The experiments were carried out with the CLOUD chamber at CERN, which has been described by Kirkby et al. (2011), Almeida et al. (2013) and Duplissy et al. (2015). In brief, the CLOUD chamber is a cylindrical electropolished stainless-steel tank with a volume of 26.1 m3.An ultraviolet (UV) light system which can control the aperture of the UV light (Kupc et al., 2011) and two stainless-steel fans for mixing vapors (Voigtländer et al., 2012) are installed in the chamber. During CLOUD7 experiments, temperature and relative humidity in the chamber were constant at 278 K (±0.5 K) and 38 % (±1 %), respectively. The experiments were classified into three groups depending on the nucleation conditions: neutral (N), ground-level galactic cosmic rays (GCRs), and charged pion beam (π). In the neutral nucleation experiments, small ions in the chamber were removed with electric fields (±20 kV). The chamber was exposed to a positively charged pion beam (Duplissy et al., 2010) during the charged-pion-beam nucleation experiments, whereas no electric clearing fields and no pion beam were used under GCR conditions. Precursor vapors such as sulfur dioxide (SO2), dimethylamine ((CH3)2NH), and α-pinene (C10H16) were continuously provided into the CLOUD chamber to produce particles.

Size distributions of particles produced in the chamber were continuously monitored with a scanning mobility particle sizer (SMPS). The sulfuric acid concentration was measured using a chemical ionization mass spectrometer (CIMS) (Kürten et al., 2011); concentrations of dimethylamine, ammonia, and α-pinene were observed with a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS) (Schnitzhofer et al., 2014). The concentrations of SO2 and O3 were also continuously measured by an SO2 detector (42i-TLE, Thermo Fisher Scientific, Inc.) and an O3 monitor (TEI 49C, Thermo Environmental Instruments), respectively. The detailed experimental conditions performed in this study can be seen in Table 1.

The nano-HTDMA system (Keskinen et al., 2011) was applied to determine the hygroscopic growth of nucleated nanoparticles at a constant subsaturated relative humidity. It consisted of two different mobility analyzers (DMA1 and DMA2; TSI 3085, USA) (Chen et al., 1998), an aerosol humidifier, and a condensation particle counter (CPC; TSI 3785, USA), as shown in Fig. 1. The TDMA measurement technique has been described in previous studies (McMurry and Stolzenburg, 1989; Hämeri et al., 2000; Sakurai et al., 2005). Briefly, nanoparticles generated in the CLOUD chamber were dried to about 10–15 % RH and then passed through a bipolar diffusion charger (85Kr, TSI) before entering the nano-HTDMA system. The nanoparticles with a certain electrical mobility were classified from charged polydisperse aerosols by DMA1. The RH of aerosol sample after passing through DMA1 was ∼ 4.5 %. The selected nanoparticles passed through the aerosol humidifier made out of GoreTex tubing with a 5 s residence time at the targeted RH. This residence time should be enough for the particles to reach their equilibrium GF (Duplissy et al., 2009). The RH of the aerosol flow, the sheath air, and the excess air in DMA2 were continuously monitored using capacitive RH sensors (Vaisala model HMP 110). The RH was kept constant to within 1.5 % of the set values. After humidifying, the size and number concentration of the particles were measured with DMA2 and the CPC to determine the change in particle size due to interaction with water vapor. Based on these results, lognormal number size distributions were fitted to the distributions to estimate the geometric mean diameter (GMD) with a standard DMA data inversion algorithm (Reischl, 1991). The use of GMD is relevant for this study as the sampled aerosol was internally mixed. In this study, the measurements were performed at 90 ± 1.5 % RH for 10 and 15 nm particles. The flow rate of the aerosol sample was 1 L min-1. The ratio of sample aerosol flow to sheath air flow of the DMA was 1 : 10. The size and RH calibration of the nano-HTDMA was carried out by using ammonium sulfate nanoparticles before, during, and after the CLOUD7 experiments. The RH calibration was done by measuring the efflorescence and deliquescence RH of ammonium sulfate particles and by comparing the values to the theoretical values.

The hygroscopic growth factor (HGF) is a measure of the diameter growth of the size-selected particles at a certain RH compared with dry conditions and is defined as HGF=dp,GMD(RH)dp,GMD(dry), where dp,GMD (RH) is the GMD of the particles at the elevated RH (ca. 90 %) and dp,GMD (dry) is the GMD for particles at dry conditions (∼ 4.5 % RH).

