*3.2. Dispersion and Distribution of Graphene Platelets Within the Nananocomposite Matrix*

Figure 4a shows the X-ray diffraction (XRD) patterns of the neat multimodal-HDPE, graphene powder, and PE-g-1% samples. The diffraction peak (002) appeared in the XRD pattern of graphene at 2θ = 26.07◦ and exhibited a broad band with a corresponding d-spacing of 0.3414 nm (Bragg's law), and average thickness of 1.941 nm (Scherrer's equation), whereas the weak diffraction peak (100) was observed at 2θ = 42.89◦ [36,37]. This indicates the sample flakes consisted of 5-6 graphene layers, which is consistent with the TEM images shown in Figure S4. The weak intensity of these two characteristic diffraction peaks is due to the 2D nature of graphene, especially those with very few layers [38]. Interestingly, the XRD pattern of the PE-g-1% is similar to that of a neat multimodal-HDPE matrix, only showing the crystalline diffraction peaks {(110) and 200)} of the neat multimodal-HDPE matrix. Clearly the XRD results demonstrated that the graphene platelets almost exfoliated into individual sheets and dispersed well in the polymer matrix after the extrusion processing [36–42].

**Figure 4.** Dispersion and distribution of graphene platelets within the polymer matrix. (**a**) XRD patterns of the neat multimodal-HDPE, graphene powder, and PE-g-1%. (**b**) Overlaid Raman spectrum of the neat multimodal-HDPE, graphene powder, and PE-g-1%. The measured 2D Raman bands with 1.96 eV laser energy of graphene (**I**) and PE-g-1% (**II**) are fitted with four and five Lorentzians, respectively. (**c**) Density measurement of graphene/multimodal-HDPE (PE-g), and carbon black/multimodal-HDPE (PE-CB) nanocomposites as a function of nanofiller loading (0.1, 0.5, 1, 2, and 5 wt.%).

Overlay Raman spectra of the neat multimodal-HDPE, graphene powder, and PE-g-1% samples, are shown in Figure 4b. The three intense peaks appeared in the Raman spectra of graphene at 1327 cm<sup>−</sup>1, 1577.5 cm−1, and 2646 cm−1, representing the characteristic D-band, G-band, and 2D-band peaks, respectively [43–45]. The G-band arises from the bond stretching of the sp2 carbon atoms (chains or rings), while the breathing modes of the sp<sup>2</sup> carbon atoms in a hexagon ring gives rise to the D-band [43–45]. The D-band, therefore, requires a defect to be activated (by disorder or at the edge) [43–45]. It originates from one iTO phonon mode around the *K* point by double resonance, whereas the overtone of the D' and D-bands gives rise to 2D' and 2D-bands [43–45]. The 2D (or 2D') peak does not require a defect for its activation, because it originates from the two iTO phonons with opposite momentum near Brillouin zone [43–45]. The position, full width at high maximum (FWHM), intensity ratio (*I*2D/*I*G), and Lorentzian fittings of the 2D peak provide good correlation with the number of layers of graphene in a flake sample [43–47]. In Figure 4bI, the 2D-band of graphene sample is fitted by five Lorentzians, with an overall FWHM of 65.52 cm−1. Z. Lin et al. [46] and E. Dervishi et al. [47] in fact used up to five Lorentzian peaks to fit the 2D-band of their few-layer graphene produced by a bottom up approach. For PE-g-1%, the three prominent characteristic D, G, and 2D peaks associated with graphene were observed at 1327 cm−1, 1582.5 cm−1, and 2658 cm−1, respectively. The 2D-band of the nanocomposite shown in Figure 4bII, is red-shifted from 2646 cm−<sup>1</sup> to 2658 cm<sup>−</sup>1, fitted by four Lorentzians, with an overall FWHM decreased from 65.52 cm−<sup>1</sup> to ~53 cm<sup>−</sup>1. Four fitted Lorentzians, each with a FWHM of ~24 cm<sup>−</sup>1, most likely arose from the asymmetry between the valence and conduction bands present in the bilayer graphene [43–47]. Besides, the increase of the (*I*2D/*I*G) from 0.98 for graphene to 1.55 for PE-g-1%, reveals the reduction of the graphene layers [43]. Overall, these results indicate that the graphene platelets are indeed dispersed (thinned) through the melt extrusion process.

Figure 4c depicts the density (*ρ*c) of the graphene/multimodal-HDPE (PE-g) and carbon black/multimodal-HDPE (PE-CB) nanocomposites at nanofiller loadings of 0.1, 0.5, 1, 2, and 5 wt.%. The PE-CB sample is a commercial grade, produced based on the same polymer matrix, but reinforced by a carbon black with a density of 1700-1900 kg·m−3. A monolayer graphene is made up of covalently-bonded sp2-hybridised carbon atoms, densely packed in a honeycomb lattice [21,22]. Therefore, the density of a defect-free monolayer graphene, with a thickness of 0.142 nm, is estimated to be around 2175 kg·m−<sup>3</sup> [48]. On the other hand, carbon black is composed of primary particles that are permanently fused together through the covalent bonds, into an aggregate structure [49]. Each primary particle is made up of imperfect crystallites of turbostratic graphite structure, which are twisted into each other throughout the aggregates [49]. Accordingly, the graphene used in this study is likely to have a density closer to the carbon black density than a monolayer graphene, i.e., defective surface structure through the oxygen-containing functional groups (see Supplementary Materials Figure S3). As is evident from Figure 4c, the density of the multimodal-HDPE matrix (*ρ*<sup>m</sup> = 950 kg·m<sup>−</sup>3) increased linearly with the addition of the nanofillers, i.e., densities of both nanocomposites increased by the same amount. The slope values are calculated at 4.003 for PE-g and 4.093 for PE-CB, suggesting that the graphene platelets were homogenously dispersed and distributed throughout the polymer matrix. An increase in the nanocomposite density is attributed to the high density of the reinforcements (*ρ*r) employed to reinforce the polymer matrix, according to the equation of the form (*ρ*<sup>c</sup> = 1/(*W*r/*ρ*r)+(*W*m/]*ρ*m)), where *W*<sup>r</sup> and *W*<sup>m</sup> are the weight fractions of reinforcement and matrix, respectively [4]. With a greater incorporation of high-density reinforcement, a higher nanocomposite density is obtained. In the case of agglomeration however, most of the graphene platelets will be lost in the accumulation, thereby the increase in the nanocomposite density remains relatively small.
