## 2 Results and Discussion
### Nonlinear Rheological Behavior
Furthermore,  
Figure 6: Normalized \(G^{\prime}/G^{\prime}{}_{0}\) and \(G^{\prime\prime}/G^{\prime\prime}{}_{0}\) as a function of \(\gamma\) for NR/SBR blends (**a,b**) and NR + SBR physical blends (**c,d**) at 100 \({}^{\circ}\)C and 1 rad/s. The straight and dashed lines are normalized \(G^{\prime}/G^{\prime}{}_{0}\) and \(G^{\prime\prime}/G^{\prime\prime}{}_{0}\) values obtained by linear numerical addition of neat NR and SBR by weight ratio. Here, the normalized moduli for the NR/SBR blends and NR + SBR physical blends with different weight ratios are vertically shifted by a factor of n to clearly show their difference. The corresponding n value is labelled in the bracket behind the NR/SBR ratio. (**e**) Onset strain \(\gamma_{\text{c}}\) for the Payne effect as a function of SBR content for the NR/SBR blends, NR + SBR physical blends, and modulus numerical addition. the modulus decay amplitude of NR + SBR physical blends is also larger than that of their corresponding numerical addition results. The critical strain for the onset of nonlinearity (\(\gamma_{\rm c}\)) increases with increasing SBR content, and the \(\gamma_{\rm c}\) values for NR/SBR blends are obviously higher than those for the NR + SBR physical blends and numerical addition results (as shown in Figure 6e), indicating that the presence of the heterogeneous structure in NR/SBR blends may extend their linear viscoelastic region and delay the occurrence of rheological nonlinearity. The \(\gamma_{\rm c}\) values for the NR + SBR physical blends are very close to that of neat NR and independent of SBR content, indicating that the strain softening of NR + SBR physical blends might be just dominated by NR. To further explore the time-dependent behavior of the Payne effect for NR/SBR blends with a heterogeneous structure, cyclic strain amplitude sweeps are applied to the NR/SBR blends and NR + SBR physical blends during a loading-unloading cycle at 100 \({}^{\circ}\)C and \(\omega\) = 1 rad/s. Figure 7 shows the \(\gamma\) dependence of normalized moduli \(G^{\prime}/G^{\prime}_{0}\) and \(G^{\prime\prime}/G^{\prime\prime}_{0}\) undergoing cyclic oscillation deformation. In the investigated \(\gamma\) region, neat NR exhibits more remarkable \(G^{\prime}\) and \(G^{\prime\prime}\) recovery hysteresis than neat SBR during a cyclic sweep at \(\gamma>10\%\). To compare the difference of modulus recovery hysteresis for NR/SBR blends and NR + SBR physical blends, the normalized moduli for the blends with different weight ratios are also vertically shifted by a factor of n. With the increase in SBR content, the \(G^{\prime}\) hysteresis of the NR/SBR blends decreases significantly, and it is much smaller than those for the corresponding NR + SBR physical blend and the numerical addition of neat NR and SBR. Furthermore, the \(G^{\prime\prime}\) hysteresis of the NR/SBR blends almost disappears, while that of the NR + SBR physical blends is even more marked than that of neat NR. Hence, the heterogeneous gel-like structure in the blends may suppress the mechanical hysteresis upon large-\(\gamma\) cyclic sweeps, especially in the co-continuous NR/SBR (50/50) blend. In the LAOS test, the Payne effect is manifested as a decrease in dynamic modulus with increasing periodic oscillatory strain. The decrease in the modulus corresponds to the change in the microstructure of the system. Once the loaded strain is removed, the material will undergo a time-dependent structural adjustment. Therefore, the time-dependent characteristics of the Payne effect could be explored from another perspective on the modulus recovery process upon loading a large strain. Here, the NR, SBR, and NR/SBR blends, as well as the NR + SBR physical blends, were sheared stepwise to \(\gamma\) = 0.05% and 50%, successively, and then sheared back to \(\gamma\) = 0.05% at 100 \({}^{\circ}\)C and \(\omega\) = 1 rad/s, with each loading step lasting for 600 s. Figure 8 shows the normalized \(G^{\prime}\) as a function of lasting time.