## 3 Results and Discussion
### Cure Acceleration  
Figure 6 shows the results of the 10 \({}^{\circ}\)C/min temperature ramp dynamic DSC experiments in which the prepared BADCy resin nanoparticles were added into the neat BADCy prepolymer at various contents (neat, 4, 8, and 10 wt%). It can be seen that the added BADCy resin nanoparticles had a strong effect on the curing temperature and enthalpy changes. The curves reveal a decrease in the curing peak temperature, \(T_{\mathrm{P}}\), as well as an increase in the curing enthalpy, \(\Delta H\), with the addition of BADCy resin nanoparticles (Table 1). This indicates that a range of BADCy resin nanoparticles can be used for accelerating curing and improving the degree of curing. This conclusion is consistent with the FT-IR spectra. The initially polymerized nanoparticles still have reactive functional groups, and can directly initiate the self-polymerization reaction. Compared with the 4 and 8 wt% systems, the curing enthalpy, \(\Delta H\), of the 10 wt% system is reduced. This is because the excessive quantity of nanoparticles results in the distance between the nanoparticles becoming small. The nanoparticles react with the matrix and also react with other nanoparticles. The heat of reaction between the nanoparticles themselves is less than that between the particles and the matrix. Therefore, the total exotherm is reduced. Figure 5: Representative SEM (**a**) and TEM (**b**) images of the BADCy resin nanoparticles. Figure 6: DSC curves of the BADCy matrix with different BADCy resin nanoparticles contents. The formation of microgel particles can occur from a thermodynamic point of view. Analogous to the thermodynamic equations of the crystallization process, the thermodynamic equations of the microgel particles can be expressed as:  
\[\Delta G=G_{cure}-G_{melt}, \tag{1}\]  
where \(\Delta G\) is the change in Gibbs free energy during the curing process and the curing reaction occurs when the \(\Delta G\) is negative. At the beginning of the curing reaction, the gel particles have a small volume and a large specific surface area. If the surface effect is considered, the total free energy of the system can be accurately expressed as:  
\[G_{cure}=G_{bulk}+\sum\sigma A, \tag{2}\]  
where \(G_{bulk}\) is the change in the matrix free energy without considering the surface effect, \(\sigma\) is the surface free energy coefficient, and \(A\) is the surface area of the gel particles. Therefore, the thermodynamic equation (Equation (1)) of the curing process can be rewritten as:  
\[\Delta G=\Delta G_{c}+\sum\sigma A. \tag{3}\]  
Here, \(\Delta G_{c}\) represents the free energy change of the matrix. \(\Delta G\) is a negative value when the reaction temperature reaches curing conditions. Since the surface free energy coefficient, \(A\), is a positive value, only at the condition of the curing temperature, \(\Delta G_{c}\), is a negative value, making \(\Delta G\) still less than zero. Therefore, curing of the resin system will proceed. Figure 7 is a schematic illustration of the free energy changes in the gel particle formation and growth stages. During the heating process of the resin systems, \(\Delta G\) is greater than zero before the formation of the thermodynamically stable gel particles, and \(\Delta G\) has a maximum value. This stage is mainly a cross-linked reaction of polymer segments and is primarily controlled by kinetic factors. Once the gel particles are formed, the growth of the gel particles can reduce the free energy of the systems and the gel particles enable automatic growth. At this stage, the viscosity of the system increases due to the growth of the gel particles, and the movement of the molecular segments is limited, so it is mainly controlled by the diffusion factors. In our study, when nanoparticles were added into the matrix, there were two reaction processes. The first is that the matrix itself undergoes a curing reaction which includes the formation and growth of gel particles.