## 3 Results and Discussions
### Isothermal Crystallization Kinetics of the Composites  
To further investigate the influence of GO and GO-H202 on the crystallization kinetics of the composites, the isothermal crystallization of the composites was investigated in this section. The isothermal crystallization curves and the relative degrees of crystallinity (\(X_{\mathrm{t}}\)) at the isothermal crystallization temperatures (\(T_{\mathrm{c}ISO}\)) of 120-124 \({}^{\circ}\)C are shown in Figure 4 as a function of crystallization time. The corresponding exothermic DSC curves are also presented in Figure 4. The \(X_{\mathrm{t}}\) is a relative value and could be defined as follows [54; 55; 56]:  
\[X_{t}=\int_{0}^{t}{(dH/dt)dt}/{\int_{0}^{\infty}{(dH/dt)dt}} \tag{1}\]  
where \(\mathrm{d}H_{\mathrm{c}}\) denotes the measured enthalpy of crystallization during isothermal time interval \(\mathrm{d}t\). The limits \(t\) and \(\infty\) denote the elapsed time during the crystallization and at the end of the crystallization process, respectively. Figure 4 reveals that for all the samples, obvious dependence of the isothermal crystallization rate on crystallization temperature \(T_{\mathrm{c}ISO}\) can be observed. As the supercooling (the difference between the melting and crystallization temperature) decreases, the exothermal peak becomes broader, indicating a decrease of crystallization rate as the \(T_{\mathrm{c}ISO}\) increases. The half crystallization time of overall crystallization (\(t_{0.5}\)) is a direct measure of overall crystallization rate, which can be defined as the half period crystallization. The reciprocal of \(t_{0.0.5}\), represented by \(G_{0.0.5}\) (Equation (2)) can be used as a parameter characterizing the crystallization rate of the sample. \[G_{0.0.5}=1/t_{0.5} \tag{2}\]  
Moreover, the Avrami model was employed to analyze the isothermal crystallization kinetics of the samples. The logarithmic form of Avrami model is expressed as Equation (3):  
\[In[-In(1-X_{t})]=Ink_{n}+nInt \tag{3}\]  
Figure 4: DSC isothermal crystallization curves and plots of relative crystallinity versus crystallization time for PP, GPP and GHPP at \(T_{\mathrm{c}ISO}\) = 120–124 \({}^{\circ}\)C.  
where \(X_{t}\) is relative degree of crystallinity at crystallization time \(t\), \(n\) is the Avrami exponent, and \(k_{n}\) represents the crystallization rate parameter involving both the nucleation and growth rate of crystals. By fitting the experimental data to Equation (3), the values of \(n\) and \(k_{n}\) can be obtained from the slope and intercept of the plots of \(\log\left[-\ln(1-X_{t})\right]\) versus \(\log t\) for each cooling rate shown in Figure 5.  
The \(t_{0.5}\), \(G_{0.5}\), \(n\), and \(k_{n}\) were calculated and plotted in Figure 6 as a function of crystallization temperature (\(T_{closed}\)). It can be seen from Figure 6 that for all samples, \(G_{0.5}\) decreases gradually with an increase in the crystallization temperature \(T_{closed}\). At a given \(T_{closed}\), the \(t_{0.5}\) decreases gradually from PP, GPP to GHPP; meanwhile, both the \(G_{0.5}\) value and the kinetic parameter \(k_{n}\) increase, indicating that the overall crystallization rate (involving both nucleation and crystal growth) increases after the addition of GO and GO-H202. After grafting hyperbranched polyester H202, the crystallization acceleration of GO-H202 becomes stronger compared with GO. Moreover, the Avrami exponent \(n\) is broadly used to describe dimensionality. The regions from lower than 2, 2 to 3, and 3 to 4 correspond to one-, two-, and three-dimensional growth, respectively. As the crystallization temperature increases, the variations of Avrami exponent \(n\) of the three samples are quite different from each other. For neat PP, the Avrami exponent \(n\) strongly depends on the isothermal crystallization temperature \(T_{closed}\), while less dependency can be observed for GPP.