## 4 Results and Discussion  
Figure 4 shows the typical flexural stress-strain curves of the neat epoxy and epoxy-CNF composites. The tendency was that the flexural modulus and strength of the epoxy resin were increased by a CNF addition, while the fracture elongation of the epoxy resin decreased with CNF addition. It is noticeable that the flexural modulus and strength were significantly increased by an extremely low CNF addition (less than 0.145 vol.%) as shown in Figure 5. Furthermore, the flexural modulus of the epoxy-CNF composites increased linearly, up to 0.145 vol.% (except for the epoxy-CNF 0.022 vol.% composite). The red line in Figure 5a is the theoretical flexural modulus of the epoxy-CNF composites estimated by FEA. The experimental flexural modulus of the epoxy-CNF composites was higher than the theoretical one, i.e., this result indicates that the flexural modulus of the epoxy-CNF composites should not be discussed as short-fiber-reinforced composites, although it seems that the flexural modulus of the epoxy-CNF composites, with a CNF of more than approximately 0.32 vol.%, is apparently compliant with the model of short-fiber-reinforced composites. However, there is currently no analysis method to explain the strengthening mechanism of the epoxy-CNF composites with an extremely low CNF addition. Figure 4: Flexural stress-strain curves of neat epoxy and epoxy-CNF 0.022 vol.% composite. Figure 3: Finite element analysis model of a three-point flexural test. Nevertheless, we deduce two strengthening mechanisms of the epoxy-CNF composite from the point of view of organic chemistry. Firstly, in view of the fact that the amine curing agent that was used, diethylenetriamine, contains mass NH\({}_{2}\) groups, we suggest the strengthening mechanism of the epoxy-CNF composite occurs via the chemical reaction between the CNF and active amide (amino CNF). [PERSON] et al. demonstrated that hydroxyl- and amino-functionalized boron nitride nanotubes, with epoxy nanocomposites, improve the strength due to the interaction of surface functional OH/NH\({}_{2}\) groups and/or covalent connections with epoxide rings [13]. Similarly, by using Fourier Transform Infrared Spectroscopy (FT-IR), [PERSON] et al. reported that active amide groups were formed by the chemical reaction between amine curing agents and CNF, leaving some unreacted amine groups [14]. The presence of carboxyl groups on the CNF was confirmed by the presence of the stretching vibration of C=O at 1730 cm\({}^{-1}\)[15]. For amine immobilized cellulose nanofibers and diethylenetriamine curing agent (AiCNF), [PERSON] et al. observed new peaks at 1560 cm\({}^{-1}\) and 1640 cm\({}^{-1}\), showing the formation of amides as a result of the reaction between C=O in the CNF with amine, and also suggested a chemical reaction theory (see Figure 6) [16]. Furthermore, the general reaction mechanism between a carboxylic acid and an amine is shown in Figure 7[17]. At a high temperature, amide groups can be formed from the ammonium carboxylate salt due to the driving off or consumption of the water. Therefore, the surface of the CNF molecule with the rich carboxylic acid groups has the potential to react with amine functions, thereby forming amide linkages [18]. Figure 5: (a) Flexural modulus and (b) flexural strength of epoxy-CNF composites. The mechanical properties of epoxy resin depend on the curing conditions [19; 20]. It means that the epoxide molecules contributing to the curing reaction react with themselves, and/or with other reactive molecules, to form a cross-linked network, whether or not a catalyst is used. Figure 8 shows the chemical reaction during amine curing of epoxy resin [21]. Besides the primary amine-epoxy additions, the other two major reactions involved in amine curing of epoxy resins are secondary amine-epoxy, and secondary amine-epoxy and hydroxyl-epoxy additions. The latter reaction only becomes more effective after an adequate increase of the \(-\)OH group concentration due to the influence of the two former reactions [22].