Organic compounds are an important contributor to the atmospheric submicron aerosol (Jimenez et al., 2009). The organic fraction is projected to increase in the future due to the confluence of a decreasing sulfate and nitrate burden and increases in the global secondary organic aerosol burden (Heald et al., 2008). An important unanswered question is how the organic influences the aerosol's ability to serve as cloud condensation nuclei (CCN), and in turn modulate climate via indirect effects of aerosols on clouds and precipitation (Andreae and Rosenfeld, 2008). Realistic prescribed variations in secondary organic aerosol hygroscopicity have demonstrable impacts on CCN number concentration (Mei et al., 2013) and can change the simulated global aerosol indirect forcing (AIF) by approx. one-sixth of the AIF simulated in a control case (Liu and Wang, 2010). To obtain a prognostic understanding of the contribution of the organic fraction to indirect aerosol forcing in future climates, models need improved schemes that map simulated organic aerosol composition to hygroscopicity and CCN activity.

Several organic aerosol types (e.g., freshly emitted diesel oil particles or first generation oxidation products of sesquiterpenes) consist of mostly hydrophobic hydrocarbon chains with few functional groups attached. Pure hydrocarbons with a carbon number less than C30 are expected to be semi-volatile and in the liquid phase. Over time the compounds evolve by functionalization, fragmentation, and oligomerization (Kroll and Seinfeld, 2008; Ziemann and Atkinson, 2012). As functional groups are added to the carbon chain, the products usually, but not always, become less volatile (Goldstein and Galbally, 2007), more dense (Kuwata et al., 2012), more viscous (Sastri and Rao, 1992), and more CCN active (Suda et al., 2014).

Laboratory (George and Abbatt, 2010; Poulain et al., 2010; Cappa et al., 2011; Massoli et al., 2010; Lambe et al., 2011; Duplissy et al., 2011; Kuwata et al., 2013; Rickards et al., 2013; Suda et al., 2014) and field studies (Jimenez et al., 2009; Chang et al., 2010; Mei et al., 2013) have demonstrated a robust link between the aerosol oxidation state and the ability of the organic fraction to promote hygroscopic water uptake and CCN activity. Proxies from mass spectrometry such as the fragmentation peak f44 or the atomic oxygen-to-carbon ratio are often used to model the increase in hygroscopicity. However, these correlations exhibit significant variability between studies and break down when applied at the compound level (Rickards et al., 2013; Suda et al., 2014).

Chemistry models are already capable of simulating the molecular identities of species present in the condensed phase during multi-day evolution of diluting air parcels (Lee-Taylor et al., 2015). Mapping this speciated aerosol composition to the aerosol hygroscopicity should ultimately permit quantification of changes in CCN number concentration (provided that the size distribution is also simulated) and associated effects on clouds and climate. Thermodynamic models should be able to predict CCN activity. Many thermodynamic models have made use of activity coefficients predicted by the universal functional group activity coefficient (UNIFAC) group contribution method (Fredenslund et al., 1975). Several investigators have compared UNIFAC predictions of organic aerosol water content to experimental data (Saxena and Hildemann, 1997; Ming and Russell, 2001; Peng et al., 2001; Choi and Chan, 2002; Mochida and Kawamura, 2004; Marcolli and Peter, 2005; Moore and Raymond, 2008). Some of these comparisons prompted proposed revisions of specific group interaction parameters, e.g., [OH] and [H2O]. Several thermodynamic models that treat complex phase equilibria of multifunctional, multicomponent organic mixtures are based on UNIFAC activity coefficients (Ming and Russell, 2002; Raatikainen and Laaksonen, 2005; Topping et al., 2005; Amundson et al., 2007; Zuend et al., 2008; Compernolle et al., 2009). The development of these models has been driven by the need to enable predictions over a wide range of conditions and compositions, including the effect of liquid–liquid phase separation on gas-to-particle partitioning (Zuend and Seinfeld, 2012; Topping et al., 2013). The prediction of CCN activity of organic compounds has received less attention. Rissman et al. (2007) used the aerosol diameter-dependent equilibrium model (ADDEM; Topping et al., 2005) with an underlying UNIFAC core to predict the relationship between critical supersaturation and dry for several dicarboxylic acid aerosols. To our knowledge no study to date has systematically focused on the prediction of CCN activity from thermodynamic models.

