## 3 Results and Discussion
### Molecular Chain Mobility  
The MCM is an important parameter to characterize various properties of nanocomposites. The movement ability of molecular chain can be described by mean square displacement (\(MSD\)) in polymer. The \(MSD\) represents the change in the position of atoms relative to their initial space during the dynamics simulation, and it is calculated by Equation (7). \[MSD=\langle\left|\overrightarrow{r_{i}}(t)-\overrightarrow{r_{i}}(0)\right|^{2}\rangle \tag{7}\]  
where \(r_{i}(t)\) is the position of \(i\) atom at time \(t\), and \(r_{i}(0)\) the initial position of \(i\) atom. A major distinction of the performance between the interface layer and the matrix is the difference in the atoms mobility. The \(MSD\) of the four models in NVT ensemble for 200 ps was calculated, as shown in Figure 9. It can be seen that the molecular mobility of the BNNS/EP composite is lower than that of the pure EP, indicating that the molecular chain mobility of nanocomposites is reduced by incorporating BNNS. In order to further characterize the mobility of molecular chains at different positions of models, the compute \(MSD\)/chunk command in LAMMPS was used to calculate the RMSD between different layers of nanocomposites. The space was divided into 50 layers along \(z\) direction, and each layer was set to be 1.2 A in this paper. This result is shown in Figure 10. The MCM of the region with a distance to BNNS less than 10 A is clearly lower, that is, the movement of atoms is restricted, which is a manifestation of the cage effect. The molecular mobility of the region with distance greater than 10 A is almost same as that of EP. Through comparing the RMSD curves of four models, it can be found that the \(MSD\) value of the interface region is relatively volatility, and the value of RMSD near the interface region is significantly lower than other locations, which indicates that MCM is reduced in the interfacial region. The strong interaction between the molecules and reduction of chain movement space are the main causes of this phenomenon. To further explore the reasons for the decrease of MCM of BNNS/EP composites, the \(CED\) and valid free volume fraction (\(VFFV\)) of compound models were calculated, as shown in Figure 11.  
The intermolecular forces of polymers have a prominent influence on many properties of the nanocomposites and is usually characterized by \(CED\). A higher \(CED\) represents a stronger interaction force between molecules. And the glass transition temperature and flexibility of the molecular chains are also related to the \(CED\)[23; 24; 33; 36; 62]. The \(CED\) value is the cohesive energy per unit volume. Figure 9: Mean square displacement (MSD) of BNNS/EP nanocomposites. Since the cross-linked EP is a networked thermoset polymer, the cohesive energy and \(CED\) can be calculated by Equations (8) and (9). \[E_{coh}=-(E_{vdw}+E_{coul}+E_{H-bond}) \tag{8}\]  
\[CED=\frac{E_{coh}}{V_{m}} \tag{9}\]  
where \(E_{coh}\) and \(V_{m}\) represent cohesive energy and volume of composites, respectively. The \(CED\) of different kinds of nanocomposites were compared, as shown in Figure 11. The \(CED\) of the BNNS/EP composites is significantly higher than that of the pure EP, which indicates that the incorporation of BNNS enhances the interaction force between molecules of nanocomposites. That is, the movement of molecular chain is restricted with the increase of \(CED\), which reduces the MCM. Moreover, it can be observed from the IBE and \(CED\) that the intermolecular interaction force is enhanced with the increase of functional density. As a result, the compatibility and flexibility of molecules become better, resulting in the molecular chain being easier to wrap around the BNNS [37; 47]. These conclusions can also explain that the functional group of CH\({}_{3}\)-(CH\({}_{2}\))\({}_{4}\)-O- is beneficial for enhancing the interfacial compatibility between BNNS and EP. Figure 11: Cohesive energy density (CED) and valid free volume fraction (VFFV) of BNNS/EP nanocomposites.