The cloud condensation nucleus (CCN) activity of organic-sulfate particles was investigated using a steady-state environmental chamber. The organic component consisted of secondary organic aerosol (SOA) generated in the dark from 24 ± 2 ppb α-pinene for conditions of 300 ± 5 ppb ozone, 40 ± 2% relative humidity, and 25 ± 1°C, with the organic mass loading in the chamber ranging from 23 to 37 μg m−3. CCN analysis was performed for 80- to 150-nm particles having variable organic-sulfate volume fractions, which were estimated from the diameter of the organic-sulfate particle relative to that of the seed as well as independently from mass spectra. Critical supersaturation, which increased for greater SOA volume fraction and smaller particle diameter, was well predicted by a Köhler model having two components, one for ammonium sulfate and another for SOA. The entire data set could be successfully modeled by a single suite of effective chemical parameters for SOA. The results suggest that the effects of limited organic solubility in mixed SOA-sulfate particles may be reliably omitted in the treatment of cloud droplet formation.
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 Tropospheric aerosol particles affect the earth's climate by several mechanisms, including among others their potential to form cloud droplets. Current understanding of the activation potential of cloud condensation nuclei (CCN) remains incomplete, especially for organic compounds, which constitute a large mass fraction of ambient fine particulate matter [Fuzzi et al., 2006]. Particulate organic matter originates from both primary and secondary sources, the latter of which include the oxidation of anthropogenic and biogenic emissions. Biogenic emissions, including isoprene, monoterpenes, and sesquiterpenes, are the larger source of global secondary organic aerosol (SOA) [Kanakidou et al., 2005].
 An environmental chamber, consisting of a constant temperature room housing a flexible Teflon bag (Welch Fluorocarbon Inc.) of approximately 5 m3, was operated continuously for several weeks in a feedback-controlled constant-volume mode, for which the flow in equaled the flow out. A schematic diagram of the experimental setup is shown in Figure S1. The conditions that were monitored and held constant were temperature (25 ± 1°C), relative humidity (RH) (40 ± 2%), and ozone concentration (300 ± 5 ppb). The NOx concentration remained below 1 ppb. For the approximation of a completely mixed flow reactor, the corresponding residence time in the chamber was 4 hours. Steady-state conditions of all measurables were reached after 24 hours and maintained indefinitely.
 Dry (NH4)2SO4 seed particles and α-pinene (Aldrich, 98%) vapor were continuously introduced into the bag. Sulfate particles from a TSI 3076 atomizer were passed through a 160-cm silica gel diffusion dryer (RH < 10%), followed by a 85Kr bipolar charger and a differential mobility analyzer (DMA1, TSI 3071). DMA1 was operated with sheath and monodisperse aerosol flows of 10 and 2 Lpm, respectively, to obtain a quasi-monodisperse seed aerosol. A syringe pump injected a 1:600 (v/v) mixture of α-pinene and 1-butanol (serving as an OH scavenger) into a bulb that was flushed with clean air. Based on the flow rates, the α-pinene available for reaction in the bag had an equivalent mixing ratio of 24 ± 2 ppb. Reaction of α-pinene by dark ozonolysis led to the formation of SOA, which condensed onto the seed particles and induced particle diameter growth. The SOA mass loading varied between 23 and 37 μg m−3 during the course of the experiments. The possibility of externally mixed organic particles was ruled out because no nucleation events were observed and because measured particles were larger than the seed particles.
 The aerosol in the outflow from the chamber passed through a diffusion tube having an outer annulus filled with ozone destruction catalyst. The flow was then split for simultaneous sampling by (1) a scanning mobility particle sizer (SMPS, TSI 3936), (2) a condensation particle counter (CPC1, TSI 3022), (3) an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) [DeCarlo et al., 2006], and (4) a DMA2 (TSI 3081, sheath:sample flow ratio of 10:1), the outflow of which was split to a CPC2 (TSI 3772) and a cloud condensation nucleus counter (CCNC, DMT Inc.) [Roberts and Nenes, 2005]. Particles were recharged before sampling by the SMPS and DMA2. Calibration of the CCNC was performed with (NH4)2SO4 at supersaturations of 0.090%, 0.26%, 0.43%, 0.60%, and 1.02% using equations described by Shilling et al.  (Table S1). Rose et al.  discuss in further detail the calibration and measurement uncertainties of the DMT CCNC. DMA2 was used to select a monodisperse aerosol from the chamber, and the activated CCN fraction (Fa) was calculated as the number concentration of activated droplets counted by the CCNC divided by the total number concentration detected by CPC2. In the experimental procedure, Fa was measured for increasing supersaturation, and the data were fit with a sigmoidal curve using a filter to omit the effect of multiply charged particles [Asa-Awuku et al., 2007]. The supersaturation at which Fa = 0.5 was defined as the critical supersaturation (Sc).
