The activation of sub-10 nm particles with water vapor requires a higher supersaturation S, which goes beyond the measurement range of most CCN counters, but falls into the range of water-based CPC. The water CPC is based on a similar working principle as a CCNC but running at a much higher S (Hering et al., 2005). High S reduces the critical activation size of particles so that “almost all” interested particles can be activated and detected (McMurry, 2000a, b). In theory, the counting efficiency curve of the CPC reflects the same composition dependence of aerosol particles as in the activation curve of the CCNC, but is extended to smaller size ranges (Fig. 3).

In practice, CPCs and CCNCs have different applications by making use of different parts of their activation curves. As shown in Fig. 3, the CPC is mainly used for the accurate particle counting, ideally operated at size ranges with activation fractions (Fact) equal to 1. The size-resolved CCN measurements are often designed to determine the whole activation curves, especially the composition-sensitive parts with Fact varying between 0 and 1.

Our nano-CCNC system adopted a similar design from previous size-resolved CCN measurements (Rose et al., 2008; Moore et al., 2010). Figure 4 exhibited the schematic of the whole system. It comprises of a nano-differential mobility analyzer (nano-DMA), a total particle counter (electrometer or ultrafine CPC with smaller critical detection size) and a nano-CCNC along with a neutralizer. The nano-CCNC is a water-based CPC with a control unit regulating the scan of S.

The measuring protocol of nano-CCNC is (1) to use a nano-DMA to select monodisperse particles of certain dry diameter (Dd); and (2) to measure the number concentration of total particles (Ntot) by the total particle counter and activated particles (Nact) at varied S by SS-CPC, respectively. This results in a size and supersaturation-resolved activation fraction, Fact=f(Dd,S). By scanning Dd and S, the whole 3-D activation spectra over the Dd-S plane can be achieved (Su et al., 2010). In practice, people can first keep Dd constant and vary S, then select another value of Dd and iterate the procedure as the “S scan” mode in CCN measurements (Dusek et al., 2006; Moore and Nenes, 2009; Snider et al., 2010). Alternatively, we could also first keep S constant and vary Dd as the “Dd scan” mode (Petters et al., 2009; Wiedensohler et al., 2009; Rose et al., 2011).

The scan of S can be achieved by (1) scanning the temperature gradient between the saturator and growth tube (by changing the saturator or growth tube temperature; Mordas et al., 2008; Kupc et al., 2013); (2) scanning the mixing ratio of saturator air and dilution air (Gallar et al., 2006) or saturator flow and aerosol flow (Vanhanen et al., 2011; Wimmer et al., 2013; Lehtipalo et al., 2014). The former approach, however, has not been actively pursued partly due to the relatively slow thermal response, limiting the time resolution of measurement to tens of minutes with current CPCs (McDermott et al., 1991). However, if we are only interested in a narrow size range, i.e., sub-10 nm or even a single size, it is still a feasible option, because relatively small number of sizes needs to be scanned. The scanning flow approach has better time resolution. In the work of Gallar et al. (2006), the flow scan is achieved by varying the mixing ratio of saturator and dilution air and their main purpose is to obtain particle size spectrum. After using fast-response flow controllers, time response of CPC (with a perfluorinated organic compound as the working fluid) could reach ∼1 second to the change of supersaturation.

Concerning the application of nano-CCNC, we proposed the following procedure. The first step is to characterize the calibration curve H(S); i.e., the cumulative supersaturation distribution of S that aerosol particles have been exposed to in the CPC, which will then be used to determine the characteristic activation supersaturation and hygroscopicity of aerosol samples for inferring chemical composition.

To demonstrate applications of the nano-CCNC, we used a WOx generator (Grimm Aerosol Technik, model 7.860; Steiner, 2006) to produce calibration tungsten oxide particles, and use an electrospray aerosol generator (TSI model 3480) to generate test nanoparticles (sodium chloride, ammonium sulfate and sucrose). The compress air and N2 were used as carrier gases for the WOx generator and electrospray aerosol generator, respectively. The salt and sucrose solutions were prepared in a standard 20 mM ammonium acetate buffer solution with a conductivity of 0.2 S m-1 (siemens per meter; Chen et al., 1995; Kupc et al., 2013).