In many cases it is useful to represent hygroscopic properties with a single hygroscopicity parameter κ, defined by Petters and Kreidenweis (2007) as κ=HGF3-1KeS-1, where S is the saturation ratio (S=RH100) and Ke the Kelvin factor, defined as Ke=exp⁡4MwσwRTρwdp. Here Mw is the molecular weight of water, σw the surface tension of the water, R the ideal gas constant, T the temperature, ρw the density of water, and dp the diameter after humidification (dp,GMD (RH) =dp,GMD (dry) × HGF). The κ values are in the range of 0 for insoluble particles such as black carbon to larger than 1 for water-soluble salt particles (Jurányi et al., 2009; Petters and Kreidenweis, 2007).

In order to obtain indirect chemical composition information from the nano-HTDMA results in experiments B–D (Table 1), we use the ZSR relation, which assumes that the water uptake volume of a mixture is the independent sum of the water uptake volume of each individual component. The organic volume fraction can then be estimated by assuming a two-component system consisting of organic and inorganic sulfate as (Keskinen et al., 2013) εDMAS=κ-κinorgκDMAS-κinorg, where κ is the hygroscopicity obtained from the nano-HTDMA measurements and κDMAS and κinorg are the hygroscopicity parameters for DMAS and inorganic sulfates, respectively. Although ammonia was not injected into the chamber during these experiments, measurements by the Thermal Desorption Chemical Ionization Mass Spectrometer (TDCIMS; Smith et al., 2004) showed that ammonium is a significant constituent of 5–20 nm particles during these new-particle-formation events (Lawler et al., 2016). Therefore, we calculated the DMAS volume fraction by assuming that the inorganic sulfates in the particles are either sulfuric acid or ammonium sulfate. Keskinen et al. (2013) showed that the hygroscopic properties of particles at a diameter of 150 nm in the presence of sulfuric acid and ammonia are in good agreement with theoretical predictions of ammonium sulfate. The κinorg values of sulfuric acid and ammonium sulfate were assumed as 0.70 (Sullivan et al., 2010) and 0.47 (Topping et al., 2005), respectively. The κDMAS was assumed as 0.28 derived from hygroscopic growth factors for dry diameters 80–240 nm measured by Qiu and Zhang (2012).

The E-AIM was used to estimate the molecular ratio of bases and acids for particles consisting of sulfuric acid, dimethylamine, and ammonia. In the model, acid deprotonation and base protonation are taken into account in the aqueous phase. Sulfuric acid is a strong acid and is assumed to deprotonate at least singly when present in aqueous solutions. It may also deprotonate a second time to form sulfate ions. Dimethylamine and ammonia are bases that have a single protonation product. Mole fractions of the deprotonated acids and protonated bases are estimated using the acid dissociation constants of the compounds defined in E-AIM (Ge et al., 2011). The density of the aqueous solution in the model is parameterized according to Clegg et al. (2013), and the surface tension is obtained from measurements by Hyvärinen et al. (2004). The E-AIM does not take into account the surface curvature of particles. Thus, when estimating the water uptake of a nanoparticle with a certain dry size and composition, the equilibrium vapor pressure for water vapor obtained from E-AIM needs to be corrected for the Kelvin effect by multiplication with the Kelvin term, which requires iterating to find the equilibrium.

Based on the TDCIMS observation (Lawler et al., 2016), we assumed that particles consisted of sulfuric acid, dimethylamine, and ammonia and that the base in the particle consisted of 50 % dimethylamine and 50 % ammonia. Also, we assumed that no particle evaporation took place in the sampling lines or in the instrument. The assumption was tested by modelling the particle evaporation in the sampling lines and inside the HTDMA, and based on the model results the evaporation was negligible (Ahlm et al., 2016). By calculating the water uptake (and the resulting HGF) in E-AIM for particles of different base / acid molecular ratios, the composition of the particles could be estimated.

