*3.4. Rheology and Thermal Stability Performance of a Nanocomposite*

Figure 6a-b shows the rheological behaviour of neat multimodal-HDPE and PE-g-1%. Shown in Figure 6a is the pseudoplastic, non-Newtonian behavior of the viscoelastic polymer. The influence of graphene on the viscoelastic response of the polymer is revealed from the change in the absolute values of the storage (*G'*) and loss (*G")* moduli, as well as their frequency dependence [33,61].

**Figure 6.** Thermal stability performance and rheological behaviors. (**a**) Dynamic frequency sweep measurements performed at 190 ◦C. *ω<sup>C</sup>* is the crossover frequency point and *GC* is the crossover modulus point in a log–log scale. (**b**) Melt flow rate (MFR) measurements of PE-g nanocomposites as a function of graphene loading (0.1, 0.25, 0.5, 0.75, and 1.0 wt.%). (**c**) Thermogravimetric thermograms performed in N2 atmosphere. (**d**) Dimensional change as a function of temperature. (**e**) Coefficient of thermal expansion (CTE) measured at temperature difference range of 30-105 ◦C.

At a high-shear rate, both materials exhibited thinning behavior, which resulted in a decrease of extensional viscosity. However, the incorporation of 1 wt.% graphene increased the melt viscosity of the nanocomposite, though the relative increase gradually lessened at high-shear rate. The presence of graphene has considerably increased the pseudoplasticity at a low shear rate region. At the angular frequency (ω) of 0.0154 rad/s, the complex viscosity increased from 0.13 MPa·s for neat multimodal-HDPE to 0.24 MPa·s for the PE-g-1%. Furthermore, the loss and storage moduli of the neat polymer increased by a value of 92% and 77% with 1 wt.% loading of graphene, respectively. The greater amount of storage and loss moduli of PE-g-1% suggests that the formation of a strong interfacial bonding between the polymer matrix and the high-modulus graphene reduced the loss tangent, the nanocomposite accordingly became more elastic [33,61–63]. This is in addition to the thorough dispersion and distribution of the nanofillers, which led to a decrease in the degree of the chain mobility of the polymers, and thus suppressed the shear flow of the polyethylene macromolecular chains [4]. In addition, the crossover modulus point (*GC*) and crossover frequency point (*ωC*) have decreased from 0.044 MPa·s and 4.5 rad/s for the neat multimodal-HDPE to 0.035 MPa·s and 1.2 rad/s

for PE-g-1%, respectively. The shift of *ω<sup>C</sup>* to lower region indicates that the nanocomposite exhibited higher average molecular mass and/or the entangled molecules were induced by the three-dimensional network of graphene platelets within the matrix [33]. However, the GC shifting to lower values after the reinforcement indicates that the polymer exhibited broader molecular weight distribution, which is evident from the increase in the polydispersity index (PDI) by 18.4%, i.e. the larger the PDI, the broader the molecular weight distribution [33]. The shift of *Gc* upon the addition of the reinforcement possibly arose also from exposing the neat polymer to high temperature, under a combination of high shear and elongation forces, for a prolonged period of time. In Figure 6b, the melt flow rate (MFR) of the extruded multimodal-HDPE decreased gradually from 13.6 g/min to only 6.42 g/min with 1 wt.% graphene loading at 21.6 kg/190 ◦C, whilst the MFR of the pristine multimodal-HDPE (non-extruded) was only was only 7.5 g/min. The lower the MFR, the higher the molecular weight or the viscosity. This indicates that graphene acted as a thermal barrier and enhanced the thermal stability of the polymer through the strong interface bonding.

The synergistic effect advantages of graphene are further investigated by thermal expansion and thermogravimetric analyses (TGA). As shown from the TGA thermograms in Figure 6c, the onset degradation temperature of PE-g-1% increased significantly by more 31 ◦C. The onset temperature at 5% mass loss (T5%) of neat multimodal-HDPE increased from 405 ◦C to 434.2 ◦C upon 1 wt.% loading of graphene (see Table 1). The reinforced polymers exhibited a greater melt strength during thermoforming such that the sagging resistance of the nanocomposite has been improved. The large aspect ratio of graphene with a platelet structure likely offered a larger interfacial surface with the polymer matrix which in turn slowed the diffusion of the decomposition products from a continuous network-structured protective layer created in the nanocomposite. It would seem as though graphene acted as an antioxidant and consequently protected the polymer from excessive thermal degradation [64–69]. The polymer could therefore be extruded in aggressive conditions, for example with a screw configuration of 37% of dispersive elements at a very low feed rate. This also implies that the amount of thermo-mechanical and thermo-oxidative degradations achieved was sufficient enough to produce an efficient reinforcement. This was achieved through the formation of a strong interfacial adhesion bond between the polymer matrix and graphene platelets, which has accordingly enhanced the thermal stability of the polymer.


**Table 1.** TGA data of the neat multimodal-HDPE and its nanocomposite.

T5%, T30%, T50%, and T80%, are the onset temperatures at 5%, 30%, 50%, and 80% mass loss, respectively.

The coefficient of thermal expansion (CTE) of the PE-g-1% was calculated to be 0.55 × <sup>10</sup>−<sup>6</sup> ◦C−<sup>1</sup> over the temperature range of 30–103 ◦C, as shown in Figure 6d-e. The CTE started to become positive after 100 ◦C confirming that graphene sheets were well bonded with the polymer matrix, and suggests the continuous interconnected network structure formed in the polymer matrix hindered the reorientation of the polymer chains. Mounet et al. [70], Zakharchenko et al. [71], Yoon et al. [72], Bao et al. [73], and others found that graphene has negative thermal expansion at low temperatures. Mounet et al. [70] used a first-principles calculation, and estimated the CTE of graphene remains negative up to 2500 K. Zakharchenko et al. [71] found that the transition from negative to positive CTE occurs at ~900 K. The CTE of a single-layer graphene measured by Yoon et al. [72] via temperature-dependent Raman spectroscopy remained negative in the temperature range of 200–400 K. Therefore, it is not yet clear at what exact point the CTE changes from negative to positive.
