Effect of Iron Oxide on Self-Healing and Thermal Characteristics of Asphalt Based on Molecular Dynamics Simulation Perspective

. To compare the efects of two powders, iron oxide and mineral, on the healing process of asphalt molecules, Fe 2 O 3 -asphalt and SiO 2 -asphalt were constructed by Material Studio software (MS). Te mean square displacement, difusion coefcient, concentration distribution of the asphalt layer, and the thermal conductivity of the two models were analyzed to evaluate the infuence of two powders on the difusion behavior of asphalt molecules on a microlevel. Te results show that the efect of Fe 2 O 3 on the difusion rate of asphalt molecules is greater than that of SiO 2 at high temperature, but the efects are similar at low temperature. Te difusion coefcient of the Fe 2 O 3 -asphalt model increases faster than that of the SiO 2 -asphalt model with increasing temperature. Compared with SiO 2 , Fe 2 O 3 is more conducive to the model’s reaching a state of uniform concentration, which is manifested as the rapid repair of cracks on a macrolevel. Te thermal conductivity of the Fe 2 O 3 -asphalt model is higher than that of the SiO 2 -asphalt model.


Introduction
Many research studies have investigated the self-healing capacity of asphalt. Most were focused on improving its dynamic modulus, fexural stifness, and viscosity to prolong its service life, as measured by mechanical tests [1][2][3]. However, those studies did not use image-analysis tools to investigate the healing performance of asphalt binder. In addition, the output of waste metal materials in the construction industry is very large. Te waste iron and steel can not only continue to bear loads but also have their own thermal physical properties can be reused. Metal materials can efectively improve the self-healing ability of asphalt, which has been widely verifed. Tose research studies have mainly focused on the factors infuencing the healing ability or on techniques for enhancing the healing efect; less attention has been paid to studying at a microscale level the mechanism of enhancing the healing ability.
To investigate the properties of asphalt at a microscale level, asphalt was divided into diferent components by some chemical composition testing techniques [4][5][6][7][8][9][10][11][12][13][14]. Te chemical composition and structure of asphalt can afect its rheological and mechanical capacities [15][16][17][18], so it is important to use an accurate molecular model for asphalt. Tere are many studies exploring asphalt components and systems using molecular models [19]. Corbett et al. separated asphalt into diferent classes: asphaltenes, polar aromatics, naphthene aromatics, and saturates [20]. A molecular model of asphalt was developed by applying statistical mechanical sampling of the positions, orientations, and confgurations in multicomponent systems of relatively few (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) molecule types [21][22][23][24]. Te Hansen solubility parameter was used to understand the components in asphalt models [7]. Researchers have built computational modeling in order to investigate the mechanism of asphalt's adhesion to a mineral surface [25]. For instance, Fan et al. used molecular dynamics (MD) simulation to study the adhesion mechanisms between asphalt and component minerals [26]. Zheng et al. found that the resin and asphaltene, polar molecules of the bitumen component, have good adhesion to the mineral surface [27]. Amirul et al. also pointed that the promotional efect of oxidation on bitumen-silica interactions through computational modeling. Sun et al. investigated the infuence of temperature on the self-healing capability of asphalt binder using MD simulation. Analyses of density, relative concentration, and mean square displacement (MSD) were performed to investigate the temperature sensitivity of the self-healing characteristics of asphalt binder [28,29]. Using small-scale MD simulation, research of the micromechanical healing mechanism of asphalt binder and the infuence of crack width on the healing property found that higher temperature would result in higher difusivity of molecules and thus a higher healing rate [30]. Te "compression" of asphalt binder volume and the "stretching" of the asphalt binder molecules were responsible for the disappearance of vacuum microcracks inside the asphalt binder [31]. Using molecular simulation as a research method, Zhou and Li analyzed the feasibility of using the values of the chemical structure indexes H/C and CH2/CH3 as evaluation indexes of asphalt's self-healing performance. Te results showed that the trend was the same as the experiment result [32]. Crack width, temperature, the state of molecular aggregation, and the aggregate have great infuence on the selfhealing behavior of asphalt binder. In addition, graphene was found to have some positive impact on the self-healing process of asphalt binder [33].
Te current studies have been very rich in the exploration of asphalt components and factors afecting asphalt's self-healing behavior, and a few types of bitumen aggregate have been evaluated under diferent substrate conditions. However, there is little research on the simulation and analysis of the infuence of iron on the healing performance of asphalt binder. A better understanding of metal iron's infuence on asphalt healing behavior can promote the application of scrap metal iron in civil engineering. In addition, iron mineral powder is one of the traditional road construction materials that belong to the pozzolanic activity of materials rich in active SiO 2 . To explore the efects of the metal iron base and mineral base on the healing behavior of asphalt, Fe 2 O 3 and SiO 2 molecular models were selected to compare their diference in heat-conduction performance in asphalt healing.

