PSI - Issue 52

Mayu Morita et al. / Procedia Structural Integrity 52 (2024) 195–202 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

199

5

structures. The cutoff distances for both Lennard-Jones (LJ) and Coulombic interactions are set to 1.0 nm. All simulations are performed using the GROMACS software. The charges of each atom are determined by density functional calculations with the B3LYP/6-31G (Hamiltonian/basis set) to reproduce the electrostatic field around each molecule. 2-2. Evaluation of mechanical properties Before calculating the mechanical properties of matrix polymer and interface energy of the interface models, the equilibrium structures of these models are obtained by following relaxation calculations. First, structural optimization of a system is performed to minimize the internal energy of the system. Second, successive relaxations are performed under NVT (temperature T = 600 K) and NPT (pressure P = 1atm and T = 600 K ) ensemble. Third, the temperature of the system is decreases from 600 K to 300 K with a cooling rate of 6.0 × 1010 K/s under constant pressure condition (P = 1atm). Finally, the equilibrated structure is obtained by the long-term relaxation under NPT (P = 1atm and T = 300 K) ensemble. To evaluate the mechanical properties of matrix polymer in bulk system, the stress-strain diagram is obtained through uniaxial tensile simulation, where the system is deformed at a strain rate of 1.0×10 9 /s in the z direction, while applying 1 atm of pressure in the x-y directions. For the interface stability between polymer and reinforcement, the interface energy per unit area ( ) is evaluated by following equation as a = total −( resin + graphene ) 2 (1) where total , resin , and graphene are the energies of the entire system, the polymer resin, and the three graphene sheets, respectively . A is the interface area. The schematic illustration for evaluating equation (1) is shown in Figure 2. 3. Results and discussion Figure 3 shows the stress-strain curves obtained from uniaxial tensile calculations in the bulk system. The orange line represents the results for EL, and the blue line represents the results for EGL. Both Youngs modulus and maximum strength are more than 10% greater for the EGL system as shown in the quantitative comparisons in Table 1. Here note that Young’s modulus is estimated from the initial slope of the stress strain curve with strain less than 0.02. The improvement of the mechanical properties is attributed to the entanglement between side chains (PEGs) with each other. EL polymer is a simple linear structure, and tensile loads are supported by the entanglement points only at its rigid main chain. On the other hand, EGL supports larger loads because the flexible side chains can entangle with different molecules. Therefore, EGL exhibits higher Young’s modulus, strength and toughness represented by the area of the stress-strain curve. Table. 1 Calculation results of the bulk properties Maximum stress (MPa) Young’s modulus (GPa) EL 243 3.32 EGL 284 3.77 Table. 2 Calculation results of the interface energy (J/m 2 ) Functional groups on graphene None -OH -O- EL -0.184 -0.204 -0.197 EGL -0.208 -0.253 -0.217