Here we build on this body of work to predict the contribution of a compound with known chemical structure to the CCN activity of a particle of known size. The proposed model uses the UNIFAC equations (Fredenslund et al., 1975) with group interaction parameters form Hansen et al. (1991), Raatikainen and Laaksonen (2005), and Compernolle et al. (2009) to model activity coefficients and free energy of mixing. Liquid–liquid phase boundaries are determined using the area method of Eubank et al. (1992). Molecular volume is estimated from elemental composition and adjustments for functional group composition using the approach of Girolami (1994). The relationship between critical supersaturation and dry diameter is then predicted using Köhler theory (Seinfeld and Pandis, 2006). The basic model mechanics are similar to those employed in multicomponent phase equilibrium models (Ming and Russell, 2002; Raatikainen and Laaksonen, 2005; Topping et al., 2005; Amundson et al., 2007; Zuend et al., 2008) but limited in scope to binary compositions and with focus on accurately representing phase and water activity at conditions relevant at the point of CCN activation only. These predictions are validated by manually mapping chemical composition to UNIFAC groupings and comparing modeled CCN activity against observations from a compiled library of recently published CCN data of mostly weakly oxidized hydrocarbons containing a mixture of alcohol, carbonyl, aldehyde, ether, carboxyl, nitrate, and hydroperoxide moieties. The model is used to predict how the addition of one or more functional groups to otherwise similar molecules promotes CCN activity. Envisioned application to multi-component aerosols and contrasts with more complete thermodynamic models are discussed.

Experimental data for validation were compiled from the literature. A detailed summary of the compound names, chemical structures, physicochemical properties, CCN observations, and observed κapp's is provided in the Supplement (Tables S3–S7). This set features compounds with mostly linear carbon backbones C4 to C18 and O : C ratio between 0.1 and 1. The data are grouped into model compounds for primary organic aerosol (POA; Table S3), functionalized hydroperoxy ethers (Table S4), hydroxy nitrates (Table S5), carboxylic acids (Table S6), and carbohydrates (Table S7). Compounds included in Table S3 are long-chain molecules that have hydrophobic tails (> 14 methylene groups) and a single terminal carboxyl or hydroxyl group. Representative example compounds are oleic acid or cetyl alcohol. Compounds in Table S4 are C14 functionalized hydroperoxy ethers that have 10–12 methylene groups, at least one hydroperoxide and ether group, and a second carbonyl, hydroperxide, or carboxyl group. Compounds in Table S5 are functionalized hydroxy nitrates featuring C10 to C15 carbon backbones with 1–3 hydroxyl and 1–4 nitrate groups. Compounds in Table S6 are C4–C10 carboxylic acids that have 1–2 carboxyl and up to one carbonyl group attached to the carbon backbone. Finally, compounds in Table S7 are C4–C18 carbohydrates that have hydroxyl groups approximately equal to the number of carbon atoms. Data in Table S3 are taken from Raymond and Pandis (2002) and Shilling et al. (2007). Data in Tables S4 and S5 are taken from the Supplement of Suda et al. (2014). Data in Tables S6 and S7 are from various sources and are summarized in the Supplement of Petters et al. (2009b), which was updated with new compounds from Christensen and Petters (2012), and data were re-screened for quality. The compounds were selected to provide systematic variation in the number and type of functional groups with otherwise similar structure, i.e., linear or weakly branched alkane backbone with variable carbon chain length.

