## 3 Results and Discussion
### Viscoelastic Properties  
Figure 5 shows the viscosity measured in a high-pressure capillary rheometer for the different materials. The measurements in the capillary rheometers are strongly related with the processing of the materials by FFF or PIM, since in both processes the material is forced to flow through a narrow nozzle at high shear rates [63]. As can be observed in Figure 5, the shear viscosity of AAHDPE00 is slightly lower than the one of HDPE00 in the range of shear rates evaluated (80 to 1000 s\({}^{-1}\)). On the contrary, the viscosity of AAHDPE30 is higher than that measured for HDPE30, especially at shear rates below 500 s\({}^{-1}\). Since the effect of the network of particles and polymer plays a more important role at lower shear rates, rotational rheology tests between 0.1 rad s\({}^{-1}\) and 500 rad s\({}^{-1}\) were conducted. Figure 4: Morphology of the strands produced in the capillary rheometer and cryo-fractured of the compounds of HDPE and AAHDPE filled with 30 vol% of zirconia. In Figure 6a, it can be observed that the complex viscosity of AAHDPE00 is slightly higher than the one of HDPE00 at low angular frequencies (\(<\)1 rad\(\cdot\)s\({}^{-1}\)), whereas HDPE00 is higher in the rest of the angular frequencies. HDPE00 shows a Newtonian plateau at low angular frequencies, whereas AAHDPE00 exhibits a pseudoplastic behavior in the range of angular frequencies evaluated. The increase in viscosity in the low shear region and the pseudoplastic behavior have been reported for long chain branched polyethylene [64; 65] as well as for polyethylene grafted with polar groups such as maleic anhydride, glycidyl methacrylate and acrylic monomers [66; 67] or silane [68]. Thus, the differences in the complex viscosity of AAHDPE00 and HDPE might be caused by the branching and partial crosslinking of the poly (acrylic acid) employed in the polymer grafting, which results in a more effective entanglement [67]; the hydrogen bonding between the carboxylic acid in the acrylic acid promotes this behavior [67]. The branching [65] or partial crosslinking [68] of the grafted polyethylene might also be the cause of the trend in the storage modulus (Figure 6b). At low angular frequencies, the G' of AAHDPE00 is higher than that of HDPE00, whereas the storage modulus of HDPE00 is slightly higher at high angular frequencies. This theory is further supported by the results observed in the loss factor of the unfilled polymers shown in Figure 6c. The slope of the loss factor is negative for HDPE00 in the whole range of angular frequencies evaluated. On the contrary, a positive slope is observed at low frequencies for the AAHDPE00, which is associated with an elastic behavior [68]. Considering the results of the mentioned studies and the trend observed in the complex viscosity (Figure 6), it can be stated that the chain entanglement or crosslinking and the reaction between the acrylic acid monomers in AAHDPE00 are the causes of the big difference in the viscoelastic properties at low angular frequencies for the unfilled polymers. In the case of the highly filled systems, the complex viscosity of AAHDPE30 is much higher than the one of HDPE30 at low shear rates (Figure 6a). It is known that, at low frequencies, the particle-particle interaction and the network of particles have the main effect on the viscoelastic properties of polymer nanocomposites [43]. As was observed in Figure 4, there are no agglomerates in AAHDPE30, whereas HDPE30 has large agglomerates. Thus, the high viscosity of AAHDPE30 is not produced by the powder's agglomerates. On the contrary, the decrease in agglomerates results in an increase in the particle surface area in contact with the polymer melt, thus increasing the viscosity [43; 69; 70; 71].