Construction of Molecular Models of Four Asphalt
Components and Asphalt Binder. Based on reference [34], the molecular structure of the asphalt used in this paper adopts a four-stage12-component system, as shown in Table 1. Te bitumen model contains three types of asphaltenes, fve types of resins, two types of saturate, and two types of aromatics. Te proportion of each component of 70 # virgin asphalt (Table 2) obtained through a four-component test is shown in Table 3.
Under periodic boundary conditions, the asphalt model with an initial density of 0.6 g/cm 3 was constructed with the amorphous cell tool. In order to minimize the energy of the asphalt model and eliminate adverse contact, the system needs to be geometrically optimized. At 298.15 K, an isothermal-isobaric (NPT) ensemble was applied at a pressure of 1 atm to run 100 ps at a time step of 1 fs to obtain a sufciently balanced model of the system. Ten, in order to obtain a stable molecular model, the canonical ensemble (NVT) was continued, and the time step remained 1 fs after another 100 ps run. In the two dynamic operations, the truncation distance was 15.5 A (1 A � 0.1 ns), the temperature control mode was velocity scale, and the temperature diference was 10 K to control the temperature of the system. Figure 1 shows a pure asphalt model with the lowest energy.

Molecular Dynamics Model Verifcation.
To ensure that the asphalt molecular model can obtain reliable data results after dynamic calculation, the density of a single asphalt model was calculated according to the literature [35]. Operating in the Forcite-dynamic module, whose force feld is COMPASS at six temperatures (298. 15 [36]. Te density of the pure asphalt model changed with simulation time, as shown in Figure 2. Te results in Figure 2 show that the density of the asphalt molecular model increases with the increase in simulation time. Ten, after 50 ps, the density tends to stabilize. In addition, the simulation results also show that the density of the model decreases with increasing temperature; this is consistent with the results obtained in reference [36], which proves that the established asphalt model is reliable.

Construction of the Crystal Structure of Minerals.
Fe 2 O 3 was used as a representative of iron oxide metal, and the model of metal-iron-mineral-asphalt was established. SiO 2 occupies a large proportion in conventional aggregates; it can usually account for more than 40% of the total composition of aggregates. (Granite is a widely used aggregate in road construction, and the proportion of SiO 2 is as high as 72% in granite). Terefore, to establish an interface model between diferent minerals and asphalt, SiO 2 was used to represent common minerals, so that the structural behavior of the mineral-asphalt interface can be studied at a microscopic scale.
Te lattice parameters of Fe 2 O 3 and SiO 2 cells are shown in Table 4. To establish two representative oxide substrates, these are the operation steps: (1) Import Fe 2 O 3 and SiO 2 cells ( Figure 3

