## 3 Results and Discussion
### Rheological Properties  
The miscibility of the binary blends was studied through the Han and Cole-Cole plot analysis because of the improvement in \(E\) concerning PLA. First, the Han plot was used to identify the polymer blend miscibility or composite materials at different temperatures and compositions [30]. The Han plots of the PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends, neat poly(S-_co_-MMA), and neat PLA analyzed at 195 \({}^{\circ}\)C are displayed in Figure 2. A significant characteristic concerning the Han plot (log G' vs. log G'') is that a slope of 2 must be observed in the terminal region or low frequency if a blend is regarded as truly homogeneous [44; 45]. The slope of the PLA\({}_{90}\)/poly(S-_co_-MMA)\({}_{10}\) blend is the highest of all the mixtures with 1.85, while PLA\({}_{50}\)/poly(S-_co_-MMA)\({}_{50}\) is the lowest, 1.62. In other words, the miscibility is present in the PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends as a function of the PLA content obtaining adequate mechanical properties. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Young’s Modulus (GPa)** & **Elongation at Break (\%)** &
\begin{tabular}{c} **Ultimate Tensile** \\ **Strength (MPa)** \\ \end{tabular} \\ \hline Neat PLA & 1.16 & 6.00 & 52 \\ PLA\({}_{50}\)/poly(S-_co_-MMA)\({}_{50}\) & 1.57 & 3.23 & 48 \\ PLA\({}_{75}\)/poly(S-_co_-MMA)\({}_{25}\) & 1.58 & 3.17 & 45 \\ PLA\({}_{90}\)/poly(S-_co_-MMA)\({}_{10}\) & 1.60 & 3.84 & 56 \\ Neat poly(S-_co_-MMA) & 1.68 & 3.00 & 46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties of neat PLA, PLA\({}_{\text{x}}\)/poly(S-co-MMA)\({}_{\text{y}}\) blends, and neat poly(S-_co_-MMA). Additionally, Figure 2b illustrates the Cole-Cole plots of neat PLA, neat poly(S-_co_-MMA), and PLA\({}_{\rm x}\)/poly(S-_co_-MMA)\({}_{\rm y}\) blends. In particular, all samples present information about the relaxation process occurring in polymeric blends. These diagrams, in particular, form or become one semicircle when they indicate miscibility; on the contrary, immiscibility is attributed when more than one semicircle appears [46]. The Cole-Cole diagrams revealed the homogeneity of amorphous PLA, showing a smooth semicircular arc. A deviation from this smooth semicircular arc was observed in the case of poly(S-_co_-MMA) neat copolymer, with a more opened arc and tail. The PLA\({}_{\rm 50}\)/poly(S-_co_-MMA)\({}_{\rm 50}\) blend displayed a non-closed semicircular arc accounting for immiscibility. Otherwise, the PLA\({}_{\rm 75}\)/poly(S-_co_-MMA)\({}_{\rm 25}\) and PLA\({}_{\rm 90}\)/poly(S-_co_-MMA)\({}_{\rm 10}\) had a similar smooth semicircular arc to the amorphous PLA, which explains the miscibility and homogeneity of these last blends [47; 48]. Similarly, the Cole-Cole plots were used by [PERSON] et al. [49] reporting two relaxation behaviors in immiscible PLA/PBAT blends, the left arc explains the polymer chain relaxation, and the right arc accounts for the droplet relaxation. Thus, [PERSON] et al. [50] reported excellent compatibility and homogeneity for PLA/ethyl-vinyl acetate (EVA) blends for a maximum EVA content of 30 wt.%. In addition, [PERSON] et al. [51] observed a tail at the end of the curves in Cole-Cole plots, confirming phase separation between PLA and acrylonitrile butadiene rubber (NBR). In the same way, [PERSON] et al. [52] studied the effect of adding epoxy functionalized graphene to PLA/PBAT blends, in which a semicircular shape was observed showing positive miscibility. Figure 3a displays the complex viscosity results, \(\eta^{\bullet}\), of neat PLA, neat poly(S-_co_-MMA), and PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends. In particular, the PLA\({}_{\text{75}}\)/poly(S-_co_-MMA)\({}_{\text{25}}\) and PLA\({}_{\text{90}}\)/poly(S-_co_-MMA)\({}_{\text{10}}\) samples presented a broad plateau in comparison to the poly(S-_co_-MMA) copolymer. However, at high frequencies, all materials converged on similar \(\eta^{\bullet}\) values at approximately 30 Hz.