Interactions of organosulfates with water vapor under sub- and supersaturated conditions

. Organosulfates (OSs) are important constituents of secondary organic aerosols, but their hygroscopic properties and cloud condensation nucleation (CCN) activities have not been well understood. In this work we employed three complementary techniques to characterize interactions of several OSs with water vapor under sub- and supersaturated conditions. A vapor sorption analyzer was used to measure mass changes in OS samples with relative humidity (RH, 0 among the 11 organosulfates examined, only sodium methyl sulfate (methyl-OS), ethyl sodium octyl sulfate (octyl-OS) were their

Abstract. Organosulfates (OSs) are important constituents of secondary organic aerosols, but their hygroscopic properties and cloud condensation nucleation (CCN) activities have not been well understood. In this work we employed three complementary techniques to characterize interactions of several OSs with water vapor under sub-and supersaturated conditions. A vapor sorption analyzer was used to measure mass changes in OS samples with relative humidity (RH, 0 %-90 %); among the 11 organosulfates examined, only sodium methyl sulfate (methyl-OS), sodium ethyl sulfate (ethyl-OS), sodium octyl sulfate (octyl-OS) and potassium hydroxyacetone sulfate were found to deliquesce as RH increased, and their mass growth factors at 90 % RH were determined to be 3.65 ± 0.06, 3.58 ± 0.02, 1.59 ± 0.01 and 2.20 ± 0.03. Hygroscopic growth of methyl-, ethyl-and octyl-OS aerosols was also studied using a humidity tandem differential mobility analyzer (H-TDMA); continuous hygroscopic growth was observed, and their growth 7136 C. Peng et al.: Interactions of organosulfates with water vapor under sub-and supersaturated conditions sorbing solar and terrestrial radiation and also indirectly by acting as cloud condensation nuclei (CCN) or ice-nucleating particles (Moise et al., 2015;Shrivastava et al., 2017). Consequently, it is important to understand the source, formation and physicochemical properties of SOA (Pöschl, 2005;Jimenez et al., 2009;Noziere et al., 2015;Peng et al., 2020). However, SOA concentrations on the global scale are significantly underestimated by many modeling studies (Heald et al., 2005;Kanakidou et al., 2005;Ervens et al., 2011;Mc-Neill et al., 2012;Shrivastava et al., 2017), indicating that there might exist unknown while important precursors and/or formation mechanisms of SOA.
As OSs are ubiquitous in the troposphere, it is important to understand their hygroscopic properties and CCN activities in order to assess their environmental and climatic effects (Kanakidou et al., 2005;Moise et al., 2015;Tang et al., 2016Tang et al., , 2019a, especially considering that OS could contribute up to 30 % of total mass of organic aerosols in the troposphere (Surratt et al., 2008;Tolocka and Turpin, 2012;Liao et al., 2015). However, to our knowledge, only two previous studies have explored their hygroscopic properties and CCN activities (Hansen et al., 2015;Estillore et al., 2016). Hansen et al. (2015) investigated hygroscopic growth and CCN activation of limonene-derived OS (with a molecular weight of 250 Da) and their mixtures with ammonium sulfate. Hygroscopicity of pure limonene-derived OS was weak, and its hygroscopic growth factors were determined to be 1.0 at 80 % relative humidity (RH) and 1.2 at 93 % RH (Hansen et al., 2015). Estillore et al. (2016) investigated hygroscopic growth of a series of OSs, including potassium salts of glycolic acid sulfate, hydroxyacetone sulfate, 4-hydroxy-2,3-epoxybutane sulfate and 2-butenediol sulfate, as well as sodium salts of benzyl sulfate, methyl sulfate, ethyl sulfate and propyl sulfate. Continuous hygroscopic growth (i.e., without obvious deliquescence) was observed for these OS aerosols (Estillore et al., 2016); in addition, their hygroscopic growth factors at 85 % RH were determined to vary between 1.29 and 1.50, suggesting that their hygroscopicity showed substantial variation. In summary, it is fair to state that hygroscopic properties and CCN activities of OS have not been well understood.