) into Materials
Studio from CRYSTAL Data Center (CCDC). (2) Set the structural surface. According to reference [37], the crystal structures of Fe 2 O 3 and SiO 2 are 2 Advances in Materials Science and Engineering   shear along the normal direction of [0, 0, 1]. Since the no-bondcut-of value is set to 9.5a in the force feld setting, the surface depth must be greater than 9.5a. In this paper, the cut-of distance is set to 15.5a. (3) Increase surface area. During the process of layer building, the model will stretch or compress if the volume parameter is diferent, this leads to distortion of the fnal calculation. Terefore, according to the volume parameters of the asphalt molecular model established above, when increasing the crystal surface volume, the size of crystal base model should be as close as possible to that of the asphalt model, and the size of the two substrates should be as similar as possible. Building vacuum slab and supercell were used to increase the surface area of the two sections by repeating in the X and Y directions, and then the period was changed from 2 to 3 dimensions. (4) Use geometric optimization to obtain an optimal structure. Finally, the mineral-crystal cell model for layer construction was obtained, as shown in Figure 4. Because of silica's strong surface reactivity, it is easily hydroxylated in the presence of water [29].
When establishing the crystal model of SiO 2 based on reference [28], a 4.5OH group/Nm 2 silicon dioxide flm representing complete hydration was added. Terefore, to increase the reliability of calculation results in the system, the hydrogenation operation was carried out after the crystal model of SiO 2 was established ( Figure 5).

Construction of Mineral-Asphalt Molecular
Model with a Crack. Models of asphalt with diferent substrates were built using the Build layers tool, and 10Å vacuum was set as a crack width in the asphalt. Te selection model size was matched according to average size. Ten, to ensure that the entire system was in a state of energy minimization, geometric optimization was carried out on the entire system again, and the number of iterations was 10000. Te optimized mineral-asphalt model is shown in Figure 6.

Healing Behavior.
In reference to the literature [28], the Forcite module was used for dynamic simulation calculations. Since asphalt is a kind of polymer material, COMPASS was used, and the dynamic simulation calculation was carried out under the constant temperature and constant volume NVT ensemble. First, it was run for 500 ps at a time step of 0.1 fs. Te atom-based summation was suitable for van der Waals interaction, and the truncation radius was set to 15.5Å to obtain accurate data. Ten, the time step was changed to 1 fs and it was run for 500 ps with the truncation radius unchanged. Finally, the same dynamic calculation was performed for two models under diferent temperature conditions. In the simulation calculation process, the control method selection of temperature is particularly important. To ensure the accuracy of the temperature, the Velocity Scale and Nose-Hoover temperature control methods were adopted successively, and the temperature diference was set at 5 K.

Difusion Coefcient.
Te difusion coefcient was used to characterize the difusion property of asphalt molecule on the surface of two minerals. Te law of

Advances in Materials Science and Engineering
Einstein expression [38], as shown in the following equation. Te limiting slope of the MSD curve as a function of time can be used to evaluate the difusion coefcient of particles. Usually, the difusion coefcient can be simplifed to this [39]: By averaging over all atoms, the MSD would have a linear dependence on time. Tus, the difusion coefcient, D, could be derived from the slope of the MSD-time relationship, as in the following equation. Te unit of D isÅ 2 / ps.
where a is the slope of the straight line ftted by MSD versus simulation time. Te unit of a isÅ 2 /ps (or 10 −8 m 2 s −1 ). Te slope of curves can be obtained by ftting the relationship between MSD and simulation time. Te difusion coefcients of asphalt fractions at diferent temperatures can be calculated according to equation (2).

Time Series Methodology.
Te time series method is a method that can predict the law of sequence development. It is also called the simple denotation method. It is a statistical method that can predict the future development trend of data based on the law of past data. Time series refers to a series of data arranged in chronological order. Time series analysis is a mathematical process used to analyze dynamic data. It is based on stochastic process theory and statistical methods to get the statistical law of the research object. Traditional statistical analysis is based on independent data series, while time series analysis focuses on the interdependent relationship between the data of the research object. General statistical analysis also includes autocorrelation coefcient (ACF) and partial autocorrelation coefcient (PACF). Based on time series theory [40], John's Macintosh Product (JMP) software was used to obtain partial autocorrelation coefcients of asphalt molecular models in the OX and OY directions at 298.15 K temperature, to judge the stability of relative concentration data.