To illustrate model initialization and model output, two example compounds from the Supplement, C12 dihydroxy nitrate and C13 trihydroxy nitrate, are presented in Table 1. For some of the compounds density and solubility data are available and those data are included in the Supplement. Table 1 shows how the molecular structure is decomposed into the subgroups understood by the UNIFAC and Girolami (1994) model framework. Detailed model output for the two example compounds is illustrated in Fig. 1. The predicted mole fraction dependence of Δgmix suggests that the C13 trihydroxy nitrate is miscible with water in all proportions while the C12 dihydroxy nitrate is not. The dashed black line connecting xa and xb encloses the maximum positive area with the Δgmix line and defines the two-phase region. Water activity derived from Δgmix is graphed in the middle panel. It shows that the miscibility gap for the C12 dihydroxy nitrate occurs at water activity close to unity. Phase gaps at water activity near unity may result in miscibility-controlled cloud droplet activation (Petters et al., 2006), which is analogous to solubility-/deliquescence-limited cloud droplet activation (Shulman et al., 1996; Hori et al., 2003; Bilde and Svenningsson et al., 2004; Kreidenweis et al., 2006; Petters and Kreidenweis, 2008). Köhler curves in the right panel demonstrate miscibility-limited activation behavior. For the C13 trihydroxy nitrate, the Köhler curve is smooth and exhibits a single maximum corresponding to the model critical supersaturation. For the C12 dihydroxy nitrate two maxima appear. The first maximum corresponds to the point of incipient phase separation xa. The height of the miscibility barrier depends on the dry diameter. For large dry particles where the Kelvin term does not play a significant role, the supersaturation of point xa is reduced and the second classical Köhler maximum will control droplet activation. Similar complex Köhler curves have been reported previously (e.g., Bilde and Svenningsson, 2004; Petters and Kreidenweis, 2008). Experiments with pure crystalline sparingly soluble organic compounds have demonstrated convincingly that the larger maximum indeed controls cloud droplet activation for solubility-limited cases (Hori et al., 2003; Bilde and Svenningsson, 2004; Hings et al., 2008). The sc vs. Dd relationship for phase-controlled activation does not result in κapp that is independent with respect to Dd (Petters and Kreidenweis, 2008). Therefore, for compounds having κ < ∼ 0.06 where phase separation might play a role, the observed sc, Dd pair is included in the data tables (Tables 1, S3–S7) and κ values are computed from the observation and the model (Eq. 12) at the same Dd. Note that the Dd-dependent κ only plays a role in a narrow range of miscibilities. Sufficiently soluble and truly insoluble substances are not affected. In summary, Table 1 and Fig. 1 demonstrate model input, illustrate model mechanics, and identify model outputs.

How well do data-derived and model-derived κapp compare? For numerical comparison both κ's are included in Tables S3–S7. A graphical illustration of these is presented in Fig. 2. To improve clarity, compounds with predicted and modeled κ < 0.001 are clustered in the lower left corner. Such low κ's correspond to compounds that are effectively CCN inactive. The range between κ=10-3 and 10-5 spans a narrow range in the sc–Dd–κ state space that characterizes CCN activity (cf. Fig. 1 in Petters and Kreidenweis, 2007). Resolving these differences is not particularly meaningful for organic dominated particles that typically have Dd < 300 nm. Furthermore, the κ of an internally mixed particle is approximately the weighted volume fraction in the mixture. For κ < 10-3 the contribution to a mixed particle's κ is insensitive to the exact value. Finally, although state-of-the-science size-resolved CCN measurements can resolve differences in κ < 10-3, compound impurities can interfere. A 1 % impurity having κ similar to ammonium sulfate would contribute ∼ 0.06 to a measured particle κ. In addition, solvent residuals (Huff Hartz et al., 2006; Shilling et al., 2007; Rissman et al., 2007) and control over the dry particle phase state (Raymond and Pandis, 2002; Hori et al., 2003; Broekhuizen et al., 2004; Bilde and Svenningson, 2004) can disproportionally bias the characterization of low κ's. Combined these points justify the definition of κ < 0.001 as effectively CCN inactive. Compounds in the CCN inactive corner include all compounds from Table S3, the C14 and C15 hydroxnitrate, and the C14 trinitrate. These compounds all have 11 or more methylene groups and O : C ratios between 0.11 and 0.65. CCN activity of these compounds is satisfactorily predicted by the model.

Nine compounds are predicted to be CCN inactive but have measurements indicating 0.001 > κobs > ∼ 0.03. These are graphed below the dashed line and include C14 di- and tetra-nitrate, C13 hydroxy nitrate, C14 and C15 dihydroxy nitrate, the remaining hydroperoxide ethers from Table S4, and cis-pinonic acid. The observed C14 di- and tetra-nitrate are barely larger than the cutoff for CCN inactive. Variation of κ between the C14 di-, tri- and tetra-nitrate (cf. Fig. 2 in Suda et al., 2014) implies that the trinitrate has lower κ than the di- and tetra-nitrate, which suggests that some random variability in the data is superimposed on the trend. Similarly, the observations show that the C14 and C15 dihydroxy nitrate are slightly more CCN active than the C13 dihydroxy nitrate. Although this is possible such behavior is not plausible due to the well-established hydrophobic nature of the added CHx groups. One possible explanation for the discrepancies is the sensitivity of observed κ's to trace contamination. Each of the compounds was purified via high-performance liquid chromatography (HPLC; Suda et al., 2014) but degree of purification likely varied between compounds. Furthermore, experimental uncertainty for the HPLC-CCN method used is slightly larger than for standard methods since it requires application of fast-flow scans. Finally, the data are from a single set of experiments. More data are needed before attributing the mismatch to either model or measurement error.

