Surface tensions of solutions containing dicarboxylic acid mixtures

Surface tensions of solutions containing dicarboxylic acid mixtures

Atmospheric Environment 89 (2014) 260e267 Contents lists available at ScienceDirect Atmospheric Environment journal homepage: www.elsevier.com/locat...

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Atmospheric Environment 89 (2014) 260e267

Contents lists available at ScienceDirect

Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv

Surface tensions of solutions containing dicarboxylic acid mixtures Jae Young Lee*, Lynn M. Hildemann Civil & Environmental Engineering Dept., Stanford University, Stanford, CA 94305, USA

h i g h l i g h t s  Surface tension of dicarboxylic acid mixture was measured using Wilhelmy plate method.  Surface tension of dicarboxylic acid mixture follows the most surface-active one.  Modified Szyszkowski equation systematically overestimates the surface tensions.  Henning’s model systematically overestimates the surface tensions.  The critical supersaturation ratio is reduced by adding dicarboxylic acids.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 July 2013 Received in revised form 18 February 2014 Accepted 21 February 2014 Available online 22 February 2014

Organic solutes tend to lower the surface tension of cloud condensation nuclei, allowing them to more readily activate. The surface tension of various dicarboxylic acid aerosol mixtures was measured at 20  C using the Wilhelmy plate method. At lower concentrations, the surface tension of a solution with equimolar mixtures of dicarboxylic acids closely followed that of a solution with the most surface-active organic component alone. Measurements of surface tension for these mixtures were lower than predictions using Henning’s model and the modified Szyszkowski equation, by w1e2%. The calculated maximum surface excess (Gmax) and inverse Langmuir adsorption coefficient (b) from the modified Szyszkowski equation were both larger than measured values for 6 of the 7 mixtures tested. Accounting for the reduction in surface tension in the Köhler equation reduced the critical saturation ratio for these multi-component mixtures e changes were negligible for dry diameters of 0.1 and 0.5 mm, but a reduction from 1.0068 to 1.0063 was seen for the 4-dicarboxylic acid mixture with a dry diameter of 0.05 mm. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Aerosol Organic aerosol Cloud condensation nuclei Climate change Surface tension Dicarboxylic acid

1. Introduction According to Köhler theory (Köhler, 1936), surface tension affects the formation and properties of clouds. The critical supersaturation required for activation of an aerosol into a cloud droplet is reduced when the surface tension decreases. Previous studies have reported that the presence of organic compounds in atmospheric aerosols lowers surface tension and critical supersaturation ratios for cloud droplets (e.g., Facchini et al., 1999; AsaAwuku et al., 2008; George et al., 2009; Aumann et al., 2010). As a result, a larger number of smaller-sized droplets is created. This contributes to the indirect effect of aerosols on climate change by increasing the cloud albedo (Twomey, 1974, 1977) and extending

* Corresponding author. E-mail addresses: [email protected], [email protected] (J. Y. Lee). http://dx.doi.org/10.1016/j.atmosenv.2014.02.049 1352-2310/Ó 2014 Elsevier Ltd. All rights reserved.

the cloud’s lifetime (e.g., IPCC, 2007; Kanakidou et al., 2005; Novakov and Penner, 1993). Organic compounds account for 20e90% of the total fine particle mass in the troposphere (e.g., Andreae and Rosenfeld, 2008; Kanakidou et al., 2005; Putaud et al., 2004). In addition, organic compounds emitted from anthropogenic and natural sources such as biomass burning are predicted to increase in the future (Andreae and Rosenfeld, 2008; Wagener et al., 2012). Among the organic components, dicarboxylic acids have been frequently measured (e.g., Sun and Ariya, 2006); oxalic, malonic and succinic acids are three of the most prevalent dicarboxylic acids in aerosols (Braban et al., 2003; Sun and Ariya, 2006). Due to their abundance in the atmosphere and relatively high solubility in water, a better understanding is needed regarding the effect of dicarboxylic acids on aerosol surface tension. Previous studies have measured surface tensions for a wide variety of single-component solutions. Inorganic salts have been reported to increase the surface tension of aqueous solutions by

