Mechanism of Rejuvenation in Aged SBS-Modified Asphalt by Density Functional Theory

Abstract

As a large area of SBS-modified asphalt pavement entered the maintenance period, the aging and rejuvenation of SBS-modified asphalt have attracted attention in recent years. In order to further study the rejuvenation of aged SBS-modified asphalt, both rheological experiments and quantum mechanical simulations were used. Complex shear modulus (G*) and phase angle (δ) were used to analyze the rejuvenation effect of aged SBS-modified asphalt. Electron density, binding energy (E_binding), and charge transfer number (Q_transfer) were used to observe the process of rejuvenation in aged SBS-modified asphalt. The results show that compared to asphalt components, SBS polymer was the least stable and most susceptible to breaking. After oxidative aging, SBS polymer with its aging products could impair the rejuvenation in aged asphalt. The interaction between aromatic components in rejuvenator and asphaltenes in aged asphalt was unstable and could be influenced by asphalt aging level. The interaction between heavy component molecules in aged asphalt with saturate component molecules in rejuvenator are closer than those with aromatic components molecules. The binding energies between saturate components in rejuvenator and asphaltenes in aged asphalt could be served as an evaluation indicator of rejuvenation.

1. Introduction

Styrene-butadiene-styrene (SBS)-modified asphalt is widely used in pavement engineering due to its excellent high-temperature stability and low-temperature crack resistance [1,2,3]. With the changes of environment and traffic loads, SBS-modified asphalt pavement has entered the stage of maintenance and repairment in China. As a result, a large amount of old SBS-modified asphalt mixtures are generated annually [4,5]. Casual handing could cause resource wastage and environmental pollution [6]. To restore the performance of aged asphalt and meet the road requirements, rejuvenators are usually added for components adjustment [7,8,9,10].

Different from virgin asphalt, the aging of SBS-modified asphalt consisted of asphalt aging and SBS degradation [11]. Carbonyl and sulfoxides content, average molecular mass, and viscosity all increased due to asphalt aging [12]. The physical and rheological properties of asphalt were affected by the degradation of SBS [13]. In linear SBS molecules, the chains of polybutadiene were broken by thermal oxidation, making C=C bonds break and combine with oxygen to form hydroxyl groups [14,15,16]. Zhang [17] et al. investigated the aging performance of SBS-modified asphalt with various aging methods, which found that the aging of SBS-90 (virgin asphalt penetration 90) was worse than that of SBS-70 (virgin asphalt penetration 70). Guo et al. [18] compared the effects on microproperties and molecular composition of aged and rejuvenated SBS-modified asphalt. It was found that based on the energy spectrum, the carbon content of aged SBS-modified asphalt decreased, while the oxygen content and sulfur content increased.

Development of density functional theory (DFT) has made significant breakthroughs in addressing quantum mechanical problems in materials science. DFT pointed out that the energy of a system was determined solely by its electronic density distribution. There existed a self-consistent relationship between electronic density and energy of the system [19,20]. Based on DFT, Qing [21] calculated the molecular charge density, electron density difference, and binding energy (E_binding) of graphene oxide (GO). As a result, the bonding between resins and GO was the most stable, followed by aromatic components with GO. And the bonding between saturate components and GO was the weakest. In addition, GO hindered the movement and volatilization of saturate components, improving the high-temperature stability and heat aging resistance of asphalt. Based on DFT, the impact of SBS on the molecular vibrations of each component in asphalt was studied [22]. Vibration spectrums and E_binding between SBS systems and molecular components of asphalt were analyzed and calculated. And Fourier-Transform Infrared Spectroscopy (FTIR) testing was performed on SBS-modified asphalt. It was found that the vibrational peak intensity of SBS with the light components in asphalt was stronger than that of the heavy components.

To ensure the correctness of quantum mechanical simulation results, it is necessary to establish a reasonable asphalt model. However, due to the complexity of asphalt composition, it is impossible to measure all molecular structures and add them to the model [23]. The American Society for Testing and Materials (ASTM) has proposed the four components method to classify asphalt into saturate (S), aromatic (A), resin (R), and asphaltene (A) components [24,25]. However, Li and Greenfield found the “pentane effect” on certain asphaltene by density functional theory (DFT) and quantum mechanical calculations. This means that although the asphaltene model is feasible for simulation, it is difficult to stabilize and maintain in actual chemical reactions, due to excessively high energy of the molecular system. Non-planar aromatic rings have emerged, which is inconsistent with the real experimental results [26]. Therefore, improvements made based on the four-component model and the asphalt AAA-1 model were proposed [27]. The asphaltene components were divided into asphaltene-phenol, asphaltene-pyrrole, and asphaltene-thiophene; the resin components were divided into quinolinohopane, thioisorenieratane, trimethylbenzeneoxane, pyridinohopane, and benzobisbenzothiophene; the saturate components were divided into squalane and hopane; and the aromatic components were divided into PHPN and DOCHN. The method is being applied by an increasing number of scholars [28].

