## 3 Results and Discussion
### Thermal Degradation Study of PLA Composites  
Figure 7 shows the TGA thermograms and Derivative Mass loss (dTG) curves of PLA composites with different metal oxide nanofillers at a heating rate of 20 \({}^{\circ}\)C/min. According to Figure 7a, there is no remarkable mass loss until 290 \({}^{\circ}\)C for PLA TiO\({}_{2}\) and PLA Ag composites, demonstrating their good thermal stability, while the mass loss curves of the samples are almost identical, suggesting a one-step procedure of thermal degradation. The presence of nanofillers is also confirmed by the residue content as the residual amount of the PLA composites was found to be close to the added filler content (1%). It may be noted that the metal oxides are inorganic and thermally stable under the applied conditions, while neat PLA is found to completely burn off. From the dTG curves in Figure 7b, the highest decomposition rates were found to be 389.5 \({}^{\circ}\)C, 391.9 \({}^{\circ}\)C, and 392.9 \({}^{\circ}\)C for neat PLA, PLA TiO\({}_{2}\), and PLA Ag composites, respectively, suggesting that the temperature of the maximum decomposition rate increases due to the presence of the TiO\({}_{2}\) and Ag nanoparticles. Because only one peak is shown in Figure 7 sb, the degradation is carried out as a one-step process for all the PLA composites. For the PLA ZnO composite, the thermal degradation and the maximum decomposition rate were found at 235 \({}^{\circ}\)C and 318.6 \({}^{\circ}\)C, respectively, far lower than the previous ones. Additionally, the dTG results indicate the catalytic effect of adding ZnO onto the PLA matrix. It can be concluded that ZnO nanoparticles cause a stronger catalytic effect than the TiO\({}_{2}\) and Ag fillers, thus decreasing PLA thermal stability [26]. Figure 5: (**a**) Dobreva plots and (**b**) nucleation activity of PLA and its nanocomposites during their non-isothermal cold crystallization after fitting the data of the heating rates 2.5, 5, 7.5, and 10 \({}^{\circ}\)C/min. Figure 6: PLM images of PLA and its nanocomposites after non-isothermal cold crystallization at various heating rates. The bars represent 100 \(\upmu\)m.  
Figure 7: (**a**) Thermogravimetric analysis (TGA) thermograms and (**b**) Derivative Mass loss (dTG) curves of PLA and its nanocomposites. The reaction rate can be defined using the general equation of solid-state reactions:  
\[\frac{da}{dt}=k(T)f(a) \tag{11}\]  
where \(k(T)\) is the reaction rate constant, \(f(\alpha)\) is the reaction model, and \(\alpha\) is the degree of conversion. The kinetic model, \(f(\alpha)\), is an algebraic expression that describes the kinetics of the solid-state reaction. The dependence of temperature on the rate of reaction is defined by the Arrhenius equation:  
\[k(T)=Ae^{-E/RT} \tag{12}\]  
where \(E\) is the apparent activation energy (kJ/mol), \(R\) is the gas constant (8.314 J/mol\(\cdot\)K), A is the pre-exponential factor (s\({}^{-1}\)), and \(T\) is the absolute temperature (K). Thermal decomposition kinetics is performed in two stages: the isoconversional and the model-fitting methods [79]. The basis of the isoconversional methods is the assumption that the conversion function, \(f(\alpha)\), does not alter with the change of the heating rate for the entire range of the degree of conversion \(\alpha\). The isoconversional methods are divided into differential and integral methods. The most frequently used methods are the Ozawa, Flynn, and Wall (OFW) analysis [43, 80] and the Friedman equation [57]. The accuracy of differential methods is sometimes limited due to a determination limit on the baseline that the method takes, and sometimes they reveal numerical instability compared to integral one. Generally, if the calculated \(E\) remains approximately the same for the whole range of the degree of conversion \(\alpha\), a single-step reaction can be concluded with certainty. A variation of \(E\) with the degree of conversion \(\alpha\) suggests a complex reaction mechanism of two or more steps, which invalidates the separation of variables.