## 3 Results and Discussion
### Rheological Properties
Equally important, the amorphous PLA effect on the blends is in the \(\eta^{\bullet}\) stabilization as a frequency function. Conversely, a poly(S-_co_-MMA) disadvantage is its high \(\eta^{\bullet}\), and a small plateau at low frequencies, which has a shear thinning behavior. It should be noted that the PS and PMMA present a similar \(\eta^{\bullet}\) curve compared to poly(S-_co_-MMA), although more identical to the PS caused by a more significant number of styrene monomer units according to the random copolymer composition [53]. Additionally, the increase or decrease in \(\eta^{\bullet}\) is the result of changes in structure when compared to starting materials. For instance, the composites present an increased \(\eta^{\bullet}\) based on the filler content in the polymer blends [54; 55; 56; 57]. On the other hand, in this study PLA and poly(S-_co_-MMA) presented differences in their \(\eta^{\bullet}\) ascribable to their molecular weight, resulting in polymer mixtures with behavior between the frontier of the neat polymers. In summary, the PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends do not show changes in structure, specifically with a physical interaction between the PLA and poly(S-_co_-MMA). Figure 3b shows the storage module (G') graph versus square frequency of polymer blends, PLA, and poly(S-_co_-MMA). In general, PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends converge at high frequencies; however, at low frequencies, the blends showed a predominant elastic behavior. The PLA showed the lower G' at low frequencies, while the poly(S-_co_-MMA) had a high value in the same range. From 7 Hz to the highest frequency, PLA\({}_{75}\)/poly(S-_co_-MMA)\({}_{25}\) presented a higher modulus than PLA\({}_{50}\)/poly(S-_co_-MMA)\({}_{50}\). For PLA\({}_{90}\)/poly(S-_co_-MMA)\({}_{10}\), there was a similar situation at approximately 30 Hz. The G' decreased with PLA concentration in the PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends. The G' decreased at low frequencies according to the rheological behavior of unlinked polymers when small molecules are in the polymer structure [58]. Moreover, blend miscibility can be analyzed in the oscillatory rheology through the storage module plot versus the frequency where the behavior should be closer to a neat homopolymer. For example, this same behavior was observed in PLA-EVA [50] and PEO/PMMA blends [54]. Additionally, the PVDF/PMMA blends showed an increase in G' compared to the neat PMMA; however, it was lower than the neat PMMA when the temperature changed [55]. Similarly, [PERSON] et al. [56] observed an increase for G' in the PMMA/PCE blends at low and high frequencies. These results were attributed to the short time for chain relaxation. Equally, [PERSON] et al. [57] reported a decrease in the rheological parameters (G' and G'') of PVC/PMMA/rubber nitrile blends as a consequence of the flexibility provided by the rubber nitrile. Figure 4 shows the G' and loss modulus (G'') curves against the angular frequency, crossing point, of neat PLA, neat poly(S-_co_-MMA), and PLA\({}_{\text{x}}\)/poly(S-_co_-MMA)\({}_{\text{y}}\) blends. It is well known that, at low frequencies, G'' > G' shows a fluid state following a typical linear polymer behavior; however, at high frequencies, G' > G'' exhibits a solid-state behavior [59; 60; 61]. Furthermore, the crossing point (G' = G'') may change according to the composition or the branch generation due to the melt blending. For the neat PLA and poly(S-_co_-MMA), the crossing points were at 72.91 and 2.06 Hz, respectively. The PLA\({}_{50}\)/poly(S-_co_-MMA)\({}_{50}\) blend presented a crossing point at 23.17 Hz, with a trend closer to the poly(S-_co_-MMA) copolymer. Subsequently, the PLA\({}_{75}\)/poly(S-_co_-MMA)\({}_{25}\) crossing point was observed at 28.35 Hz. Finally, the PLA\({}_{90}\)/poly(S-_co_-MMA)\({}_{10}\) had a crossing point at 57.32 Hz.