In a word, based on DFT, the interaction between polymers and asphalt could be further studied with quantum mechanical simulation by electron densities, E_binding, and so on. However, compared to molecular dynamic simulation, the quantum mechanical simulation was not used widely. There is still a lack of research on the rejuvenator components and aged SBS-modified asphalt components, which plays an important role in the deep study of rejuvenation mechanisms. To this end, this study used quantum mechanical simulation based on DFT to further analyze the interaction between rejuvenators and aged SBS-modified asphalt.

2. Materials and Experiments

2.1. Raw Materials

The SBS-modified asphalt was supplied by Jinya Maintenance Emergency Support Base in China. Its technical indicators are displayed in

Table 1. SBS-modified asphalt technical indicators.

Properties		Experiment Values	Technical Requirements
Penetration/0.1 mm		72	60–80
Softening point/°C (ringball method)		80.5	≥55
Ductility/cm		36	≥30
Viscosity/Pa·s−1		2.175	≤3
Flash point/°C		285	≥230
Solubility/%		99.5	≥99
Residual asphalt binder remaining after RTFOT	Mass loss/%	0.56	≤1
	Penetration ratio/%	78	≥60
	Ductility/cm	44	≥20

. Experiment values were tested according to the Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [29]. All the values met the restricted range defined.

The rejuvenator was supplied by Jiangsu Kelaifu Pavement Maintenance Co., Ltd. in Nanjing, China. Actually, the rejuvenator is a softening agent, which provides abundant light components to make aged asphalt rejuvenated. Significantly, the content of aromatic components plays a decisive role in the rejuvenation effect [30]. Due to the bad compatibility between asphaltenes and saturate components, few or no saturate components in the rejuvenator is better. The technical indicators of the rejuvenator are displayed in

Table 2. Rejuvenator technical indicators.

Properties	Viscosity/Pa·s−1	Flash Point/°C	Density/g·cm−3	Residual Asphalt Binder Remaining after RTFOT/%	Aromatic Components/%	Saturate Components/%
Experiment values	109	208	0.932	−2.5	36	7

.

2.2. Aged SBS-Midified Asphalt

The Rolling Thin Film Oven Test (RTFOT) was used to prepare the short-term aged asphalt, at a temperature of 163 °C for 85 min. An amount of 35 g of asphalt was injected into a dry sample bottle, which would be placed on a circular rack to rotate, with a speed of 15 revolutions per minute. Finally, hot air with a flow rate of 4000 mL/min was introduced into the sample, and after 85 min, the short-term aged asphalt is prepared.

A pressure aging vessel (PAV) (Koehler Instrument Company, Inc., Bohemia, NY, USA) was utilized to accelerate the long-term aging test of asphalt. The short-term aged asphalt was used for the long-term aged asphalt, with a temperature of 100 °C and a pressure of 2.1 MPa for 20 h.

2.3. Rejuvenated SBS Modified Asphalt

The short-term and long-term aged asphalt are heated and poured into a high-speed shear mixer. Rejuvenator was also added, with a 10% dosage of asphalt, which was a regular dose determined by empirical method. To ensure uniform dispersion of rejuvenator during the mixing process, mixing speed was set at 1800 r/min and mixing time was 30 min. And the temperature was 135 °C.

3. Quantum Mechanical Simulation

Asphalt and Rejuvenator Models

Based on the AAA-1 model [27], an asphalt molecular model was constructed, as shown in Figure 1. Due to their stable and inactive nature, the models of saturate components are unchanged in the aging process [31]. Previous studies [31] had found that the aging process of asphalt could be divided into two different stages. In the first stage, the asphalt underwent rapid initial oxidation reactions within the hydrocarbon structure and as a result, some functional groups were generated, such as sulfoxide groups, aromatized benzene rings, and hydroxyl groups. In the other stage, hydroxyl groups were further oxidized into ketones.

