## 3 Results and Discussion
### Dynamical Mechanical Analysis  
#### 3.3.1 Monofrequency DMTA Analysis and Vicat Grade  
The dimensional stability and the dependency of the viscoelastic properties from the temperature is a key parameter in the design of engineering plastics for packaging applications. Therefore, DMTA analysis was carried out on PLA and the relative nanocomposites. In Figure 5a-d the trends of the dynamic moduli (E\({}^{\prime}\), E\({}^{\prime\prime}\)), of the loss tangent (tan8), and of the thermal expansion coefficient (CTE) from DMTA tests performed at 1 Hz are reported. The most important results from DMTA analysis (E\({}^{\prime}\) at different temperatures, \(T_{g}\) and thermal strain at 65 \({}^{\circ}\)C) are summarized in Table 4.  
It is worth noting that nanosilica introduction determined an important increase of E\({}^{\prime}\) with respect to the neat PLA. For instance, the E\({}^{\prime}\) at 25 \({}^{\circ}\)C passed from 2180 MPa for the unfilled PLA to 2710 MPa (+24%) with a filler amount of 24 vol%. A similar stiffness increase was detected under quasi-static conditions in our previous paper on these systems [46]. As often happens with filled amorphous polymers, the stiffening effect above the \(T_{g}\) was even more pronounced, as previously observed in PLA/hydroxapatite composites [21]. The relative E\({}^{\prime}\) increase experienced at 60 \({}^{\circ}\)C for the 24 vol% filled samples was 1500%. This is due to the fact that the stiffening effect provided by silica nanoparticle was more evident when the difference between the elastic modulus of the filler and that of the matrix increased. The stabilizing effect due to nanosilica introduction could also be detected in the systematic lowering and shifting of damping peak (see Figure 5b and Table 4), reducing consequently the dissipation energy in the glass transition zone. In the present case, the E\({}^{\prime}\) increase at 60 \({}^{\circ}\)C evidenced \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Storage Modulus E\({}^{\prime}\)**} & \multicolumn{2}{c}{**E\({}^{\prime}\) Peak**} & \multicolumn{2}{c}{**TanS Peak**} & \multicolumn{2}{c}{**Thermal**} & \multirow{2}{*}{**VST**} \\  & \multicolumn{2}{c}{**(MPa)**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C)**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C)**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C)**} & \\  & **at 25 \({}^{\circ}\)C/40 \({}^{\circ}\)C/60 \({}^{\circ}\)C** & & \multicolumn{2}{c}{**(\({}^{\circ}\)C)**} & \multicolumn{2}{c}{**(\({}^{\circ}\)C/\({}^{\circ}\)C)**} & \\ \hline PLA & 2180/2100/11.1 & 55.6 & 56.6/2.99/6.2 & 11.2 & 62.6 + 0.2 \\ PLA-Ar805-2 & 2220/2123/41.3 & 56.8 & 60.6/2.61 /6.2 & 6.1 & 62.8 + 0.4 \\ PLA-Ar805-4 & 2410/2280/28.9 & 55.8 & 59.4/2.31/6.9 & 3.5 & 63.1 + 0.3 \\ PLA-Ar805-8 & 2580/2440/63.2 & 56.1 & 60.2/1.96/7.4 & 2.6 & 63.9 + 0.6 \\ PLA-Ar805-24 & 2710/2520/170 & 56.3 & 61.1/1.12/0.1 & 1.2 & 70.6 + 0.2 \\ \hline \hline \end{tabular}  
* \(T_{g}\) determined at max of the damping peak; 2 width determined at half of the damping peak.  
\end{table} 
Table 4: Results of DMTA analysis and Vicat softening temperature (VST) of PLA and relative fumed silica nanocomposites. Figure 5: DMTA tests (heating rate 10 \({}^{\circ}\)C/min; 1 Hz) of PLA and relative nanocomposites at 2, 4, 8, and 24 vol% of FS. **(a)** Storage modulus, **(b)** loss factor (tan\(\delta\)), **(c)** thermal strain, and **(d)** coefficient of thermal expansion (CTE) below and above \(T_{g}\). for nanofilled samples was partly related to the \(T_{g}\) shift due to silica introduction. In fact, a \(T_{g}\) increase of about 4 \({}^{\circ}\)C could be registered for all silica nanocomposite samples (see Figure 5b and Table 4). The \(T_{g}\) shift was also confirmed by the damping curves, as depicted in Figure 5c. The glass transition temperature increase observed in DMTA tests was in contrast with the conclusion reported in DSC tests (see Table 3).