Molecular Dynamics-Based Study of Graphene/Asphalt Mechanism of Interaction

Abstract

This study employed molecular dynamics simulation to investigate the mechanism of action of graphene-modified asphalt. A series of molecular models of graphene-modified asphalt were constructed and validated using thermodynamic parameters. The impact of the graphene (PGR) size and number of layers on its interaction with asphalt components were examined, and the self-healing process and mechanism of action of PGR-modified asphalt were analyzed. The results demonstrated that the size and number of layers of PGR significantly influenced its interaction with asphalt components, with polar components demonstrating a stronger affinity for PGR. When the size and number of layers of PGR were held constant, the interfacial binding energy between it and ACR-modified asphalt was the highest, followed by SBS-modified asphalt, and 70# matrix asphalt exhibited the lowest interfacial binding strength. This interfacial binding strength is primarily attributed to intermolecular van der Waals interactions. Furthermore, the incorporation of multi-layer PGR can markedly enhance the mechanical properties of matrix asphalt, whereas small-sized PGR is more efficacious in improving the low-temperature performance of polymer-modified asphalt. PGR can act as a bridge between asphalt molecules through rapid heat transfer and π-π stacking with aromatic ring-containing substances, which markedly increases the free diffusion ability of asphalt molecules, shortens the healing time of asphalt, and enhances the collective self-healing performance of asphalt. This study provides an essential theoretical basis for understanding the mechanism and application of PGR in asphalt modification.

1. Introduction

With the development of nanotechnology, nanomaterial-modified asphalt is increasingly being widely used in road construction. Researchers have tried to add a variety of nanomaterials such as nano-zno, nano-clay, nano-TiO₂, nano-CaCO₃, nano-SiO₂, graphene, and graphene oxide to the asphalt and mix to strengthen the mechanical properties of the pavement, aging resistance, fatigue resistance, adhesion properties, etc. [1,2,3,4,5]. Compared with other nanomaterials, graphene has a large specific surface area, excellent physical properties (mechanical, thermal, optical), and stable chemical structure [6,7,8] while having significant “small size effects”, “quantum size effects”, and “surface and boundary effects” [9,10,11]. It has been proved that the binder’s mechanical strength, aging resistance, and high-temperature stability can be significantly improved by introducing graphene nanosheets into asphalt material. In particular, using graphene composite rubber powder as a new modifier has attracted extensive attention to improving the storage stability, high-temperature rutting performance, and aging performance of asphalt adhesives [12,13]. On the other hand, graphene tends to agglomerate and accumulate, which is not conducive to its large-scale application [8], and the interaction mechanism between graphene and asphalt binders is still unclear.

In recent years, molecular dynamics simulation methods have been widely used to explore the mechanism of asphalt–aggregate interface interaction [14], asphalt aging [15], and asphalt self-healing [16] and have made breakthrough progress. Molecular dynamics (MD) simulation, as a kind of computerized virtual simulation test, can break through the limitations of traditional testing instruments, effectively make up for the shortcomings of macroscopic tests, and reveal the microscopic mechanisms of the macroscopic properties of asphalt from the molecular or even atomic scale [17,18].

Shishehbor et al. [17] explored the adhesion properties and interaction behavior between graphene and asphalt four components (SARA) and aggregate with the help of the molecular dynamics (MD) simulation method; the simulation results showed that the adhesion work between asphaltene and aromatic fractions and GNPs was 30% higher than that of colloidal and saturated fractions. However, adding GNPs did not significantly affect the adhesion enhancement between asphalt and aggregate. Rickgauer et al. [19] used molecular dynamics to comparatively evaluate the adhesion behaviors between CNTs, GNPs with aggregates, and SARA, and the simulation results showed that the interfacial strength and adhesion work between GNPs and SARA was higher than that between CNTs and SARA, where the CNTs-SARA interfacial interactions were mainly achieved through van der Waals forces. Lau et al. [11] found through MD simulations that hydrogen binding plays a vital role in the reinforcement of asphalt nanocomposites; significantly modified graphene (hydroxylated and epoxy-modified) can form more robust interactions with the polar components of asphalt, which improves the shear resistance. Qing Zeng [20] further verified the binding relationship between the four elements of asphalt and the GOs based on density-functional theory (DFT) calculations, and the results showed that the gums were most stabilized with the GOs. In addition, GOs can effectively hinder the movement of saturated fractions and enhance the high-temperature stability and thermal aging resistance of asphalt; GOs are uniformly and stably dispersed in the asphalt matrix mainly through non-chemical binding.