3. Multiple-Component Köhler Model
 The model used to describe the CCN activity of internally mixed organic-sulfate particles is based on Köhler  theory, which expresses the vapor pressure of water over an aqueous droplet as follows:
where s is the saturation ratio relative to a flat surface of liquid water, aw is the water activity of the solution, σ is the solution-vapor surface tension, Mw is the molecular weight of pure water, R is the universal gas constant, T is the solution temperature, ρw is the density of pure water, and Daq is the aqueous particle diameter. The maximum of equation (1) (smax) corresponds to the critical supersaturation Sc = smax − 1.
 The water activity for a multi-component solution is given by:
where nw is the number of moles of water, nk is the number of moles of species k in solution, and ik is the corresponding van't Hoff factor. The possibility of limited solubility of species k is incorporated by using an expression adapted from Henning et al. :
where Csat,k is the saturation concentration of species k (g g−1·H2O), ρw′ is the density of water in solution (taken equal to ρw for dilute conditions), ɛk is the volume fraction in the dry particle, ρk is the density, D0 is the diameter of the dry particle, and Mk is the molecular weight.
4. Results and Discussion
 CCN activity was investigated for particles having midpoint mobility diameters of 80, 100, 120, and 150 nm, each varying in organic volume fraction depending on sulfate seed diameter (27, 31, 41, 51, 59, 71, or 88 nm). Figure 1a shows a typical number size distribution of particles exiting the chamber for a seed diameter of 71 nm. The organic volume fraction (ɛSOAd) was calculated from the increase in particle diameter relative to the seed particle. Spherical dry particles were assumed. In addition, the size-dependent sulfate and organic mass loadings were measured with the HR-ToF-AMS, from which the organic mass fraction was calculated and converted using organic density to a second, independent measurement of volume fraction (ɛSOAmass) (Figure 1b). The organic density (ρSOA = 1.4 ± 0.1 g cm−3) was determined from the mode diameters of the vacuum-aerodynamic size distribution and the mobility size distribution, assuming a spherical particle shape and including a correction for the density of ammonium sulfate [DeCarlo et al., 2004; Katrib et al., 2005]. A scatter plot of ɛSOAd and ɛSOAmass shows good agreement (Figure 1c). AMS measurements also confirmed that the SOA chemistry was stable during the course of experiments (Figure S3). A full V-mode ToF-AMS spectrum of SOA having a 71-nm ammonium sulfate core is also shown in Figure S2. For example, the ratio of the signal intensity at m/z 43 to that at m/z 44 fell between 1.24 and 1.41 for all experiments.
 Critical supersaturation (Sc) increased for greater SOA volume fraction and smaller particle diameter (Figure 2 and Table S2). The curves in Figure 2 show the least-squares fit of a two-component model that uses equations (1) to (3). The model consists of ammonium sulfate as one chemical component and SOA as a second effective chemical component (i.e., SOA is a mixture consisting of many organic species). The effective SOA molecular weight (MSOA) was obtained as an optimized model fit to the entire data set shown in Figure 2 for fixed values of the surface tension (σ), the effective SOA density (ρSOA), and the effective van't Hoff factor of SOA (iSOA) (Table 1). The optimization had no sensitivity to the effective saturation concentration of the organic component (Csat,SOA) provided that a lower limit of 0.070 g g−1·H2O was exceeded. The values of iSOA and σ were assumed equal to 1 and 0.0725 N m−1, respectively. MSOA, the target of the global optimization, was constrained as 178 ± 3 g mol−1 based on the least-squares fit of the entire data set using a Monte Carlo approach to vary Sc values within their uncertainties.
Table 1. Parameters Used in Köhler Model to Calculate Sca
 The sensitivity of the modeled Sc was evaluated by applying perturbations of approximately 10% to each input parameter (σ, ρSOA, iSOA, and MSOA). For the range of perturbations investigated, Table S3 shows that changes in σ have the greatest effect on the modeled Sc. Correspondingly, the constrained value of MSOA depends most strongly on the assumed value of σ. Further sensitivity studies were therefore performed by simultaneously optimizing for both σ and MSOA, obtaining values of 0.0702 N m−1 and 202 g mol−1, respectively. This value of σ, which is close to that of pure water, suggests the absence of significant surface-tension lowering by organic molecules. For values of σ between 0.0702 and 0.0725 N m−1, MSOA ranges from 178 to 202 g mol−1.
