## 3 Results and Discussion
### Thermal Properties
#### 3.2.2 Calorimetric Characterization (DSC) and Kinetics Analysis of Crystallization
(**a**) Relative crystallinity at different temperatures of PLA; (**b**) relative crystallinity at different temperatures of PLA-Ar805-8; (**c**) \(k\)-coefficient; and (**d**) \(n\)-coefficient of the Avrami equation. The PLA-Ar805-8 composition was selected because it represents the best compromise between processability of PLA nanocomposite systems and their mechanical properties (stiffness, toughness, and creep stability), as reported in our previous paper [46]. In Figure 4a,b, relative crystallinity values as a function of the testing time in a temperature interval between 80 and 125 \({}^{\circ}\)C are reported, while in Figure 4c,d the trends of the \(k\) and \(n\) coefficients of the Avrami model (see Equation (2)) at different temperatures are shown. Considering DSC thermograms reported in Figure 4a, it is interesting to note how, in the testing time of 10,000 s, the neat PLA sample was able to reach a plateau \(W_{c}\) value of about 25% for temperatures higher than 85 \({}^{\circ}\)C. The fastest crystallization rate can be detected for a temperature of 100 \({}^{\circ}\)C, while a further temperature increase determines a slowing of the crystallization process. This behavior can be explained considering that crystallization dynamics in semicrystalline polymers are governed by a balance between crystal nucleation and growth processes. At low temperatures, crystal nucleation is favored, but their growth is hindered by the limited molecular mobility. At higher temperatures, the opposite trend can be detected. From the thermograms of the PLA-Ar805-8 nanocomposite sample (Figure 4b), it is possible to notice that the plateau \(W_{c}\) value (i.e., 25%) could be reached at a temperature of 100 \({}^{\circ}\)C, and the maximum crystallization rate could be registered at 110 \({}^{\circ}\)C. Analyzing the trends of the kinetic constant of the Avrami equation (\(k\)), reported in Figure 4c, it is possible to notice that nanocomposite sample followed substantially the same behavior of the neat matrix, with a theoretical maximum crystallization rate located at about 105 \({}^{\circ}\)C. From the trends of the \(n\) coefficient, reported in Figure 4d, it is possible to conclude that for neat PLA, \(n\) assumed a value of 3.2 in correspondence with high crystallization rate temperatures (around 100 \({}^{\circ}\)C), while at 85 and 120 \({}^{\circ}\)C \(n\) was about 4.0. This trend could be tentatively explained considering that at lower crystallization rates a better crystallite order could be achieved, and \(n\) assumed thus a higher value. For the nanocomposite sample, the \(n\) coefficient seemed to be practically unaffected by the testing temperature and assumed a fairly constant value near to 4.0. In literature, it is generally reported that \(n\) values for PLLA between 2 and 3.5 could be associated with the formation of crystals with spherulitic morphology [64; 65; 66]. Therefore, it can be concluded that the presence of the nanosilica did not substantially affect the crystallization kinetics of the materials, nor the morphology of the crystals. The poor influence of fumed silica nanoparticles on the crystallization properties of polymer matrices was already detected in our previous paper on polyolefin-fumed silica nanocomposites [25]. In those papers, this behavior was explained considering that the amorphous nature of silica nanoparticles did not promote the nucleation of crystals around the nanofiller surface, as previously observed for PLA at high enantiomeric purity [67].