## 2 Materials and Methods
### Conductance Measurements  
The determination of the conductance in function of RH, and thus the determination of both DRHs and CRHs of the collected aerosol samples was performed in a specifically designed Aerosol Exposure Chamber (AEC) [8; 18; 19]. The AEC is a sealed 1 m\({}^{3}\) glass chamber in which the collected aerosol samples are exposed to humidification and dehumidification cycles, from 30 to 90% RH and vice versa, with RH steps of 1%. The RH is varied inside the chamber by introducing either dry or moist pure air in it (Aria Zero, Sapio), while the temperature is kept constant at 25 \({}^{\circ}\)C (the fixed temperature cooling of the Free-Cooling data center, see [PERSON] et al. [18; 20]). Temperature and relative humidity were monitored by means of a thermo-hygrometric sensor (DMA672 coupled with an ELO008 Data-Logger, LSI-Lastem, \(\pm\)1% RH and \(\pm\) 0.1 \({}^{\circ}\)C accuracy) during the whole cycle. As reported in D'Angelo L. [80], equilibration tests were performed monitoring the electrical response and RH with 30 min step each within the AEC in order to observe the time needed to reach the equilibrium in conductance measurements. Figure S2a (Supplementary Materials) shows a typical equilibration time experiment. During 30 min, the RH conditions resulted to be constant with a fluctuation of less than 0.5% RH and this produced a constant electrical response (Figure S2a, Supplementary Materials). However, whenever RH exhibit small variations (e.g., in Figure S2b,c at 56% and 58% RH) the electrical conductance followed RH in perfect agreement (R\({}^{2}\) = 0.915). Moreover, Figure S3 reports conductance for each RH steps at 0 s, 180 s, 1200 s and 1800 s for the sample showed in Figure S2a. As the conductance was constant and reached very fast (i.e., seconds) the equilibration, the conductance measurements were carried out waiting two minutes after that the RH reached the target value to avoid any random fluctuations. As a result, each experiment (humidification and dehumidification) lasted \(\sim\)4 h.  
Within the AEC, up to 6 aerosol samples can be housed at a time in specifically-designed PTFE filter holders, each provided with a pair of electrodes that allowed the measurement of the electrical resistance of the deposited aerosol at each RH step. The electrodes were set at a fixed calibrated distance of 5 mm (a balance between inter soldier parts on PCB board, size of PTFE filters) and the electrical measurements were performed with a 3421A Data Acquisition Unit (Hewlett-Packard, 0-30 M\(\Omega\) measured resistance range). With respect to the electrodes, any influence of their mechanical pressure applied to samples is negligible as previously demonstrated [80]. This result was obtained by measuring via AEC the conductance signal on the same PM\({}_{2.5}\) sample (collected on PTFE filters) a second time. In this respect an example of a sample exposed to two RH cycles is reported in Figure S4 (Supplementary Materials): the profiles highlighted a good repeatability (R\({}^{2}\) = 0.99, slope = 1.032) of the measurements. During the humidification phase, the hygroscopic components of the aerosol samples promote water uptake and a steep increase in the samples' conductance can be observed in correspondence to the deliquescence of water-soluble compounds, because of the formation of a conductive electrolytic solution. On the contrary during dehumidification, when a strong decrease in conductance is measured, the crystallization of water-soluble compounds occurs. Thus, DRH and CRH values of each sample can be determined in correspondence to the maximum conductance gradient in the humidification and dehumidification curves respectively, according to the method reported by [PERSON] et al. [18] and validated in [PERSON] et al. [8]. A typical plot of the measured conductance as a function of the RH applied in the chamber is shown in Section 3.1.