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many researchers (e.g., Tuckermann, 2007; Weissenborn and Pugh, 1996; Abramzon and Gaukhberg, 1993). Various organic species, on the other hand, have been shown to decrease the surface tension. Tuckermann (2007) tabulated the surface tension data for pure organic solutions available in the literature. Aumann et al. (2010) also measured the surface tension for a large number of pure organic solutions including saccharides, dicarboxylic acids, aromatic polycarboxylic acids, alkanoic acid salts, and humic substances. Hyvärinen et al. (2006) studied the surface tension of dicarboxylic acid and cis-pinonic acid solutions as a function of temperature. The surface tension of multi-component solutions also has been examined in previous studies. Tuckermann (2007) measured the surface tension of aqueous solutions containing an organic component (cis-pinonic acid) and an inorganic salt such as sodium chloride. The author observed that the effect of inorganic salt on the overall surface tension depends on the concentration of cis-pinonic acid in the solution. Other experiments on multi-component solutions have been carried out by Abramzon and Gaukhberg (1993), Shulman et al. (1996), Li et al. (1998), Fainerman et al. (2002), Kiss et al. (2005), Henning et al. (2005), Topping et al. (2006), Prisle et al. (2011), and Lee and Hildemann (2013). A common approach for predicting the surface tension of aqueous solutions containing mixed water soluble organic compounds is to use a linear combination of the surface tensions for the individual components (Tuckermann and Cammenga, 2004; Henning et al., 2005). To combine surface tensions, Tuckermann used a weighted sum based on concentrations of the individual components, while Henning used a weighted sum based on a carbon content ratio. However, there are still relatively few experimental studies on the surface tension of organic mixture solutions. Even though real atmospheric samples are composed of complex mixtures of organics, the interactions between species in multicomponent aqueous solutions are poorly understood. In this study, the surface tension of aqueous solutions containing dicarboxylic acid mixtures was measured to examine the effect of organic mixtures on the overall surface tension. The surface tension of various types of dicarboxylic acid mixtures containing two, three or four components (e.g., malonic/glutaric acid mixtures, oxalic/malonic/succinic acid mixtures) was measured at 20  C based on the Wilhelmy plate method. Our surface tension measurements were fitted to the Szyszkowski equation and compared with the predictions made using the modified Szyszkowski equation and Henning’s model (Henning et al., 2005). In addition, the Köhler equation was used to analyze the effect of the surface tension reduction on the critical saturation ratio.

2. Experimental procedures 2.1. Materials The properties of the dicarboxylic acids tested in this study are listed in Table 1, including the chemical formula, molecular mass (g/

261

Fig. 1. Schematic of surface tension measurement apparatus. This drawing shows the interconnections between: (1) a tensiometer; (2) a programming monitor; (3) a thermostat regulator; (4) a refrigerated chiller; and (5) a double boiler system.

mol), density (g/cm3), solubility (g/100 g of water), and manufacturer information for each of these water soluble compounds. 2.2. Surface tension measurements To measure the surface tension of a solution, methods used in previous studies have included the Du Noüy ring method (Henning et al., 2005; Tuckermann, 2007), the pendant drop method (Svenningsson et al., 2006; Asa-Awuku et al., 2008), and the Wilhelmy plate method (Hyvärinen et al., 2006; Aumann et al., 2010). In this study, a thermostated tensiometer (Krüss K11, Germany), based on the Wilhelmy plate method, is used to measure the surface tensions of organic solutions. A thin, small plate made of platinum, which hangs on the balance, can measure the equilibrium surface tension of the aqueous solution at the air-liquid interface. Fig. 1 shows a schematic of the tensiometer apparatus. The solutes were each weighed using a digital balance with an uncertainty of 0.01 g (less than 1% of the total mass). Thus, the uncertainty in solute concentration was less than 1%. An aqueous mixed organic solution was prepared using Milli-Q purified water (18.2 M) and placed on the insulated metal holder jacket inside of the tensiometer. The temperature of this metal holder was controlled by a refrigerated chiller (Cole Parmer EW-01283-40, USA) ((3) in Fig. 1) and a programmable bath (Cole Parmer EW12107-20, USA) ((4) in Fig. 1). The target temperature, 20  C with an uncertainty of 0.1  C in this study, was maintained for at least 30 min to reach equilibrium. When the organic solution at target temperature was ready, a small plate was rinsed by pure water (Milli-Q, 18.2 M) and acetone several times and then dried with flames to remove all residual chemicals on its surface. After the cleaning steps, the surface tension of the aqueous solution was measured by submerging a small platinum plate several times. During this process, the temperature of plate equalized with the temperature of the solution, and the surface tension data stabilized. Only the stabilized data were used.

