## 4 Properties
### Thermal Properties
#### 4.1.1 Dsc  
Differential scanning calorimetry has been widely applied in the investigation of the polymer and polymer nanocomposite thermal transitions, namely glass transition, melting, and crystallization temperatures and related enthalpies. Usually DSC thermal analysis in AP-based systems is conducted by performing three different scans. The first scan is used to evaluate any processing effect on the polymeric material, or to delete the thermal history. The second scan, i.e., a cooling scan, can be conducted at a slow or at a fast rate (quenching), depending on whether the crystallization ability needs to be suppressed (e.g., to highlight the glass transition phenomenon) or not. One last heating scan is run to evaluate the characteristic thermal transitions. The thermal transition temperatures of the most well-known APs are reported in Table 1 together with those of PBS and PBCE. With the exception of PGA and PLA-based homopolyesters, they all display a T\({}_{\text{g}}\) below room temperature. It can be noted that the T\({}_{\text{g}}\) of PBCE is higher than that of PBS because of the chain rigidity imparted by the aliphatic ring [74]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polymer** & **T\({}_{\text{g}}\) (\({}^{\circ}\)C)** & **T\({}_{\text{m}}\) (\({}^{\circ}\)C)** & **Ref.** \\ \hline
**PLLA** & 55–65 & 170–200 & [27] \\
**PDLLA** & 50–60 & Amorphous & [27] \\
**PGA** & 35–45 & 220–233 & [27] \\
**PCL** & (\(-\)65)–(\(-\)60) & 56–65 & [33] \\
**PHB** & 9 & 175–180 & [36] \\
**PBS** & (\(-\)37)–(\(-\)30) & 111–115 & [19] \\
**PBCE** & 12 & 167 & [20] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thermal properties of the main aliphatic polyesters. In random copolymers, glass transition is often a monotonic function of composition and the most common equation employed to foresee it as a function of comonomer amount is the Fox one [75]  
\[1/\mathrm{T_{g}}=\omega_{\mathrm{A}}/\mathrm{T_{g,A}}+\omega_{\mathrm{B}}/ \mathrm{T_{g,B}} \tag{1}\]  
where \(\mathrm{T_{g,A}}\) and \(\mathrm{T_{g,B}}\) are the glass transition temperatures of the homopolymers and \(\omega_{\mathrm{A}}\) and \(\omega_{\mathrm{B}}\) the corresponding weight fractions. In this regard, APs random copolymers make no exception. Studies have demonstrated the linear variation of \(\mathrm{T_{g}}\) with the molar composition in PBS-based copolyesters and the applicability of a Fox-type equation for the determination of the \(\mathrm{T_{g}}\) of fully amorphous PBS [76]. It has been observed that the insertion of ether and thioether linkages along the macromolecular backbone of APs has a significant influence on the glass transition temperature. Two opposite factors play a role in this respect, and one of the two can prevail depending on the copolymeric system. On one hand, there is a flexibility enhancement that causes a decrement of \(\mathrm{T_{g}}\)[42; 51; 52]. On the other hand, the presence of polar atoms can raise the \(\mathrm{T_{g}}\) because of stronger interchain interactions [76]. Notwithstanding a similar chemical structure, blends of two APs can be immiscible, thus presenting two distinct \(\mathrm{T_{g}}\)[19]. The reactive blending strategy permitted to overcome this limitation, already for short reaction times, i.e., long copolymeric sequences, as a single \(\mathrm{T_{g}}\) was observed [19; 50; 51]. The chain extension of hydroxyl-terminated prepolymers, which led to the formation of multiblock copolymers, also evidenced a complete miscibility of the final materials in the amorphous phase [53; 54; 55]. As to the melting process, DSC traces of APs may show multiple melting peaks that have been imputed to melt-recrystallization phenomena that take place during the DSC scan [13]. Furthermore, a decrease of \(\mathrm{T_{m}}\) is usually recorded by increasing the content of comonomeric units in random copolymers.