## 3 Results and Discussion  
### Effect of the BGE Diluent on Reaction Kinetics  
The differential thermal curves of the epoxy diluted with BGE at 12.5%, 15%, 17.5%, and 20%, are shown in Figure 2 at different heating rate. The curves reveal that the healing agent has two major exothermic peaks, and the first exothermic peak is significantly sharper than the second one. This indicates that the curing reaction occurred in two stages [31; 32], and the reaction rate in the first stage was greater than that in the second stage. With the increase of the heating rate, the initialtemperature (\(T_{i}\)), peak temperature (\(T_{P}\)), and the termination temperature (\(T_{f}\)) of the system shifted in the direction of the high temperature. However, the higher the heating rate, the broader the exothermic peak. The heat is more concentrated at the low heating rate. The values \(-\)ln(\(\beta/T_{P}\)) are plotted against \(1000/T_{P}\) in Figure 3A according to the temperature of the first peak of the curing reaction at different heating rates, and they show a good linear relationship. This indicates that it should be reasonable to study the kinetics of the above system while using the Kissinger equation (Equation (2)). The activation energy E of the curing reaction was calculated from the slope of the regression straight line according to Equation (2). In the same manner, the plotting of \(-\)ln\(\beta\) against \(1000/T_{P}\) (Figure 3B) also shows a good linear relationship. Accordingly, it is feasible to use the Crane equation to study the kinetics of the system. The order of the curing reaction can be calculated from the slope and activation energy. The activation energy and reaction order with different BGE mass fractions shown in Table 1 reveal that a BGE content of 17.5% produces the lowest activation energy, which implies that the system has the greatest reactivity. This suggests that the most favorable BGE content in the epoxy healing system should be about 17.5%. For different BGE contents, the height of the peak for the first exothermic curve of each system is different, which indicates that BGE may have an impact on the curing reaction. On the other hand, there is not so much difference between the second exothermic peak of each system, which is basically very gentle. A likely explanation for this is that the curing agent MC120D is a microencapsulated latent curing agent. Accordingly, after the first peak, the wall of the curing agent MC120D is completely softened, which leads to the disappearance of the hysteresis  
Figure 2: Differential thermal analysis of the healing system with different mass fractions of BGE (a. 5 K/min, b. 10 K/min, c. 15 K/min, d. 20 K/min). (**A**) 12.5% BGE; (**B**) 15% BGE; (**C**) 17.5% BGE; and, (**D**) 20% BGE. effect of the wall material on the curing reaction, thereby resulting in the consistent reactivity being shown by the system. The reaction order \(n\) of the curing process is determined by the type of chemical reaction and the interaction of various reactions. The change in \(n\) should reflect the changes in the mechanism of the curing reaction. Thus, as the BGE content increases, basically, the reaction order of the curing process decreases. (See Table 1). This indicates that BGE is involved in the cross-linking of E-51. In addition, the curing reaction order of each system is less than one, indicating that the curing reaction is very complicated. Also, the finding that the values of the reaction order are relatively close indicates that there was no significant difference among the reactions of all the systems. A comparison of the values of the frequency factor A (Table 2) of the respective heating rates at different BGE contents reveals that the value of A is relatively low when the BGE content is in the range of 17.5-20%. This indicates that this amount of BGE induced the largest resin curing degree. At this stage, the initial temperature and peak temperature are both relatively low. It can also be seen that the \(k\) value of each BGE content is not much different.