Table 1 Chemical properties of organic compounds. Compound name Oxalic acid Malonic acid Succinic acid Glutaric acid a b

Chemical formula C2H2O4 C3H4O4 C4H6O4 C5H8O4

(HOOCeCOOH) (HOOCeCH2eCOOH) (HOOCe(CH2)2eCOOH) (HOOCe(CH2)3eCOOH)

Lide (2009). Summarized in Saxena and Hildemann (1996).

Molar mass (g/mol) 90.03 104.06 118.09 132.12

Density (g/cm3) a

1.900 1.619a 1.572a 1.429a

Solubility (g/100 g) at 25  C

Manufacturer

12b 161b 8.8b 116b

SigmaeAldrich Alfa Aesar SigmaeAldrich Alfa Aesar

262

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To ensure that no systematic error was added during the measurement process, the surface tension of Milli-Q purified water (18.2 M) was measured at 20  C. Compared to the known surface tension of pure water, our measured surface tension showed an error of less than 0.1 mN/m. A double boiler system was used, where a small beaker with the organic solution was surrounded by a big beaker with water ((5) in Fig. 1). This transferred heat more uniformly to the solution and minimized the volume of organic solutions needed for measurements. 3. Results 3.1. Single component solutions For validation of the method, equilibrium surface tensions of single organic solutions were measured at 20  C. Concentrations varied from 0.05 to 0.5 mol/l for the oxalic and succinic acids, and from 0.05 to 1 mol/l for malonic and glutaric acids. The surface tension measurements were analyzed with the Szyszkowski equation (Eq. (1)) which describes how surface tension changes as solute concentration varies (Szyszkowski, 1908).



s ¼ s0  Gmax RT$ln 1 þ

C

b

 (1)

where s ¼ surface tension of an aqueous solution (mN/m); s0 ¼ surface tension of pure water (mN/m); Gmax ¼ maximum surface excess (mol/m2); R ¼ universal gas constant (mN m/K$mol); T ¼ temperature (K); C ¼ solute concentration (mol/l); b ¼ inverse Langmuir adsorption coefficient (mol/l). The Szyszkowski equation has been widely used by previous investigators (Tuckermann, 2007; Asa-Awuku et al., 2008; Aumann et al., 2010) to fit their experimental measurements. In this equation, the maximum surface excess (Gmax) and Langmuir adsorption coefficient (b) were empirically obtained by fitting the experimental surface tension measurements (s) over a range of solute concentrations (C) at 293 K (T). For a smaller inverse Langmuir adsorption coefficient (b), the surface tension of the mixture will start decreasing at lower solute concentrations, as illustrated in Fig. 2. On the other hand, for a smaller maximum surface excess (Gmax), the slope of the surface tension curve at high solute concentrations will be smaller. Our surface tension measurements for oxalic, malonic, succinic, and glutaric acids are shown in Fig. 3 (see Table 2 for the numerical measurements). The lines show the fit of the data to the Szyszkowski equation, with the best fit parameters listed in Table 3. As shown in Fig. 3, the surface tension of all acids decreased as the

Fig. 3. Surface tension of pure dicarboxylic acid solutions. Each data point is the average of at least 3 replicate measurements; lines are the best fit Szyszkowski equation. Standard deviations for all experimental points are less than 0.3 mN/m.

