## 3 Results and Discussion
### Dynamical Mechanical Analysis
#### 3.3.1 Monofrequency DMTA Analysis and Vicat Grade
This discrepancy could be attributed to the different testing configuration of the two techniques, and to the different thermal processes to which the samples were subjected in these tests. A slight increase of the \(T_{g}\) due to nanosilica addition was also reported in other papers of our group on other amorphous systems [28]. In these works, the increase in the material stiffness and of \(T_{g}\) found for nanocomposites was generally attributed to the reduction of chain mobility due to physical filler/matrix interactions. The stiffening effect and the reduction of polymer chain mobility in the \(T_{g}\) zone due to nanofiller introduction were also confirmed by the trends of the width of the loss tangent curves, as reported in Table 4. The positive contribution played by silica nanoparticles on the stability of the prepared nanocomposites was also reflected in the progressive reduction of thermal strain (Figure 5c) and the consequent strong reduction of the thermal coefficient expansion (CTE) over the whole range of considered temperatures, as shown in Figure 5d. In particular, below \(T_{g}\), nanosilica introduction at a concentration of 24 vol% determined a reduction of the CTE from \(1.83\times 10\) to \(0.94\times 10^{4}\) K\({}^{-1}\), i.e., more than 40%. It should be noted that the observed reduction was even more effective for lower filler contents (i.e., 2-8 vol%), because of the better nanofiller dispersion. Moreover, the effect was also evident above the glass transition temperature, where an almost linear decrease of CTE was observed, from \(35.5\times 10\) of PLA to \(16.8\times 10^{4}\) K\({}^{-1}\) of PLA-Ar805-24 sample. The loss modulus peak (alpha transition) could also be properly used for the evaluation of the interphase in composite as a function of filler fraction \(\phi_{f}\) according to the expression of the Sumita model, reported in Equation (3) [68]:  
\[\frac{E^{\prime\prime}{}_{PLA\_FS}}{E^{\prime\prime}{}_{PLA}}=(1-\phi_{e})^{- 1}=\left(1-\phi_{f}B\right)^{-1} \tag{3}\]  
where \(\phi_{e}\) is the effective particle volume fraction, \(B\) parameter is the effective volume per single particle, and \(E^{\prime\prime}{}_{PLA\_FS}\) and \(E^{\prime\prime}{}_{PLA}\) represent the maximum values of the loss modulus peak of the composites and the neat matrix, respectively. The results are shown in Figure 6. The effective particle volume fraction \(\phi_{e}\) generally increased with the filler content, evidencing a relative minimum at 4 vol%. On the other hand, the large initial decrease of the \(B\) parameter suggested that the extent of the particle agglomeration increased, as previously determined also in nanocomposite polyolefin fibers with hydrotalcite [69] or fumed silica [32]. However, above 4 vol% the \(B\) parameter exhibited an almost constant value until 24 vol% of fumed silica, suggesting a relatively minimum level of aggregation in the tested composition range, in agreement with the results of morphological analysis (see Figure 1). Correspondingly, Vicat tests also confirmed the positive effect played by nanosilica on the stability of the prepared materials. In Figure 7, Vicat penetration curves of PLA and relative nanocomposites are reported, while in Table 4 the numeric results are summarized. It is evident that nanosilica addition promoted an evident decrease of the slope of the penetration curves above the glass transition temperature. Therefore, a Vicat grade of PLA-Ar805-24 sample was 8 \({}^{\circ}\)C higher than that of the neat PLA. These results are of relevant importance in the design of PLA-based components for packaging applications.