Another notable outlier is adipic acid. Here, the observed κ < 0.01 corresponds to the solubility-limited value that is referenced against its solid crystalline phase state. In contrast, the predicted value κ=0.14 is in good agreement with the molar volume prediction (κ=0.17; cf. Fig. 4 in Christensen and Petters, 2012) and observed κ that adipic acid particles express when solubility limitations are removed (cf. Fig. 1 in Hings et al., 2008). This scenario was selected to illustrate the inability of the UNIFAC model to treat solid phases. It therefore cannot capture deliquescence and deliquescence-/solubility-limited activation. In atmospheric OA multiple organic compounds likely form an amorphous supercooled melt (Marcolli et al., 2004) and metastable aqueous solutions are ubiquitous (Rood et al., 1989). Thus the metastable prediction would be valid to account for adipic acid in the context of atmospheric OA.

A series of carboxylic acids and carbohydrates cluster near the 1 : 1 line at κ > ∼ 0.06. These compounds are generally highly functionalized having at least two carboxyl, hydroxyl, or carbonyl groups for every four carbon atoms. The O : C ratio always exceeds 0.5 and is close to 1 for many of the compounds. For the predictions, activity coefficients approach unity, compounds are miscible in water in all proportions, and model κ's closely track the prediction based on estimated molar volume. Overall comparison of predicted vs. observed κ is approximately within a factor of 2 and this range is similar to predictions that are based on actual molar volume (cf. Fig. 2 in Petters et al., 2009b).

The series of hydroxy nitrates, dihydroxy nitrates, and trihydroxy nitrates for different carbon chain lengths also clusters near the 1 : 1 line. The spread is within approximately a factor of 2 and similar to that of the carboxylic acids and carbohydrates. These compounds span the entire range from κ < 0.001 to κ∼ 0.1 and have as few as two hydroxyl and one nitrate group per 13 carbon atoms (C13 dihydroxy nitrate). The model appears to accurately predict the influence of the methylene and hydroxyl groups on the transition from immiscible and CCN inactive to sufficiently miscible and CCN active according to the molar volume of the compound. For the C11, C12, and C13 dihydroxy nitrates, the predicted miscibility-limited activation demonstrated in Fig. 1 seems to adequately explain the transition. The accurate model prediction of this sensitive transition regime is encouraging, especially since no adjustment was made to the amn group interaction parameters for [OH], [CHx], and [H2O] groups.

In summary, Fig. 2 demonstrates four capabilities of the model. First, the model has good skill in correctly classifying effectively CCN inactive compounds (κ < 0.001). Second, the model captures the molar volume-dependent activation of highly functionalized compounds (low molecular weight dicarboxylic acids and polysaccharides). Scatter between predicted and observed κ is approximately within a factor of 2 and considered acceptable taking into account the considerable diversity in the underlying CCN data. We note that uncertainties in molar volume estimation of vs∼±10 % stemming from the Girolami (1994) method correspond to ±10 % error in predicted κ for these compounds, which is significantly less than the observed scatter in the data (Petters et al., 2009b). Third, the model predicts that miscibility limitations are the cause for poor CCN activity of weakly functionalized hydrocarbons, and the phase separation information can be used to quantitatively predict the transition between sufficiently miscible and effectively immiscible species. Finally, the model seems to accurately capture the main functional group dependencies observed previously (Suda et al., 2014): a strong promoting effect of hydroxyl, a weak promoting effect for hydroperoxides, a negligible or inhibiting effect of nitrate, and inhibiting effect of methylene groups on CCN activity. How, then, can one quantify the model sensitivity of κ to the addition of functional groups to otherwise similar molecules?

