# Molecular Dynamics-Based Study of Graphene/Asphal Mechanism of Interaction
## 3 Results and Discussion
### 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 A 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 A to 10 A. 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 A, while the saturated fraction shows a weak peak near 15 A. As the PGR size increases (e.g., Figure 9d,e), the interaction between PGR and the saturated  
Figure 8: Variation of molecular modeling system parameters (PGR for u = v = 7 monolayer graphene molecule (G7-1)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Asphalt** & _CED_ @ **298 K (J/m\({}^{3}\))** & \(\delta\) @ **298 K ((J/cm\({}^{3}\))\({}^{0.5}\))** & **Solubility Parameter \& Range @ **298 K ((J/cm\({}^{3}\))\({}^{0.5}\))** \\ \hline
70\# & 3.164 \(\times\) 10\({}^{8}\) & 17.787 & \\ PGR + 70\# & 3.170 \(\times\) 10\({}^{8}\) & 17.805 & \\ SBS & 3.162 \(\times\) 10\({}^{8}\) & 17.783 & \\ PGR + SBS & 3.159 \(\times\) 10\({}^{8}\) & 17.775 & \\ ACR & 2.998 \(\times\) 10\({}^{8}\) & 17.315 & \\ PGR + ACR & 3.038 \(\times\) 10\({}^{8}\) & 17.429 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cohesion energy density CED and solubility parameter \(\delta\) for molecular modeling of bitumen. fraction in the bitumen is enhanced in the range of 5-10 A, 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 \(\pi\)-\(\pi\) 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.  
Figure 10: _Cont._  
Figure 9: Radial distribution function between graphene and matrix asphalt components. Upon addition of a monolayer of small-sized PGR (e.g., Figure 9(a)) to SBS-modified asphalt, PGR peaks with SBS molecules near 5 A. The peak of PGR with the saturated fraction (Sa) is located at 10 A, while the peak with gums is only near 20 A. The peak of PGR with SBS molecules is around 5 A, and that with gums is around 20 A. This indicates that PGR preferentially interacts with SBS molecules, followed by saturated fractions and gums. Increasing the number of PGR layers (e.g., Figure 9(b),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 9(d),e shows that the interaction between saturated fraction and PGR is more significant when increasing the PGR size and number of layers.