With the help of molecular dynamics simulation, Hu Kui et al. [18] found that GOs have the potential to enhance the performance of SBS-modified asphalt by reducing the diffusion coefficient of the molecules, enhancing the strength of the three-dimensional network structure of SBS-modified asphalt, and thus improving its ability to resist permanent deformation.

As aforementioned, the experimental research has characterized comprehensive properties and mechanisms of PGR. In contrast, they need to be clarified at a molecular scale. Although several studies have shown that the addition of an appropriate amount of PGR can enhance the healing ability and self-healing rate of asphalt binder, how the interaction between graphene and asphalt components affects the self-healing behavior of asphalt materials needs to be further explored. Thus, it is necessary to understand them at a molecular scale. In this study, the MD simulation method was selected to explore the interactions between molecules in different graphene-modified asphalt systems and their action mechanisms from the molecular scale, which provides a new research idea for the study of modified asphalt, especially for the action mechanism of inorganic modifiers, and at the same time, it partially explains the enhancement mechanism of the self-healing performance of asphalt after graphene addition, thus providing a specific reference value for the future large-scale application of graphene in asphalt pavements. At the same time, this study partially explains the enhancement mechanism of self-healing performance after graphene incorporation, which provides a specific reference value for the large-scale application of graphene in asphalt pavements in the future.

2. Models Establishment and Simulation Methods

2.1. Molecule Models

2.1.1. Molecule Model for Virgin Asphalt

Asphalt is a highly complex chemical composition of organic polymer mixtures; according to the physical and chemical properties of asphalt, it is believed that asphalt is defined by the saturated fraction (Sa), aromatic fraction (Ar), gum (Re), asphaltene (Asp) composition. To further improve the accuracy of the simulation, the molecular model containing the four components of asphalt12 [21] was used in this study. The molecular structure and composition of the asphalt model are shown in Figure 1 and

Table 1. Number and proportion of representative molecules in the four components of asphalt.

Fraction	Encodings	Representation	Number	Simulated Content (%)	Measured Content (%)
Asphaltenes	Asp-1	C51H62S	2	12.78	12.78
	Asp-2	C42H54O	3
	Asp-3	C66H81N	2
Saturates	Sa-1	C30H62	6	12.87	12.89
	Sa-2	C35H62	5
Aromatics	Ar-1	C30H46	22	52.26	52.47
	Ar-2	C35H44	24
Resins	Re-1	C18H10S2	3	22.09	21.86
	Re-2	C36H57N	4
	Re-3	C40H59N	3
	Re-4	C40H60S	4
	Re-5	C29H50O	4

.

2.1.2. Molecule Model for Crumb Rubber

Rubber powders are mainly composed of natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR), etc., where NR and BR are polymerized from cis-1,4-polyisoprene monomers and cis-1,4-polybutadiene monomers, respectively. SBR is a random copolymer with the synthetic monomers of 1,4-butadiene and styrene [22]. In the present study, taking into account the efficiency of the computer dynamics simulation, the above NR, BR, and SBR were further integrated into one macromolecule to represent microwave-activated rubber powder (ACR), and the molecular structures of the three synthetic monomers and rubbers are shown in Figure 2 and Figure 3.

2.1.3. Molecule Model for GR

This study used cutting graphite crystals, expanding crystal cells, and adjusting hydrogenation (edge passivation) to construct molecular models of graphene with different sizes and numbers of layers, as shown in Figure 4 and Figure 5. Referring to the XRD test results of PGR, the interlayer distance of PGR was determined to be 3.85 Å.

The representative number of molecules and mass percentages of modifiers used in this study are shown in

Table 2. Modifier molecule types and numbers.

Modifier Type	Number	Formula	Floors/Pieces	Mass (%)
PGR	G5-1	C61H34	1	1.99
	G5-2	C122H68	2	3.99
	G5-3	C183H102	3	5.98
	G7-1	C113H46	1	3.65
	G7-2	C226H92	2	7.30
	G9-1	C181H58	1	5.80
SBS		C107H176	1	3.80
ACR		C248H352S18	2	20.33

The a of Ga-b in the table represents the number of graphene planar transverse (longitudinal) benzene rings; b represents the number of graphene layers.

. Considering the size effect of graphene PGR and the computational efficiency of kinetic simulation, the PGR content was controlled to be less than 8%, and the number of PGR layers was not more than 3. SBS was added to the asphalt matrix as single long-chain macromolecules, and the number of ACR molecules was controlled to be two to be close to the experimental dosage.