As the rejuvenator used in this study is a softening agent, the asphaltene model and saturate model were chosen from Zhang and Greenfield’s research [32], which was used to represent the chemical families found in paving asphalts. The resin model was chosen from Murgich et al.’s research [33], and the aromatic model was chosen from Verstraete et al.’s research [34]. The rejuvenator components models are exhibited in Figure 2.

The SBS molecule comprised a styrene molecular monomer (hard segment) and 1,3 butadiene molecular monomer (soft segment). To balance the rigid and flexible molecules, an SBS molecular model was constructed with a ratio of styrene to butadiene as 3:7, as shown in Figure 3. After oxidation, the SBS polymer chains were broken at the C=C bonds in polybutadiene segments. One of the aging products was oxidized to form hydroxyl groups, another was oxidized to form carboxyl groups [35], which were shown in Figure 4. Due to severe degradation and loss of modified functionality [36], the SBS molecules in long-term aged asphalt were not considered in this study.

All molecular models were established in Materials Studio. In order to study the interaction between the component molecules of rejuvenator and aged SBS-modified asphalt, amorphous cells were built, containing one rejuvenator component molecule and one asphalt molecule or SBS molecule. The cell size is 12 Å × 12 Å × 12 Å. Due to space limitations, only amorphous cells consisting of aromatic components of rejuvenator and SBS-modified asphalt components were presented, as shown in Figure 5. And the lattice has been removed for better observation.

All molecular simulations were completed in DMol3 package of Materials Studio. As the local density approximation (LDA) could not be used to study hydrogen bonding interactions, the generalized gradient approximation (GGA) method was used to calculate the exchange–correlation energy. GGA also had higher calculation accuracy. To save calculation cost, there was no special treatment of nuclear electrons, which means that all electrons were included in the calculation. The energy tolerance accuracy was set to 2.0 × 10⁻⁵ Ha. The force convergence tolerance was set to 0.004 Ha/Å. The basis set was DND. The SCF tolerance was set to 1 × 10⁻⁵ Ha. The maximum number of SCF cycles was 50. And the global orbital cutoff was 3.3 Å.

4. Results and Discussion

4.1. 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 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. E_single of SBS molecular and its aging products.

Properties	Esingle/Ha	Properties	Esingle/Ha
Asphaltene-phenol	1706.47	PHPN	1358.78
Asphaltene-pyrrole	2615.86	DOCHN	1169.59
Asphaltene-thiophene	2376.79	Hopane	1369.45
Benzobisbenzothiophene	1487.37	Squalne	1179.13
Pyridinohopane	1459.27	SBS	4043.67
Quinolinohopane	1612.76	SBS molecular aging product 1	2096.41
Thioisorenieratane	1956.70	SBS molecular aging product 2	2171.62
Trimethylbenzeneoxane	1209.10

exhibits E_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].

From Table 3, it can be observed that E_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_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_single of a molecule is related to the size. The larger the molecule, the greater the E_single, leading to greater instability.

E_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_binding indicates the interaction potential strength of the interactions between molecules. And the calculation formula for E_binding is shown in Equation (1).

$$E_{\mathrm{binding}}=E_{\mathrm{AB}}-\left(E_{\mathrm{A}}+E_{\mathrm{B}}\right)$$

(1)

where E_AB is the single-point energy of the combination of A and B; E_A, E_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_binding between aromatic molecules in rejuvenator and the components molecules in aged asphalt are presented in

Table 4. E_binding between aromatic components in rejuvenator and heavy components in short-term aged asphalt.

Properties	Ebinding/Ha
Aromatic—Benzobisbenzothiophene (S)	−0.107
Aromatic—Asphaltene-thiophene (S)	0.096
Aromatic—Asphaltene-phenol (S)	0.091
Aromatic—Asphaltene-pyrrole (S)	−0.079
Aromatic—Thioisorenieratane (S)	−0.030
Aromatic—Pyridinohopane (S)	0.024
Aromatic—Quinolinohopane (S)	−0.006
Aromatic—Trimethylbenzeneoxane (S)	0.003

and

Table 5. E_binding between aromatic components in rejuvenator and heavy components in long-term aged asphalt.

