## 3 Results and Discussion  
### Non-Isothermal Cold Crystallization  
Cold crystallization of PLA and its composites occurred during all the applied heating rates, up to 20 \({}^{\circ}\)C/min. The scans are presented in Figure S1, and the thermal characteristics in Table S1. In Figure 1, the effect of the heating rate on the final % crystallinity and the peak temperature of cold crystallization are presented. Increasing the heating rate leads to increase of the \(T_{\rm cc}\) (cold crystallization peak temperature), while the onset of melting remains unaffected (Figure S1). The \(T_{\rm cc}\) increases because of thermal delay, which occurs at fast heating rates in all polymers. In the slow heating rates up to 5 \({}^{\circ}\)C/min for PLAand 7.5 \({}^{\circ}\)C/min for its composites, multiple melting is observed, which is caused by the presence of two populations of lamellae, a typical multiple melting behavior for PLA [37; 38]. First, there was small lamellae melt in the temperature range of the first melting peak, followed by the melting of the more perfected crystals. With a further increase of the heating rate, both crystallization and melting peaks decrease significantly in size, as there is not enough time for the macromolecular chains to reorganize and form crystals. As a result, the multiple melting behavior also disappears, with the second melting peak gradually shifting to lower temperatures and finally merging with the first one. Consequently, the larger the heating rate, the less perfected the formed crystals of PLA. Similarly, as shown in Figure 1, the \(T_{\rm cc}\) decreases in the presence of the fillers in slow heating rates only. This lower recrystallization temperature implies that the nanocomposites have more nuclei [22; 39]. More specifically, Ag and TiO\({}_{2}\) decrease the \(T_{\rm cc}\) in heating rates 2.5-10 \({}^{\circ}\)C/min, and ZnO in heating rates 2.5 and 5 \({}^{\circ}\)C/min. The increase of the degree of crystallinity is also more prominent in the small heating rates. This suggests that the fillers can efficiently act as cold crystallization nucleation sites in these heating rates [40; 41]. Based on the assumption that the evolution of crystallinity is linearly proportional to the evolution of heat released during the crystallization, the relative crystallinity, \(X(t)\), can be calculated according to the equation:  
\[\mathrm{X}(t)=\frac{\int_{0}^{t}\Bigl{(}\frac{dH_{\rm c}}{dt}\Bigr{)}dt}{\int _{0}^{\infty}\Bigl{(}\frac{dH_{\rm c}}{dt}\Bigr{)}dt} \tag{2}\]  
where \(dH_{\rm c}\) is the measured enthalpy of crystallization during an infinitesimal time interval, \(dt\). The limits \(t\) and \(\infty\) denote the elapsed time during crystallization and at the end of the crystallization process, respectively. Figure 1: Effect of the heating rate and fillers on the final % crystallinity and the peak temperature of cold crystallization. The crystallization temperature, \(T_{c}\), can be converted to crystallization time, \(t\), with the well-known relationship for non-isothermal crystallization that is strictly valid when the sample experiences the same thermal history as designed by the DSC furnace:  
\[t=\frac{(T_{o}-T_{c})}{\alpha} \tag{3}\]  
where \(\alpha\) is the constant heating rate, \(T_{o}\) is the temperature at the beginning of crystallization, and \(T_{c}\) is the crystallization temperature at time, \(t\). The relative crystallinity of the samples as a function of time is shown in Figure S2, and the resulting crystallization half-times are presented in Figure 2. All fillers reduce the \(t_{1/2}\) of PLA during non-isothermal cold crystallization, revealing their role as sites of heterogenous nucleation. ZnO was able to also accelerate the crystallization half-time of poly(3-hydroxybutyrate) during non-isothermal cold crystallization [42].