Calculation Methodology of Termal Conductivity.
If the density of the model system is not uniform during the calculation process of thermal conductivity, it would afect the thermal conductivity calculation, leading to a result that does not conform to the actual situation. Since the existence of voids would reduce the transmission rate of heat fow between divided layers, the goal was to obtain a model with uniform density and as few voids as possible. Terefore, the model, as shown in Figure 7 was adopted, and the dynamic calculation was carried out after the modeling was completed. COMPASS was used for the force feld, the temperature was set at 298.15 K, and the time step was 1 fs. Te calculation time was 1000 ps, and then the thermal conductivity was calculated.
First, the force feld setting of atoms in the model should be changed to universal, and the current charge should be used by default before the calculation of thermal conductivity. Ten, the script of thermal conductivity should be run. To reduce the time cost of calculation and ensure the accuracy of calculation results, the number of layers along the Z-axis was set at 40 in this section. To obtain the infuence of two diferent base models on the temperature distribution and transfer of the asphalt model, the temperature feld results were calculated. Set the time step to 1 fs and the number of steps to 250 fs. Te temperature control method was Berender, and the temperature attenuation constant was set to 0.1.

Results and Analyses
3.1. Mean Square Displacement. Mean square displacement (MSD) can be used to refect the change of molecular displacement with simulated time so that the law of molecular difusion can be studied. And the damage-healing behavior of asphalt material is a macroscopic manifestation of molecular motion, so MSD can indirectly refect the healing behavior of asphalt. Figure 8 shows the calculated results of MSD from Fe 2 O 3asphalt and SiO 2 -asphalt models at diferent temperatures. For both models, MSD increased with the increase of simulation time, which corresponds to the fact that things always develop in the direction of entropy increase. In addition, the slope of the MSD curves of the two models increased with the increase in temperature, which indicates that a higher temperature leads to a faster difusion rate of molecules.

Molecular Difusion Coefcients.
Te difusion coefcients obtained by formula (2) are shown in Tables 5 and  6. Te difusion coefcients (D) of the Fe 2 O 3 -asphalt model were both greater than those of the SiO 2 -asphalt model at a temperature which was greater than 333.15 K, and the growth rate of the D value of the Fe 2 O 3 -asphalt model was greater with the increase of temperature. When the temperature was 298.15 K and 313.15 K, MSD curve of two models were close, which means that the difusion behavior of asphalt molecule is not obvious in two models, that is, the repair ability of asphalt molecule is weak at these two temperatures [29]. However, when the temperature was lower than 333.15 K, the difusion coefcient of the Fe 2 O 3asphalt and SiO 2 -asphalt model were unstable, which may be caused by the relatively low temperature, the diference of infuence of Fe 2 O 3 and SiO 2 on the difusion behavior of asphalt was not very large. In addition, combined with the conclusions obtained from reference [35], it can also be shown that under a certain condition, Fe 2 O 3 has a stronger promoting efect on the difusion behavior of asphalt, and this efect would be more signifcant at a higher temperature, indicating a higher rate of completion of the healing process.
By ftting the relationship between difusion coefcient and temperature with an exponential function, the results were obtained, as shown in Figure 9. It can be seen that the difusion coefcient of the Fe 2 O 3 -asphalt model grew faster 6 Advances in Materials Science and Engineering

Relative Concentrations in OX and OY Directions.
Te distribution of atomic concentration in the asphalt molecule can be used to refect its motion characteristics and rules. Terefore, the concentration distribution can be obtained by calculating the atomic density of periodic structures with cracks parallel to each coordinate axis, so as to evaluate the motion behavior of the asphalt molecule, and then evaluate its damage healing efect and rate. After dynamic simulation, the relative concentrations in the OX, OY, and OZ directions were obtained, as shown in Figures 10 and 11. Te fgures show that the relative concentrations of the asphalt model in the OX and OY directions were almost constant. Tis was consistent with the total concentration, and the concentration distribution was more uniform with a higher temperature. It can be concluded that in the process of crack repair, in both the Fe 2 O 3 -asphalt model and the SiO 2 -asphalt model, the motion of asphalt in the direction of OX and OY tended to be stable. Tis is the same as the motion of atoms in OX and OY directions under the pure asphalt model [29]. It showed that the healing behavior in the OX and OY directions was not obvious, since there was no damage crack, the asphalt molecules were in a relatively balanced state, and their motion behavior was relatively gentle.