2.1.4. Construction of Asphalt Binder Bulks

This section used the Amorphous Cell module in Materials Studio 2020 to build the virgin asphalt and PGRMA bulks. ① Molecular models of representative compounds and modifiers of asphalt components were drawn, and a specified number of the above molecules were placed in amorphous cells. ② In order to eliminate molecular overlap and obtain a reasonable structure, the initial density of the amorphous cell was set to 0.5 g/cm³, and the structure was optimized with the help of the Forcite module to obtain the configuration with the lowest molecular structure potential energy. ③ Five consecutive annealing treatments were carried out in the NPT systematic at one standard atmospheric pressure in the temperature range of 200 K~600 K to eliminate unreasonable energies in the molecular model. ④ A 100 ps dynamic simulation in the NVT system was used to realize the initial relaxation of the model system. ⑤ A 100 ps dynamic simulation was performed in the NPT system to obtain the asphalt molecular model close to the actual asphalt state and finally obtain the asphalt molecular model in the stable state, as shown in Figure 6. ⑥ The dimensions of the simulation boxes for different asphalt formulations were as follows: the box for the 70# asphalt measured 39.8 Å × 39.8 Å × 39.8 Å. For the SBS-modified asphalt, the dimensions were 40.4 Å × 40.4 Å × 40.4 Å, while the ACR-modified asphalt had dimensions of 42.8 Å × 42.8 Å × 42.8 Å. When polymer-grafted graphene (PGR) was incorporated, the box sizes adjusted accordingly: PGR combined with 70# asphalt resulted in a box size of 40.7 Å × 40.7 Å × 40.7 Å; with SBS asphalt, the dimensions were 41.3 Å × 41.3 Å × 41.3 Å; and with ACR asphalt, the size increased to 43.7 Å × 43.7 Å × 43.7 Å. It should be noted that the PGR molecules in the figure are uniformly set as u = v = 7 single-layer graphene molecules (G7-1). The optimized molecular volume model of the asphalt binder is shown in Figure 6.

2.1.5. Modeling Molecular Self-Healing of Asphalt

Self-healing models of asphalt in the presence of 70# matrix asphalt, SBS-modified asphalt, ACR-modified asphalt, and PGR were constructed in the “Build Layer” module of Materials Studio 2020. The asphalt molecular model is on both sides of the healing model, while the crack or PGR molecular model is in the center; the cracks are represented by a vacuum layer with a length of 20 Å in the OZ direction [15,23]. Given that G9-1-type graphene is efficacious in improving its interaction with asphalt components and interfaces, as well as its geometry is relatively close to the geometric characteristics of graphene in the modified asphalt prepared in the test chamber, G9-1 is used as a representative of PGR in the healing model of graphene-modified asphalt. Figure 7 shows the schematic diagram of the 70# matrix asphalt self-healing model and PGR-modified asphalt. The self-healing models of PGR/SBS and PGR/ACR composite-modified asphalt were also constructed according to the above steps.

2.1.6. Simulation of Self-Healing Processes

To simulate the self-healing process of asphalt materials, firstly, 5000 steps of structural optimization were carried out for the two-layer diffusion model; then, 150 ps kinetic calculations were carried out with the help of the “Forcite” module for the self-healing model of different types of graphene-modified asphalt in NPT system and one standard atmospheric pressure.

2.2. Molecular Dynamics Simulation Methods

In this study, the software Materials Studio 2020 developed by Accelrys was conducted for the MD investigation. The technique is a molecular simulation based on theoretical chemistry and computer technology, which is primarily based on Newton’s kinematics law to predict the trajectory and thermodynamic properties of any atom in a molecular system under specific conditions. The molecular dynamics simulation generally involves the selection of force field potential energy functions, coefficients, and periodic boundaries [23]. The COMPASS force field enables condensed matter atom-level simulations, which has obvious advantages in studying organic molecular equilibrium states. Therefore, the COMPASS force field is used in this study for molecular dynamics simulations.

2.2.1. Solubility Parameter

The solubility parameter is an important indicator used for identifying the interaction between material molecules and the compatibility of reaction mixture systems [24]. In this study, the solubility parameter characterization (δ) was introduced to characterize the storage stability of modified bitumen. As shown in Equation (1), the solubility parameter (δ) can be calculated by the square root of the cohesive energy density (CED); the smaller the difference in Δδ, the better the compatibility between asphalt and modifier.

$$\delta =\sqrt{CED}$$

(1)

2.2.2. Radial Distribution Function (RDF)

The radial distribution function (RDF) is the probability of other particles appearing in the space around a given particle at a distance r. It is often used to characterize the spatial aggregation of particles and the orderliness of molecular arrangement in the molecular model of asphalt [15], and the calculation formula is shown in Equation (2).

$$g\left(r\right)=\frac{\rho \left(r\right)}{\rho }$$

(2)

where $g\left(r\right)$ is the radial distribution function; r is the distance (Å) from the given particle; $\rho \left(r\right)$ is the particle density (g/cm³) at a distance of r around the given particle; and $\rho$ is the average particle density (g/cm³) of the molecular simulation system.

