## 1 Introduction
In addition, according to the percolation theory [40], the aerosol loading has to exceed a critical surficial concentration value in order to create a continuous conductive path. A further factor that affects electrical bridging caused by deposited particles is that the conductance of aerosols can be different as a function of their physical state. If the aerosol particles are hydrated (i.e., over the DRH with increasing RH or over the CRH if RH is decreasing from above the DRH) the ionic components spontaneously dissolve, creating a conductive electrolytic solution. Therefore, hygroscopic particles can potentially originate conductive paths and cause electrical leakage [41]. Consequently, in literature, hygroscopic aerosol is believed to be the major responsible for printed circuit boards (PCBs) failures [1; 38; 39; 42; 43]. The aerosol induced failures in indoor environment are also extremely connected with energy consumption. In recent studies, [PERSON] et al. [18; 20] performed aerosol conductance measurements in function of RH in order to set-up safe thermodynamic ranges for the electronic equipment installed indoor in \"green\" Free-Cooled Data Centers to avoid any failure. Green Free-Cooled Data Centersconsists of data centers in which outdoor air is used to cool the information technology equipment (i.e., high-performance calculators) within a data center. However, traditionally, in order to avoid any corrosion and failure, data centers cool the hot air produced by the information technology using air-conditioning units through a closed-loop air cycle also drying the recycled air. This approach is responsible for a \(\sim\)35-50% of energy consumption in a data center just for the cooling process [33; 34; 44]. As a result, data centers are responsible for more than 2% of worldwide electricity consumption [45]. In an alarmist scenario, [PERSON] and [PERSON] [46] suggested that the global power demand of data centers could reach as much as 13% of global electricity use in 2030, corresponding to a 14-fold increase compared with the 1.1 to 1.5% of the global electricity use, in 2010 [47]. However, [PERSON] [48] revised this value to 3% in 2025. [PERSON] et al. [18; 20] demonstrated that a safe use (i.e., avoiding ions deliquescence) of the Free-Cooling approach (which avoid the air-conditioning usage) leads to an energy saving up to 80% of the cooling process allowing to avoid the emissions of tens of ktons of CO\({}_{2}\) and other absorbing material into the atmosphere. This is beneficial also in a climate change mitigation perspective [49; 50]. In this respect, it is well-known that aerosol components other than the ionic inorganic fraction are hygroscopic, consequently be involved in this kind of phenomena [51; 52]. Examples are carboxylic acids and other organic compounds classes [53; 54; 55; 56; 57; 58]. Most important, it has been demonstrated that even non-electrolyte substances (e.g., sucrose) can induce a deterioration of PCB components [59]. Among the non-electrolyte substances, the elemental carbon (EC) could play a significant role. Briefly, elemental carbon indicates carbonaceous particles deriving from combustion processes and composed of graphene layers with small contents of heteroatoms, especially oxygen and hydrogen [60; 61; 62]. Often the term \"soot\" is improperly used as a synonymous of elemental carbon especially when laboratory flame carbonaceous material is generated. Here this term is introduced as it was proven that flame generated soot can be electrically conductive [63], even if the measured conductivity values (between 10\({}^{-6}\) and 10\({}^{-2}\)\(\Omega^{-1}\) cm\({}^{-1}\), depending on the sample density and on the fuel used for soot production) could be lower than those of pure graphite (between 10\({}^{-3}\) and 10\({}^{-1}\)\(\Omega^{-1}\) cm\({}^{-1}\), depending on the sample density).