In this work, three complementary techniques were used to investigate hygroscopic properties and CCN activities of a series of OSs, including sodium methyl sulfate, sodium ethyl sulfate, sodium octyl sulfate, sodium dodecyl sulfate, potassium hydroxyacetone sulfate, potassium 3-hydroxy phenyl sulfate, potassium benzyl sulfate, potassium 2-methyl benzyl sulfate, potassium 3-methyl benzyl sulfate, potassium 2,4dimethyl benzyl sulfate and potassium 3,5-dimethyl benzyl sulfate. A vapor sorption analyzer was employed to measure mass change in these OS samples as a function of RH. In addition, hygroscopic growth (change in mobility diameters) and CCN activation of submicron aerosol particles were studied for sodium methyl sulfate, sodium ethyl sulfate and sodium octyl sulfate, using a humidity tandem differential mobility analyzer (H-TDMA) and a cloud condensation nuclei counter (CCNc). Due to their very limited quantities, we could not carry out H-TDMA and CCNc measurements for other OS samples which were synthesized by us. In addition, we also investigated the impacts of sodium methyl sulfate, sodium ethyl sulfate and sodium octyl sulfate on hygroscopic properties and CCN activities of ammonium sulfate.
2 Experimental section

VSA experiments
A vapor sorption analyzer (VSA), commercialized by TA Instruments (New Castle, DE, USA), was used to measure mass change in organosulfates as a function of RH. Experimental details can be found in our previous studies (Gu et al., 2017;Chen et al., 2019;Guo et al., 2019;Tang et al., 2019b) and are thus described here briefly. Experiments were conducted at 25 ± 0.1 • C and in the RH range of 0 %-90 %. A high-precision balance was used to measure the sample mass at different RHs with a stated sensitivity of < 0.1 µg, and the dry mass of samples used in this work was typically around 1.0 mg.
Changes in RH and normalized mass of a CH 3 SO 4 Na sample with time are displayed in Fig. 2 as an example to illustrate the VSA experimental procedure. As shown in Fig. 2, the mass of OS samples at different RHs was determined by the VSA using the following method. RH was set to < 1 % to dry the sample; after the sample mass was stabilized, RH was increased to 90 % stepwise with an interval of 10 % per step; at the end, RH was changed back to < 1 % to dry the sample again. The sample was considered to reach the equilibrium at a given RH when the mass change was measured to be < 0.1 % within 30 min. All the experiments were conducted at least three times in our work. The sample mass at a given RH (m) was normalized to that at < 1 % RH (m 0 ) to determine the mass growth factor, defined as m/m 0 .

H-TDMA experiments
A custom-built hygroscopicity tandem differential mobility analyzer (H-TDMA) was used to measure the mobility diameters of OS aerosol particles at different RHs (5 %-90 %) at 24 ± 1 • C. The instrument was detailed elsewhere Peng et al., 2016), and therefore only a brief introduction is given here. A commercial atomizer (MSP 1500) was used to produced polydisperse aerosol particles from dilute OS solutions in water (around 0.1 wt %), and the generated aerosols were dried to < 5 % RH by passing the aerosol flow through a Nafion dryer (MD-110-12S) and then a silica gel diffusion dryer. The dry aerosol flow was subsequently split into two flows. One aerosol flow was sent to the vent, and the other aerosol flow (0.3 L min −1 ) was passed through the first differential mobility analyzer (DMA) to produce quasimonodisperse aerosol particles with a mobility diameter of 100 nm. After that, the aerosol flow was humidified to a desired RH by flowing through a humidification section, which was made of two Nafion tubes (MD-700-12F-1) connected in series, and the residence time in the humidification section was ∼ 27 s. Finally, the size distribution of humidified aerosols was measured by a scanning mobility particle sizer (SMPS), which consisted of the second DMA coupled to a condensation particle counter (CPC 3776, TSI). The RHs of the aerosol flow and the sheath flow in the second DMA were maintained to be equal and monitored using a commercial dew-point hygrometer (Michell, UK) with a stated uncertainty of ±0.08 % RH. In addition, the flow rate ratio of the sheath flow to the aerosol flow was set to 10 : 1 for both DMAs.
Hygroscopic growth factors (GFs), defined as d/d 0 (d is the mobility diameter at a given RH and d 0 is the mobility diameter at RH < 5 %), were reported. All the experiments were conducted in triplicate. During our experiments, am-monium sulfate was used to calibrate the H-TDMA system routinely, and the absolute differences between the measured and theoretical GF at 90 % RH were found to be within 0.04, confirming the robustness of our measurements.