2.2.3. Binding Energy

Interfacial energy is essential for evaluating the mixing ability and compatibility between components in a mixing system [25]. Generally speaking, the total energy of a mixed system is always lower than the sum of the components’ energies used to maintain the system’s stability; the interfacial binding energy and the interaction energy are opposite [22,23]. The interfacial binding energy in this study refers to the energy barrier that needs to be overcome to separate different types of graphene from asphalt. The larger the interfacial binding energy, the higher the interaction strength between the graphene and the asphalt system. The interfacial bind energy is calculated as shown in Equation (3).

$$\Delta E_{binding}=E_{Asphalt}+E_{Modifier}-E_{Modifier/Asphalt}$$

(3)

where ${∆E}_{binding}$ is the interfacial binding energy; $E_{Asphalt}$ is the total energy of the system containing only asphalt components; $E_{Modifier}$ is the total energy of the system containing only modifier; $E_{Modifier/Asphalt}$ is the total energy of the system containing both asphalt components and modifier.

2.2.4. Glass Transition Temperature

The glass transition is a reversible transition that occurs in the amorphous region of an amorphous or semi-crystalline polymeric material and manifests itself as a change from the rubbery state to the glassy state during temperature reduction. Tg can be used to evaluate the low-temperature properties of asphalt and asphalt mixtures. Asphalt binder phase change is the behavior that occurs with the change of temperature and is an embodiment of the inherent properties of asphalt binder; the glass transition occurs between the asphalt glass state and the rubber state transition, reflecting the form of molecular movement of the asphalt binder under low-temperature conditions. The ideal state of asphalt binder application is that its Tg is less than the lowest temperature.

2.2.5. Relative Concentration of Asphalt Molecules (RDF)

The self-healing of asphalt materials involves the initial interfacial interaction and subsequent diffusion of asphalt molecules to the microcrack interface. The distribution state of asphalt molecules during the healing process can directly reflect the healing characteristics of asphalt [15]. The relative concentration ($C_i$) can qualitatively analyze the spatial density distribution of molecules in the mixture system and characterize the distribution state of asphalt molecules during the self-healing process [23]. The relative concentration of selected molecules was calculated directly in the “Analysis” function of the “Forcite” module of the Materials Studio 2020 software, as shown in Equation (4).

$$C_i=\left(N_i/V_i\right)/\left(N_t/V_t\right)$$

(4)

where $C_i$ is the relative concentration of i molecules in the selected space system; $N_i$ is the number of i molecules in the selected spatial system; $V_i$ is the volume of molecules in the selected space system; $N_t$ is the total number of molecules in the simulated space system; $V_t$ is the total molecular volume of the simulated system.

2.2.6. Mean Square Displacement

Self-healing of asphalt is accompanied by diffusion and miscibility of asphalt molecules, which will move with the force field and tend to diffuse from the original position during kinetic simulation. Mean square displacement (MSD) has been used reflect the displacement change of certain molecules with the increase in the simulation time [26]. The diffusion coefficient (D), which is calculated by the slope of the MSD curve, has been used to characterize the diffusion or motion capacity of molecules [27]. The MSD curve is obtained from the system at an equilibrium state. The MSD and D are calculated in Equations (5) and (6).

$$MSD\left(t\right)={\left|r_i\left(t\right)-r_i\left(0\right)\right|}^2$$

(5)

$$D=\underset{t\to \infty }{\mathit{lim}}\frac{{\left|r_i\left(t\right)-r_i\left(0\right)\right|}^2}{6t}=\underset{t\to \infty }{lim}\frac{MSD\left(t\right)}{6t}=\frac{m}{6}$$

(6)

where $MSD\left(t\right)$ presents the root mean square displacement of particle i at moment t; r_i(0) and r_i(t) are the initial and current positions, respectively; t is the time; and m is the slope of the MSD(t) function. The unit of D and m is Ų/ps, which is equivalent to 10⁻⁸ m²/s.

