Effect of styrene-butadiene-styrene copolymer on the aging resistance of asphalt: An atomistic understanding from reactive molecular dynamics simulations

Abstract

To reveal the potential influence of styrene-butadiene-styrene (SBS) polymer modification on the anti-aging performance of asphalt, and its mechanism, we explored the aging characteristics of base asphalt and SBS-modified asphalt by reaction force field (ReaxFF) and classical molecular dynamics simulations. The results illustrate that the SBS asphalt is more susceptible to oxidative aging than the base asphalt under oxygen-deficient conditions due to the presence of unsaturated C=C bonds in the SBS polymer. In the case of sufficient oxygen, the SBS polymer inhibits the oxidation of asphalt by restraining the diffusion of asphalt molecules. Compared with the base asphalt, the SBS asphalt exhibits a higher degree of oxidation at the early stage of pavement service and a lower degree of oxidation in the long run. In addition, SBS polymer degrades into small blocks during aging, thus counteracting the hardening of aged asphalt and partially restoring its low-temperature cracking resistance.

Graphical abstract

Keywords

SBS asphalt / oxidative aging / asphalt hardening / ReaxFF / molecular dynamics

1 Introduction

Asphalt is susceptible to oxidative aging during its service life due to long-term exposure to heat, light, and oxygen. With the oxidation of asphalt, several highly polar oxygen functional groups are introduced into asphalt compositions, and the light fractions are aggregated into heavy asphaltenes [1–3]. Therefore, the intermolecular interactions within asphalt are enhanced, and the fluidity of asphalt is restricted, resulting in an increased stiffness and a decreased ductility for flexible pavement. This hardening is undesirable because it causes cracking and leads to considerable deteriorations in the structural strength and durability of pavement [4–7].

In recent years, polymer-modified asphalt (PMA) has been widely used in flexible pavement, mainly to improve the rutting resistance. In addition, it can reduce the risk of cracking by improving the binder failure strain [8,9]. In practice, the modification of asphalt with styrene-butadiene-styrene triblock copolymer (SBS) accounts for most cases of polymer modification. Oxidative aging causes deleterious influences on both base asphalt and SBS asphalt [10]. However, the influence of SBS modification on the aging resistance of asphalt, which matters with regards to the extension of pavement service life and the rejuvenation of a high content of reclaimed SBS modified asphalt pavements (SBS-RAP) [11], and its potential mechanisms have not yet been well understood. Several studies have indicated that the performance of SBS asphalt subjected to aging was better than that of asphalt [12,13]. Woo et al. [14] suggested that the SBS polymer degraded to a smaller molecular size during aging and revealed the opposite trend to the aggregation of asphalt compositions, thus counteracting oxidation hardening. Another factor of concern is the formation of oxygen functional groups such as carbonyl, hydroxyl, and sulfoxide, which is direct evidence of asphalt oxidation [15,16]. Zhao et al. [17] observed oxygen functional groups with Fourier transform infrared (FTIR) spectroscopy and found that the SBS polymer inhibited the formation of carbonyl groups. Yut and Zofka [18] evaluated the oxidation levels of various PMAs, including SBS asphalt, using the attenuated total reflection (ATR)-FTIR technique. However, the results indicated that the polymers did not inhibit the generation of oxygen functional groups, and there was no clear evidence that the polymers degraded after PMA aging. Ruan et al.’s [19] research showed that polymers had little effect on inhibiting asphalt oxidation, and he suggested that asphalt oxidation would increase the temperature sensitivity of the asphalt’s stiffness and viscosity, but the addition of polymers could significantly reduce this temperature sensitivity of aged asphalt.

Among these potential mechanisms by which SBS polymer improves the aging performance of asphalt, the most critical one that needs to be clarified for recycling purposes is whether the addition of SBS polymer inhibits the generation of oxygen functional groups. If it does have an inhibitory effect, the degree of aging of SBS-RAP should be lower than that of unmodified RAP, and thus the theoretical maximum dosage of SBS-RAP should be improved when designing recycled asphalt mixtures. However, previous studies have not agreed on this issue. This is because the technique (FT-IR) used to characterize the formation of functional groups is not accurate enough to directly measure the number of functional groups in the asphalt. It can only qualitatively observe the presence of functional groups by analyzing their absorption peak characteristics [20].

Since it is difficult to observe the aging process of asphalt at the sub-nano scale by experimental measurements, computational simulation has become an important method [21]. Ab initio molecular dynamics (AIMD) simulations based on quantum mechanics (QM) can accurately predict the oxidation behavior of organic compounds. The only inputs into the AIMD simulation are physical constants; therefore, the calculation results can reflect the essential characteristics of the material without the influence of external conditions, which overcomes the shortcomings of the experimental research [22]. However, QM calculations, even the density functional theory (DFT) method that has undergone some approximation treatments, are very computationally expensive and are not suitable for asphalt molecules containing thousands of atoms. An alternative method is molecular dynamics (MD) simulation with reactive force field (ReaxFF) [21]. This method significantly reduces the computing resource requirements and provides an accuracy close to DFT for predicting chemical reactions; thus it is applicable to the oxidation simulation of asphalt. Recently, to investigate the mechanism of asphalt aging, the ReaxFF MD method was used to investigate the thermodynamic and kinetic characteristics of asphalt oxidation [23]. The simulation results agreed well with the experimental research. More interestingly, this method showed unique advantages in determining the intermediate free radical products and the free radical chain reactions during asphalt oxidation.

