Role of molecular size in cloud droplet activation

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L22801, doi: /2009gl040131, 2009 Role of molecular size in cloud droplet activation M. D. Petters, 1,2 S. M. Kreidenweis, 1 A. J. Prenni, 1 R. C. Sullivan, 1 C. M. Carrico, 1 K. A. Koehler, 1 and P. J. Ziemann 3 Received 22 July 2009; revised 27 September 2009; accepted 5 October 2009; published 17 November [1] We examine the observed relationships between molar volume (the ratio of molar mass and density) and cloud condensation nuclei (CCN) activity for sufficiently soluble organic compounds found in atmospheric particulate matter. Our data compilation includes new CCN data for certain carbohydrates and oligoethylene glycols, as well as published data for organic compounds. We compare predictions of CCN activity using water activities based on Raoult s law and Flory-Huggins theory to observations. The Flory-Huggins water activity expression, with an assumed surface tension of pure water, generally predicts CCN activity within a factor of two over the full range of molar volumes considered. CCN activity is only weakly dependent on molar volume for values exceeding 600 cm 3 mol 1, and the diminishing sensitivity to molar volume, combined with the significant scatter in the data, limits the accuracy with which molar volume can be inferred from CCN measurements. Citation: Petters, M. D., S. M. Kreidenweis, A. J. Prenni, R. C. Sullivan, C. M. Carrico, K. A. Koehler, and P. J. Ziemann (2009), Role of molecular size in cloud droplet activation, Geophys. Res. Lett., 36, L22801, doi: /2009gl Introduction [2] Organic particulate matter contributes 30 80% to the non-refractory, submicron, atmospheric aerosol mass burden [Zhang et al., 2007]. Many organic compounds are water soluble and therefore contribute to the hygroscopicity of the aerosol, which in turn influences the ability of individual particles to serve as cloud condensation nuclei (CCN). By altering number and chemical composition of CCN populations, organic compounds also indirectly affect cloud droplet number concentrations and precipitation intensity, and in turn modify the Earth s radiation budget [Andreae and Rosenfeld, 2008]. Maria et al. [2004] estimated that the organic aerosol indirect effect contributes 1 W m 2 Tg 1 to the top of atmosphere forcing. However, this estimate is highly uncertain because most of the organic aerosol is uncharacterized, making it difficult to assess the ability of organic aerosols to serve as CCN. 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, USA. 2 Now at Department of Marine Earth and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina, USA. 3 Air Pollution Research Center, University of California, Riverside, California, USA. Copyright 2009 by the American Geophysical Union /09/2009GL [3] Köhler theory provides a link between pure compound properties and the water supersaturation that must be exceeded before a particle of known size activates as a CCN. In its most basic form it describes the saturation ratio, S, over a curved droplet S ¼ a w exp A D ; where a w is the water activity of the solution, D is the diameter of the droplet, A = s s/a /T, s s/a is the surface tension of the solution/air interface in J m 2, T is temperature in Kelvin, and volume additivity is assumed. The critical saturation ratio, S c, required for a dry particle to activate as a CCN is computed from the maximum of equation (1), with respect to diameter. The water activity term must either be measured as a function of water content or alternatively can be calculated from a theory that applies to aqueous solutions. If Raoult s law is chosen, analytically obtained relations between the particle dry diameter, D d, and critical supersaturation, s c = S c 1, can be derived [Seinfeld and Pandis, 1998]. The so-derived s c D d relationship depends on the dry particle chemical composition and indicates the efficiency with which a particle can serve as CCN in the atmosphere. More efficient CCN are those particles that activate at lower supersaturation when compared to another particle of equal diameter. In this framework, the chemical properties that determine the CCN efficiency are the molecular weight and density of the solute, the non-ideality of the solution, the surface tension of the dilute aqueous solution and the ability of the compound to dissociate in solution. Using Raoult s law as the model for the water activity-composition relationship, several recent studies have used measurements of s c and D d to infer some of these chemical properties, often with emphasis on deriving an effective molecular weight [Asa- Awuku et al., 2009; Engelhart et al., 2008; King et al., 2007; Moore et al., 2008; Padro et al., 2007; Shilling et al., 2007]. This type of analysis tacitly assumes that CCN efficiency scales with molecular weight, as predicted by Raoult s law, and that all compounds are sufficiently soluble to be fully dissolved at dilutions relevant to those found near the wet critical diameter where s c is reached. These assumptions seem justfied since prior studies suggest that the CCN behavior of many compounds is well modeled using Raoult s law [e.g., Rosenørn et al., 2006]. On the other hand, water soluble polymers are much more active than anticipated by Raoult s law [Petters et al., 2006], but it is unclear if atmospherically relevant high molecular weight compounds ( g mol 1 ) [Dinar et al., 2006] strongly deviate from Raoult s law. The purpose of this work is to examine the observed relationship between molar ð1þ L of5