3. Results and Discussion

3.1. Verification for Binder Models

The correctness of the molecular model and stance parameters of the original asphalt (virgin asphalt) was verified with the help of its thermodynamic parameters (system energy, density, temperature, and solubility parameters). The changes in the total system energy and density of different types of PGR-modified asphalt calculated in this study during a kinetic simulation at 100 ps are shown in Figure 8. As seen in the figure, after 40 ps kinetic calculations, the total energy and density in the six asphalt systems remained almost unchanged, indicating that the simulated systems have reached a stable state. After stabilization, the density of the simulated systems remained in the range of 0.950 g/cm³~0.980 g/cm³, which is roughly comparable to the actual asphalt density (0.95 g/cm³~1.05 g/cm³) [23], indicating that the PGR-modified asphalt model constructed in this study is reasonable and reliable.

The cohesion energy density CED and solubility parameter δ of the molecular models of different types of PGR-modified asphalt are summarized in

Table 3. Cohesion energy density CED and solubility parameter δ for molecular modeling of bitumen.

Type of Asphalt	CED @ 298 K (J/m3)	δ @ 298 K ((J/cm3)0.5)	Solubility Parameter δ Range @ 298 K ((J/cm3)0.5)
70#	3.164 × 108	17.787	15.3~23.0
PGR + 70#	3.170 × 108	17.805
SBS	3.162 × 108	17.783
PGR + SBS	3.159 × 108	17.775
ACR	2.998 × 108	17.315
PGR + ACR	3.038 × 108	17.429

PGR modifier uniformly set to u = v = 7 monolayer graphene molecule (G7-1).

. In Table 3, it can be seen that the solubility parameters of graphene and graphene/polymer composite modified asphalt simulation systems are roughly distributed in the range of 16.384–17.354 (J/cm³)^0.5, which is between the solubility proposed by Li et al. [15,23], and parameters indicate that this asphalt’s molecular modeling and stance parameters are more reasonable.

3.2. Interaction between Graphene and Asphalt Components

3.2.1. Radial Distribution Function Analysis

The last frame of the 298 K steady-state molecular model was extracted for radial distribution function analysis, and the results are shown in Figure 9.

It was found by radial distribution function (RDF) analysis that PGR exhibits a significant peak in the range of 0~5 Å concerning asphaltenes or resins in the bitumen. This phenomenon suggests that polar components such as asphaltenes and resins aggregate around graphene when added. Notably, when the graphene size is kept constant (e.g., Figure 9a–c), with the number of graphene layers increasing, these peaks become more significant, and the distance corresponding to the peaks extends from 5 Å to 10 Å. Especially when the number of PGR layers is two, the interaction with asphaltenes is the strongest, and the peaks are closer. When the number of layers increases to three, the resins start to aggregate in the range of 10~15 Å, while the saturated fraction shows a weak peak near 15 Å. As the PGR size increases (e.g., Figure 9d,e), the interaction between PGR and the saturated fraction in the bitumen is enhanced in the range of 5~10 Å, indicating that the larger size of graphene is more likely to interact with nonpolar or weakly polar bitumen components. The aggregation of asphaltenes and colloids was more rapid when further increased to the G9-1 size. This phenomenon reveals that graphene mainly interacts with polar asphaltene components containing aromatic structures to form π-π stacks [28], which order the asphaltene molecules in specific regions, which is favorable for improving the thermodynamic and functional properties of asphaltene.

The radial distribution functions in the molecular systems of different types of PGR/SBS composite-modified bitumen are shown in Figure 10.

Upon addition of a monolayer of small-sized PGR (e.g., Figure 10a) to SBS-modified asphalt, PGR peaks with SBS molecules near 5 Å. The peak of PGR with the saturated fraction (Sa) is located at 10 Å, while the peak with gums is only near 20 Å. The peak of PGR with SBS molecules is around 5 Å, and that with gums is around 20 Å. This indicates that PGR preferentially interacts with SBS molecules, followed by saturated fractions and gums. Increasing the number of PGR layers (e.g., Figure 10b,c) significantly decreases the peaks of PGR with asphalt fractions and SBS molecules, and the greater the number of PGR layers, the more the aromatic fractions interact with the PGR in the front position. This is because increasing the number of PGR layers reduces its surface tension and weakens the adsorption with polar components. In contrast, the weakly polar aromatic components are more likely to move around the PGR and entangle with the asphaltene due to their smaller molecular mass and faster moving speed, thus affecting the physicochemical properties of the PGR/SBS composite-modified asphalt.

Figure 10d,e shows that the interaction between saturated fraction and PGR is more significant when increasing the PGR size and number of layers. Further growing the PGR size to G9-1 (Figure 10f), the peak of the aromatic fraction is slightly higher than that of PGR-Sa but appears closer, indicating that the interaction between large-size PGR and the aromatic fraction is more intense, mainly due to the formation of a strong π-π stacking interaction.