In this study, a combined approach of ReaxFF and classical MD simulations was employed to investigate whether SBS modification can inhibit the oxidative aging of asphalt under certain potential mechanisms. First, the inhibitory effect of SBS modification on the oxidative aging of asphalt in terms of chemical reactivity was studied. Specifically, ReaxFF MD simulations were used to model the chemical reactions of base asphalt and SBS asphalt with oxygen. The evolution of the amount of oxygen-containing functional groups was analyzed in the two asphalts with aging time. After that, the effects of SBS modification on the diffusion behavior of asphalt molecules in terms of physical activity were explored. In this part, the classical MD simulation was carried out to model the thermodynamic motions of base asphalt and SBS asphalt and calculate their diffusion coefficients to determine whether SBS modification can reduce the movement of asphalt molecules and thereby reduce their contact with oxygen. Finally, the effects of degradation of the SBS polymer during aging on its aging-related properties were examined, including the construction of aged asphalt molecular models based on ReaxFF MD simulations and calculations of the viscosity and modulus by classical MD simulations. This study is expected to improve the understanding of the anti-aging behavior of SBS asphalt and provide theoretical guidance for the rejuvenation of SBS-RAP.

2 Methodology

The detailed processes of the methodology are as follows. Section 2.1 introduces the classical and ReaxFF molecular dynamic methods to be used. Section 2.2 determines the molecular models of asphalt and SBS polymer. Section 2.3 illustrates the computational details of analysis of the influence of SBS modification on asphalt oxidative aging from both chemical and physical aspects and briefly describes the materials and methods of the ATR-FTIR test to verify the MD simulations. Section 2.4 describes the computational details used in analysis of the reduction effect of the SBS polymer on the hardening of aged asphalt.

2.1 Classical and ReaxFF molecular dynamics

MD simulations were brought into asphalt research by Zhang and Greenfield in 2007 and were subsequently widely applied by other researchers [24–26]. Classical MD simulations based on a nonreactive force field, Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies II (COMPASS II) [27], were conducted to calculate thermodynamic parameters related to asphalt hardening in this study. COMPASS II is an optimized ab initio force field suitable for investigating the characteristics of organic and inorganic materials in a wide temperature and pressure range, and thus it is widely used in asphalt performance prediction [28]. Classical MD methods use Newton’s equations to calculate the motion and trajectory of molecules, thus greatly expanding the applicable calculation size compared to QM calculation [29]. However, the connectivity between atoms in classical MD methods is predefined and remains unchanged during the simulation, and thus these methods cannot investigate the oxidation characteristics and pathways of asphalt related to chemical reactions.

Although QM calculations can predict chemical reactions, their inherent characteristics determine their high computational cost and severely limit the modeling scale. The ReaxFF reactive force field proposed by the research group of van Duin exactly bridges this gap [21]. In MD simulation with the ReaxFF force field, bond orders are empirically calculated from the interatomic distances and used to determine the bonding connectivity. The bond orders change dynamically during the simulation, indicating that bond breaking and formation always occur, and thus the chemical reaction can be predicted in the ReaxFF MD simulation. ReaxFF parameter sets are obtained by training the energy and structural data from QM calculations, which greatly reduces the computational cost and ensures that the calculation accuracy is close to that of QM. The classical treatment of reactive chemistry enables the ReaxFF methodology to simulate chemical reactions in large systems that could not previously be studied by computational methods. There are currently two intra-transferable groups of ReaxFF parameter sets: the combustion branch and the aqueous branch. The parameter sets on the same branch can be directly combined. Since the ReaxFF description of each element is transferable across phases, the ReaxFF simulation can model a reactive event at the gas, liquid and solid interfaces. The transferability and a lower computational expense compared to QM allow ReaxFF to predict reactive phenomena such as oxidation, combustion, heterogeneous catalysis and atomic layer deposition [ 30].