2 from molecular weight, density, and dissociation for a single compound from [Kreidenweis et al., 2009] k Raoult ¼ n r sm w r w M s ¼ n f w f s ; ð3þ Figure 1. Expected relationships between molar volume and apparent hygroscopicity from traditional Köhler theory based on Raoult s law (solid black line), Flory-Huggins Köhler (FHK) theory with zero enthalpy of mixing (red lines), and modified Köhler theory based on Raoult s law and including solubility (black dashed lines). Grey shadings indicate range of apparent hygroscopicity for a surface tension reduction down to J m 2, 10% lower than for pure water. volume and CCN efficiency for a broad range of organic compounds. 2. Theoretical Considerations [4] The lack of detailed chemical information for ambient particles has led to semi-empirical formulations of Köhler theory where chemical effects are expressed by a single parameter [Hudson and Da, 1996; Petters and Kreidenweis, 2007; Rissler et al., 2006; Svenningsson et al., 1994; Wex et al., 2007]. Although each formulation is tied to slight variants in the starting equation, and thus is only applicable to ranges that do not violate the initial assumptions (e.g., dilute solution approximations, volume additivity), all single parameter representations are identical in spirit, namely that they obviate the need to explicitly specify physicochemical parameters for each compound. Here we use the formalism of Petters and Kreidenweis [2007] who defined the hygroscopicity parameter k through D 3 D 3 d SD ð Þ ¼ D 3 D 3 d ð1 kþ exp A D : ð2þ Although the derivation of equation (2) is grounded in Raoult s law, equation (2) can be applied to any pair of s c and D d to obtain an apparent hygroscopicity, k app [Sullivan et al., 2009; Pöschl et al., 2009]. In the most basic interpretation, k app -values can be understood to simply pinpoint the observed CCN activity in s c D d space, with higher values of k app indicating greater CCN activity. Because surface tension is assumed to equal that of pure water when fitting k app to s c D d data, and solubility is not included in equation (2), k app can contain contributions from water activity, solubility, and solution surface tension in unknown proportions. On the other hand, if surface tension and solubility do not play a role, and Raoult s law holds (i.e. the solution behaves ideally), k can be computed where f w = M w /r w and f s = M s /r s are the molar volumes of water and solute, respectively. Non-ideal behavior can be included in equation (3), and we discuss this later. For a non-dissociating compound, ln(k Raoult )=lnf w ln f s and thus k is expected to decrease linearly with solute molar volume when plotted in log-log space (Figure 1, solid black line). [5] Statistical mechanics conceptualizes Raoult s law as a liquid lattice where each cell is occupied by a single molecule, either solute or solvent. For molecules where the solute is much larger than the solvent, the lattice model underestimates the number of states into which the system can arrange, because segments of solute molecules can partially mix with solvent molecules. Flory [1953] showed how to account for this and developed an equation for the water activity of an idealized solution for arbitrary values of f s when accounting for partial mixing of molecular segments. Using this expression for water activity in an analog of equation (2), Flory-Huggins Köhler (FHK) theory is given by [Petters et al., 2006] SD ð Þ ¼ 1 D3 d D 3 exp 1 f w f s D 3 d D 3 exp A D ; where we assumed that the Flory interaction parameter c = 0. The resulting s c D d pair can then be used to compute a corresponding k app from equation (2) and the predicted relationship is superimposed on Figure 1 for two assumed dry diameters (red lines). For small molecules, i.e., f w /f s 1, Raoult s law and FHK give similar predictions for k app. Significant deviations from Raoult s law are only seen for f s > 200 cm 3 mol 1 (M s g mol 1, typically compounds with more than eight carbon atoms in the molecular structure), where FHK predicts that particles are more CCN active than would be expected from Köhler theory assuming ideality throughout the activation process and no dissociation of the solute. [6] Neither form of Köhler theory presented here accounts for the solubility of compounds in water. Solubility was introduced into Köhler theory by Shulman et al. [1996] and several variants of their formulation have been used to model experimental data of