## 3 Results and Discussion
### Interfacial Bonding Strength  
The interfacial binding energy reflects the bonding strength and compatibility between the matrix and the nanomaterial, and the interfacial bonding strength of composite materials can be described using IBE and ISS. A greater binding energy means that the interface strength of the composites is higher and compatibility is better. The calculation method of IBE is described as follows. The total energy (\(E\)) of the molecular system is the sum of kinetic energy (\(E_{kinetic}\)) and potential energy (\(E_{potential}\)). Molecular potential energy includes intramolecular potential energy and intermolecular potential energy and interaction energy. The intermolecular potential energy (\(E_{non-bond}\)) includes Van der Waals energy (\(E_{vdw}\)), electrostatic energy (\(E_{coul}\)), and hydrogen bonding energy (\(E_{H\text{-}bond}\)).  
\[E=E_{kinetic}+E_{potential} \tag{1}\]  
\[E_{non-bond}=E_{vdw}+E_{coul}+E_{H\text{-}bond} \tag{2}\]  
The IBE of different BNNS/EP composites can be calculated by the Equation (3):  
\[E_{interface}=E_{T}-(E_{BNNS}+E_{EP}) \tag{3}\]  
where \(E_{BNNS}\), \(E_{EP}\), and \(E_{T}\) are the potential energy of BNNS, EP, and BNNS/EP composite, respectively.  
The interfacial shearing strength is another way to characterize interfacial bonding strength. The ISS can be deduced by \(E_{pullout}\) that is the energy required to completely extract the nanomaterials from the composites and equals to the value of \(E_{interface}\). The ISS is calculated by Equations (4) and (5).  
\[E_{pullout}=\left|E_{interface}\right|=\int_{x=0}^{x=l}A\tau_{i}dz=\int_{x=0}^ {x=l}2S\tau_{i}dz=\int_{z=0}^{z=l}2h(L-x)\tau_{i}dz=h\tau_{i}L^{2} \tag{4}\]  
\[\tau_{i}=\frac{\left|E_{interface}\right|}{hL^{2}} \tag{5}\]  
where \(S\), \(h\), and \(L\) are the surface area, the width, and length of the BNNS, respectively. \(z\) is the coordinate of the drawing direction. \(\tau_{i}\) is the shear stress. Since BNNS of this paper is not a square, \(\tau_{i}\) in the different direction as \(X\) and \(Y\) are calculated and averaged, shown as Equation (6).  
Figure 6: RDD (radial distribution density) of BNNS/EP nanocomposites.  
\[\tau=\frac{\tau_{X}+\tau_{Y}}{2} \tag{6}\]  
The potential energy curves of each model for 100 ps of the balance process were taken, as shown in Figure 7. It can be seen that the curves are basically stable, indicating that the model is already in equilibrium. Furthermore, the potential energy of the BNNS/EP composites is significantly higher than that of the pure EP. The IBE and ISS of the BNNS/EP composites with different functional densities were calculated, as shown in Figure 8. It can be found that the IBE of BNNS/EP, 4 BNNS/EP, and 8 BNNS/EP is \(-397\) kcal/moL, \(-584\) kcal/moL, and \(-692\) kcal/moL, respectively, and corresponding ISS is \(9.5\) MPa, \(13.9\) MPa, and \(17.7\) MPa. In other words, the interfacial strength of BNNS/EP composites increases with the functional density rising. Furthermore, the higher IBE and ISS values of the interface imply that the bonding strength of the interface between BNNS and EP is larger, so that the region near BNNS is more compact within a certain range, and the mass density in the vicinity of BNNS is significantly higher than that of the matrix. Besides, existing researches [37; 38; 51; 52] showed that interfacial compatibility is positively correlated with interfacial bonding strength, so the compatibility of BNNS/EP also becomes better with the increase of functional density according to Figure 8, which means that the functional group of CH\({}_{3}\)-(CH\({}_{2}\))\({}_{4}\)-O- is appropriate for BNNS. And the favorable interfacial compatibility will contribute to molecular entanglement near BNNS, which is beneficial for enhancing interfacial bonding strength.  
Figure 8: IBE (interfacial binding energy) and ISS (interfacial shear strength) of BNNS/EP nanocomposites.  
Figure 7: Potential energy of BNNS/EP nanocomposites for 100 ps.