Two different types of plastic, PP T30S and LDPE 2102TN26, were purchased from Dalian and Qilu Petro China, respectively. The melt flow rate (MFR) of PP and LDPE was measured at 230°C and 190°C, respectively, using a 2.16 kg weight. The density was measured at room temperature. The measured values are listed in Table 1.

PP and LDPE samples were dried using an electric blast drying oven at 80°C for 12 h. A high-speed mixer from Fuxin Light Industry Machinery Factory in Liaoning, China was then used to mix the PP/LDPE blend at a weight ratio of 50/50. To analyze the phase morphology, other weight ratios such as 30/70, 40/60, 60/40, and 70/30 were also prepared. The PP/LDPE blends were extruded using a co-rotating twin screw extruder from Rubber and Plastic Machinery Factory in Guangzhou, China at 210°C, and blended particles were obtained using a granulator. The blended samples were then dried at 85°C for 12 h using an electric blast drying oven. Sample disks with diameters of 25 mm were prepared for rheological measurement using a compression mold at 210°C and 10 MPa.

Scanning electron microscope (SEM): The samples of PP/LDPE blends were brittlely fractured after being kept in liquid nitrogen for half an hour.

The weight ratios of the blends were 30/70, 40/60, 50/50, 60/40, and 70/30. Gold was sprayed on the cross sections of the samples and micrographs were taken using a scanning electron microscope (SEM) LE0438VP from Hitachi Co., Japan. The average size of the dispersed phase was calculated using Nano Measurer 1.2.0 software.

Rheological measurement: A rotational rheometer with a parallel-plates geometry manufactured by Anton Paar GmbH was employed to measure the dynamic rheological properties of the polymer samples. The parallel plates have a diameter of 25 mm with a gap of 1 mm between them. The angular frequency ranged from 0.028 to 300 rad/s at two different temperatures—210°C and 230°C. The samples were subjected to an applied strain of 4%, which was within the linear viscoelastic region determined through strain sweeping. Nitrogen gas was employed during the rheological measurement to prevent possible oxidation of the polymer samples at high temperatures. The samples were allowed to rest on the rheometer for 5 min to remove any thermal history before conducting the rheological measurement.

Fig. 1 shows SEM images of the PP/LDPE blends. In the PP/LDPE (30/70) blend, dispersed morphology can be observed. PP and LDPE are the dispersed droplet and matrix, respectively. The condition for phase inversion can be expressed as follows [14]: (4) ψ1/ψ2=η1/η2where ψ_i and η_i represent the volume fraction and melt viscosity of component i, respectively.

At 210°C and 230°C, the ratio of ψ₁/ψ₂ (PP/LDPE) is 35/65 and 44/56, respectively, and the viscosity is zero shear one. Models that use the viscosity ratio approach face difficulties in predicting the phase inversion at low shear rates [15]. However, Wu’s work [15] shows that this model accurately predicted the phase inversion region at a shear rate of about 40 s⁻¹. Similarly, in this work, the ratio of ψ₁/ψ₂ (PP/LDPE) at a shear rate of 40 s⁻¹ is 48/52 and 51/49 at 210°C and 230°C, respectively, which corresponds to the phase inversion. The models predict that it is much more likely for the less viscous phase to be the continuous phase [16–18].

Figs. 2b–2d show the morphologies of the 40/60, 50/50, and 60/40 blends, respectively. These blends do not exhibit dispersed morphologies. It is difficult to confirm a distinct co-continuous morphology, as the optical contrast of PP and LDPE is not high enough. On the other hand, the 70/30 blend clearly shows a dispersed morphology, which is different from the 30/70 blend (Figs. 2a and 2e). In the 70/30 blend, LDPE is the dispersed phase, and PP is the matrix. The average diameter of the 30/70 blend and 70/30 blend is 0.57 and 0.55 µm, respectively.

The storage modulus of the PP/LDPE binary blend shows an interesting trend as the LDPE content is varied. Initially, it increases with increasing LDPE content, reaching a peak at around 30%. After this point, it slowly drops until 70% of LDPE content is reached, beyond which it drops quickly. This trend suggests a phase inversion of the binary blend, which is consistent with the morphology shown in Fig. 3. It also implies a transition from dispersed to co-continuous morphology, as per studies [19,20].