The energy contributions of the ReaxFF force field consist of the following items:

(1)\begin{array}{rl}{E}_{\text{system}}=& E_{\mathrm{b}\mathrm{o}\mathrm{n}\mathrm{d}}+E_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}}+E_{\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}+E_{\text{angle}}+E_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}}\\ & +E_{\mathrm{v}\mathrm{d}\mathrm{W}}+E_{\mathrm{C}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{o}\mathrm{m}\mathrm{b}}\text{+}{E}_{\text{Specific}},\end{array}

where E_bond is the bond energy that describes the energy associated with forming bonds between atoms. E_over and E_under are energy penalties preventing the over- and under-coordination of atoms, which are based on the valence theory of bonding (e.g., an over-coordination energy penalty is employed if a C atom forms more than four bonds). E_angle is the valence angle energy associated with a three-body valence angle strain. E_tors is the torsion angle energy associated with a four-body torsional angle strain. E_vdW and E_Coulomb are dispersive and electrostatic interactions between atoms that are not connected by covalent bonds. E_Specific are specific corrections to the ReaxFF potential of the system when necessary, such as conjugation, lone-pair, and hydrogen binding contributions. A more detailed description of the functional forms can be found in the work of van Duin et al. [31]. The computational difficulty of the ReaxFF MD simulation for asphalt aging is that there is no ReaxFF parameter set specifically established for asphalt molecules. However, the C/H/O/N description and the S description established by Strachan et al. [32] for studying the combustion of coal can be used to simulate asphalt aging because both coal and asphalt are materials composed of complex molecules with polycyclic aromatic hydrocarbons [33].

2.2 Molecular models of asphalt and SBS polymer

Since the molecular composition of asphalt is very complex, it is difficult to distinguish and identify all molecules in asphalt. Based on Corbett’s liquid chromatography method, asphalt is divided into saturates, aromatics, resins and asphaltenes (SARAs) according to functionality and molecular size [34]. Greenfield et al. proved that by referring to the microstructural characteristics of each asphalt SARA fraction, it is possible to simulate real bitumen to a certain extent by representing these fractions with specific compound molecules and combining them in a certain proportion to build an asphalt molecular model [5,24]. The most widely used representative molecules of asphalt fractions were proposed by Li and Greenfield [35] by integrating earlier developed models, as shown in Fig. 1. In this study, these representative molecules were combined in the proportion determined by Li and Greenfield to simulate the AAA-1 asphalt of the Strategic Highway Research Program (SHRP), as presented in Table 1.

Although the dosage of SBS in conventional SBS-modified asphalt ranges from 3% to 4.5%, for porous asphalt concrete facing more serious oxidative aging, its SBS dosage is increased to achieve better high-temperature performance and anti-raveling properties [36]. Some studies have suggested that the economic dosage of SBS in high content PMA is 9% [37,38]. Therefore, a SBS content of 9% was applied in the simulations of this study. The SBS polymer is a triblock copolymer composed of polystyrene and polybutadiene.

The difficulty in modeling the SBS asphalt is to determine the degree of polymerization (DP) of the SBS polymer. If the DP value is too large, the SBS dosage of the SBS asphalt in the simulation is much greater than the actual SBS dosage in engineering practice, and if the DP value is too small, the SBS chain cannot show the effect of polymer modification on asphalt because its molecular structure is similar to that of the saturates in the asphalt. High viscosity is one of the most salient features of SBS asphalt; therefore, the suitability of the set DP can be judged according to the viscosity change of the asphalt model after adding the SBS polymer. If the viscosity does increase after adding SBS, it indicates that the set DP is appropriate and vice versa.

In this study, a SBS_6-37-6 chain (made up of a polystyrene with a DP of 6, a polybutadiene with a DP of 37, and another polystyrene with a DP of 6) and three SBS_2-12-2 chains were used to represent SBS asphalt models. The SBS chains with different degrees of polymerization are shown in Fig. 2.

Then, the shear viscosities of the base asphalt and SBS asphalt models were calculated and compared to evaluate the suitability of the SBS chains with different DPs, as shown in Fig. 3. The data of Fig. 3 were obtained from three duplicate simulations (similarly hereinafter). The detailed process of viscosity calculation is described in Section 2.4. Compared with the base asphalt, the viscosity of SBS_6-37-6-modified asphalt increases while the viscosity of SBS_2-12-2-modified asphalt decreases, indicating that the SBS_6-37-6 chain more feasibly represents the SBS polymer in MD simulations. This is because polymer modification can be achieved only when the size of the added SBS polymer is much larger than the size of asphalt molecules. In contrast, the molecular structure of the small SBS polymer is similar to that of the saturates in asphalt, and its addition will increase the dispersion medium of asphalt colloids and dilute the asphaltenes, thus decreasing the viscosity of asphalt.

2.3 Analysis of SBS polymer inhibiting asphalt oxidation

2.3.1 Modeling the oxidation of asphalt binders

The products of asphalt oxidation are oxygen functional groups such as carbonyl, hydroxyl, and sulfoxide [39,40]. By modeling the oxidative aging of SBS asphalt and base asphalt with ReaxFF MD simulations and then quantifying the number of oxygen functional groups, it can be determined whether the SBS polymer inhibits the reactivity of asphalt oxidation. The oxidation simulation in this study was carried out using open source software, the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [41]. Before the simulation, the asphalt molecules (with or without SBS chains) were blended with oxygen molecules to create a reaction system with periodic boundary conditions, as shown in Fig. 4.

