# Molecular Dynamics-Based Study of Graphene/Asphal Mechanism of Interaction
## 3 Results and Discussion
### Interaction between Graphene and Asphalt Components
#### 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 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 \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type of PGR**} & \multirow{2}{*}{\(\mathbf{\Delta E_{Binding}}\) **(kcal/mol)**} & \multicolumn{3}{c}{**Non-Bonding Energy (kcal/mol)**} \\ \cline{2-5}  & & \(\mathbf{E_{\text{adW}}}\) & \(\mathbf{E_{\text{LRC}}}\) & \(\mathbf{E_{Coulomb}}\) \\ \hline 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 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Changes in binding energy of graphene/matrix asphalt interfacial system. Figure 11: Radial distribution function between PGR- and ACR-modified asphalt components. the number of graphene layers, which enhances the interactions (van der Waals forces and \(\pi\)-\(\pi\) 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 11(b), 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 11(c), the interfacial bind energy between different PGR and ACR-modified asphalt is enhanced with increasing graphene layers.