CCN experiments
The CCN activity of aerosol particles was determined using a commercial cloud condensation nuclei counter (CCNc, CCN-100, Droplet Measurement Technologies, Longmont, CO, USA) described in previous studies (Roberts and Nenes, 2005;Lance et al., 2006;Moore et al., 2010). Polydisperse aerosol particles were generated using a commercial atomizer (TSI 3076), in which concentrations of solutions used were around 0.1 g L −1 . The wet aerosol flow generated was passed through two silica gel diffusion dryers to reduce its RH to < 5 % RH. After that, a dry aerosol flow (∼ 800 mL min −1 ) was passed through a DMA (TSI 3081) in size scanning mode to produce quasi-monodisperse aerosols, and subsequently the aerosol flow was split into two streams: one stream (∼ 300 mL min −1 ) was sampled into a commercial CPC (TSI 3775) to measure total number concentrations of aerosol particles ([CN]), and the second flow (∼ 500 mL min −1 ) was sampled into the CCNc (CCN-100) to measure number concentrations of CCN ([CCN]).
Activation fractions ([CCN] / [CN]) of size-resolved dry particles were determined using the scanning mobility CCN analysis (SMCA) method described elsewhere (Moore et al., 2010). In brief, the DMA was operated in the scanning voltage mode, and thus one activation curve (activation fractions as a function of dry diameter) could be obtained in 60-120 s. The multiple charge effect was also corrected in this method, and in our work the supersaturation (SS) was set in the range of 0.45 %-1.13 % with the stated uncertainty to be ±0.01 %. As shown in Fig. 3, activation fractions of sodium methyl sulfate (methyl-OS) and its internally mixed aerosols with ammonium sulfate were measured at four different SSs with dry mobility diameters between 20 and 100 nm. Activation fractions were fitted versus dry diameters, and the critical particle diameter (d 50 ) was determined as the dry diameter at which the activation fraction is equal to 0.5. During our measurements, ammonium sulfate was used to calibrate supersaturations, and the Pitzer ion interaction model was applied in the calibration procedure to account for incomplete dissociation of ammonium sulfate at droplet activation (Pitzer and Mayorga, 1973;Clegg and Brimblecombe, 1988). The corrected supersaturations were reported in our work.  OS) and potassium hydroxyacetone sulfate, and the data are also listed in Table 1. Figure 4a suggests that methyl-OS was deliquesced when RH was increased from 40 % to 50 %, and after that mass growth factors increased further with RH. The mass of ethyl-OS was moderately increased (by ∼ 11 %) when RH was increased from 40 % to 50 %, and a further increase in RH to 60 % led to an additional although small increase in sample mass (by ∼ 2 %); the increase in sample mass at 50 % and 60 % RH may be because ethyl-OSs were partially deliquesced at this stage (Ling and Chan, 2008;Mikhailov et al., 2009). When RH was increased to 70 %, ethyl-OS was completely deliquesced, and a further increase in RH (to 80 % and 90 %) resulted in a further increase in sample mass. Octyl-OS was only deliquesced when RH was increased from 80 % to 90 %, whereas no significant water uptake was observed for dodecyl-OS even at 90 % RH. The mass growth factors at 90 % RH were determined to be 3.65 ± 0.06, 3.58 ± 0.02 and 1.59 ± 0.01 for methyl-OS, ethyl-OS and octyl-OS, respectively.