Three equivalent oxygen levels (1, 0.5, and 0.25) were applied in the simulations to represent the different oxygen contents in the reaction system. The equivalent oxygen level (EOL) was defined as the ratio of the number of oxygen molecules in the reaction system to the number of oxygen molecules required to completely oxidize the asphalt molecules (including the SBS polymer, similarly hereinafter) into CO₂, H₂O, SO₂, and NO₂. It should be noted that due to our limited research data, these three oxygen levels cannot yet establish a corresponding relationship with the actual oxygen content in practical engineering. To accelerate the simulated oxidation reaction, the simulation temperature was higher than the actual asphalt aging temperature. As shown in Fig. 5, the oxygen content of the oxidized asphalt in the ReaxFF MD simulations was significantly influenced by the simulation temperature. According to the authors’ previous work, the temperature suitable for the simulation was 1200K (Kelvin scale, similarly hereinafter), the system density was 0.1 g/cm³, and the dimensions of each system were determined according to the density. These model parameters accelerated the oxidation reaction and ensured that the asphalt molecules underwent mild oxidation rather than intense combustion [23].

There is no need to worry that the simulation temperature of 1200K is higher than the ambient temperature; the asphalt aging process obtained through the simulation is not consistent with the actual situation. According to the Boltzmann distribution law [42], at ambient temperature, a small portion of asphalt molecules have translational energy higher than the activation energy of the asphalt aging reaction, which leads to the aging reaction of these molecules. In practical engineering, it takes years for these weak aging reactions to be observed. However, in the simulations in this study, by increasing the temperature to make the translational energy of the asphalt molecules reach the activation energy of the aging reaction, asphalt aging will occur rapidly, but their aging pathways will not be changed.

The ReaxFF MD simulation started with energy minimization for the reaction system, followed by equilibration for 100 ps at the canonical ensemble (NVT) and a temperature of 298K. The time step was set as 0.1 fs to provide a balance between calculation accuracy and computational expense. The simulation temperature was controlled by rescaling the velocities of molecules by the Berendsen thermostat with a damping constant of 0.1 ps. Afterwards, a 2 ns reaction simulation was carried out at 1200K and under the NVT ensemble with a damping constant of 0.5 ps and a time step of 0.1 fs. The bond order cutoff for recognition of the newly generated chemical species was set to 0.3. The raw data about bond breaking and formation were recorded using the fixed reax/c/bonds command of LAMMPS. The computational cost of the ReaxFF MD simulation is higher than that of the classic MD simulation. The 2 ns production simulation in this study took more than 12 d on a high-performance computing platform (a 64-bit 28-core Intel Xeon Platinum 8173 M processor and 192 GB of RAM).

ATR-FTIR tests were conducted on SBS-modified and unmodified asphalts with different aging levels by a Thermo Nicolet iS10 spectrometer to determine the formation of oxygen functional groups and verify the reliability of the ReaxFF MD simulation. Short-term aged asphalt was prepared with the rolling thin-film oven test (RTFOT) by referring to the AASHTO T 240 standard [43]. Long-term aged asphalt was prepared with the pressure aging vessel (PAV) test by referring to the AASHTO R 28 standard [44]. The base asphalt used was a performance grade (PG) asphalt binder of PG 64-22 produced by the SK company, and the SBS-modified asphalt reached PG 76-22.

2.3.2 Quantifying the diffusion of asphalt molecules

SBS modification increases the asphalt viscosity by improving the internal frictional force between the asphalt compositions. Therefore, in addition to the possibility of directly inhibiting the reactivity of asphalt oxidation, SBS polymer may also inhibit asphalt oxidation by restraining the free motion of asphalt molecules and restricting their contact with oxygen molecules. The term diffusivity, which refers to the random movement of particles, was applied in this study to measure the diffusion of asphalt molecules. The diffusivity D is defined as follows [45]:

(2)D=\frac{1}{6N}\underset{t\to \mathrm{\infty }}{lim}\frac{\text{d}}{\text{d}t}\sum _{n=1}^N{\left[x_n(t)-x_n(0)\right]}^2,

where N is the number of particles to be averaged and x_n(0) and x_n(t) are the positions of each particle at the initial time and the current time, respectively. Diffusivity is difficult to calculate directly but can be derived from the mean square displacement (MSD). The MSD refers to the deviation of the particle positions with respect to their initial positions over time and is defined as follows:

(3)MSD=\frac{1}{N}\sum _{n=1}^N{\left[x_n(t)-x_n(0)\right]}^2,

where the terms are the same as in Eq. (2). Therefore, the diffusivity D can be obtained as follows:

(4)D=\frac{a}{6},

where a is the slope of the straight line fitted by the MSD with respect to the simulation time and the unit of a is Ų/ps. The diagram of Eq. (4) is shown in Fig. 15(a).

