## 2 Materials and Methods
### Instrumental Methods  
Quasi-static nanoindentation and nanoscratch measurements were perpetrated on Hysitron TI 980 instrument (Bruker, Billerica, MN, USA) by using a 2D transducer assembly (both normal and lateral force) equipped with a Berkovich probe. A typical radius of curvature for a standard Berkovich indenter would be approximately 150 nm. Three distinct maximum loads of 100 \(\upmu\)N, 1000 \(\upmu\)N, and 10,000 \(\upmu\)N were selected in the nanoindentation study of the composite samples seeking to confirm the conjecture of presence of indentation size effect as a function of the elastic deformation and indentation depth [17; 18]. The viscoelastic polymer nature of the materials required to add a hold segment in the setting of trapezoid load function and to establish a loading and an unloading rate of 200 \(\upmu\)N/s. The load was maintained for 2 s in the hold segment at every indentation peak force aiming to reduce the creep effect. Nanoscratch experiments were carried out at constant load scratch function consisting of nine segments by applying peak force of 1000 \(\upmu\)N and total scratch length of 10 \(\upmu\)m. The coefficient of friction was extracted from the segment of interest, where the peak load is being kept constant for 15 s, matching with the substantial move of the probe into the composite surface, as already reported in a previous paper on nanomechanical characterization of polymer surfaces [19]. A test procedure of tip-to-optic calibration helping to select an experimental area with satisfactory surface roughness was performed prior to every one single nanoscratch. Evaluation of both the average surface roughness and the residual side pile-up formed past a groove has been made by analysis of _in-situ_ SPM image of nanoscratched sample surface area using the TriboView 5.9 instrumental software. The thermal conductivity of the composites was measured by using an LFA 467 HyperFlash (Netzsch, Selb, Germany). The samples were prepared by pressing them into a mold with a diameter of 25 mm and a thickness of 2 mm. Using thermal diffusivity values (\(\alpha\)), density (\(\rho\)), and specific heat capacity (Cp), the thermal conductivity (\(\lambda\)) values were calculated according to the following Equation (1): \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Carbon** & **Diameter** & **Length** & **Purity** & **Aspect Ratio** & \begin{tabular}{c} **Average** \\ **Thickness** \\ \end{tabular} & \
\begin{tabular}{c} **Specific Surface** \\ **Area (SSA)** \\ \end{tabular} &
\begin{tabular}{c} **Volume** \\ **Resistivity** \\ \end{tabular} \\ \hline MWCNTs & 9.5 nm (NC7000) & 1.5 \(\upmu\)m (OD) & 90\% & 150 & – & 250–300 m\({}^{2}\)/g & 10\({}^{-4}\)\(\Omega\).cm \\ \hline TNGNPs & 5\(-\)10 \(\upmu\)m & – & 99.5\% & 500 & 4–20 nm & – & 4 \(\times\) 10\({}^{-4}\)\(\Omega\).cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical data of the employed carbon nanomaterials. \[\lambda=\alpha\cdot\rho\cdot Cp. \tag{1}\]  
LFA and the reference sample were used to determine the specific heat capacity. In order to evaluate the influence of temperature on the thermal conductivity of the composites, the measurements were carried out at the following temperatures: 25, 50, and 75 degrees. A thermal imaging camera (TIM106S, Micro-Epsilon, Ortenburg, Germany) was used to monitor the temperature of the specimens during the electrical measurements. A hotplate stirrer was employed to heat the samples. The temperature was increased from 20 \({}^{\circ}\)C to 100 \({}^{\circ}\)C with a step of 10 \({}^{\circ}\)C. For value validation purposes, every measurement was repeated at least three times. The electrical resistance was determined by an oscilloscope (LCR Bridge HM8118, HAMEG Instruments, Mainhausen, Germany) with 0.5 s of acquisition time for 5 min. The morphology of the HDPE-based nanocomposites was observed by a scanning electron microscope (SEM, SH 4000M, Hirox, Oradell, NJ, USA).