## 3 Results and Discussion
### Effect of SBS Architecture, Content, and Molecular Weight
On the other hand, the complex viscosity \(\,\mathrm{1}\eta^{*}\,\mathrm{1}\) and G\({}^{\prime}\) are two sensitive parameters reflecting the composite structural phase [26], with changes in interfacial interactions and dispersion state of the components usually manifest at low-frequency regions [27]. In particular, G\({}^{\prime}\) represents microstructure elasticity; therefore, the increase in G\({}^{\prime}\) indicates elastic strength enhancement of the melt ascribed to a form relaxation process [28; 29]. Figure 2 shows the effect of SBS content on G\({}^{\prime}\) of the PPE/HIPS/SBS blends processed by TSE and IM. The SBS411R (radial architecture and the highest molecular weight (M\({}_{w}\))) blends processed by TSE presented a slightly higher G\({}^{\prime}\) than those with SBS416R (radial architecture and medium M\({}_{w}\)); in contrast, the blends with SBS4301L (linear structure and the  
Figure 1: Storage modulus (G\({}^{\prime}\)) and viscous modulus (G\({}^{\prime\prime}\)) as a function of SBS content (Y = 6, 12, 18, and 24 wt%) of the PPE/HIPS/SBS411R, PPE/HIPS/SBS416R, and PPE/HIPS/SBS4301L formulated by twin-screw extrusion (Z = TSE) (**a–d**) and internal mixing (Z = IM) (**e–h**). Relaxation time (\(t_{r}\)). lowest M\({}_{\rm w}\)) are different, resulting in lower G\({}^{\prime}\) values, see Figure 2a-c. The PPE/HIPS/SBS blends processed by IM exhibit a similar behavior, see Figure 2d-f. Hence, the higher G\({}^{\prime}\) modulus is due to the radial architecture and the high or medium M\({}_{\rm w}\) of SBS411 and SBS416, respectively. These findings confirm that the mechanical and micromechanical properties of the block copolymer are directly influenced by the architecture and M\({}_{\rm w}\), even when their nanostructures are equivalent. For instance, styrene/isoprene graft copolymers with four branch points showed acceptable mechanical performance depending on the enhanced degree of physical cross-linking sites, e.g., star block copolymer systems, versus linear copolymers [30,31]. In the present study, radial SBS (411R and 416R) possesses superior mechanical properties than linear SBS (4301L) [32, 33, 34]. The viscoelastic behavior of PPE can be influenced by interactions between SBS and HIPS. In addition, a significant quantity of dispersed rubbery phase (PB) and hard PS blocks that serve as entanglement points to make a network structure, resisting the motion of macromolecular chains, are responsible for the plateau in the curve [25]. These factors induce the increment of blend elasticity, interfacial interactions, and, accordingly, an increase in relaxation time due to the increase of the total interfacial area of the components and interfacial energy [27,35,36]. Figure 3 illustrates the G\({}^{\prime}\) at 0.01 Hz of PPE/HIPS/SBS411R blends processed by TSE and IM. Compared to all PPE/HIPS/SBS blends (PPE/HIPS/SBS411R, PPE/HIPS/SBS416R, and PPE/HIPS/SBS4301L) formulated, both methods exhibited similar behavior. Nevertheless, the blends processed by TSE have a higher elasticity. For example, PPE/HIPS/SBS411R-18-TSE and PPE/HIPS/SBS411R-18-IM G\({}^{\prime}\) were 19,280 Pa and 16,950 Pa, respectively. Consider as another example, PPE/HIPS-TSE and PPE/HIPS-IM, G\({}^{\prime}\) was 2700 Pa and 1830 Pa, respectively. The difference was related to significant dispersive action with rupture and distribution of the soft phase within the matrix using TSE [12,37]. The PPE/HIPS/SBS416R  
Figure 2: Storage modulus (G\({}^{\prime}\)) as a function of SBS content (Y = 6, 12, 18, and 24 wt%) in the blends versus PPE/HIPS-22-TSE or PPE/HIPS-22-IM: (a) PPE/HIPS/SBS411R-Y-TSE; (b) PPE/HIPS/SBS416R-Y-TSE; (c) PPE/HIPS/SBS4301L-Y-TSE; (d) PPE/HIPS/SBS411R-Y-IM; (e) PPE/HIPS/SBS416R-Y-IM; (f) PPE/HIPS/SBS4301L-Y-IM. Table S1 illustrates the correlations of the Pearson time-product matrix for PPE/HIPS/SBS blends. These correlation coefficients range from \(-1\) to \(+1\) and measure the strength of the linear relationship between variables.