 An implication of Csat,SOA > 0.070 g g−1·H2O is that the mixed organic-sulfate particles were fully solvated at activation, up to the largest measured organic fraction. The raw data further support this model-based conclusion, notably through the absence of an abrupt discontinuity in Sc for increasing ɛSOAd in Figure 2, contrary to the behavior of a limited-solubility system (inset b) [Henning et al., 2005]. Moreover, adjustments in the values of the SOA parameters in Table 1 do not allow the data of Figure 2 to be fit by a limited-solubility assumption (analysis not shown). As indicated in inset b, the ɛSOAd at which the discontinuity occurs depends on Csat,SOA. Thus, the lower limit of Csat,SOA for this study can be calculated from the largest measured ɛSOAd for which there is no discontinuity. This lower limit is, however, much higher than expected given the chemical composition of dark ozonolysis α-pinene SOA [Glasius et al., 2000]. To explain the greater apparent organic solubility, we hypothesize that the high effective SOA solubility arises because the particles are either supersaturated aqueous solutions of organic material at 40% RH [Bilde and Svenningsson, 2004] or liquids or amorphous solids even at low water activity [Marcolli et al., 2004].
 Using the effective SOA parameters, we can predict the CCN activity of pure SOA particles and thereby compare with previous CCN studies that were performed in the absence of inorganic seed particles. CCN data from three studies of the dark ozonolysis of α-pinene SOA are shown in Figure 3 [Hartz et al., 2005; VanReken et al., 2005; Prenni et al., 2007]. The solid line corresponds to the effective SOA parameters of this study, thus implicitly assuming no solubility-limited behavior for ɛSOAd → 1. The dotted line is calculated using the parameters of Hartz et al. . Both model results agree with the data of Prenni et al.  and with each other, which is expected because the MSOA: ρSOA ratio of 146 cm3 mol−1 from Hartz et al. is similar to that of 127 ± 12 cm3 mol−1 determined in this study (see equation (3)). The ρSOA value of 1.2 g cm−3 assumed by Hartz et al. is lower than our measured ρSOA value of 1.4 ± 0.1 g cm−3. The MSOA value of 178 to 202 g mol−1 of this study is slightly greater than the value of 175 g mol−1 of Hartz et al., who estimated MSOA using literature-based reports of α-pinene SOA products. Possible hypotheses to explain the different values of MSOA include (1) that the product species reported in the literature omit high molecular weight oligomers or (2) that SOA composition and hence MSOA are not fixed quantities, possibly depending on reaction conditions and mass loadings. The results for MSOA can also differ depending on the theoretical framework used for analysis of CCN observations, most notably in the treatment of water activity. For example, the model described in this study assumes the additivity of species (see equation (2)) because of the absence of knowledge on the interaction terms between SOA molecules and ammonium sulfate ions. Therefore, MSOA should be regarded as an effective molecular weight and not a physical molecular weight.
5. Conclusions and Atmospheric Implications
 The results of this study show that the CCN behavior of mixed multi-component organic-sulfate particles is well predicted by a two-component Köhler model. The critical supersaturations for a range of atmospherically relevant sizes and compositions lie between 0.1% and 0.5%, well within the range of possible atmospheric conditions. Findings from this and other related laboratory studies of CCN activity serve as the physical basis to describe aerosol-cloud interactions in general circulation models as well as in explicit cloud-resolving models. Many treatments have supposed the necessity of employing a modified Köhler theory that incorporates the effects of limited solubility [Nenes and Seinfeld, 2003]. Our study implies that computations of CCN spectra can be simplified (yet remain accurate) by omitting the consideration of limited solubility for the mixed organic-sulfate particles prevalent in the atmosphere, at least for the range of conditions and types of particles considered in this study.
 This material is based upon work supported by the National Science Foundation under Grant ATM-0513463. SMK acknowledges support from the EPA STAR fellowship program. TR acknowledges support from the Danish Agency for Science Technology and Innovation under Grant 272-06-0318. We thank the Carnegie Mellon University Air Quality Laboratory for helpful consultation.