In this study, nonreactive simulations for calculating the physical properties of asphalt, including the MSD, were conducted on the commercial software Accelrys Materials Studio with the COMPASS II force field [46]. The first step of the unreactive simulation was to establish the models of SBS asphalt and base asphalt. The target density of the models was set to 1.0 g/cm³. Figure 6 presents the model of SBS-modified asphalt for unreactive simulations. Then, the newly built model was subjected to geometry optimization with 5000 iterations, followed by equilibration for 500 ps at the NVT ensemble and a temperature of 180°C to imitate the mixing conditions of asphalt. The time step was set to 1 fs, and the cut off was set to 15.5 Å. Subsequently, another 500 ps equilibration was implemented at the isothermal isobaric ensemble (NPT) at a temperature of 60°C and a pressure of 1 atm. The resulting trajectory file was used to calculate diffusivity by performing the MSD analysis.

2.4 Analysis of SBS polymer reducing the hardening of aged asphalt

Asphalt hardening is highly susceptible to oxidation, and the hardness of asphalt increases with the degree of oxidative aging. However, since the polybutadiene block of the SBS polymer can increase the rubber-like flexibility of asphalt, SBS modification may improve the low-temperature crack resistance of aged asphalt by reducing its hardening caused by its susceptibility to oxidation [47]. The modulus and viscosity of virgin and aged asphalt models were calculated with the MD method to evaluate whether the SBS polymer reduces the hardness growth of aged asphalt. The compositions of aged asphalt used in this study were the same as those of virgin asphalt. The representative molecules of compositions for the aged asphalt and SBS polymer were determined from the ReaxFF simulation results. The simulation process was similar to that in Section 2.3.1 except that this simulation required development of oxidation reaction systems for individual asphalt molecules and the SBS polymer rather than for the integral asphalt binder. A detailed description of the modeling can be found in the authors’ previous study [23]. The proportion of representative molecules to establish the aged model was the same as that of the virgin model in Table 1.

After establishing the virgin and aged models of SBS-modified and unmodified asphalts, geometry optimization and 500 ps NVT equilibration at 180°C were carried out. The time step was set to 1 fs, and the cut off was set to 15.5 Å. Then, 500 ps NPT equilibration at 25°C and 1 atm was carried out to obtain the equilibrated geometry for calculating the bulk modulus. In addition, the cohesive energy densities (CEDs) and the solubility parameters of virgin and aged asphalts at 25°C were also calculated to measure the effects of SBS modification and oxidative aging on the composition compatibility of asphalt. Meanwhile, another 500 ps NPT equilibration was performed at 60°C and 1 atm, and the obtained equilibrated geometry was used to calculate the shear viscosity. The viscosity was determined according to the Green-Kubo formula from the resulting trajectory document of a 3000 ps NVT-shear simulation with a shear rate of 0.0001 ps⁻¹ at 60°C. The Green-Kubo formalism relates viscosity to the autocorrelation function of the stress/pressure tensor, as shown in Eq. (5):

(5)\eta =\frac{V}{k_{\mathrm{B}}T}\underset{0}{\overset{\mathrm{\infty }}{\int }}⟨P_{\text{αβ}}(t)P_{\text{αβ}}(0)⟩\mathrm{d}t,

where P_αβ is the three off-diagonal elements of the instantaneous pressure tensor, t is the time, V is the volume, k_B is the Boltzmann constant, and T is the temperature.

3 Results and discussion

3.1 Oxidation characteristics of SBS-modified and unmodified asphalts

3.1.1 Evaluating the effect of SBS polymer on asphalt oxidation

The results of ReaxFF MD simulations of SBS-modified and unmodified asphalts at different oxygen levels are presented in Fig. 7. As shown in Figs. 7(a)−7(c), the three bonds related to carbonyls, hydroxyls, and sulfoxides increase with the simulation duration. The fastest growth of C−O bonds indicates that the number of carbonyls formed in oxidized asphalt is the largest, followed by H−O bonds related to hydroxyls, and the number of S−O bonds related to sulfoxides is the least. Figure 8 presents the ATR-FTIR spectra of SBS-modified and unmodified asphalts before and after aging. The bands appearing at 1740−1700 cm⁻¹ are the absorbance peaks of the carbonyl group (C=O). The bands appearing at 1070−1030 cm⁻¹ are the absorbance peaks of the sulfoxide group (S=O). The inconspicuous bands at approximately 1150 cm⁻¹ are the absorbance peaks of the bond connecting the carbon atom and the hydroxyl (C−OH). These characteristic peaks verified the correctness of the ReaxFF MD simulation.

The addition of SBS polymer and the change in oxygen levels influence the formation of the three types of chemical bonds. Since the trends of the formation of the three types of bonds were similar, it is more meaningful to discuss them together. The total number of C/H/S−O bonds in Fig. 7(d) is the sum of the bond numbers in Figs. 7(a)−7(c), based on which the oxygen contents of the simulated oxidized asphalt binders were calculated and are presented in Fig. 7(e). A higher oxygen content indicates a higher degree of oxidation for asphalt. Figure 7(f) presents the number of oxygen molecules consumed by the oxidation of asphalt during the simulation. Each consumed oxygen molecule can provide a pair of oxygen atoms, and thus the total number of C/H/S−O bonds should theoretically be equal to twice the number of consumed oxygen molecules. However, the former is greater than twice the latter in Fig. 7. This is because some oxygen atoms near the asphalt molecules are mistakenly identified as being connected by chemical bonds. In addition, the oxygen atom in the hydroxyl group repeatedly corresponds to a H−O bond and a C−O bond simultaneously. Nevertheless, this discrepancy has little effect on the overall trend of the chemical bonds to be analyzed.