sparingly soluble compounds [e.g., Bilde and Svenningsson, 2004; Hori et al., 2003; Raymond and Pandis, 2003]. Petters and Kreidenweis [2008] extended the k-framework to explicitly include solubility (C), where C is expressed as volume of solute per unit volume of water present in a saturated solution. Characteristic C values can be used to classify compounds into three distinct types [Hori et al., 2003;Petters and Kreidenweis, 2008]. Type I compounds (C > 0.1) are sufficiently soluble and calculated critical supersaturations are not sensitive to C. Type II compounds ( < C < 0.1) are moderately soluble and values of C have a strong effect on the experimentally determined critical supersaturations, resulting in values ranging from 0 < k app < intrinsic hygroscopicity parameter. The intrinsic hygroscopicity parameter ð4þ 2of5

3 is the k-value that would be observed in the absence of solubility limitations [Sullivan et al., 2009]. Type III compounds (C <510 4 ) are practically insoluble and classified by k app =0. [7] Here we follow the method described by Sullivan et al. [2009] to calculate k app. However, in contrast to Sullivan et al. [2009] who fixed D d, k Raoult and varied solubility, we choose a molar volume, calculate k Raoult using Raoult s law, and construct isopleths of k app as functions of molar volume, assuming a constant particle dry diameter and solubility. These isopleths are depicted in Figure 1 by the dashed lines for C = 0.1 and 0.5, and D d = 50 and 100 nm. The dashed lines intersect with the prediction based on Raoult s law (solid line). For molar volumes smaller than that at the intersection, the chosen solubility is sufficiently large to have no effect on droplet activation. For example, the CCN activity of a 50 nm particle with C = 0.5 is not expected to be solubility limited for f s < 300 cm 3 mol 1. At larger molar volumes solubility limitation results in a decrease in k app. The dependence of apparent k on molar volume arises through variations in saturated solution water activities. Individual saturated solutions of two compounds with different molar volumes, but the same solubility, will have identical volume fractions of water, but the water activity at saturation (a w,sat ) is larger for the compound with larger molar volume. This raises the solubility-controlled critical saturation ratio, given by a w,sat exp A D d for single component particles [Kreidenweis et al., 2006], for compounds with larger molar volume. The isopleths in Figure 1 describe the ranges of molar volumes where the transitions from classical activation to solubility-limited activation occur. [8] Many organic compounds, especially those that have large molecular volumes and structures with hydrophobic and hydrophilic ends, are preferentially located near the liquid/air interface, resulting in a depression of the solution surface tension. Measurements of surface tension depression in bulk solutions suggest that this effect may be important for many atmospherically-relevant organic compounds [e.g., Facchini et al., 1999]. Unfortunately, including measured surface tension depression into Köhler theory is not straightforward because surface-to-bulk partitioning alters k Raoult and s s/a simultaneously [Li et al., 1998; Sorjamaa et al., 2004], with often intractable complications for multicomponent systems. Further, if solubility is unknown k app is insufficient to constrain the water content at activation [Petters and Kreidenweis, 2008] and since surface tension depression is a function of water content it is unclear what value should be chosen to evaluate the solution surface tension near activation. Nevertheless, several studies have attempted to indirectly constrain s s/a from a combination of hygroscopic growth and CCN measurements [Engelhart et al., 2008; King et al., 2009; Shilling et al., 2007; Wex et al., 2009]. Combined, these studies suggest that s s/a > J m 2 for surface active organic compounds at the point of activation, a 10% reduction from the value of pure water. Kreidenweis et al. [2009] examined the basic sensitivity of the critical supersaturation to parameters in the Köhler equation by expressing relative changes in surface tension to equivalent changes in k app and found that a 10% reduction in surface tension is equivalent to a 30% increase in k app, neglecting bulk-surface partitioning, solubility limitations, and assuming k > 0.1. We indicate this range by the grey shadings in Figure Data and Methods [9] Our objective is to amass a sufficient number of experimental data points to fill the state space of k app versus molar volume, and compare these to the predicted relationships displayed in Figure 1. We surveyed the literature for CCN measurements of organic compounds with known molecular weights, solubilities, and densities, and fit the s c D d data to derive k app. A detailed list of compounds selected, their properties, and their k app values are given in the auxiliary material. 