# Heat-Resistant Behavior of PLA/PMMA Transparent Blends Induced by Nucleating Agents
## 3 Results and Discussion
### Melting and Crystallization Behavior
The relationship between the relative crystallinity \(\mathrm{X_{t}}\) and time obtained according to this formula is shown in Figure 3.  
As shown in Figure 3, when different blends were subjected to isothermal crystallization at 90 \({}^{\circ}\)C and 100 \({}^{\circ}\)C, the time required for the same blends to reach the same crystallinity decreased as the isothermal crystallization temperature increased. At the same temperature, different blends reached the same crystallinity at different times, following a trend consistent with the non-isothermal crystallization process, indicating that nucleating agent addition to PLA minimally affected the time required to reach the same crystallinity. However, although the presence of PMMA significantly increased the time necessary, adding a nucleating agent to the PLA/PMMA system reduced the time to varying degrees, confirming the previous conclusion regarding the non-isothermal crystallization process. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{3}{c}{**Tg (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Tm (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Xc (\%)**} \\ \cline{2-10}  & **80 \({}^{\circ}\)C** & **90 \({}^{\circ}\)C** & **100 \({}^{\circ}\)C** & **80 \({}^{\circ}\)C** & **90 \({}^{\circ}\)C** & **100 \({}^{\circ}\)C** & **80 \({}^{\circ}\)C** & **90 \({}^{\circ}\)C** & **100 \({}^{\circ}\)C** \\ \hline PLA & 61.1 & 59.3 & 60.6 &To further quantify the crystallization rate, the Avrami equation was employed to describe the isothermal crystallization process [23], which was formulated as follows:  
\[1-\mathrm{X_{C}(t)}=\exp(-\mathrm{kt^{n}}) \tag{4}\]  
Figure 3: The relative crystallinity of the PLA blends, crystallized isothermally at (a) 90 \({}^{\circ}\)C and (b) 100 \({}^{\circ}\)C.  
Figure 2: The DSC thermal characteristic curves of the PLA blends during (a) 80 \({}^{\circ}\)C, (b) 90 \({}^{\circ}\)C, and (c) 100 \({}^{\circ}\)C isothermal crystallization. where K is the crystallization rate constant of the polymer, representing the crystal nucleation and crystal growth rate of the polymer, and \(n\) is the Avrami index, which is closely related to the nucleation mechanism and growth mode of the polymer. Although the spherulite \(n\) value of three-dimensional PLA growth is typically between 2 and 4 [24], it is affected by the growth conditions during the actual crystallization process. To facilitate analysis and calculation, both sides of the equation are often subjected to simultaneous logarithmic operations to obtain the following formula [23]:  
\[\ln[-\ln(1-X_{t})]=\ln k+\ln t \tag{5}\]  
Figure 3 is plotted using the \(\ln[-\ln(1-X_{t})]\) and \(\ln t\) in this formula as the \(Y\)-axis and \(X\)-axis, respectively, and the results are shown in Figure 4. Although the obtained curves exhibited a satisfactory linear relationship during the intermediate crystallization stage, they deviated from this association during the initial and final stages. This can be attributed to initial nucleation and subsequent secondary crystallization. The data in Figure 4 were subjected to linear fitting, where the resulting slope and intercept corresponded to the Avrami exponent (\(n\)) and lnk (natural logarithm of k) values, respectively. To minimize analysis errors, only the data points representing 10% to 90% relative crystallinity were included in the fitting process. The corresponding parameters obtained from the fitting are presented in Table 3.  
The nucleating agent acted as a heterogeneous nucleation site during the cooling of the PLA melt, effectively adsorbing PLA molecular segments and facilitating their arrangement and growth. At 90 \({}^{\circ}\)C, the \(n\) value of the blends remained relatively constant, ranging from 1.8 to 2.2, while it displayed a notable increase at an isothermal crystallization temperature of 100 \({}^{\circ}\)C. The specific influence of nucleating agents on the crystallization mechanism depended on the type of nucleating agent and the isothermal crystallization conditions.