# Nano-Interaction Mechanism Between Crumb Rubber and Asphal Components: A Molecular Dynamic Study
## 2 Modeling and Simulation Method
### Asphalt Modeling
#### 2.1.2 Model Validation  
In order to ensure the accuracy of the constructed model, the model validity was verified by multiple indexes, such as density, glass transition temperature (\(T_{\mathrm{g}}\)), cohesive energy density, and solubility parameter (\(S_{p}\)), using the aforementioned post-annealing model as a benchmark. The applicability of the model was ensured by comparing and analyzing existing literature or experimental data.  
Density  
The dynamics calculation of the asphalt model was carried out using the Forcite module Dynamics function. Calculation of the NPT ensemble, the temperature of 298 K (24.85 \({}^{\circ}\)C), and the laboratory density test used (25 \({}^{\circ}\)C) is the same. The calculation of pressure to take the standard atmospheric pressure was 1.01 \(\times\) 10\({}^{-4}\) GPa. The calculation time could be determined by the trial calculation. When the density change tended to stabilize, it could be stopped. This study took the time of the calculation to be 1000 ps.  
Figure 3 shows the time course curve of the density variation of the asphalt model. It could be seen that the density stayed in a stable vibration state when running for 200 ps. In order to make the results more representative, the last 200 ps density average was selected as the representative density. After calculation, the steady-state density of the asphalt model is 0.972 g/cm\({}^{3}\). It was consistent with the simulation results in related literature [29; 30].  
Glass Transition Temperature (\(T_{g}\))  
As an essential index of amorphous polymer materials, the \(T_{\mathrm{g}}\) has a reference value for the cognition of the substances' physical and chemical properties. The specific volume (\(V_{\mathrm{specific}}=1/\rho\)) curve method was used to determine the \(T_{\mathrm{g}}\). The specific volume versus temperature curve is shown in Figure 4. It calculated that the \(T_{\mathrm{g}}\) of the present model was 298 K, which was consistent with the simulation results (298 K) from the literature, as well as the experimental measurements (223 K\(\sim\)303 K) [19; 31].  
Cohesive Energy Density and Solubility Parameters (\(S_{p}\))  
The cohesion energy is defined as the energy required to transfer a unit molecule of a substance to the range of intermolecular forces. The cohesion energy density (CED) is the size of cohesion energy per unit volume, which can be used to assess the intermolecular interactions of asphalt. \(S_{P}\) is a physical constant, which measures the compatibility of polymer materials. It can be obtained by squaring the CED. The CED and \(S_{\mathrm{P}}\) are calculated as shown in Equation (1) below [32]:  
\[S_{P}=\sqrt{CED}=\sqrt{\delta_{vdw}^{2}+\delta_{ele}^{2}} \tag{1}\]  
Figure 3: Asphalt model density variation time course curve.  
where \(\delta_{vdw}\) and \(\delta_{ele}\) are the \(S_{p}\) components resulting from van der Waals and electrostatic forces, respectively.  
The comparison between the simulation results at room temperature (298 K) and the test values in the relevant literature is shown in Table 2. Results revealed that the simulation results agree with the measured values, indicating that the model selection of asphalt components and the setting of analytical parameters such as standpoint have good accuracy. Asphalt component model selection, position, and other analytical parameters were set accurately.