0713 e and 0.0461 e, respectively.