## 1 Introduction  
The modelling and experimental activities performed in the last decades to study the formation process of soot particles in combustion systems has led to substantial progresses [1, 2]. Flame-generated particulate matter is rightly considered an environmental issue. Several studies have pointed out that ultra-fine combustion-formed particles are responsible for different adverse effects on human health [3, 4]. Furthermore, soot particle emissions can lead to severe affection of the climate system [5]. On the other hand, a flame can be also seen as a reactor for the synthesis of engineered novel carbonaceous nanomaterials [6, 7, 2]. In light of the above, a deep understanding of the chemistry and the morphology of flame-formed carbon nanoparticles is required to control the synthesis of soot particles in flames for both the aforementioned objectives. Some of the properties that characterize soot particles and soot particle films have been already studied and analyzed, including particle size, morphology, carbon and nanostructure [8, 9, 10, 11], optical and electronical features [6, 12, 13, 14, 15, 16, 17], surface properties and interaction forces [18, 19, 20]. However,very little is known about the mechanical properties, such as hardness and elastic modulus. Some theoretical and experimental works have been published [21; 22; 23], showing that the mechanical properties of different singlet carbon particles can provide an indication for the crosslinking and the carbonization degree [22; 23]. The mechanical behavior and the physical nanostructure of soot particles also proved to be useful in understanding tribological effects, such as the enhanced wear of mating surfaces covered with soot particles [24]. This mechanism is particularly relevant in internal combustion engines which use soot-contaminated oil and lubricants [25] and it could be applied also for designing diesel particulate filters and their regeneration processes. Recently, the fabrication of coatings using flame-formed carbon nanoparticles has become very attractive as a novel approach for the synthesis of surfaces with enhanced properties. Nanostructured thin films of carbon nanoparticles from different flame synthesis reactor configurations are produced as water-repellent, superhydrophobic surfaces [26; 27; 28], electrode materials for supercapacitors [29] and hole extractor for perovskite solar cells [30]. The characterization of the mechanical properties provides novel information to tune and modify the synthesis process for realizing more robust, durable and stable soot particle films, as required for the aforementioned applications. Consequently, an experimental investigation of the mechanical properties of flame-formed soot nanoparticles collected as nanostructured films could be a useful addition to the literature, as well as a piece of work of great relevance from a material science point of view. Several well-established techniques exist on the macro-scale and on the micro-scale to characterize the mechanical behavior of a given material. Particularly, the indentation technique allows measuring the mechanical properties by indenting the material, i.e., by pressing a probe at a defined force on the sample surface in order to deform it. Techniques with nanometric resolution are required to characterize and test nanosized and nanostructured materials [31]. To this aim, nanoindentation characterizations based on Atomic Force Microscopy (AFM) are becoming increasingly attractive. The most important advantages of AFM nanoindentation are the measurement of mechanical properties simultaneously with surface topography, the unique force sensitivity of the technique (down to nNewton) and the probe size in the order of nanometers, which are essential to perform indentation and molecular pulling experiments at the nanoscale [32; 33; 34]. In this paper, an experimental investigation of nanomechanical properties of flame-formed carbonaceous particles has been performed for the first time by means of AFM nanoindentation.