Simulation of homologous series can be used to derive these sensitivities. Figure 3 shows modeled κ's for a series of functionalized n-alkanes. The gradual decreasing trend of κ with increasing carbon number is due to the increase in molar volume. A steep decline is observed when a critical carbon number is exceeded. Beyond this point the additional methylene groups reduce the miscibility with water and render the compound effectively CCN inactive. For example, CCN activity for a C16 trihydroxy alkane is controlled mostly by molar volume while C18 trihydroxy alkane is effectively CCN inactive. The critical carbon number is C7, C12, C16, C20, and C24 for the mono-, di-, tri-, tetra-, and penta-hydroxy alkanes, respectively. Starting with an n-alkane, the most dramatic effect of adding functional groups is to render the molecule miscible with water. Contrasting the critical carbon number for different homologous series can be used as a measure of a particular groups' ability to transform the molecule such that it is sufficiently miscible in water and can express its molar volume κ. The hydroxy alkane series shows that approximately one hydroxyl group is needed to compensate for the addition of four methylene groups (i.e., to maintain miscibility at the composition of the critical carbon number), expressed as a ratio, Δ[CHn] /Δ[OH] ∼ -4/1. Similar ratios for the other groups are derived from the shifts in the dihydroxy alkane series upon further functionalization: Δ[CHn] /Δ[C(=O)OH] ∼ -5/2, Δ[CHn] /Δ[CHnC(=O)] ∼ -2/3, Δ[CHn] /Δ[HC(=O)] ∼ -4/2, Δ[CHn] /Δ[CHn(O)] ∼ -2/4, Δ[CHn] /Δ[CHn(OOH)] ∼ -2/2, Δ[CHn] /Δ[CHnC(=O)] ∼ -2/3, and Δ[CHn] /Δ[CHnONO2] ∼ 2/3. This leads to a sorting of relative effectiveness of the groups in promoting miscibility, hydroxyl (-4) > acid (-2.5) > aldehyde (-2) > hydroperoxide (-1) > carbonyl (-0.66) > ether (-0.5) > nitrate (0.66), where the number in parentheses corresponds to the Δ[CHn] /Δ[n]. According to this model the addition of nitrate groups is in the same direction as methylene groups; i.e., it reduces miscibility. This finding is consistent with CCN experiments on alkenes reacted with NO3 radicals (Suda et al., 2014, their Supplement), and the known low miscibility of organic nitrates in water (Boschan et al., 1955). Furthermore, sorting of the different functional groups is qualitatively consistent with the sensitivity of κ to the addition of functional groups derived from CCN data (Table S5, Suda et al., 2014).

This paper describes how functional group contribution methods can be used to estimate the CCN activity of pure organic compounds. Group interaction parameters were taken from a mix of sources and used without further tuning. Model fidelity was evaluated against a database of published CCN data. Weakly functionalized alkanes are correctly classified as effectively CCN inactive (defined as κ < 0.001). Highly functionalized and water-soluble molecules are predicted to activate in accordance with the estimated molar volume and generally predictions agree with observations within a factor of 2. Liquid–liquid phase separation is predicted to occur for compounds with few functional groups and phase separation is predicted to control κ. The model adequately reproduces the observation that hydroxyl groups strongly promote CCN activity while nitrate groups inhibit CCN activity. A few outliers in the model evaluation may be explained by the combination of CCN measurement uncertainty, compound purity, uncertainty in dry particle phase state, and insufficiently tuned group interaction parameters. However, more systematic data on weakly functionalized compounds, including repeat studies, are needed before a retuning of parameters is justified. The model makes new predictions about the relative effectiveness of the groups in promoting miscibility. Most notably, it predicts that hydroperoxides have much less of an effect than hydroxyl, which is slightly surprising since one would expect the hydrogen bonding to be similar. The model state space can serve as a rough guide to define test conditions to quantify via experiment the effectiveness of adding one or more functional groups to a carbon backbone.

Although this work is limited to a few functional groups, the presented framework is general since interaction parameters are available for a wide range of groups. For atmospheric purposes, amines, olefins, and aromatic compounds are the most relevant groups that need to be added. Few, if any, systematic CCN data for these groups are available. However, the success of the current model to estimate κ without the need to tune parameters could be taken as an indication that first-order predictions can be obtained until such data become available.

Source code and example scripts demonstrating model initialization for the compounds presented in this study are available as Supplement to this manuscript.