solute concentration increased. In addition, as the carbon chain length increased, surface tension decreased; oxalic acid has the shortest and glutaric has the longest chain length among the four dicarboxylic acids. Fig. 4 shows the comparison of our measurements (shown as solid lines) with previous studies’ data (shown as dotted lines; constructed based on the Szyszkowski equation parameters listed in Table 3). As shown in Fig. 4(a) and (b), our surface tension data for individual dicarboxylic acids agree with other studies to within 2%, except for glutaric acid. The surface tension of glutaric acid showed a maximum difference of 6.3% for the highest concentration tested. Table 3 compares our Szyszkowski equation parameters with previous publications. Although the difference in the surface tension is less than 6.3%, as shown in Fig. 4, the Szyszkowski equation parameters from our study and other previous studies show sizeable differences. This is mainly because small changes in the surface tension can result in much larger changes in Szyszkowski equation parameters, thereby resulting in large deviations (as shown in Fig. 2). While there were small differences in the measurement temperatures between studies, this has been reported to have no significant effect on the parameters (Aumann et al., 2010); however,

Table 2 Surface tension measurements from equi-molar mixed organic solutions at 20  C. The concentrations of the mixtures are total moles of all solutes per liter of water. Concentration (mol/l)

Fig. 2. Illustration of how the maximum surface excess (Gmax) and inverse Langmuir adsorption coefficients (b) affect the shape of the Szyszkowski equation.

Malonic acid Surface tension Glutaric acid (mN/m) Oxalic acid Succinic acid Concentration (mol/l) Malonic/Glutaric acids Malonic/Succinic acids Succinic/Glutaric acids Oxalic/Glutaric acids Concentration (mol/l) Oxalic/Malonic/Succinic acids Malonic/Succinic/Glutaric acids Concentration (mol/l) Oxalic/Malonic/Succinic/Glutaric acids

0.05

0.1

0.3

0.5

1

3

72.1 70.9 72.4 71.8 0.05 70.9 71.6 71.1 70.7 0.05 71.5

71.9 69.9 72.4 71.3 0.1 70.3 71.2 70.1 70.1 0.1 71.4

70.9 67.0 71.6 68.8 0.3 67.9 69.2 67.2 68.5 0.15 70.3

70.0 65.1 71.1 68.1 0.5 66.1 68.4 65.7 66.1 0.3 69.5

67.7 63.9 62.7 58.6

70.3

70.0 68.7

67.6 65.6 64.7

0.05 0.1 0.2 70.8 70.4 68.5

0.3 0.4 0.5 68.1 67.8 66.5

1 64.0

0.5 0.9 68.5 67.7

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3.3. Mixture of two dicarboxylic acids

Table 3 Szyszkowski equation parameters measured from dicarboxylic acid solutions.

Gmax (106 mol/m2); b (103 mol/l)

Compound name

Our study (20  C)

Other studies (25  C)

Oxalic acid

1.16  0.14; 643  192

Malonic acid Succinic acid

2.00  0.12; 586  88 1.35  0.06; 149  22

Glutaric acid

1.66  0.06; 92  10

1.54  0.39; 0.31  0.04; 1.14  0.06; 2.13  0.15; 1.10  0.08; 1.4; 268c 2.78  0.08; 2.5; 248c 3.12  0.17;

a b c d

1670  501a 35  15b 225  44b 319  32a 74  12b 184  11a 188  45d

Aumann et al. (2010). Calculated in Tuckermann (2007), originally from Hyvärinen et al. (2006). Summarized in Tuckermann (2007), originally from Gaman et al. (2004). Calculated in Tuckermann (2007), originally from Shulman et al. (1996).

differences between studies in the highest concentration tested might have influenced the fit.