1 Here we focus on compounds with C > 0.1 to highlight the relationship between soluble organic compounds and molar volume. [10] We also performed new measurements on certain carbohydrates and oligoethylene glycols to better explore the range of molar volumes shown in Figure 1. Our measurement protocols are described in detail by Petters et al. [2007]. In brief, our system consists of a Droplet Measurement Technologies (DMT) CCN counter, a differential mobility analyzer (DMA), and a condensation particle counter (CPC). The DMA/CPC system measures the aerosol size distribution in DMPS mode ( nm) while simultaneously measuring size resolved CCN activity at constant supersaturation. The calibration procedure, the specific compounds studied, the multiple charge correction and the derivation of the measured k app -values are reported in the auxiliary material and in prior publications [Petters and Kreidenweis, 2007; Petters et al., 2007]. 4. Discussion [11] Figure 2 illustrates the observed k app as a function of molar volume. The data show that most compounds, on average, obey Raoult s law at low molar volumes and Flory- Huggins at all molar volumes. Nevertheless, the data scatter by a factor of two around the Flory-Huggins prediction and we attribute this to a combination of measurement uncertainties/calibration differences, surface tension effects, and non-ideal solution effects. The purity of the commercially available compounds varies and ranges from %. A contaminant of 1% sodium chloride by volume would add to a particles k app [Bilde and Svenningsson, 2004; Petters and Kreidenweis, 2007]. Further, the unknown initial phase state, particle microstructure, and unquantified losses due to evaporation during the measurement for compounds with higher vapor pressures can result in erroneous estimates of the dry solute volume and may lead to biased k app [Mikhailov et al., 2004; Koehler et al., 2006]. Surface active compounds may result in an increased k app but our earlier analysis suggests that for typical surface active organic compounds this effect is <30%. To bring the most obvious outliers (points #5 and #33 35 in Figure 2) into agreement with Raoult s law, an unrealistic surface tension value of J m 2 must be assumed at the point of activation. Similarly, to explain the deviation of point #33 1 Auxiliary materials are available in the HTML. doi: / 2009GL of5

4 [14] Acknowledgments. This research was funded by the Office of Science (BER), U.S. Department of Energy, under DE-FG02-05ER Figure 2. Apparent hygroscopicity obtained from CCN measurements versus molar volume, for sufficiently soluble single compounds. Vertical bars show the range of hygroscopicity and estimate the uncertainty in the individual CCN measurement. Uncertainties in molar volume are contained within the symbol size. Red and black symbols indicate compounds contributed by this study and the literature survey, respectively. Numbers identify individual compounds listed in Table S1 of Text S1. Compound # 1 6: organic acids, 7 18: carbohydrates, 19 26: synthetic oligomers, 27 33: fulvic acid fractionated by molecular weight, atmospheric humic like substances. References and data quality screening methods are discussed in the auxiliary material. The lines show expected relationships between apparent hygroscopicity and molar volume calculated for Flory-Huggins (100 nm dry diameter) and Raoult s law water activity (independent of dry diameter). Dashed lines show ±100% deviation from the FH prediction. from Raoult s law with uncertainty in molar volume, an unrealistic density of 10 g cm 3 would be required. [12] Non-ideal effects can lead to positive and negative deviations from Raoult s or FHK calculations. If Raoult s law is chosen to represent the ideal state, k app / F [Kreidenweis et al., 2009], where F is the practical osmotic coefficient and F = 1 corresponds to the reference ideal solution. Typical values of F for dilute organic acids are 0.7 < F < 1.3 [Clegg and Seinfeld, 2006], corresponding to a ±30% relative change in k app, leading to similar deviations from the ideal state due to surface tension effects as shown by the grey bars in Figure 1. [13] Overall the data in Figure 2 suggest that the Flory- Huggins water activity expression (or Raoult s law for low molecular weight compounds), predicts CCN activity expressed as apparent hygroscopicity within a factor of two. This is twice as large as the average uncertainty in individual CCN measurements as indicated by the vertical bars in Figure 2. Methods that rely on CCN measurements to infer chemical parameters such as molecular weight will be limited by this uncertainty. For low molar volumes, where Raoult s law is valid, a 100% relative uncertainty in k app corresponds to an equal relative uncertainty in molar volume. At larger molar volumes, e.g., 1000 g mol 1,a 100% relative uncertainty in k app corresponds to a >500% relative uncertainty in inferred f s on the basis of FHK, because k app becomes insensitive to changes in molar volume. 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