As shown in Fig. 7(e), when the EOL is 0.25, the oxygen contents of SBS-modified and unmodified asphalts are the lowest during the simulation, indicating that the reaction systems are under oxygen-deficient conditions at this oxygen level. The oxygen content of SBS asphalt is higher than that of base asphalt, which indicates that the reaction activity of SBS asphalt is higher when oxygen is deficient. This is because there are many C=C unsaturated bonds in the SBS polymer, which are easily attacked by oxygen to form carbonyl groups. This opinion is supported by the evidence as shown in Fig. 7(a) that the number of C−O bonds of SBS asphalt is higher than that of base asphalt at an EOL of 0.25. In the oxygen-deficient reaction system, the number of collisions between oxygen and asphalt molecules is limited. If collisions occur on SBS polymer rich in unsaturated bonds, the probability of oxidation reaction is higher than when collisions occur on asphalt compositions. Therefore, the SBS asphalt has a higher degree of oxidation than the base asphalt.

As the EOL increases to 0.5, the number of collisions between oxygen and asphalt molecules increases, thus improving the degree of oxidation of both asphalts during the simulation. However, when the EOL is 0.5, the mechanism of SBS modification to promote the oxidation of asphalt at an EOL of 0.25 is no longer effective, and the degree of oxidation of SBS asphalt is lower than that of base asphalt. What is more surprising is that when the EOL is further increased to 1, the degrees of oxidation of both asphalts are reduced rather than increased.

Whether the oxidation reaction occurs between oxygen and asphalt molecules during their collision depends on the kinetic energy of these colliding particles (molecules or atoms). Therefore, it is suspected that the particle velocities may decrease when the EOL is 1, thus causing a decrease in the collision energy and inhibiting oxidation. In response to this suspicion, the velocities of atoms in the simulation systems were calculated, as shown in Fig. 9. However, the results suggested that the velocities of atoms were only related to the temperature but not to the oxygen levels and the addition of SBS polymer.

In addition to the kinetic energy of colliding particles, the intensity of the oxidation reaction is also related to the system pressure. Therefore, it is assumed that the decreased degree of oxidation of asphalt at high oxygen levels is due to the drop in system pressure. Accordingly, the system pressures under different oxygen levels were calculated, as shown in Fig. 10. The results demonstrated that the pressure of the system increased with the oxygen level, which was unfortunately again contrary to the expectation.

Since the influences of atomic velocity and system pressure have been ruled out, it is reasonable to speculate that part of the reason for the decreased asphalt oxidation at an EOL of 1 is that the amount of oxygen in the system exceeds the optimal amount required to oxidize the asphalt molecules. The term mean free path was applied to understand the complex issues in the reaction system. The mean free path refers to the average distance a particle moves between successive collisions [48], which is calculated as follows:

(6)\lambda \text{=}\frac{k_{\text{B}}T}{\sqrt{2}\text{π}{d}^{2}p},

where k_B is the Boltzmann constant, T is the temperature, d is the particle diameter, and p is the pressure. According to Eq. (6), the mean free path of a particle is inversely proportional to the pressure and the square of the diameter. As the EOL rises, the pressure of the system increases, and the mean free path of the oxygen molecules decreases. Therefore, when the EOL rises to 1, the oxygen molecules far from the asphalt molecules may never be able to contact them, resulting in a situation in which the oxygen in the system is excessive.

On the other hand, the oxidation of asphalt is essentially the reaction between the atoms in the asphalt (C, H, S, N) and the oxygen atoms when they collide; therefore, the number of collisions in the system, which affects the degree of asphalt oxidation, should be directly determined by the concentration of the reactant atoms (the total number of atoms in unit volume) rather than the pressure. The concentrations of reactant atoms for systems at different oxygen levels are shown in Fig. 11. The density of the systems is constant, but the mass of the oxygen atom (16 amu) is larger than the average mass of asphalt atoms (5.8 amu), and thus the reactant concentration decreases as the oxygen level rises. Therefore, the number of collisions between reactant atoms in the system with an EOL of 1 is decreased compared to that at an EOL of 0.5, which leads to the reduced degree of oxidation of asphalt.

The reason why the degree of oxidation of SBS asphalt is lower than that of base asphalt at EOLs of 0.5 and 1 is also related to the mean free path. With the addition of SBS polymer, the size of the asphalt molecules as a whole becomes larger, and the corresponding mean free path decreases according to Eq. (6). This indicates that as the overall size of the asphalt molecules rises, the collision frequency between the asphalt and oxygen molecules increases, resulting in the slower diffusion of asphalt molecules. However, on average, for each atom of asphalt, the number of collisions with oxygen molecules does not increase but decreases because the diffusion of asphalt molecules slows down. Consequently, SBS asphalt is less oxidized than base asphalt at EOLs of 0.5 and 1.

