## 3 Results and Discussion
### Viscosity  
The viscosity of a polymer blend depends on the components, composition, and interfacial interactions [38]. Figure 4 illustrates an overall increase \(\mid\eta^{*\mid}\) with SBS content of any type and processing method at the low-frequency region, which affects the viscosity of all blends [8]. A higher viscous phase, SBS411R, SBS416R, and SBS4301L, attached to a less viscous phase, PPE > HIPS, hinders flowability and increases overall system viscosity, see Figure S4 [8]. For all PPE/HIPS/SBS blends, \(\mid\eta^{*\mid}\) obeys throughout the frequency range, a shear-thinning response, as evidenced by the viscosity decrease with increasing frequency, representing the typical characteristic of a pseudoplastic fluid. Although PPE and PS are completely miscible [39], PPE and PB are immiscible [32]; as a result, the blends were expected to be phase-separated. According to [PERSON] et al. [40], in poly(phenylene ether)/polydivinylbenzene(polyisobutylene-\(b\)-polystyrene) blends, melt viscosity reduction with increasing frequency was expected because of a progressively disrupted phase segregation in the melt. At low frequencies, phase separation prevailed, and the degree of entanglement of polymeric chains dominated the flow, whereas, at increasing frequencies, phase separation became increasingly disturbed, and the alignment in flow direction dominated, facilitating the flow, causing a sudden decrease in melt viscosity [25]. Compared with PPE/HIPS/SBS416R-24-IM, the improved flow behavior (lower viscosity) of PPE/HIPS-40-IM was due to a higher content of HIPS, because PS derivatives, i.e., HIPS, improves the PPE processability and toughness, see Figure S5 [41]. Moreover, TSE could imply a significant dispersive action, with rupture and distribution of the soft phase into the matrix compared to IM [12; 37]. Therefore, the increase in \(\mid\eta^{*\mid}\) is due to sturdy interfacial adhesion between PB and PPE, and consequently, the stress can be transferred from one phase to another upon applying shear forces, hindering flowability and enhancing the system viscosity [8]. Figure 3: Storage modulus at 0.01 Hz (G\({}^{\prime}\), 0.01 Hz) as a function of type of SBS (X = 411R, 416R, and 4301L) and its content (Y = 6, 12, 18, and 24 wt%) for PPE/HIPS/SBSX-Y-Z. (**a**) \(Z\) = IM; (**b**) \(Z\) = TSE. [PERSON]'s plot, [PERSON], and [PERSON] help examine the miscibility and morphology of blends from linear viscoelastic data [38]. In the rheological criterion established by [PERSON] et al., the plot of log G\({}^{\prime}\) vs. log G\({}^{\prime\prime}\) is used to determine the rheological miscibility of polymer blends. There are distinctive differences between the [PERSON]'s plot of homogeneous polymers and multiphase systems. [PERSON]'s plot must be independent of temperature and composition. Additionally, the terminal region slope of 2 must indicate that a mixture is truly homogeneous or molecularly compatible. Otherwise, the blend is deemed to be immiscible or phase-separated [42; 43; 44]. The difference in the slope suggested differences in morphology [38]. Figure 5 shows [PERSON]'s plot for all PPE/HIPS/SBS blends, varying SBS content and method processing. As observed, the G\({}^{\prime}\)-G\({}^{\prime\prime}\) curve of all blends showed a clear dependence on the composition, exhibiting a nonlinear correlation and an upturning shape at low frequencies, indicating the existence of phase separation or immiscibility [45]. In addition, the slope deviated from 2. However, when the SBS content increased at 18 wt%, a considerable enhancement of G\({}^{\prime}\) at low frequencies arose, revealing poorer compatibility and high interfacial tension between the PPE-PS phase and PB with a significant change in blend microstructure [38; 46]. Finally, the findings reveal insignificant changes in the behavior of [PERSON]'s plot when comparing both processing methods.