## 2 Results and Discussion
### Fourier-Transform Rheology Analysis  
Lissajous curves are a way to transform the time domain of stress into a stress-strain domain, and can be also used to reflect the nonlinear characteristics of the materials under LAOS on the basis of closed loops for normalized stress versus normalized strain [50]. Figure 9 shows the Lissajous curves of the NR, SBR, and NR/SBR blends, as well as the NR + SBR physical blends, at 100 \({}^{\circ}\)C and \(\omega=1\) rad/s. The Lissajous curves of all the samples at low strain amplitude are elliptical, corresponding to the predominately elastic stress response. As the strain increases, the Lissajous curves deviate significantly from the ellipse due to strain softening [51]. The distortion at mediate and high \(\gamma\)s for NR/SBR blends is dependent on the SBR content and the blend morphology, while the distortion for the NR + SBR physical blends is very close to that of pure NR. The distortion of SBR is much weaker than that of NR, and the presence of SBR in the NBR/SBR blend may weaken its distortion. It should be noted that the Lissajous curves for the co-continuous NR/SBR (50/50) blend are even able to almost maintain an elliptic shape at high \(\gamma\) (100%), indicating that the microscopic strain amplification of SBR and the additional elastic contribution which resulted from the co-continuous domain deformation may weaken their strain softening. During the unloading process, it could be observed that the NR + SBR physical blends also show more obvious elliptical distortion than the NR/SBR blends with the corresponding composition, indicating that the recovery of NR + SBR physical blends is remarkably slower than that of the NR/SBR blend, and that the microscopic heterogeneous structure in NR/SBR blends may weaken their nonlinear viscoelastic and elliptical distortion characteristics.  
Figure 9: Normalized Lissajous curves generated from oscillatory shearing measurements at different strain amplitudes for NR/SBR blends and NR + SBR physical blends at 100 \({}^{\circ}\)C and 1 rad/s. Here, L represents loading and U represents unloading.  
In order to further explore the effect of blend morphology on their nonlinear viscoelastic response, the high-order harmonics \(i_{\rm n}\) can be separated by using a Fourier transformation of the stress and strain signals. The stress (\(\sigma(t)\)) could be expressed as follows [52]:  
\[\Sigma i_{\rm n}\mathrm{sin}(n\omega_{0}\;t+\delta_{\rm n}) \tag{2}\]  
where \(\omega_{0}\) is the frequency of the fundamental wave, and \(\delta_{\rm n}\) is the phase angle. Among the high-order harmonics, the intensity of odd-numbered harmonics is higher than that of even-numbered harmonics, and the intensity of harmonics gradually decreases as the order increases. Since the third harmonic contributes the most to the nonlinearity, the ratio of the intensity of the third harmonic (\(i_{3}\)) to the intensity of the first harmonic (\(i_{1}\)) (\(i_{3}/i_{1}\)) is generally used to quantify the degree of nonlinearity. Figure 10 shows the \(\gamma\) dependence of \(i_{3}/i_{1}\) for the NR/SBR blends and the NR + SBR physical blends. It could be seen that the two blend systems exhibit slightly different nonlinear characteristics, and that the nonlinearity of NR is more obvious than that of SBR. Furthermore, the \(i_{3}/i_{1}\) of the two systems generally increase with the increase in \(\gamma\), which is attributed to the orientation and stretch of polymer chains [53]. Here, \(i_{3}/i_{1}\) for the NR + SBR physical blends is close to that of virgin NR, while \(i_{3}/i_{1}\) for NR/SBR blends is similar with that of virgin SBR, indicating that the microscopic heterogeneous structure in NR/SBR blends may weaken their nonlinearity [54].