In summary, under the condition of insufficient oxygen, due to the large amount of unsaturated bonds in the added SBS polymer, the degree of oxidation of SBS asphalt is higher than that of base asphalt. As the oxygen level rises, the oxidation of SBS asphalt and base asphalt becomes more severe. However, the addition of SBS polymer reduces the diffusion of asphalt molecules and decreases the collision frequency of oxygen molecules with each asphalt atom. Therefore, SBS modification inhibits the oxidation of asphalt under the condition of sufficient oxygen. Given so many parameters affect the response of the asphalt aging prediction model, a sensitivity analysis shall be carried out in future to evaluate the reliability of the model [49–51].

However, the oxygen content in the air is almost constant, and thus the question remains of how the influence of the oxygen level on the aging of SBS asphalt can be reflected in actual engineering. One solution is to convert the oxygen level in the spatial dimension to the oxygen level in the time dimension. The amount of oxygen to which asphalt is exposed increases with the service life of pavement; therefore, the initial stage of pavement service corresponds to the oxygen-deficient condition for asphalt aging, while the later stage corresponds to the condition of sufficient oxygen. Accordingly, compared with the base asphalt, the SBS asphalt exhibits a higher degree of oxidation at the early stage of pavement service and subsequently exhibits a lower degree of oxidation. This conclusion is validated by experimental measurements reported by Zhao et al. [17]. They observed that SBS asphalt has a higher degree of oxidative aging when the aging time is less than 6 months, and after 6 months, the degree of aging of base asphalt is higher.

3.1.2 Determining the molecular structures of oxidized asphalt and SBS polymer

By visualizing the dump files of individual asphalt molecules and the SBS polymer obtained from the ReaxFF MD simulations using visual molecular dynamics (VMD) software [52], the oxidation mechanisms of asphalt and SBS polymer can be analyzed. Asphaltene is the most easily oxidized component in asphalt, and its oxidation is accompanied by the cracking of aromatic rings, as shown in Fig. 12(a). The detailed pathway of the oxidation of asphaltene is that oxygen molecules first attack the unsaturated bonds on the aromatic ring, generating two intermediate semiquinone groups, and then, the aromatic ring cracks to generate two carbonyl groups. The oxidation of the asphaltene molecule mainly occurs on the aromatic rings rather than on the side chains, demonstrating that the chemical reactivity of the polycyclic aromatic hydrocarbon (PAH) region is higher than that of the side chains. This phenomenon is consistent with the finding by Xing that the naphthalene ring is easier to oxidize than its side chain. This reaction mechanism can be understood by the Clar theory describing the localization of aromatic sextets in PAHs, which suggests that many C–C bonds on PAHs are true double bonds with high reactivity, and thus the PAH region of asphaltene is easily oxidized.

There are two pathways for the thermal degradation of the SBS polymer. One is the homolytic cleavage that occurs on the saturated C−C bond, which results in polymer chain breaking; the second is that oxygen attacks the unsaturated C=C bonds to form carbonyl groups, with or without the cleavage of these bonds. Since the chemical stability of the benzene ring is higher than that of aliphatic hydrocarbons, the oxidation of the SBS polymer mainly occurs in the polybutadiene blocks rather than the polystyrene blocks. Sugano et al. [38] explored the effect of asphalt substrate on the decomposition of SBS in polymer-modified asphalt, with results indicating that the degradation of SBS was enhanced by the low molecular weight components in asphalt but inhibited by the high content of asphaltene. This is because asphaltenes with a large molecular weight limit the movement of SBS, thereby reducing its contact with oxygen and decreasing its degradation. Therefore, SBS also inhibits asphalt aging based on this mechanism.

The representative molecules of the oxidized asphalt were determined according to the results of ReaxFF MD simulations. The degree of oxidation of asphalt molecules gradually increases with the simulation time, and thus the molecular structures of oxidized asphalt change continuously. In this study, the molecular structures of asphalt molecules with the highest degree of oxidation, but which were not pyrolyzed, were used to represent the oxidized asphalt compositions, as presented in Fig. 13. The saturates are so chemically stable that their structures remain unchanged when the other asphalt compositions are oxidized.

The oxidation of the SBS polymer is accompanied by the breaking of the polymer chain; therefore, the number of molecules in the simulation system continues to increase, as shown in Fig. 14(a). However, the number of molecules remained unchanged at 1000−2000 ps, indicating that the degradation of the SBS polymer reached a stable state during this period. Therefore, the molecular structure of the SBS polymer at this time was used to represent the oxidized SBS polymer, as shown in Fig. 14(b). The representative molecules presented in Figs. 13 and 14 were applied to establish models of aged asphalts to calculate the physical parameters in sections 3.2 and 3.3.