Properties	Ebinding/Ha
Aromatic—Thioisorenieratane (L)	0.211
Aromatic—Pyridinohopane (L)	0.107
Aromatic—Benzobisbenzothiophene (L)	−0.094
Aromatic—Asphaltene-pyrrole (L)	−0.046
Aromatic—Quinolinohopane (L)	−0.033
Aromatic—Asphaltene-phenol (L)	0.030
Aromatic—Asphaltene-thiophene (L)	−0.027
Aromatic—Trimethylbenzeneoxane (L)	−0.026

. And E_binding between saturate molecules in rejuvenator and the components molecules in aged asphalt are presented in

Table 6. E_binding between saturate components in rejuvenator and heavy components in short-term aged asphalt.

Properties	Ebinding/Ha
Saturate—Thioisorenieratane (S)	0.200
Saturate—Asphaltene-phenol (S)	0.168
Saturate—Asphaltene-pyrrole (S)	0.157
Saturate—Benzobisbenzothiophene (S)	−0.132
Saturate—Asphaltene-thiophene (S)	−0.034
Saturate—Quinolinohopane (S)	−0.028
Saturate—Pyridinohopane (S)	−0.015
Saturate—Trimethylbenzeneoxane (S)	0.006

and

Table 7. E_binding between saturate components in rejuvenator and heavy components in long-term aged asphalt.

Properties	Ebinding/Ha
Saturate—Asphaltene-thiophene (L)	0.279
Saturate—Asphaltene-phenol (L)	0.105
Saturate—Asphaltene-pyrrole (L)	0.098
Saturate—Quinolinohopane (L)	0.092
Saturate—Benzobisbenzothiophene (L)	0.085
Saturate—Thioisorenieratane (L)	−0.063
Saturate—Pyridinohopane (L)	−0.037
Saturate—Trimethylbenzeneoxane (L)	0.037

.

From Table 4, Table 5, Table 6 and Table 7, it is found that the absolute values of E_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. 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. E_binding between light components in rejuvenator and SBS molecule with its aging products.

Properties	Ebinding/Ha
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

presents E_binding 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 (Q_transfer)

Q_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_transfer was less than 0.5 e. The chemical interactions were more likely to occur when Q_transfer was more than 0.5 e [38,39,40]. The calculation formula for Q_transfer is shown in Equation (2).

$$Q_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{f}\mathrm{e}\mathrm{r}}=Q_{\mathrm{A}\mathrm{B}}-Q_{\mathrm{A}}$$

(2)

where, Q_transfer is the charge transfer number between A and B; Q_AB is the total charge number of A and B; Q_A is the charge number of A.

Q_transfer between aromatic molecules in rejuvenator and components molecules in aged asphalt are presented in

Table 9. Q_transfer between aromatic components in rejuvenator and heavy components in short-term aged asphalt.

Properties	Qtransfer/e
Aromatic—Pyridinohopane (S)	0.1477
Aromatic—Asphaltene-phenol (S)	0.0937
Aromatic—Quinolinohopane (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

and

Table 10. Q_transfer between aromatic components in rejuvenator and heavy components in long-term aged asphalt.

Properties	Qtransfer/e
Aromatic—Asphaltene-pyrrole (L)	0.1171
Aromatic—Trimethylbenzeneoxane (L)	0.1040
Aromatic—Asphaltene-phenol (L)	0.0811
Aromatic—Benzobisbenzothiophene (L)	0.0709
Aromatic—Asphaltene-thiophene (L)	−0.0519
Aromatic—Quinolinohopane (L)	0.0364
Aromatic—Pyridinohopane (L)	0.0287
Aromatic—Thioisorenieratane (L)	−0.0121

. Q_transfer between saturate molecules in rejuvenator and components molecules in aged asphalt are presented in

Table 11. Q_transfer between saturate components in rejuvenator and heavy components in short-term aged asphalt.

Properties	Qtransfer/e
Saturate—Benzobisbenzothiophene (S)	−0.2015
Saturate—Asphaltene-pyrrole (S)	−0.1930
Saturate—Asphaltene-phenol (S)	−0.0972
Saturate—Pyridinohopane (S)	0.0462
Saturate—Thioisorenieratane (S)	−0.0384
Saturate—Trimethylbenzeneoxane (S)	−0.0244
Saturate—Asphaltene-thiophene (S)	−0.0111
Saturate—Quinolinohopane (S)	−0.0020

and

Table 12. Q_transfer between saturate components in rejuvenator and heavy components in long-term aged asphalt.