As demonstrated in Fig. 4, the generated particles were passed through a neutralizer (Kr85, TSI model 3077), and a TSI nano-DMA (model 3085) was used to select positively charged monodisperse particles. A water-based CPC (TSI model 3788) was used as a nano-CCNC to measure Nact and a Faraday cup electrometer (Grimm Aerosol Technik, model 5.705) was used to measure Ntot. The variation of S distribution was achieved by varying the saturator temperature (Ts) from 284 to 296 K, while the growth tube temperature (Tgt) was fixed at 348 K. In total, seven H(S) distributions were measured and each temperature adjustment takes 150 s for stabilization.

As previously demonstrated, WOx particle was used to determine the H(S) under the different saturator temperatures. The S distribution that particles experienced inside the nano-CCNC was achieved by measuring the counting efficiency spectra from 2 to 10 nm. Following Eq. (2), we retrieve H(S) from the counting efficiency spectra for WOx particles (Fig. 6). As expected, H(S) was changed considerably by tuning the saturator temperature. Increasing the saturator temperature will reduce the temperature gradient and the supersaturation inside the growth tube. During the data retrieval process, we found that the activation curves for WOx particles represent a bimodal distribution. The following expression of a bimodal lognormal CDF was used to fit the activation curves: Fact=(50-a)⋅1+erfDd-D1σ12+a⋅1+erfDd-D2σ22.

Here, “erf” is the Gauss error function, a is the number fraction for one mode, D1 and D2 are the geometric mean values of particle diameter, and σ1 and σ2 are the standard deviations of the cumulative Gaussian distribution function.

For the conversion of Dd to Scri, we adopt the multilayer adsorption theory accounting for the very low solubility and hygroscopicity for WOx particles. The basic idea is to include an adsorption isotherm (FHH (Frenkel, Halsey and Hill) isotherm in this study) in the traditional Köhler theory instead of the solute term: S=exp⁡4σMwRTρwDexp⁡-AΘ-B, where D is the diameter of solution droplet. The parameter A characterizes interactions between adsorbed molecules and between the surface and adjacent adsorbate molecules, while B characterizes the attraction between the solid surface and the adsorbate in subsequent layers. For further details concerning the derivation and explanation of Eq. (10), we refer the reader to Sorjamaa and Laaksonen (2007).

The evaluation of parameters A and B in Eq. (10) are determined by the best fitting between measured and calculated activated fractions Fact for AS particles at 2.5 nm (Fig. 7), with values of 0.1 and 2.1, respectively. These values are located in the range of previous literature reports (0.1 < A < 3, 0.5 < B < 3; Sorjamaa and Laaksonen, 2007, and references therein). Our calculations suggest that with the appropriate parameter values, the activated fractions can be well predicted by the modified Köhler equation with FHH isotherm for the insoluble particles. For NaCl particles, it is difficult to predict Fact due to its uncertain shape factor. However, if we assume the volume equivalent diameter of ∼2.1 nm, we will get similar results as shown in Fig. 7.

For the determination of Scri, we choose 2.5 nm as the target diameter and select monodisperse NaCl, AS and sucrose particles as examples. The activation fractions were determined from results of the electrometer and SS-CPC. Similarly, seven saturator temperatures were tested in our experiments. Figure 8a shows distinct activation curves of various chemical compounds at 2.5 nm. For the same Ts (or S), NaCl shows the highest activation fraction Fact while WOx shows the lowest, which is consistent with their hygroscopicities. To reach the same Fact as NaCl, AS would require a ∼4 K lower Ts, i.e., a larger temperature gradient and S while a further lower Ts (∼10 K) is needed for sucrose. Such difference in the temperature gradient is significant enough in discriminating the investigated nanoparticles, much higher than the instrument noise ∼0.1 K. The hygroscopic-TDMA has been applied with Dd down to ∼6 nm (Biskos et al., 2006a, b; Swietlicki et al., 2008), while size-resolved measurements by traditional CCN counters are limited to Dd > 30 nm as previously mentioned. We now push this limit down to 2.5 nm.