In this section, the role of dimethylamine or secondary organic compounds from the oxidation of α-pinene in defining the hygroscopicities of nanoparticles is investigated (Exps. A and D–F). The concentrations of sulfuric acid, dimethylamine, and α-pinene in the chamber for the different experiments are shown in Table 1. The κ values of 10 and 15 nm particles produced by sulfuric acid, sulfuric acid–dimethylamine, and sulfuric acid–organics are shown in Fig. 2. In Exp. A, the hygroscopicities of particles in the presence of sulfuric acid only were examined. The κ values (± standard deviation) of nucleated nanoparticles were 0.64 ± 0.02 and 0.52 ± 0.02 for 10 and 15 nm, respectively (the HGF of 10 and 15 nm particles were 1.55 ± 0.02 and 1.56 ± 0.02, as shown in Table 1). Here the error bars represent the standard deviation of the measurements from the mean value. The κ values are slightly lower than previous results for sulfuric acid (κH2SO4∼ 0.7) reported elsewhere (Shantz et al., 2008; Sullivan et al., 2010). Also, the theoretical value for κH2SO4 for 10 nm particle at 90 %, corresponding to our experimental conditions (residual water taken into account) and calculated by E-AIM, is 0.7 (at 90 % RH). In should be noted that the sulfuric acid solution droplet is highly unideal. Hence, the calculated κ value from E-AIM depends strongly on both humidity and particle size. The reason for the lower measured κ values of the nucleated nanoparticles can be twofold: (1) existence of trace levels of contaminants such as ammonia and dimethylamine in the chamber and/or (2) residual water in the nanoparticle after passing through DMA1. Although we supplied only sulfuric acid to the chamber and an overnight cleaning cycle (100 ∘C for 12 h) was performed to remove contaminants before experiments, the atmospheric pressure interface time-of-flight mass spectrometer (APi-TOF) measurements showed that trace levels of ammonia and dimethylamine still remained in the clusters (< 2 nm) (Bianchi et al., 2014), most probably due to wall adsorption from previous experiments. Ammonia and dimethylamine were also found in the nanoparticles (< 40 nm) from TDCIMS measurements (Lawler et al., 2016). This observation suggests that trace levels of these ammonia and dimethylamine in the chamber may be present in the nucleated nanoparticles, hence decreasing the κ values.

The hygroscopic properties of nucleated nanoparticles in the presence of sulfuric acid and dimethylamine were determined in Exp. D. Although dimethylamine was continuously supplied into the chamber to maintain a concentration of 23.8 ppt, the observed κ values for 10 nm particles agree to within 4 % with the results for particles in the presence of sulfuric acid, as can be seen in Fig. 2. In the case of the 15 nm particles, however, the hygroscopicities of sulfuric acid–dimethylamine particles were 12 % lower than those for sulfuric acid particles. This decline of hygroscopicity for 15 nm particles is probably caused by an increasing amount of aminium salts during the growth process. The E-AIM model results show that the observed decreases in κ values could be explained by decreasing particle acidity with increasing particle size, as shown in Table 2. Our results indicate that the ratio of dimethylamine to sulfuric acid increases when particles grow from 10 to 15 nm. It should be noted that the monodisperse particle growth model MABNAG (Model for Acid-Base chemistry in NAnoparticle Growth) predicts lower acidity in the 10 and 15 nm particles than do the HTDMA-based estimates under the same experimental conditions (Ahlm et al., 2016). The reason for this discrepancy is still unknown; it may be related to measurement uncertainties in the 10–15 nm size range, or to the incomplete understanding of the growth process of particles formed from sulfuric acid and dimethylamine. Chan and Chan (2013) observed evaporation of dimethylamine from aminium sulfate particles upon drying at 3 % RH using an electrodynamic balance. Ouyang et al. (2015) also concluded that dry particles consisting of dimethylamine and sulfuric acid in the size range of 5–8.5 nm would be unstable under ambient conditions. In our HTDMA measurements the particles were dried before measuring the growth factor; therefore some of the dimethylamine may have evaporated from the particles prior to growth factor measurements, increasing the acidity of the particles. Based on the thermodynamic condensation model simulation, the base / acid molar ratio may have decreased in the sampling line as much as 15 % (in the experiment with 40 ppt of dimethylamine) (Ahlm et al., 2016) compared to the value in the chamber. However, the difference between the base / acid ratio of growing particles predicted with the model and that derived from measured growth factors is much larger than this. It is, therefore, unlikely that evaporation of dimethylamine alone would explain this discrepancy.

