## Materials and Methods
### Characterization Techniques  
Field emission scanning electron microscopy (FESEM) observations were carried out on cryofractured specimens by using a Zeiss Supra 40 microscope, operating at an acceleration voltage of 10 kV. Melt flow index (MFI) measurements were performed in accordance with the ASTM D1238 standard by using a Dynisco 4003 DE plastometer. PLA and compounded materials were tested at three different temperatures (170, 190, 210 \({}^{\circ}\)C) under an applied load of 2.16 kg. At least 10 measurements were performed for each composition. Thermogravimetric analyses (TGA) were carried out through a Mettler TG50 thermobalance (Schwerzenbach, Switzerland) in a temperature interval from 30 to 700 at 10 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\) under an air flow of 100 mL\(\cdot\)min\({}^{-1}\). In this way, the temperatures associated with a mass loss of 5% (T\({}_{5\%}\)), the decomposition temperature (T\({}_{\rm d}\)), taken as the temperature associated with the maximum mass loss rate, and the relative mass residue at 700 \({}^{\circ}\)C (m\({}_{700}\)) were determined. Differential scanning calorimetry (DSC) tests were performed through a Mettler DSC30 calorimeter with a heating-cooling-heating cycle in the range 0-200 \({}^{\circ}\)C at \(\pm\)10 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\) under a nitrogen flow of 100 mL\(\cdot\)min\({}^{-1}\). The glass transition temperature (\(T_{g}\)) was determined as the inflection point of the thermograms, whereas the crystallinity content (\(W_{c}\)) was computed from the melting enthalpy (\(\Delta H_{m}\)) normalized to the standard enthalpy of the fully crystalline poly(L-lactic acid), i.e., P-L-LA, (\(\Delta H_{0}\)), taken as 93.6 J\(\cdot\)g\({}^{-1}\)[56], according to Equation (1):  
\[W_{c}=\frac{\Delta H_{m}}{\Delta H_{0}(100-f)} \tag{1}\]  
where \(f\) is the weight percentage of the filler. Crystallization kinetics was investigated on neat PLA and on PLA-r805-8 nanocomposite sample (i.e., the composition that showed the best balance of the mechanical properties, as previously reported [46]), by using the same DSC equipment, 160 \(\mu\)L crucibles, and a nitrogen flow of 100 mL\(\cdot\)min\({}^{-1}\). Isothermal DSC tests were performed at different temperatures (80, 85, 90, 100, 110, 120, and 125 \({}^{\circ}\)C), and the evolution of the relative crystallinity (\(W_{c}\)) with the testing time was analyzed through the Avrami approach [57; 58; 59]. This model considers the evolution of the crystallization process of amorphous solids under isothermal conditions. Under the hypothesis of homogeneous nucleation on the material, the evolution of the relative crystallinity with the time \(W_{c}\)(\(t\),\(T\)) can be expressed through a sigmoidal trend, as reported in Equation (2). \[\frac{W_{c}(t,T)}{W_{\rm cos}}=1-e^{(-k_{(T)},t^{n})} \tag{2}\]  
where \(W_{\rm cos}\) is the maximum crystallinity degree, \(k_{(T)}\) is the kinetic constant, and \(n\) is the Avrami coefficient. The kinetic constant depends on the temperature, while the Avrami coefficient depends on the morphology of the crystallites during the isothermal process. In the literature, an \(n\) value comprised between 1 and 5 is generally reported. Vicat softening temperature was determined in accordance with the ASTM D1525 standard through an ATS-FAAR mod. MP/3 machine (Milan, Italy). Rectangular samples 10 long, 5 wide and 4 mm thick were tested, imposing a load of 10 N at 2 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\) in the range 40-100 \({}^{\circ}\)C. The results represent the average of three specimens. Dynamic mechanical thermal analysis (DMTA) tests were carried out in tensile mode with a MkII Polymer Laboratories (Loughborough, UK) analyzer, in the temperature range from 0 to 100 \({}^{\circ}\)C at a heating rate of 3 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\), by imposing a pre-stress of 0.2 MPa and a sinusoidal displacement with a peak-to-peak amplitude of 32 \(\upmu\)m and a frequency of 1 Hz. Rectangular specimens 0.8 mm thick and 5 mm wide were tested, with a gage length of 17 mm.