Figure 8b shows the calculated Scri for various chemical compounds at 2.5 nm. Good agreement between the estimated and theoretical supersaturation has been achieved for AS particles, as indicated in Fig. 7. In summary, our results demonstrate that based on the determined H(S) distributions, the chemical compounds with different hygroscopicity can be separated distinctly, especially between representative inorganic (AS, S=55 % ± 5 %) and organic (sucrose, S= 67 % ± 1 %) compounds.

By measuring the activation behavior of sucrose-AS mixtures, we performed a preliminary test of the relationship between aerosol hygroscopicity and organic mass fraction (forg). The result shows a near-linear relationship between κ and forg for nanoparticles of 2.5 nm (Fig. 9). Here, forg is the mass fraction of sucrose in mixed solutes that were used to generate aerosol particles. In analogy to the ambient CCN measurements (Gunthe et al., 2009, 2011; Dusek et al., 2010; Rose et al., 2011, 2013), κ of lab-generated aerosols (mixtures of sucrose and AS) shows a decreasing trend with the increasing organic mass fraction. Note that the κ value of ∼ 0.4 for 2.5 nm AS particles is lower than the values reported for larger AS particles (∼ 0.5–0.8; Petters and Kreidenweis, 2007; Rose et al., 2008; Mikhailov et al., 2009, 2013), which can be attributed to the concentration dependence of aerosol particle hygroscopicity and nano-size effects on the thermodynamic properties of AS (Cheng et al., 2015).

As previously mentioned, the detection sensitivity of the electrometer precludes its application in ambient measurement. We suggest using the relative activation ratio RH/H0 as an alternative parameter. As shown in Fig. 10, different compounds exhibit distinct RH/H0 distributions (the ratio of Fact,T to Fact,11∘C). Their characteristic Scri can also be determined from RH/H0 by Eq. (6). Previous studies (Kulmala et al., 2014, and references therein) have demonstrated that both the ammonium sulfate and organics contribute to the subsequent growth of newly formed particles, which corresponds to the envelope between the AS and WOx profiles.

According to the Köhler equation, different temperatures will also lead to changes in Scri, introducing more complexity in the use of relative activation ratio. To solve this problem, we can take the scanning flow approach for the purpose of varying S so that the temperatures of the saturator and growth tube do not need to change.

The concept of scanning supersaturation (SS) is not limited to water-based CPCs, and may also work for CPCs with other working fluids, such as butanol, perfluorotributylamine (Gallar et al., 2006) as well as diethylene glycol (DEG; Vanhanen et al., 2011; Wimmer et al., 2013). In analogy to aerosol “hygroscopicity” describing the affinity for water, we introduce the term “solvoscopicity”, which from a broad sense, is the ability of a substance to attract and hold solvent molecules. Substances showing higher solvoscopicity for one working liquid may have lower solvoscopicity for another working liquid (Kangasluoma et al., 2014). For example, Fig. 11a–b show that NaCl is more hygroscopic (higher Scri and lower Dcri) than Ag but become less “solvoscopic” in butanol vapor.

The solvoscopic parameter can be used as “footprint” to estimate/distinguish the aerosol composition. However, it does not work once different substances show similar solvoscopicities, e.g., as sucrose and emery oil in butanol (Fig. 11c). This problem can be solved by performing additional measurements with water-based CPC, in which sucrose and emery oil show distinct hygroscopicities. Therefore, we suggest running multiple CPCs with different working fluids in a SS mode, which gives a SS-CPCB system. Compared to a single SS-CPC, SS-CPCB results in a multiple dimension of Scri enabling better inference of chemical composition. As shown in Fig. 11c, different inorganic and organic substances as well as metal can be easily distinguished in the 2-D solvoscopicity matrix. The existing CPCB systems (Kulmala et al., 2007; Riipinen et al., 2009; Kangasluoma et al., 2014) can be readily extended to a SS-CPCB system and produce multiple dimensional solvoscopicity matrix.