We also investigated the hygroscopicities of nanoparticles produced in the chamber in the presence of α-pinene, sulfuric acid, and O3 (Exps. E and F). In these experiments, hydrogen (H2) was added to suppress OH radicals from α-pinene ozonolysis in order to probe the role of ozonolysis alone on new particle formation (Praplan et al., 2015). Although the concentrations of sulfuric acid were higher during the sulfuric acid–organics experiments than during the sulfuric acid–dimethylamine experiments, the HGFs of particles in the presence of sulfuric acid and organics were much smaller than those of particles in the presence of sulfuric acid and dimethylamine, as can be seen in Table 1. As shown in Fig. 2, the hygroscopicity of 10 nm particles when α-pinene ozonolysis products are present is significantly lower than observed in the sulfuric acid or sulfuric acid–dimethylamine experiments; moreover it decreases with increasing size. It has previously been reported that the hygroscopicity of organics from α-pinene oxidation is clearly lower than the hygroscopicity of sulfuric acid (or ammonia-containing sulfate compounds) (Qiu and Zhang, 2012; Massoli et al., 2010). Hence, the present results indicate that the organic-oxidation products contribute significantly to the composition of both 10 and 15 nm particles and, thereby, to their growth.

We also investigated the effect of sulfuric acid concentration on the hygroscopicity of 10 and 15 nm particles (Exps. B–D); while SO2 and dimethylamine were continuously added to the chamber at a constant rate, the UV light intensity was varied by changing the light aperture. The sulfuric acid monomer concentrations at an aperture of 20, 40, and 100 % UV were 5.1 ×106, 7.6 ×106, and 12.3×106 molecules cm-3, respectively; in the discussion that follows we will refer to these concentrations as low, medium, and high, respectively. The growth rate (GR) of particles from 4 to 15 nm diameter increases from 2.35 to 8.41 nm h-1 with increasing sulfuric acid concentration from 5.1×106 to 12.3×106 molecules cm-3. The large increase in the GR is probably due to a combination of the enhanced kinetic condensation of sulfuric acid (and dimethylamine) molecules and the increase in the number concentration of the formed particles, enhancing growth by coagulation (Ahlm et al., 2016). However, there were no remarkable differences among the hygroscopicities of 10 nm particles, as shown in Fig. 3a. The κ values (± standard deviation) of the 10 nm particles were 0.58 ± 0.01, 0.60 ± 0.01, and 0.61 ± 0.02 for low, medium, and high sulfuric acid concentrations, respectively. This suggests that the composition of 10 nm particles does not change significantly over this range of sulfuric acid and dimethylamine gas-phase concentrations.

In contrast to the insensitivity of hygroscopicity for 10 nm particles to sulfuric acid levels, the hygroscopicity of 15 nm particles increases with increasing gas-phase sulfuric acid (i.e., with increasing UV intensity). The κ values (± standard deviation) were 0.31 ± 0.01, 0.42 ± 0.02, and 0.45 ± 0.02 for low, medium, and high sulfuric acid concentrations, respectively. Especially, the κ value for the low gas-phase sulfuric acid concentration was close to that of DMAS at 90 % RH (κDMAS∼ 0.28) (Qiu and Zhang, 2012). This suggests that more aminium salts were involved in 15 nm particles with decreasing gas-phase sulfuric acid concentrations. The DMAS volume fractions (± standard deviation) derived from Eq. (4) using experimentally derived sulfuric acid hygroscopicity for the inorganic sulfate (κinorg= 0.70) varied from 0.29 ± 0.03 to 0.20 ± 0.05 for 10 nm particles and from 0.92 ± 0.02 to 0.58 ± 0.03 for 15 nm particles depending on the gas-phase sulfuric acid concentrations (Fig. 3b). Due to the observation of ammonia in the particles the DMAS volume fraction in 10 nm particles was also calculated assuming that the inorganic fraction was ammonium sulfate (κinorg= 0.47) to investigate how much the uncertainty in inorganic composition can affect the calculations. This assumption resulted in lower DMAS volume fractions for 15 nm particles compared to the assumption of inorganic sulfate being sulfuric acid (Fig. 3c). The measured κ of 10 nm particles were too high to be explained with a combination of ammonium sulfate and DMAS. In summary, with each value of κinorg there is a clear increase in the DMAS volume fraction from 10 to 15 nm. Hence our measurements support the view that the contribution of dimethylamine to particle growth increases with increasing particle size.