Figure 11a–c shows that in ACR-modified asphalt, small-sized PGRs interact significantly with gums and asphaltenes primarily, aromatic fraction secondarily, and gum powder molecules the least and that an increase in the number of PGR layers enhances their aggregation with asphaltenes and decreases their aggregation with gums. Figure 11d shows that PGR interacts significantly with the saturated fraction, and increasing the number of PGR layers (Figure 11e) enhances the degree of adsorption of gum powder with asphaltenes. In contrast, large-size monolayer graphene (G9-1) will moderately reduce the peak radial distribution function between PGR and ACR-modified asphalt fractions, thus weakening the interaction between the two.

In summary, adding small-sized PGR to polymerized modified asphalt facilitates the enhancement of the interaction of polar components in the modified asphalt, and the large-sized multilayer graphene contributes to the enhancement of asphalt matrix properties.

3.2.2. Binding Energy

The binding energy refers to the required energy for separating a component from the mixed system, and the magnitude of the power can explain how strongly these components combine [29]. Further, the simulation cannot directly output the binding energy, while it can be calculated based on the internal energy.

Table 4. Changes in binding energy of graphene/matrix asphalt interfacial system.

Type of PGR	∆EBinding (kcal/mol)	Non-Bonding Energy (kcal/mol)
		EvdW	ELRC	ECoulomb
G5-1	61.79	58.47	1.58	1.74
G5-2	111.37	99.30	3.08	8.99
G5-3	174.00	168.44	4.54	1.03
G7-1	97.74	91.23	2.77	3.75
G7-2	166.11	158.63	5.34	2.14
G9-1	198.26	192.60	4.26	1.40

summarizes the interfacial bind energies of different types of graphene with 70# matrix asphalt and their compositional changes. The table shows that the bind strengths of the interfaces of various types of graphene and asphalt are all greater than zero, indicating an interaction between graphene and asphalt molecules, consistent with the radial distribution function analysis results.

The contribution of chemical binding energy (binding energy) to the interfacial binding energy is zero, indicating no chemical reaction between graphene and asphalt matrix, consistent with the results of infrared spectroscopy tests. The interfacial binding energy between graphene and asphalt is mainly composed of non-bonded energies such as van der Waals’ action energy (EvdW), long-range corrected action energy (ELRC), and Coulomb force action energy (ECoulomb), in which the van der Waals’ action is the main factor and the Coulomb force action is the secondary factor. The interfacial binding energy between PGR and polymer-modified asphalt is similar to matrix asphalt and mainly consists of physical reactions. Still, modified asphalt’s interfacial bind strength value is higher than that of PGR and matrix asphalt.

The variation of the binding strength and its composition between different types of PGR and three asphalt matrices is shown in Figure 12. Figure 12a shows that the size and number of graphene layers significantly affect its interfacial binding energy with the matrix bitumen. The interfacial binding energy increased dramatically by 182% when the PGR was increased from one to three layers. This is primarily due to the increase in the number of graphene layers, which enhances the interactions (van der Waals forces and π-π stacking) between the PGR and the asphaltene and resin components, thereby improving the interfacial bonding strength. When the number of PGR layers was the same, the interfacial bind energy increased by about 58% when the PGR was changed from G5-1 to G7-1, indicating that increasing the number of graphene layers was more favorable for the graphene/matrix asphalt interfacial bind strength.

In Figure 12b, it can be seen that increasing the number of small-sized graphene (G5-1) lamellae does not effectively enhance the interfacial binding energy with SBS-modified asphalt because the increase in the number of PGR layers results in the migration of nonpolar saturated fractions in the asphalt to graphene, which in turn affects the binding effectiveness. Increasing the PGR size (e.g., G5-2 to G7-2) increased interfacial bind strength by approximately 39%. At a PGR of G9-1, the interfacial bind energy of the PGR/SBS composite-modified asphalt reaches its peak, mainly due to a significant increase in the interaction of the PGR with the colloidal and saturated fractions.

According to Figure 12c, the interfacial bind energy between different PGR and ACR-modified asphalt is enhanced with increasing graphene layers. For the same number of layers of PGR, larger graphene sizes (e.g., G9-1) resulted in a more incredible interfacial binding energy. This binding energy is mainly due to the close connection of PGR with the gum, activated gum powder, and saturated fraction in the ACR-modified asphalt, so the gum powder fully absorbs the lightweight components in the asphalt and forms a dense and flexible polymer network.

