Bisphenol A diglycidyl ether (BADGE), 1,6-hexanediol diglycidyl ether (HDGE), and 3,4-epoxycyclohexylmethyl-3',4'-epoxycyclohexanecarboxylate (EHMHC) were used as epoxy resin monomers, with cyclohexane-1,2,4-tricarboxylic acid- 1,2-anhydride (H-TMAn), 1,3-bis(aminomethyl)cyclohexane (BAC), and isophoronediamine (IPDA) utilized as curing agents (Figure 1).

In the microdroplet test, performed using an HM410 instrument (Tohei Sangyo Co.), the melted resin was attached to a single carbon fiber extracted from the bulk. All samples were prepared at a constant temperature of 23˚C and a relative humidity of 55%.

Compositional optimization was performed using the B3LYP hybrid density functional with a 6-31G(d) basis set, and the epoxy binding energy was estimated for the optimized structure. Charge densities for each optimized structure were calculated at MP2 (second-order Møller-Plesset perturbation, full)/6- 31G(d) levels and also using the ChelpG method [12] . In our Ab initio calculations, graphene was substituted by benzene to reduce the number of atoms in the model and thus facilitate computation. Similarly to previous studies [13]

[14] , a COOH functional group was attached to benzene and allowed to react with epoxy monomers, as shown in Figure 2, with its binding energy estimated by the Ab initio method. The above calculations were performed using Gaussian09 software [15] . k₁ was showed the C?O bond of a COOH functional group. k₂ was showed the C?O bond which was generated after carbon atom of epoxy ring attached a COOH functional group.

Interactions between epoxy compounds were modeled using GROMACS 5.1.2 [16] molecular modeling software implementing a version of AMBER03 [17] . All force field MD calculations were performed in an NPT ensemble at 300 K for 30 ns under the condition of a constant number of atoms and pressure using the Nose-Hoover thermostat [18] and the Parrinello-Rahman barostat [19] . Prior to NPT simulation, we conducted structural relaxation in an NVT ensemble at 800 K for 10 ns, utilizing a unit cell with 256 molecules. The LINCE algorithm [20] was applied to all constrained bonds in epoxy monomers. The simulation time step equaled 1 fs, and calculations utilized the epoxy monomer charge density estimated by the Ab initio method.

The experimentally determined shear stress (Table 1) varied between 59 and 65 MPa, with the maximum corresponding to the BADGE/IPDA resin.

The C?O bond binding energies of k₁ and k₂ were estimated as shown in Figure 2, with the corresponding numerical values listed in Table 2.

For BADGE-benzene, k₁ and k₂ were determined as 561 and 431 kcal∙mol^?1∙ Å^?2, respectively, with the corresponding values of HDGE-benzene equaling 372 and 282 kcal mol^?1∙Å^?2. For EHMHC-benzene, k₁ was calculated as 331 kcal mol^?1∙Å^?2, whereas k₂ could not be obtained due to the non-convergence of performed calculations. Consequently, we compared the calculated binding energies and the shear strength values determined by the microdroplet test, revealing that these two parameters were not correlated. Thus, bonds between the functional groups of the carbon filer and the epoxy resin were hard to break. In addition, the calculation of binding energies was very time-intensive due to the multi-atom nature of the simulated compounds, implying that the adopted calculation method was not suitable for estimating the carbon fiber/epoxy interfacial fracture toughness.

Subsequently, we estimated interactions for each epoxy compound monomer by MD simulations. Its interaction energy meant the intermolecular interaction energy between resins in a bulk phase. The intermolecular interaction energy increased with the hardness and/or heat resisting of material [21] . The energy of bulk epoxy monomers, i.e., the interaction energy, was obtained by averaging the energies of the last 10 ns of simulation time, as indicated by Equation (1).

Since the above interactions become stronger with increasing number of atoms per molecule, the total energies of bulk epoxy monomers were divided by the number of molecules in the calculation cell to allow meaningful comparison, affording interaction energies of 39.54, 0.13, 51.04, 18.14, and 40.64 kJ∙mol^?1∙nm^?3 for BADGE/BAC, BADGE/H-TMAn, BADGE/IPDA, EHMHC/H- TMAn, and HDGE/H-TMAn combinations, respectively. The above interaction energies increased correspond to the shear strength value of microdroplet test, implying that the detachment force for the carbon fiber/epoxy resin interface is influenced not only by interfacial energy but also by the interaction energy of epoxy monomers.