## 2 Materials and Methods
### The Process of Crosslinking  
The principle of cross-linking between EP and curing agent follows the two main reaction formulas, as shown in Figure 3. Two epoxy functional groups can theoretically react with one secondary amine functional groups. Each EP molecule has two epoxy functional groups, and each DETDA molecule includes two secondary amine functional groups. The cross-linked degree of the actual system is generally in the range of 80-95% [55]. Therefore, the cross-linked degree was selected as 85% in this study.  
The structure of the above molecular model was optimized, then the energy minimization calculation was performed with Forcite module until the geometry of them reached convergence.  
Figure 1: Molecular models for DGEBA (diglycidyl ether of bisphenol A) and DETDA (diethyl toluene diamine).  
Figure 3: Cross-linking reaction principle.  
Figure 2: Molecular models for boron nitride sheets (BNNS) with different functionalization density.  
After that, a stoichiometric mixture of 64 DEGBA molecules and 32 DETDA molecules was established by employing the amorphous cell module. Next, the above model was balanced and relaxed until the structure and energy became quite steady. This model was balanced once by canonical ensemble (NVT), in which the temperature of ensemble maintained 300K, the step of time was 0.5 fs, and this process kept 100 ps. Then, the model was subsequently relaxed twice by isothermal-isobaric ensemble (NPT) with pressure 1.0 GPa and 0.1 MPa (simulation time 100 ps and time step 0.5 fs). Afterwards, the structure of this model was optimized and balanced again. Through the above process, the uncross-linked model was obtained. The force field of this molecular dynamics (MD) simulation is universal force field (UFF), and the method of thermostat and barostat is Andersen and Berendsen, respectively [56].  
Based on the established model, the cross-linked process was performed by using Perl scripting language according to the procedures in [55]. The main steps are described with four steps.  
Step 1: Define the values of simulation parameters. The initial and final cross-linked cutoff distances are 3.5 A and 12.5 A, respectively. The step length is selected as 0.5 A, and the reaction temperature keeps 300K. The number of iterations is 3. The ultima cross-linked degree is set as 85%.  
Step 2: The distance between the unreacted atoms (R1, R2) is identified. If the reaction atoms of epoxy groups are located within the reaction cutoff distance, the ring of epoxy groups is opened. Then the reaction atoms of epoxy groups react with unreacted secondary amine to form new C-N chemical bonds. The reactive principle is shown in Figure 3.  
Step 3: If three times of iterations are finished or there are no unreacted atoms within the reaction cutoff distance, the cutoff distance increases with steps of 0.5 A. The geometry is optimized and balanced until this model reaches the most stable status. The simulating condition of this process is the same as that of building the uncross-linked model.  
Step 4: The program repeats Steps 2-3, and when the cross-linked degree or the maximum reaction cut-off distance is reached, this process stops.  
After above cross-linked process, the structure of this model was optimized and balanced again. The built cross-linked EP model is with density of 1.12 g/cm\({}^{3}\) and cell size of \(25.4\times 25.4\times 59.8\) A, as shown in Figure 4.