Properties	Qtransfer/e
Saturate—Asphaltene-thiophene (L)	0.3400
Saturate—Asphaltene-phenol (L)	0.2403
Saturate—Trimethylbenzeneoxane (L)	0.2011
Saturate—Pyridinohopane (L)	−0.1258
Saturate—Thioisorenieratane (L)	0.1208
Saturate—Quinolinohopane (L)	−0.1119
Saturate—Asphaltene-pyrrole (L)	−0.0801
Saturate—Benzobisbenzothiophene (L)	0.0332

.

From Table 9 and Table 10, it is found that in short-term aged asphalt, the absolute values of Q_transfer 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, Q_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_binding 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 Q_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. Q_transfer between light components in rejuvenator and SBS molecule with its aging products.

Properties	Qtransfer/e
Aromatic -SBS	0.1270
Aromatic—SBS molecular aging product 1	0.1367
Aromatic—SBS molecular aging product 2	0.0878
Saturate—SBS	−0.1263
Saturate—SBS molecular aging product 1	−0.1709
Saturate—SBS molecular aging product 2	−0.2066

presents Q_transfer between aromatic and saturate components in rejuvenator with SBS and its aging products. The conclusion could be summarized as Q_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.

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. Molar mass of each molecule and their respective proportions in AAA-1 model [27].

Asphalt Components	Molar Mass/g × mol−1	Numbers	Mass/%
Asphaltene-phenol	575.8	3	9.11
Asphaltene-pyrrole	888.5	2	14.08
Asphaltene-thiophene	707.2	3	11.21
Benzobisbenzothiophene	290.4	15	4.60
Pyridinohopane	530.9	4	8.41
Quinolinohopane	554.0	4	8.78
Thioisorenieratane	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

.

To further analyze the correlation between simulation results and experiment results, the E_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_binding 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. E_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_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 asphaltenes, as well as resins, remained in a stable state throughout. E_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.

$$P_{rej}={\displaystyle \frac{\left|G^{*\prime }-G^{*}\right|}{G^{*}}}\times 100\%$$

(3)

where P_rej 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 P_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_rej. In the same temperature, the P_rej 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 E_binding between saturate components with asphaltenes. Compared to original asphalt, E_binding 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 E_binding 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, Q_transfer of each molecule was recalculated. And the weighting calculation is presented in Figure 11a,b, which shows Q_transfer between the light components in rejuvenator and heavy components in SBS-modified asphalt.

From Figure 11a,b, Q_transfer 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 Q_transfer 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 Q_transfer that in long-term aged asphalt, Q_transfer 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, Q_transfer between saturate molecules with asphaltenes and resins molecules were higher, at 0.0713 e and 0.0461 e, respectively.

5. Conclusions

(1)

In SBS-modified asphalt, SBS molecules are the least stable and prone to fracture. The energy difference between SBS and aromatic components is the largest, and that between SBS and asphaltenes is the smallest. This indicates that SBS has the best compatibility with aromatic components and the poorest compatibility with asphaltenes. The value of energy is related to the structure and size of molecules.

(2)

The interaction between aromatic components in rejuvenator with asphaltenes in aged asphalt is not stable. And it could be affected by the asphalt aging level. The interaction between heavy components molecules in aged asphalt with saturate components molecules in rejuvenator are closer than those with aromatic component molecules, which could be related to the molecular structure.

(3)

The interaction between light components in rejuvenator with SBS exhibits great interaction potential and closeness of molecular force. After rejuvenator is added into the aged SBS-modified asphalt, a certain amount of rejuvenator reacts first with the SBS molecules, leading to a certain degree of reduction of rejuvenation.

(4)

E_binding between saturate components in rejuvenator with asphaltenes in aged SBS-modified shows good consistency with G* of aged SBS-modified asphalt before and after rejuvenator is added. Therefore, the results of E_binding can be used as a qualitative evaluation indicator for rejuvenation of aged SBS-modified asphalt.

The types of aged asphalt prepared in this study are limited. It is necessary to supplement with a variety of aged asphalts in subsequent experiments to validate and improve the correlation between rheological test results and quantum simulation results. Only one rejuvenator was investigated in this study. In the future, it is necessary to supplement with different rejuvenators to validate the applicability of the conclusions. Furthermore, this study lacks discussion on the practical implications and potential applications of these findings in real-world scenarios. Exploring the practical benefits and limitations would be the next job in the future.