Mass growth factors of seven potassium organosulfates were also investigated: potassium hydroxyacetone sulfate, potassium 3-hydroxy phenyl sulfate, potassium benzyl sulfate, potassium 2-methyl benzyl sulfate, potassium 3-methyl benzyl sulfate, potassium 2,4-dimethyl benzyl sulfate and potassium 3,5-dimethyl benzyl sulfate. All the compounds did not show measurable water uptake at 80 % RH. When RH was increased to 90 %, as shown in Fig. 4b, a significant increase in mass was observed for potassium hydroxyacetone sulfate particles, suggesting the occurrence of deliquescence, and the mass growth factor was determined to be 2.20 ± 0.03 at 90 % RH. Furthermore, no significant water uptake was observed for the other six potassium organosulfates even when RH was increased to 90 %. We should men-  1.00 ± 0.01 -1.00 ± 0.01 -30 1.00 ± 0.01 -1.00 ± 0.01 -40 1.00 ± 0.01 -1.00 ± 0.01 -50 1.00 ± 0.01 -1.00 ± 0.01 -60 1.00 ± 0.01 -1.00 ± 0.01 -70 1.00 ± 0.01 -1.00 ± 0.01 -80 1.01 ± 0.01 -1.00 ± 0.01 -90 1.59 ± 0.01 7.63 ± 0.02 2.20 ± 0.03 12.84 ± 0.18 tion that occasionally small increase in sample mass (up to 10 %-20 %) was observed for a few samples when RH was increased from 80 % to 90 %, and such small increase in sample mass may be caused by water uptake of impurities (such as potassium hydroxide) contained in these synthesized com-pounds. When such increased sample mass was observed when RH was increased from 80 % to 90 %, we carried out at least four duplicate experiments, and all the other experiments confirmed that the mass increase was insignificant. For deliquesced samples, measured mass changes can be converted to water-to-solute ratios (WSRs), defined as the molar ratio of H 2 O to sulfur. The WSRs data are summarized in Table 1 for sodium methyl sulfate, sodium ethyl sulfate, sodium octyl sulfate and potassium hydroxyacetone sulfate. As shown in Table 1, WSRs at 90 % RH were determined to be 19.75 ± 0.34, 21.19 ± 0.14, 7.63 ± 0.02 and 12.84 ± 0.18 for sodium methyl sulfate, sodium ethyl sulfate, sodium octyl sulfate and potassium hydroxyacetone sulfate at 25 • C.

Organosulfates
H-TDMA was employed to measure hygroscopic growth factors of 100 nm methyl-, ethyl-and octyl-OS aerosols as a function of RH (up to 90 %), and the results are shown in Fig. 5 and Table 2. In addition, no significant hygroscopic growth was observed for dodecyl-OS for RH up to 90 %. We did not investigate hygroscopic growth of other OS aerosols due to the very small quantity of these synthesized compounds.
As shown in Fig. 5, methyl-, ethyl-and octyl-OS aerosols all exhibited continuous hygroscopic growth without obvious phase transitions. To our knowledge, only one previous study (Estillore et al., 2016) investigated hygroscopic growth of methyl-and ethyl-OS aerosols using an H-TDMA, and continuous hygroscopic growth was also observed. The continuous growth behavior can be attributed to the amorphous state of aerosol particles, which would take up water at very low RH. For methyl-OS aerosols, GFs were determined in our work to be 1.53 ± 0.01, 1.63 ± 0.01 and 1.83 ± 0.03 at 80 %, where a, b and c are coefficients obtained from fitting using Eq. (1). As shown in Fig. 5, hygroscopic growth factors of methyl-, ethyl-and octyl-OS aerosols can be fitted by Eq. (1), and the obtained coefficients (a, b and c) are summarized in Table 3. Figure 4 shows that obvious deliquescence transitions were observed for methyl-, ethyl-and octyl-OS in the VSA experiments because samples used in VSA experiments may be crystalline salts; in contrast, as revealed by Fig. 5, continuous hygroscopic growth without obvious phase transitions was observed for methyl-, ethyl-and octyl-OS aerosol particles in H-TDMA measurements, suggesting that these aerosol particles, which were produced by drying aqueous droplets to < 5 % RH, may exist in an amorphous state. Estillore et al. (2016) employed an H-TDMA to investigate hygroscopic properties of several OS aerosols, and similarly they found that those aerosols, including methyl-OS, ethyl-OS and potassium hydroxyacetone sulfate, which were also examined in our work, displayed continuous hygroscopic growth.