3.2.3. Glass Transition Temperature

A lower Tg generally indicates a better low-temperature performance of the asphalt material because it is still flexible at lower temperatures, thereby reducing the likelihood of cracking. In this study, 100 ps kinetic calculations were carried out at 200 K, 220 K, 240 K, 260 K, 280 K, 300 K, 320 K, and 340 K temperatures under the NPT system (one standard atmospheric pressure) for the asphalt molecular model that reached the steady state, and the 80th ps to 100 ps density data were extracted for each test temperature and statistically analyzed. The reciprocal of the average density value at this stage (specific volume) was used as the dependent variable to plot the change in a particular volume of graphene-modified asphalt at different test temperatures.

Figure 13 shows the specific volume of 70# and PGR (G7-1) modified 70# matrix asphalt at different temperatures. This study defines the intersection of the two specific volume-fitted straight lines in the asphalt material as the glass transition temperature.

The glass transition temperatures Tg of different types of graphene-modified asphalt are shown in Figure 14. The increase in the size and number of layers of PGR leads to an increase in the Tg of the 70# matrix asphalt. Still, the fluctuation range of the Tg is not more than 5 K when the size of the PGR does not exceed G9-1, which indicates that the addition of PGR has a slight effect on the low-temperature performance of asphalt but is not sufficient to change the low-temperature performance class.

The Tg of SBS-modified asphalt decreased after adding Small PGR (e.g., G5-2), and the increase in the number of PGR layers increased the Tg, thus reducing its low-temperature cracking resistance. However, this effect is negligible, considering that the PGR incorporation in the test was not more than 1%, which is much lower than the percentage used in the simulation.

For ACR-modified asphalt, although its Tg is much higher than that of 70# and SBS asphalt, which suggests that the low-temperature performance of ACR is not as good as that of the latter two, the opposite is true. It should be noted that Tg is not a fixed value but a range. This study focuses on the law of influence of different types of PGR on the Tg of asphalt matrix. Figure 14 shows that small-sized graphene slightly reduces the Tg of ACR-modified bitumen, while the opposite is true for increasing the number of layers. Overall, adding graphene can appropriately enhance the low-temperature performance of ACR-modified asphalt without exceeding the size of G9-1.

3.2.4. Relative Concentration of Asphalt Molecules

The healing temperatures of the asphalt were selected as the corresponding optimal healing temperatures, i.e., the test temperatures of 70# and PGR-modified 70# asphalt were set to 318 K (45 °C), the test temperatures of SBS and PGR/SBS composite-modified asphalt were fixed to 353 K (80 °C), and the test temperatures of ACR and PGR/ACR composite-modified asphalt were set to 333 K (60 °C), respectively. For the 70# and SBS-modified asphalt systems, the concentration of asphalt molecules along the OZ direction of the asphalt self-healing model at the moments of 0 ps, 30 ps, 60 ps, 90 ps, 120 ps, and 150 ps were calculated, respectively. For the ACR-modified asphalt system, the asphalt molecular concentration of the asphalt self-healing model along the OZ direction at 0 ps, 20 ps, 40 ps, 60 ps, 80 ps, and 100 ps were calculated, respectively.

The relative concentration changes of the PGR-modified different types of asphalt molecules along the OZ direction are shown in Figure 15, where the initial asphalt model shows high-concentration peaks on both sides of the crack and a 20 Å crack with zero concentration in the middle. The addition of PGR resulted in a slight decrease in the concentration peaks on both sides of the asphalt.

For 70# asphalt, the concentration peaks decreased, the cracks narrowed after 30 ps, and the cracks healed further after 90 ps and approached complete healing at 150 ps. The addition of PGR accelerated the healing process of 70# asphalt. The healing process was completed at 90 ps, which was 60 ps faster than that of the unmodified asphalt, and this accelerated healing process was attributed to the π-π force between the PGR and asphalt molecules (aromatic structural substances) and the bridging effect of the PGR mesh structure, which promoted the migration of small molecules (saturated fractions) to increase the healing efficiency, which is in line with the result of the heat-induced self-healing test. This is consistent with the results of the heat-induced self-healing test.

For SBS and ACR-modified asphalt, the presence of long-chain polymers hinders the mobile diffusion of asphalt molecules. Therefore, higher temperatures and longer diffusion times are needed to heal the microcracks gradually. For the 150 ps diffusion of SBS-modified asphalt, the relative concentration of asphalt molecules is close to 1, indicating that the molecules of SBS-modified asphalt are generally self-healing at this time. After 120 ps kinetic calculations, composite-modified asphalt can be realized after the relative concentration of 1, so 30 ps shortens the healing time.