Partial Autocorrelation Coefcient.
Te change in relative concentration can indicate that the asphalt molecules move during the process of asphalt healing, thus showing the healing behavior. When the asphalt concentration around the crack increases, it indicates that the crack is being repaired.
It can be seen from Figures 12 and 13 that the development trend of partial autocorrelation coefcient of each diferent lag number was 0, which indicates that the time series data studied was stable. In other words, the relative concentrations of the asphalt model in the OX and OY directions of the two models were consistent with the total concentration, and remained almost unchanged after the dynamic simulation was started. Terefore, it can be concluded that the motion of asphalt molecules in these two directions tends to be stable at a density of 1.0.

Relative Concentrations on OZ Direction.
Trough the calculation on the direction of (0, 0, 1) to estimate the relative concentration of asphalt molecular aggregation distribution in the OZ direction, Figure 14 shows the asphalt molecular distribution in the OZ direction. It can be seen from the diagram, for the initial model, the vast majority of asphalt molecules were distributed at both ends of the model, and the atomic concentration at the cracked part was 0. After a dynamic calculation at diferent temperatures, the atomic concentration of the cracked part began to increase. Tis was due to the atoms in the two layers of asphalt molecules being close to each other to repair the cracked area, so the relative concentration gradually increased. In addition, at diferent ambient temperatures, with the increase in temperature, the atomic concentration of the cracked part increased gradually, and the concentration value after healing was progressively closer to 1.0 g/cm 3 .
However, it is not enough to analyze only the concentration distribution of asphalt in the composite model; the numerical diference of its relative concentration was not very signifcant, which makes it difcult to distinguish the infuence of Fe 2 O 3 and SiO 2 on the motion of asphalt molecules. Terefore, the standard deviation of relative concentration in the asphalt molecular model was calculated at diferent temperatures to obtain the infuence of the  Advances in Materials Science and Engineering two diferent substrates on the uniformity of the asphalt concentration distribution in the models. Te results are shown in Figure 15. It can be seen that with an increase in temperature, the standard deviation became progressively smaller, indicating that the distribution of asphalt components was more uniform. Compared with the SiO 2 -asphalt model, the standard deviation of the relative concentration in the Fe 2 O 3 -asphalt model was smaller. It can be concluded that the distribution of the asphalt components in the Fe 2 O 3 -asphalt model was more uniform. At higher temperatures, asphalt components in the Fe 2 O 3 -asphalt model could reach the equilibrium state more rapidly and complete the repair of cracks. When the temperature was lower, the composition distribution uniformity of the two models was relatively close. Tat is because the fow performance of asphalt at a lower temperature is poor, and it is not enough to complete the crackrepair process; therefore, the overall standard deviation value is larger, and the relative concentration of the two

Conclusions
Te Fe 2 O 3 -asphalt model and a SiO 2 -asphalt model were established, and dynamic simulations and thermodynamic calculations were carried out under diferent temperature conditions. Te mean square displacement, difusion coefcient, concentration distribution of the asphalt layer, and the thermal conductivity of the two models were analyzed. Maybe the infuence of other metal oxide on the healing property of asphalt on microlevel and macrolevel could also be researched in the future. It would enrich the research of asphalt area. Te main fndings of this study can be drawn as follows: (1) A higher temperature leads to a larger difusion rate of molecules. At diferent temperatures, the mean square displacement (MSD) of Fe 2 O 3 -asphalt and SiO 2 -asphalt model increased with the increase of simulation time. Te slope of MSD curve increased with an increase in temperature. (2) Fe 2 O 3 has a better efect on the difusion rate of asphalt molecules than SiO 2 at a higher temperature, but it is similar at a lower temperature. At a temperature greater than 333.15 K, the difusivity of the Fe 2 O 3 -asphalt model was greater than the difusivity of the SiO 2 -asphalt model.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.