Comparison between VSA and H-TDMA measurements
For completely deliquesced particles, if it is assumed that the particle is spherical and that the particle volume at a given RH is equal to the sum of the dry particle volume and the volume of particulate water, particle mass change, measured using the VSA, can then be converted to hygroscopic GF, using Eq. (2): where ρ 0 and ρ w are the density of the dry sample and water, respectively. The densities of methyl-, ethyl-and octyl-OS particles were reported to be 1.60, 1.46 and 1.19 g cm −3 with an uncertainty of 20 %-30 % (Kwong et al., 2018;Chemistry Dashboard, 2021). Figure 6 compares VSA-derived GFs and those measured using H-TDMA for methyl-, ethyl-and octyl-OS, and it can be concluded that for the RH at which the samples used in the VSA experiments were deliquesced, GFs derived from mass change measured using VSA agree relatively well with those directly measured using H-TDMA. For example, at 90 % RH GFs were measured by H-TDMA to be 1.83 ± 0.03, 1.79 ± 0.02 and 1.21 ± 0.02 for methyl-, ethyl-and octyl-OS, while at the same RH their GFs derived from VSA measurements were found to be 1.74 ± 0.01, 1.68 ± 0.01 and 1.19 ± 0.01, only 6 % (or less) smaller than those measured using H-TDMA. The small but systematical differences between VSA and H-TDMA results, as evident from Fig. 6, could stem from the volume additivity assumption used to convert mass growth to diameter growth, uncertainties in OS densities, and DMA sizing errors.

Internally mixed aerosols
We also investigated hygroscopic properties of methyl-, ethyl-and octyl-OS aerosols internally mixed with ammonium sulfate (AS), and the results are summarized in Table 4. Figure 7a displays GFs of 100 nm methyl-OS / AS mixed aerosols with mass ratios of 1 : 1 and 1 : 5. The 1 : 1 mixed aerosol particle showed a deliquescence transition at 70 % RH, while the 1 : 5 mixed aerosols showed a deliquescence transition at 75 % RH, which was lower than the deliquescence RH (DRH, 80 %) of AS. Here the DRH is defined as the RH at which the mixed aerosols are completely del-iquesced (Choi and Chan, 2002). Figure 7a suggests that before full deliquescence, significant hygroscopic growth was also observed, i.e., pre-deliquescence of mixed particles occurred when RH was lower than their DRH. Predeliquescence was widely reported in previous studies which investigated hygroscopic properties of inorganic / organic mixed aerosols (Choi and Chan, 2002;Prenni, 2003;Wise et al., 2003;Brooks, 2004;Marcolli and Krieger, 2006;Wu et al., 2011;Lei et al., 2014;Jing et al., 2016;Estillore et al., 2017). For example, Choi and Chan (2002) investigated hygroscopic behaviors of internally mixed particles which consisted of water-soluble organic compounds and AS and found that the internal mixing with organics (such as malonic and citric acids) could reduce the DRH of AS, due to the ability of organics to absorb water at low RH.
Internal mixing with ethyl-and octyl-OS could also reduce the DRH of AS. As shown in Fig. 7b, ethyl-OS / AS mixed aerosols were deliquesced at 70 % RH when the mass ratio of ethyl-OS to AS was 1 : 1 and at 80 % RH when the mass ratio was 1 : 5. In addition, Fig. 7c suggested that the deliquescence of octyl-OS / AS aerosols took place at 75 % RH for the 1 : 1 mixture and at 80 % for 1 : 5 mixture.
The Zdanovskii-Stokes-Robinson (ZSR) method (Stokes and Robinson, 1966) has been widely used to predict hygroscopic growth of internally mixed aerosol particles, assuming that the interaction among individual species is negligible and that individual species in the mixed particles take up water independently. According to the ZSR method, the GF of a mixed particle, GF mix , can be calculated using Eq. (3) (Malm and Kreidenweis, 1997): where GF i is the GF of ith species that the dry mixed particle contains. The volume fraction of the ith species in the dry mixed particle, ε i , can be calculated using Eq. (4): where m i and ρ i are the mass fraction and density of the ith species. GFs of pure OS, measured in our work using H-TDMA and presented in Sect. 3.2.1, and GFs of AS, calculated using the extended aerosol inorganics model (E-AIM) (Clegg et al., 1998;Wexler and Clegg, 2002), were used as input to predict GFs of methyl-, ethyl-and octyl-OS internally mixed with AS. Comparisons between measured and predicted GFs are displayed in Fig. 7 for OS / AS mixed aerosols. As shown in Fig. 7a, GFs of methyl-OS / AS mixed aerosols (both the 1 : 1 and 1 : 5 mixtures) could be well predicted using the ZSR method when RH was < 60 % or > 80 %, while the ZSR method underestimated their GFs at 70 % and 75 % RH. Such underestimation at 70 % and 75 % RH is likely to due to the circumstance that inorganic compounds (AS, in our work) may dissolve partially in the organics / water solution (which can be formed at much lower Table 4. Hygroscopic GF of methyl-, ethyl-and octyl-OS internally mixed with AS (their mass ratios are 1 : 1 and 1 : 5) at different RHs. All the errors given in this work are standard deviations.

