## 3 Results and Discussions
### Self-Nucleation Isothermal Crystallization Kinetics  
In the isothermal crystallization study above, both primary nucleation and crystal growth contribute to the overall crystallization kinetics of PP. Unfortunately, the information about the single nucleation kinetics or the crystal growth kinetics can hardly be obtained. In order to separate the contributions of these two factors, the self-nucleation isothermal crystallization kinetics was carried out. It is assumed that the sample is fully nucleated during the self-nucleation process before the subsequent isothermal crystallization [49; 57; 58; 59]. After that, the sample is rapidly cooled down and isothermally crystallized at the desired temperature (denoted as \(T_{cSN}\)). In this way, the subsequent isothermal crystallization can be used to study the crystal growth kinetics. In this study, the temperature of self-nucleation treatment was 167 \({}^{\circ}\)C and the value of \(T_{cSN}\) was 141-145 \({}^{\circ}\)C. The crystallization curves, as well as the curves of the relative degree of crystallinity (\(X_{\rm t}\)) as a function of crystallization time at \(T_{cSN}\) are shown in Figure 7.  
From Figure 7, the half-crystallization time for crystal growth, \(t_{c0.5}\), and the crystal growth rate parameter, \(G_{c0.5}\), were calculated and plotted in Figure 8 as a function of the crystallization temperature \(T_{cSN}\). Figure 8: (**a**) Half crystallization time for crystal growth, \(t_{c0.5}\), and (**b**) Crystal growth rate parameter, \(G_{c0.5}\), as a function of crystallization temperature \(T_{cSN}\) for PP, GPP and GHPP. Figure 7: Self-nucleation isothermal crystallization curves (**a**) neat PP, (**b**) GPP and (**c**) GHPP and plots of relative crystallinity vs. crystallization time for (**d**) neat PP, (**e**) GPP and (**f**) GHPP when self-nucleated at 167 \({}^{\circ}\)C for 5 min and subsequently isothermally crystallized at \(T_{cSN}\) = 141–145 \({}^{\circ}\)C.  
As can be seen from Figure 8, at the same \(T_{c\text{SN}}\), from PP, GPP to GHPP, \(t_{c0.5}\) decreases monotonously while \(G_{c0.5}\) increases gradually, indicating that the crystal growth rate of PP increases gradually after the addition of GO and GO-H202. To understand fully, [PERSON] and coworkers [60; 61] proposed an equation based on the Turnbull and Fisher equation which is usually referred to as Lauritzen-Hoffman theory (Equation (4)):  
\[G=G_{0}\exp\left[\frac{-U^{*}}{R(T_{c}-T_{\infty})}\right]\exp\left[\frac{-K_{ g}}{T_{c}(\Delta T)f}\right] \tag{4}\]  
where \(G\) is the crystal growth rate, \(G_{0}\) is the constant and includes all the terms that are temperature-insensitive, \(U^{*}\) is the transport activation energy, \(R\) is the gas constant, and \(R\) = 8.314 J/(mol\(\cdot\)K), \(U^{*}\) = 6276 J/mol. \(K_{g}\) is the nucleation parameter, \(T_{\infty}\) is the temperature below at which motion ceases and is usually taken as \(T_{\infty}\) = \(T_{g}-30\)K, \(T_{c}\) is the crystallization temperature, \(\Delta T=T_{m}{}^{0}-T_{c}\) is the degree of undercooling, \(T_{m}{}^{0}\) is the equilibrium melting temperature, and \(f\) is a factor that accounts for the variation in the enthalpy of fusion, \(\triangle h_{f}\), with temperature, and is obtained by \(f=2T_{c}/\left(T_{m}{}^{0}+T_{c}\right)\). By rearranging Equation (4), Equation (5) is obtained:  
\[InG=InG_{0}-\left[\frac{U^{*}}{R(T_{c}-T_{\infty})}\right]-\left[\frac{K_{g}}{ T_{c}\cdot\Delta T\cdot f}\right] \tag{5}\]  
\(K_{g}\) is also expressed as Equation (6)  
\[K_{g}=n_{c}b_{0}\sigma\sigma_{e}T_{m}{}^{0}/\Delta h_{f}k \tag{6}\]  
where the \(n_{c}\) value depends on the crystallization regime according to Lauritzen-Hoffman theory. At Regime I and Regime III, which occur at low and high undercoolings, respectively, \(n_{c}\) = 4. However, at Regime II, which occurs at medium undercooling, \(n_{c}\) = 2. \(\sigma\) and \(\sigma_{e}\) are the lateral and end surface free energies of the growing crystal, respectively.