## 4 Results
### Isothermal crystallization kinetics
Figure 4: DSC signal recorded upon heating PEI\({}_{17.1}\)T after different crystallization isotherms at 170 \({}^{\circ}\)C. The duration of the isotherms is embedded in the figure. From the plots in Figure 5c,d, the crystallization half time t\({}_{1/2}\), Avrami index n, and crystallization rate constant K were obtained using the following Avrami equation:  
\[X(t)=1-e^{-(K\times t)^{n}}, \tag{7}\]  
where X(t) is the relative crystallinity at time t, K is the crystallization rate constant (min\({}^{-1}\)), and n is the Avrami exponent linked to the geometry of crystals. This equation may also be expressed in the following form:  
\[\log{[-\ln(1-X)]}=\mathrm{nlog(t)}+\mathrm{nlog(K)}. \tag{8}\]  
This second form of the Avrami equation gives easy access to parameters n and K, as well as t\({}_{1/2}\), corresponding to the half crystallization time. Those three essential parameters to describe the crystallization kinetics of polymers are gathered in Table 2.  
Table 2 gathers the Avrami parameters measured on PET and PEIT with varying isosorbide contents. Those parameters were obtained by fitting experimental crystallization kinetics with the Avrami equation (Equation (7)). Examples of such a fit are presented in Figure 5c,d. It firstly appears from Table 1 that the isosorbide content slowed down the crystallization kinetics of PEIT. The t\({}_{1/2}\) was actually multiplied by 100 between PEI\({}_{4.9}\)T and PEI\({}_{20.8}\)T (t\({}_{1/2}\) = 8 min and t\({}_{1/2}\) = 813 min, respectively at 170 \({}^{\circ}\)C). In parallel, it is to be noted that the isosorbide content did not clearly have an impact on the value of parameter n. Actually, n always remained in the range 2-3. Higher values of parameter n were obtained for PEI\({}_{20.8}\)T at 150 \({}^{\circ}\)C and 180 \({}^{\circ}\)C (3.73 and 3.41, respectively). However, for those particular cases, crystallization kinetics were so long that a limited number of points were taken into account for Avrami equation fitting. This limited number of points was most probably at the origin of a less accurate fitting, leading to higher values of parameter n. More generally, n values shown in Table 2 tended to show that the geometry of PET crystals was not modified by the introduction of isosorbide molecules in the structure of the polymer (for the isosorbide content range between 0 and 20 mol.%). Figure 5: Weight fraction crystallinity X\({}_{t}\) versus isothermal crystallization time t (**a**,**b**) and Log(\(-\ln(1-X_{t})\)) versus Log(t) (**c**,**d**) for several crystallization temperatures. The two PEIT samples presented here are PEI\({}_{4.9}\)T (**a**,**c**) and PEI\({}_{17.1}\)T (**b**,**d**). Figure 6 presents the evolution of t\({}_{1/2}\) values given in Table 2 as a function of temperature for isothermal crystallization of PEIT with varying isosorbide contents. Results presented in Figure 6 give a good overview of the impact of the isosorbide content on the crystallization kinetics of PEIT. It also clearly appears from Figure 6 that the crystallization kinetics of PET and PEIT presented a maximum speed at around 170 \({}^{\circ}\)C. This temperature remained the same over the isosorbide range studied. This variation of the half crystallization time is well known for polymers. It is actually the result of the competition between the thermodynamic driving force and the mobility of the molecules. When decreasing the temperature from the melt, the first increases while the second decreases. On the one hand, between the melting temperature and the maximum crystallization speed temperature, the thermodynamic effect was predominant which was caused by an increase in crystallization speed  
Figure 7 presents the impact of the isosorbide molar content on the crystallization half time at the maximum crystallization speed temperature (170 \({}^{\circ}\)C). This graph highlights that the increase in the molar content of isosorbide induced an exponential increase of t\({}_{1/2}\).