ACR-modified asphalt after 100 ps diffusion can repair most of the microcracks; at this time, the relative concentration curve in the middle of the depression area still exists; for PGR/ACR composite-modified asphalt after 100 ps diffusion, the concentration curve in the middle of the depression area almost disappeared, the minimum value of the relative concentration of the microcracked area was more than 0.92, and the concentration of the two sides of the molecules was in the range of 1.2~1.4. The above analysis confirms that PGR can also promote the polymer-modified asphalt healing time, which the presence of PGR can achieve. This presence can also encourage the self-healing of polymer-modified asphalt molecules.

3.2.5. Mean Square Displacement and Diffusion Coefficient

Self-healing of asphalt is accompanied by the diffusion and miscibility of asphalt molecules, which will move with the force field and tend to diffuse from the original position during the kinetic simulation.

Figure 16 shows that the MSDs of PGR-modified asphalt in the range of 0 to 150 (100 ps) at different temperatures increase with the simulation time and test temperature. At the same test temperature, the MSD of PGR-modified asphalt molecules is always higher than the corresponding asphalt molecules, indicating that PGR can enhance the diffusion ability of asphalt molecules.

For 70# and PGR-modified asphalt, for the first 50 ps of the simulation, the movement of the asphalt molecules toward the microcracked regions at both ends is relatively smooth due to the presence of microcracks. However, as the microcracks close, the movement of the asphalt molecules is influenced by the opposite molecules. Therefore, the molecular motion within 0~50 ps best reflects the healing process. In this study, the MSD curve of 0~50 ps was analyzed, and the slope of the MSD curve was used to calculate the diffusion coefficient D.

Figure 17 shows the diffusion coefficients of different types of graphene-modified asphalt molecular models at different test temperatures D. The results show that the diffusion coefficients D of the PGR-modified asphalt are higher than those of the corresponding asphalt at the same test temperatures, indicating that the PGR can enhance the free diffusion ability of the asphalt molecules, thus improving the self-healing efficiency of the asphalt binder. On the one hand, this enhanced healing ability is due to the good thermal conductivity of graphene, which increases the kinetic energy of the asphalt molecular system and helps the asphalt molecules to overcome the interaction force and stimulate the diffusion behavior. On the other hand, graphene forms a π-π stacking effect with the gums, asphaltenes, aromatic fractions, and other aromatic ring-rich structural substances in the asphalt molecules, which plays the role of bridging the asphalt gels and transferring molecules and jointly improves the self-healing performance of the asphalt. In summary, the dual effects of PGR modification and graphene significantly improved the self-healing efficiency of asphalt.

4. Conclusions

In this study, the interaction between different types of graphene and asphalt was systematically analyzed based on molecular dynamics simulation technology to explore the enhancement mechanism of graphene on the self-healing performance of asphalt, and the conclusions pointed out the following:

(1)

The 4-component, 12-molecule model was used to construct the molecular model of matrix asphalt and polymerization-modified asphalt; the molecular model of graphene with different sizes and layers was successfully constructed by using cut graphite and supercrystalline constructions, etc., and the reasonableness of the model was verified by indexes such as energy, density, and solubility parameters.

(2)

The size and number of layers of PGR have a significant effect on its interaction with asphalt components, and the polar components in asphalt interact more strongly with PGR; when the size and number of layers of PGR are fixed, its interfacial binding with ACR-modified asphalt is the highest, followed by SBS-modified asphalt, and 70# matrix asphalt is the worst; the interfacial binding between PGR and asphalt mainly relies on the van der Waals interaction between interfacial molecules; multilayer graphene molecular modeling was successfully constructed with different sizes and numbers of layers, and the model was verified by energy, dissolution parameters, and other indicators. Van der Waals interaction: multilayer graphene on the mechanical properties of matrix asphalt strengthens the role of more apparent, and small-sized graphene is more suitable for enhancing the low-temperature performance of polymer-modified asphalt.

(3)

Based on the relative molecular concentration and MSD function, the self-healing process and mechanism of PGR-modified asphalt were comprehensively evaluated. PGR bridged asphalt molecules through rapid heat transfer and π-π stacking with aromatic ring-containing substances, which significantly improved the free diffusion ability of asphalt molecules, shortened the asphalt healing time, and enhanced the overall self-healing performance of asphalt.

(4)

Despite the above findings, the study may need to improve the realism of the simulation and the accuracy of the model construction. Future research could consider experimental validation of the simulation results and explore the effects of different modifiers and asphalt formulations on the self-healing ability.