## 2 Molecular Dynamics Simulations
### Simulation Results  
The relaxation process of asphalt molecules is shown in Figure 2. The relaxation was used to reach the energy minimization state of the asphalt molecular structure. It can be seen that the relaxation process would influence the structure of asphalt molecules, where agglomeration and densification occurred. Figure 1: Constructed asphalt in amorphous cell. Figure 2: The relaxation process of asphalt molecules. In the study, molecular dynamics simulation were exerted on the asphalt layer, where \"region\" and \"group\" commands were applied to set different regions in the asphalt molecule ensemble. The velocity command was used to set the velocities of different groups at 0.3 A/fs along the \(y\) axis to simulate the state of tension. The ensemble temperature was set to room temperature, which is 298.15 K. For every 100 time steps, the simulation temperature was adjusted. For asphalt molecular ensemble, the energy minimization process was firstly conducted to achieve the stability of the system, and then the simulation of the stretching process was conducted. The time step was set to 0.003 fs, and a total operation time with 6000 steps was conducted. In the OVITO (Open Visualization Tool) software, asphalt molecules were sliced (Figure 3), where the internal development of asphalt molecules under tension could be observed. Figure 3a shows the complete whole microstructure and Figure 3b shows the half-sliced part. It was found that, along with the applying of continuous tension loading, obvious gaps could be found in the internal asphalt molecule structure (Figure 4), where these locations may be the weak regions and prone to easily crack. The radial distribution function (RDF) is an important parameter to describe molecular structure. The essence of the radial distribution function \(g_{\text{ab}}\) (\(r\)) is the atomic ratio of local density and average density in the system [26]. When A and B atoms are distributed uniformly in the spherical shell, the probability is calculated as follows:  
\[\rho_{A}=\frac{n_{A}}{V} \tag{2}\]  
\[\rho_{B}=\frac{n_{B}}{V} \tag{3}\]  
Figure 4: Development of gap under tension loading. Figure 3: Slicing of the asphalt molecules. \[P_{A}=4\rho_{A}r^{2}\delta r \tag{4}\]  
\[P_{B}=4\pi\rho_{B}r^{2}\delta r \tag{5}\]  
where \(V\) is the total volume of the simulation system, \(n_{A}\) and \(n_{B}\) are the number of A and B atoms, \(\rho_{A}\) and \(\rho_{B}\) are the average density of atoms in the simulation system, and \(P_{A}\) and \(P_{B}\) are the uniform distribution probabilities of A and B atoms. By calculating the radial distribution function between different atoms, the local distribution of different atoms could be studied, as shown in Figure 5. It is observed that there existed a small difference in RDF before and after tension loading. For the asphalt microstructure before tension loading, when the distance was 2.375 A, a maximum value of 16.5250 occurred; for the asphalt microstructure after the tension loading, when the distance was 2.375 A, maximum value of 17.039 occurred. The trends of the curves of the two curves were completely consistent, indicating that most of the atoms in the asphalt microstructure did not significantly change their locations while a small portion changed the locations. It was further concluded that the applied tension loading would not only result in the whole asphalt microstructure change, but also in some of the specific locations. The application of tension loadings on the asphalt molecular structure was done by setting a constant speed in its \(y\) direction (vertical direction) of different regions, resulting in the stretching of the asphalt microstructure. Figure 6 shows the morphological changes of asphalt microstructures. Note that different color represents different atom types on the top and three different divisions on the bottoms.