Fig. 4 shows the dynamic rheological curves of the PP/LDPE (50/50) blend as well as neat polymers at 210°C and 230°C, respectively. It is obvious PP has higher viscosity than LDPE. In the PP/LDPE blend with a weight ratio of PP/LDPE less than 1, LDPE forms the continuous phase as it is less viscous than PP, which is the dispersed phase. The viscosity curve and loss modulus of the blend lie between the two components, but the storage modulus does not. At both temperatures, the storage modulus of the 50/50 blend shows a plateau at low frequencies, beyond those of PP and LDPE. This plateau occurs due to an increase in the interfacial area between the two phases, rather than the shape relaxation of the dispersed droplets [21]. A larger interfacial area results in a higher interfacial modulus [22], as more time is needed for the interface between the two phases to relax. This unique characteristic at low frequency invalidates the G-M model [23] and Palierne model [6], which only consider dispersed morphology. The 70/30 and 30/70 PP/LDPE blends have droplet morphology and do not show an elasticity plateau at low frequency, which is not shown in this work.

Yu model (Eq. (1)) was used to fit the G′ data for the PP/LDPE (50/50) blend. According to [24], the interfacial tension of the blend is 0.214 mN/m at 210°C and 0.098 mN/m at 230°C. Yu model has two parameters: K_B or K_C and K_B/K_C. However, only K_B/K_C was shown in Yu’s fitting work. The value of K_B or K_C was not presented in the fitting. Although K_B/K_C may be small, K_C may be very large! As explained earlier, the interfacial tension has little contribution to the B-type deformation. Only the tilt of the cylinder has an impact. On the other hand, C-type has a significant impact on the interfacial deformation of the blend due to the shape change of the cross-section of the cylinder. This work has been done to show their different influences in dynamic shear flow. If K_B/K_C = 0.1, K_C should be much larger than K_B. Fig. 6 exhibits the fitting curves at two temperatures. For the fixed K_B/K_C ratio and different K_C values, the fitting results are different. Fig. 6a demonstrates that the larger the value of K_C, the closer the fitting curve. However, when K_C value is too low (0.07 and 0.7), the fitting curves are located below the data. Conversely, when K_C value is large enough (7), Yu model fits the data well. However, if K_C value is too high, the fitting curve will lay beyond the data (not shown in Fig. 6a). Fig. 6b shows the fitting curve for the data at 230°C. If K_C value is lower than 8.3, the fitting curves will lay below the data. The fitting curve with K_C value of 8.3 agrees well with the data. At the two temperatures shown, the characteristic length is 6 µm, and the K_B/K_C ratio is 0.1.

A further fitting was carried out with fixed K_C and varying K_B/K_C ratios, as presented in Fig. 7. Fig. 7a indicates that if K_C is low, adjusting the ratio or K_B value, has no effect on the fitting outcome. The fitting curve at low frequency is below the data if K_C is not enough. In fact, if K_C is insufficient, the fitting curve falls below the data at low frequency, which means the model with low K_C value underestimates the data. However, when K_C is increased to a higher value, as demonstrated in Fig. 7b, the K_B/K_C ratio or K_B has no impact on the fitting when K_B/K_C is less than 1. If K_B/K_C is 1, i.e., when K_B is considerably increased, the fitting curve overestimates the data at low frequency. Since type B deformation has little contribution to the stress of the blend, it is unnecessary to emphasize the value of the K_B co-efficient during the fitting process. When K_B/K_C is less than 1, the K_B co-efficient can be neglected in Eq. (1), and only K_C should be retained. Thus, Eq. (1) can be rewritten as Eq. (5) by removing the K_B item.

(5) G ′=G components ′+Kc8αSVf2ω2τ2f12+ω2τ2

The simplified model (Eq. (5)) is applicable only when the K_B/K_C ratio is less than 1. In Yu’s research [10], the K_B/K_C ratio for the best-fitting curves is 0.12, 0.2, 1, and 0.4 in Figs. 4 to 6, respectively, most of which are less than or equal to 1. This simplified model is effective in most cases where orientation and distortion are present, with only two fitting parameters, K_C and lc.