## 4 Results and Discussion  
The implemented experimental procedure was preliminary tested by measuring the mechanical properties of reference materials. PEN substates were chosen as a medium soft material. Figure 2a shows a semi-contact AFM image of an indent caused during indentation measurements by the tip on the PEN surface. Figure 2b shows the same image cropped and analyzed with the Gwyddion software, where the indent was overlaid with a red mask used to calculate the projected area. The mean value of projected area of the intend resulted \(A_{P}\approx\) 14,000 \(\pm\) 500 nm\({}^{2}\). From several force-distance curves acquired on different locations of the sample and using a Poisson ratio \(v_{sample}\) = 0.3 [47], the mean mechanical properties of PEN were measured to be equal to \(H\) = 0.70 \(\pm\) 0.05 GPa and \(E\) = 3.8 \(\pm\) 0.3 GPa, in quite good agreement with values reported in the literature [48]. HOPG is a high purity graphitic structure and can be considered as a reference in the analysis of the properties of soot particles. Figure 3 shows a semi-contact AFM image of an indent on the HOPG surface (Figure 3a) and the same image cropped and analyzed with the Gwyddion software (Figure 3b). The hardness measured on HOPG samples by AFM from the mean projected area, \(A_{P}\approx\) 18,000 \(\pm\) 700 nm\({}^{2}\), was found H = 2.40 \(\pm\) 0.10 GPa. This value is in good agreement with previously reported measurements performed on HOPG [21; 44; 49]. Instead, the analysis of the retraction curves with the DMT model using a Poisson ratio \(v_{sample}\) = 0.2 [44] resulted in an underestimation of the [PERSON]'s modulus. The mean measured by [PERSON]'s modulus was \(E\) = 7.5 \(\pm\) 0.3 GPa, significantly lower than the reported values \(E\) = 15-20 GPa [44; 50]. This difference is possibly due to the experimental  
Figure 2: Semi-contact AFM image of an indent on PEN surface (**a**); same image as in the upper panel after cropping and analysis with the software Gwyddion (**b**). set-up. The tip used in this study is characterized by a spring constant which has proved to be suitable for measuring the elastic modulus, as well as the hardness, on medium-soft samples (_E_ < 10 GPa). On the other hand, the spring constant of the cantilever is likely too low to properly perform an elastic deformation at small indentation depths on a medium-hard sample such as HOPG (_E_ > 10 GPa), thus affecting the accuracy of the calculation of the Young's modulus from the retraction force-distance curve using the DMT model. This deviation could likely be corrected by using a cantilever with a higher spring constant (_Kc_ > 100 N/m) on such a hard sample. We now shift our attention to flame-formed carbon nanoparticle samples. Sample #1 films were produced in flame conditions characterized by a bimodal particle size distribution with a first particle mode of 2-4 nm and a second mode of 12-15 nm [51]. Sample #2 films were produced in flame conditions in which >10 nm soot particles and aggregates are mainly produced and characterized by a higher graphitization degree compared to Sample #1 particles [6; 18]. The two samples for indentation measurements were collected by thermophoretic sampling inserting the substrate in the flame 100 times (Sample #1) and 25 times (Sample #2), with a fixed residence time of 100 min. The thermophoretic sampling procedure was already used to synthesize nanostructured films of carbon nanoparticles in similar flame reactors [6; 52]. The thicknesses of the two samples were estimated using a model for the calculation of the particle film growth rate based on the thermophoretic velocity previously developed [52; 53] and found to be 100 \(\pm\) 25 nm for Sample #1 and 200 \(\pm\) 25 nm for Sample #2. In this study, the procedure and the total sampling times were chosen to produce thick nanoparticle films covering the whole substrate, so avoiding any interaction between the AFM tip and the mica muscovite substrate that may affect the nanoindentation measurement of the samples.