3.2 Effect of SBS polymer on asphalt diffusion

Section 3.1 analyzes the mechanism by which the SBS polymer reduces the oxidation of asphalt by slowing down the motion of asphalt molecules based on the mean free path theory. The mean free path is a measurement suitable for gas systems, thus making it applicable to ReaxFF MD simulation systems at 1200K. However, asphalt binders are viscoelastic fluids at the actual aging temperature. Therefore, the MSD and diffusivity suitable for fluids were used to evaluate the restraining effect of SBS polymer on asphalt molecules in this section. The curve of the MSD over time does not increase linearly at the early stage of the simulation, and a large fluctuation may arise from the decreased statistical accuracy at the end stage. Therefore, the linear regression line of the MSD was fitted using the data from 50 to 250 ps, as shown in Fig. 15(a). According to the slopes of the fitted lines, the diffusivities of SBS asphalt and base asphalt were calculated and are presented in Fig. 15(b).

The oxidative aging of asphalt introduces many highly polar oxygen functional groups, thus increasing the intermolecular interactions within asphalt and reducing the diffusivity of asphalt molecules. Similarly, with the addition of SBS polymer, the diffusivities of asphalt molecules decrease and approach that of aged asphalt. This is attributed to the aggregation and clumping of polystyrene blocks of the SBS polymer. The calculation of the MSD and diffusivity demonstrates that the SBS modification does reduce the oxidative aging of asphalt pavement by reducing the diffusivity of asphalt molecules and restricting their contact with oxygen. This is supported by previous research, which concluded that a higher viscosity of SBS asphalt results in slower asphalt flow and reduces the chance of oxidation [17].

3.3 Effect of SBS polymer on the hardening of aged asphalt

To verify the accuracy of MD simulations based on the COMPASS II force field, several thermodynamic parameters of the virgin asphalt and aged asphalt were calculated and compared with the experimental values, as presented in Table 2. The calculated density surface free energy and solubility parameters are within the range of the experimental values [53–55], which indicates that the accuracy of the MD simulations is acceptable for calculating the physical properties of asphalt.

The viscosity and modulus related to the hardening of asphalts were calculated and are shown in Figs. 16(a)–16(b). The viscosity of asphalt increases with the addition of SBS polymer or the oxidative aging of asphalt. However, the viscosity growth of SBS asphalt is not as fast as that of aged asphalt. This is because the DP value of 49 of the SBS polymer in this study is much smaller than the actual DP value of thousands of polymers, and the effect of SBS modification has not been fully reflected. The viscosity of the aged SBS asphalt is larger than that of the virgin SBS asphalt but significantly smaller than that of the aged base asphalt. This demonstrates that the degradation of SBS polymer into small blocks does increase the dispersion medium in the asphalt colloid, thereby diluting the more viscous asphaltenes and polar aromatics and decreasing the susceptibility of asphalt viscosity hardening to oxidation. However, the degradation of the SBS polymer can only partly counteract the viscosity growth of aged asphalt and cannot restore the viscosity to the unaged level. The bulk modulus of asphalt is greatly affected by oxidative aging due to the introduction of highly polar oxygen functional groups. However, it is hardly affected by the addition of SBS polymer because although the polystyrene blocks in the SBS polymer improve the stiffness of asphalt, the polybutadiene blocks also increase the asphalt flexibility.

Changes in the CED and solubility parameters may also account for the hardening of aged asphalt. CED is the energy required to separate a unit volume of molecules from neighboring molecules to infinite separation, mainly reflecting the interaction between functional groups. Materials with a larger CED have higher molecular polarities and intermolecular interactions and are therefore difficult to deform. The solubility parameter is the square root of the CED. Figure 16(c) shows that the CED and solubility parameter of asphalt increase significantly with oxidative aging but remain almost unchanged with the addition of SBS polymer. This demonstrates that the SBS polymer is a nonpolar compound, and its addition does not significantly change the polarity of asphalt.

4 Conclusions

This study characterized the oxidation and hardening of SBS-modified and unmodified asphalts subjected to aging with MD simulations and concluded that SBS modification improved the aging resistance of asphalt binder under various mechanisms. The following conclusions can be drawn.

1) The degree of oxidation of SBS asphalt is higher than that of base asphalt under oxygen-deficient conditions. However, under the condition of sufficient oxygen, the addition of SBS polymer decreases the collision frequency of oxygen molecules and asphalt atoms and therefore inhibits the oxidation.

2) Compared with the base asphalt, the SBS asphalt exhibits a higher degree of oxidation in the initial aging state of pavement but later exhibits a lower degree of oxidation.

3) The MSD and diffusivity calculations demonstrate that the addition of SBS polymer can indeed reduce the diffusion of asphalt molecules, thus inhibiting their contact with oxygen molecules and decreasing the oxidative aging of asphalt.

4) During the oxidation of SBS asphalt, the SBS polymer degrades into smaller blocks and dilutes the more viscous asphaltenes. Therefore, it can counteract the hardening of aged asphalt and partly restore the low-temperature cracking resistance of aged asphalt, although the hardness cannot be restored to the unaged level.

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