Cloud condensation nucleation activities
Figures 3, S2 and S3 in the Supplement show CCN activation curves obtained at four supersaturations for methyl-, ethyl-and octyl-OS aerosols and their internal mixtures with ammonium sulfate. Each activation curve was fitted using a Boltzmann sigmoid function to derive the corresponding critical particle diameter (d 50 ), which was then used to calculate κ ccn using Eqs. (5a)-(5b) (Petters and Kreidenweis, 2007): where S c is the critical saturation ratio (1 + SS) of water, d 50 is the critical particle diameter, and A is a constant which describes the Kelvin effect on a curved surface of a droplet and depends on the surface tension (σ s/a ), molecular weight (M w ), density (ρ w ) of water, temperature (T ) and the universal gas constant (R). Table 5 summarizes critical diameters at different supersaturations for aerosol particles examined in this work and their κ ccn values. As shown in Table 5, κ ccn values were determined to be 0.459 ± 0.021, 0.397 ± 0.010 and 0.206 ± 0.008 for methyl-, ethyl-and octyl-OS, decreasing with alkyl chain length, and this suggests that the addition of hydrophobic hydrocarbon functional groups to OS reduced their hygroscopicity. A decrease in the hygroscopicity of OS compounds with the increase in the number of carbon atoms was also observed under subsaturated conditions (Sect. 3.2). In addition, we investigated CCN activities of alkyl-OS / AS mixed aerosols with a mass ratio of 1 : 5, and κ ccn values were determined to be 0.453 ± 0.027, 0.458 ± 0.024 and 0.436 ± 0.009 for methyl-OS / AS, ethyl-OS / AS and octyl-OS / AS.

Comparison between H-TDMA and CCN activities measurements
It is suggested that the single hygroscopicity parameter, κ, could describe aerosol-water interactions under both sub-and supersaturated conditions (Petters and Kreidenweis,Figure 8. Comparison of κ values derived from hygroscopic growth (κ gf ) with those derived from CCN activities (κ ccn ) for methyl-, ethyl-and octyl-OS aerosols as well as their internal mixtures with ammonium sulfate (the mass ratio was 1 : 5).
2007). The κ values derived from CCN activity measurements, κ ccn , have been illustrated above; the κvalues derived from H-TDMA measurements, κ gf , can be calculated using Eq. (6) (Petters and Kreidenweis, 2007;Tang et al., 2016): In this work GFs measured at 90 % RH were used to calculate κ gf values, which are also listed in Table 5. Equation (6) does not take into account the Kelvin effect as the effect is small for 100 nm particles (Tang et al., 2016). Figure 8 compares κ ccn and κ gf values for the six types of aerosol particles examined. For pure OS, κ ccn values of methyl-OS (0.459 ± 0.021) and ethyl-OS (0.397 ± 0.010) were smaller than their κ gf values (0.537-0.604 and 0.505-0.548), but the relative differences do not exceed 25 %. Such a difference (< 25 %) may not be significant if all the uncertainties associated with deriving κ from measured hygroscopic growth and CCN activities are considered (Petters and Kreidenweis, 2007). Octyl-OS appears to be an exception, and the average κ ccn (0.206) was ∼ 2.4 times larger than the average κ gf (0.086). In addition, no significant difference was observed between κ ccn and κ gf for all the alkyl-OS / AS mixed aerosols.
