# A Coarse-Grained Molecular Model for Simulating Self-Healing of Bitumen
## 2 Establishment of Molecular Model
### Coarse-Grained Model  
The core of CGMD is to determine the distribution structure and number of atoms corresponding to a coarse-grained bead, i.e., to determine the mapping scheme. If the number of atoms in the CG bead is too small, the simulation is limited in scale and the calculation efficiency is low. If too many atoms are included, important molecular \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Calculation** & **Reference Value** \\ \hline Density (g/cm\({}^{3}\)) (at 288 K) & 0.996 & 1.025 [8] \\ Diffusion coefficient(cm\({}^{2}\)/s) (at 298 K) & 0.4 \(\times\) 10\({}^{-6}\) & 0.092 \(\times\) 10\({}^{-6}\)[23] \\ Glass transition temperature (K) & 262.9 & 261.7 [24] \\ Solubility parameter (J/cm\({}^{3}\))\({}^{\beta.5}\) & 17.6–18.2 & 13.3–22.5 [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculation and reference values of properties of bitumen all-atom molecular model. Figure 1: All-atom molecular model of bitumen. information (e.g., molecular topology structure and branched chain form) will be lost with insufficient accuracy of the model. Considering that bitumen molecules are mainly composed of polycyclic aromatic hydrocarbons, unsaturated cyclic aromatic compounds, non-polar hydrocarbons with straight and branched chains and aliphatic cycloalkanes, we considered 16 kinds of coarse beads classified in Table 3 after repeated calculation. During the division of the coarse-grained beads, the DMol3 module was used to minimize the energy of the functional groups to be coarse-grained, and the GGA-PBE generalization with the DNP group was selected to calculate the optimized structure with the lowest energy. All hydrogen atoms are not abstracted by the structure (including functional groups of hydrogen atoms), and all the chemical formulas on the number of hydrogen atoms are expressed in n, this is due to the fact that the relative atomic mass of hydrogen atoms is small compared with other heavy atoms, besides, the internal forces of the bitumen system are not dominated by hydrogen bonds; the differences in the number of hydrogen atoms within the same CG bead have less influence on the properties of the beads, thus this effect is ignored in this work. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Bead** & **Structural** & **Chemical** & **Mapping** & **Legend** & **Bead** & **Structural Formula** & **Chemical** & **Mapping** & **Ratio** & **Legend** \\ \hline C3 & C3 Hn & 3 & S1 & C5 HnS & 6 & & & \\ C4a & C4 Hn & 4 & B1 & C6 Hn & 6 & & & \\ C4b & C4 Hn & 4 & B2 & C4 Hn & 4 & & \\ C5a & C5 Hn & 5 & B3 & C5 Hn & 7 & & \\ C5b & C5 Hn & 5 & B4 & C5 Hn & 9 & & \\ C6 & C6 Hn & 6 & B5 & C6 HnO & 10 & & \\ N1 & C2 HnN & 3 & B6 & C6 HnS & 7 & & \\ N2 & C6 HnN & 7 & B7 & C4 HnO & 5 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Beads of bitumen CG molecular model. In the model, the coordination ratio of a bead is usually three to seven atoms. C3, C4a, C4b, C5a, C5b, and C6 are hydrocarbon structures without a benzene ring structure, N1, N2, and S1 are non-hydrocarbon structures without a benzene ring structure, B1, B2, B3, B4, B5, B6, and B7 are chemical structures with a benzene ring structure. In order to maintain the integrity of the benzene ring and to preserve as much as possible the characteristics of the benzene functional group, we have done the following special treatment of the benzene ring structure: without splitting the benzene ring structure that exists alone, the relevant structure is mapped as one of the CG beads B1, B4, B5, or B6; for the structure of a compound benzene ring (i.e., structures in which multiple benzene rings share carbon atoms), the mapping is completed with one of B2, B3, or B7 (the red circle in Table 3) attached to B1. For example, naphthalene (C10H8) is mapped as two beads, one B1 and the other B2. Based on the building block approach [26] to build a CG molecule model, the CG structure is kept as all-atoms by the confining effect of the force field.