## 3 Results and Discussion
### Effect of SBS Architecture, Content, and Molecular Weight  
Rheological analysis of polymer blends and composites is an efficient method to provide insight into their microstructures, interfacial interactions, and processing behaviors [18; 19]. The storage modulus (G\({}^{\prime}\)) and loss modulus (G\({}^{\prime\prime}\)) represent the elastic portion and viscous component of the characteristic viscoelastic behavior as a function of time, respectively. Nevertheless, in some cases, the G\({}^{\prime}\) is more sensitive to changes in the micro- or nano-structure of viscoelastic systems in frequency sweep tests, whereby a significant change in its rheological behavior provides information about the transition from viscous to elastic behavior [20]. A comparison of the G\({}^{\prime}\) and G\({}^{\prime\prime}\) magnitude, the rheological behavior can be defined as viscoelastic, solid, or liquid. When G\({}^{\prime}\) > G\({}^{\prime\prime}\), the system is dominated by viscoelastic solid-like behavior; in contrast, if G\({}^{\prime}\) < G\({}^{\prime\prime}\) (at low frequencies), it has viscoelastic liquid-like behavior [21]. Figure 1 displays the viscoelastic behavior of all PPE/HIPS/SBS blends. For example, the PPE/HIPS/S416R-6-TSE, Figure 1a, presents a viscoelastic liquid-like behavior (G\({}^{\prime\prime}\) > G\({}^{\prime}\) at low frequencies). However, the transition from liquid to viscoelastic solid occurs for PPE/HIPS/SBS416R-12-TSE, see Figure 1b. Finally, a viscoelastic solid-like behavior (G\({}^{\prime}\) > G\({}^{\prime\prime}\)) at higher concentrations (18 and 24 wt%) of the S416R copolymer was observed, seen in Figure 1c,d, respectively. Notably, the increase in G\({}^{\prime}\) and G\({}^{\prime\prime}\) modules occurred at low frequencies, suggesting the presence of the slow relaxations inherent to a vast portion of a macromolecular network [22]. In summary, the dynamic rheological measurements revealed that all the PPE/HIPS/SBS blends have identical viscoelastic behavior to the PPE/HIPS/SBS416R blends, see Figure 1. Figures S1 and S2 compares the PPE/HIPS-22 (0 wt% SBS) and PPE/HIPS/SBS411R-6 blends processed by IM and TSE, respectively, which have similar behavior, where, at low frequencies, the viscous component dominates. Compared to PPE/SBS416R-40-IM, the PPE/HIPS/SBS416R-24-IM blend has a similar behavior specifically as viscoelastic solid, notwithstanding it has a lower G\({}^{\prime}\). In contrast, PPE/HIPS-40-IM (0 wt% SBS416R) exhibits behavior such as a viscoelastic liquid due to the significant difference in PB content, see Figure S3. Moreover, the relaxation time is calculated from the inverse of the crossover frequency, i.e., when G\({}^{\prime}\) and G\({}^{\prime\prime}\) are equal [23], indicating the relaxation time after applying deformation or stress. Likewise, crossover frequency and zero shear viscosity are important viscoelastic properties of the polymer related to the degree of entanglement. A higher crossover frequency with increased SBS content indicates lower entanglements among the molecules and a lower characteristic relaxation time [24]. In contrast, the shifts towards lower frequencies indicate a higher relaxation time of the polymer chains. This relaxation delay could be attributed to more entanglements and weaker mobility of the chain segments in the PPE/HIPS/SBS blends. In other words, SBS acts as a physical barrier to the relaxation process, restricting the chain mobility of the PPE/HIPS matrix [25; 26]. Additionally, the PPE/HIPS/SBSX-6 and PPE/HIPS/SBSX-12 display relaxation time, namely as \(t_{r}\), Figure 1a,b,e,f. For PPE/HIPS/SBS blends with 18 and 24 wt% of SBS content, G\({}^{\prime}\) is always higher than G\({}^{\prime\prime}\) (Figure 1c,d,g,h), i.e., the transition of solid behavior to liquid behavior is absent with increasing frequency, indicating an enormous elasticity [23]. Similarly, behavior is observed for PPE/SBS416R-40-IM blends, see Figure S3.