Significant differences between κ gf and κ ccn were reported in previous studies Wex et al., 2009;Hansen et al., 2015), attributed to several factors discussed below. Petters and Kreidenweis (2008) demonstrated that cloud droplet activation was highly sensitive to the solubility for sparingly soluble compounds in the range of 5 × 10 −4 -2 × 10 −1 , expressed as volume of solute per unit volume of water (Petters and Kreidenweis, 2008). Compared to the highly soluble methyl-and ethyl-OS (their solubilities are 0.127-0.219 and 0.075-0.151), the solubility of octyl-OS Table 5. Single hygroscopicity parameters derived from hygroscopic growth (κ gf ) and CCN activity measurements (κ ccn ) for methyl-, ethyland octyl-OS and their internal mixtures with ammonium sulfate (AS). All errors given were standard deviations.  , 2021) is rather limited, and incomplete dissolution at subsaturated condition in H-TDMA measurements may lead to underestimation of κ gf values for octyl-OS; as a result, the solubility limit may explain the observed difference between κ gf and κ ccn for octyl-OS. Furthermore, surface tension is a key factor to influence critical supersaturations at which aerosol particles are activated to cloud droplets (Petters and Kreidenweis, 2013). We measured surface tensions of alkyl-OS and alkyl-OS / AS (the mass ratio was 1 : 5) solutions, and the results are shown in Table S1 and Fig. S4. The surface tension of octyl-OS is much lower than that of pure water, leading to a significant reduction in critical supersaturations and thus an overestimation of its κ ccn value; for comparison, the surface tension depression is also visible but much less pronounced for octyl-OS / AS mixed aerosols. Overall, we proposed that the solubility limit and surface tension reduction may both contribute to the observed discrepancy between κ gf and κ ccn values for octyl-OS aerosols. We note that some numerical models Kreidenweis, 2008, 2013;Riipinen et al., 2015) are available to quantitatively assess the contribution of the solubility limit and surface tension reduction to the discrepancy between κ gf and κ ccn .

Conclusions
Organosulfates (OSs) may contribute significantly to secondary organic aerosols in various locations over the globe; however, their hygroscopic properties and CCN activities have not been well understood. In this work, three complementary techniques -a vapor sorption analyzer (VSA), a hygroscopicity tandem differential mobility analyzer (H-TDMA) and a cloud condensation nuclei counter (CCNc)were employed to investigate interactions of several OSs with water vapor under sub-and supersaturated conditions, trying to obtain a comprehensive picture of their hygroscopic properties and CCN activities. VSA was used to measure mass change in OS samples with RH (0 %-90 %). Obvious deliquescence was found for sodium methyl sulfate (methyl-OS), sodium ethyl sulfate (ethyl-OS), sodium octyl sulfate (octyl-OS) and potassium hydroxyacetone sulfate, and their mass growth factors at 90 % RH were determined to be 3.65 ± 0.06, 3.58 ± 0.02, 1.59 ± 0.01 and 2.20 ± 0.03, respectively. No significant water uptake was observed up to 90 % RH for the other OS compounds examined, including sodium dodecyl sulfate, potassium 3-hydroxy phenyl sulfate, potassium benzyl sulfate, potassium 2-methyl benzyl sulfate, potassium 3-methyl benzyl sulfate, potassium 2,4-dimethyl benzyl sulfate and potassium 3,5-dimethyl benzyl sulfate. Hygroscopic properties of methyl-, ethyl-and octyl-OS aerosols were also studied using H-TDMA, which measured mobility diameters of aerosol particles as a function of RH. Continuous hygroscopic growth was observed for methyl-, ethyl-and octyl-OS aerosols, and their growth factors at 90 % RH were measured to be 1.83 ± 0.03, 1.79 ± 0.02 and 1.21 ± 0.02.
We further investigated CCN activities of methyl-, ethyland octyl-OS aerosols, and their single hygroscopicity parameters, κ ccn , were determined to be 0.459 ± 0.021, 0.397 ± 0.010 and 0.206 ± 0.008, respectively. For methyland ethyl-OS aerosols, single hygroscopicity parameters derived from CCN activities (κ ccn ) agree reasonably well with those derived from H-TDMA measurements (κ gf ) with relative differences being < 25 %. However, κ ccn was found to be ∼ 2.4 times larger than κ gf for octyl-OS, and we show that the solubility limit and surface tension reduction may both contribute to such a discrepancy as observed.
Data availability. Data used in this paper can be found in the main text or the Supplement.
Author contributions. MT conceived this work; RJH, YZ, XD and XW chose and provided samples investigated in this work; CP, LC, YZ and XD conducted VSA measurements; CP, WW and MG conducted H-TDMA measurements; PNR, KAM and AAAA conducted CCN activity measurements; CP, PNR, KAM, AAAA and MT analyzed the data and prepared the paper with contributions from all the other coauthors.
Competing interests. The authors declare that they have no conflict of interest. Review statement. This paper was edited by Alex Lee and reviewed by two anonymous referees.