3.2. Modified Szyszkowski equation for mixture The Szyszkowski equation (Eq. (1)) can be extended to apply to a mixture (where details of the derivation are given in Lee, 2013)

(P

ai )

i Gmax; i $bi

s ¼ s0  RT$

P an n bn

$ln 1 þ

X an n

bn

! $C

(2)

Here, s ¼ surface tension of an aqueous solution (mN/m); s0 ¼ surface tension of pure water (mN/m); Gmax,i ¼ maximum

surface excess of species i (mol/m2); R ¼ universal gas constant (mN m/K$mol); T ¼ temperature (K); C ¼ total solute concentration (mol/l); Ci ¼ solute concentration of species i (mol/l); ai ¼ Ci/C; bi ¼ inverse Langmuir adsorption coefficient (mol/l) of species i. The maximum surface excess and the inverse Langmuir adsorption coefficient for the mixture, respectively, are given by

P

Gmax; mix ¼ 1

bmix ¼ P

an

n bn

ai

i Gmax; i $bi

P an

263

(3)

n bn

(4)

To examine the surface tension of solutions containing two dicarboxylic acids, four different mixtures were tested. All mixtures consisted of 50:50 M ratios of two individual organic compounds. In Fig. 5, solid gray lines (with hollow symbols) show the surface tensions of single-component organic solutions, and the solid black lines (with solid symbols) show surface tensions of the 50:50 M mixtures. Our results show that the surface tensions measured for all of our 50:50 mixtures closely follow whichever of the two individual organics has the lower surface tension. The maximum surface excess (Gmax) and inverse Langmuir adsorption coefficient (b) from the Szyszkowski equation for these two dicarboxylic acid mixtures are listed in Table 4. Our surface tension measurements were compared with the modified Szyszkowski equation for mixtures (Eq. (2)) and Henning’s model (Henning et al., 2005). Henning’s model predicts the surface tension of mixtures using a weighted average of each surface tension that is proportional to the carbon content of each compound. In Fig. 5, the modified Szyszkowski equation for the mixtures, shown as dashed lines, and Henning’s predictions, shown as dotted lines, agree well with each other, but both are systematically higher than our measurements. The maximum deviations between the surface tension measurements and the modified Szyszkowski equation (Eq. (2)) are 1.4%, 1.0%, 0.8% and 1.4%, while the maximum deviations between the measurements and the Henning’s predictions are 0.7%, 1.1%, 0.7% and 1.3% for oxalic/glutaric, malonic/glutaric, malonic/succinic and succinic/glutaric acid mixtures, respectively. To examine how surface tension is dependent on the molar mixing ratios in organic mixtures, further experiments were done involving a range of molar ratios for: (i) succinic/glutaric acids (a mixture of less soluble and highly soluble organics), and (ii) malonic/glutaric acids (both highly soluble). In Fig. 6(a), solid gray lines with hollow markers show the surface tensions of pure succinic and glutaric acid solutions. The black lines show three different mixing ratios for the mixture. At lower concentrations, the surface tension of the mixture closely follows that of glutaric acid regardless of the mixing ratio. This indicates that even a small amount of glutaric acid can exert the dominant influence on the overall surface tension at lower concentrations. However, at higher concentrations, the effect of the mixing ratio on surface tension becomes more pronounced. Similar behavior is seen for the mixtures of malonic and glutaric acids. As plotted in Fig. 6(b), the surface tensions of the three different mixing ratios all are close to that of glutaric acid at lower

Fig. 4. Surface tension of pure dicarboxylic acid solutions. Error bars on measured data represent 1 S.D. (0.3 mN/m). Lines from previous studies were constructed based on the Szyszkowski equation parameters listed in Table 3.

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Fig. 5. Surface tension of two-dicarboxylic-acid solutions. Each data point represents the average of at least 3 replicate measurements. Solid lines represent the best fit Szyszkowski equation. Standard deviations for all data points are less than 0.3 mN/m; error bars are depicted for only one compound, for simplicity.

concentrations, but as the solute concentration increases, the effect of malonic acid on the surface tension becomes apparent. 3.4. Mixture of three dicarboxylic acids Two types of equi-molar three-dicarboxylic-acid solutions were tested: oxalic/malonic/succinic and malonic/succinic/glutaric. As shown in Fig. 7(a), the overall surface tension of the first organic mixture was found to be similar to that of the succinic acid solution alone, especially at the lower concentration levels. Similarly, as shown in Fig. 7(b), the second organic mixture closely followed the surface tension of glutaric acid solution alone, especially at lower concentrations. In both cases, the surface tension of the mixture most closely resembled the single organic solution having the lowest surface tension among the three components. The maximum surface excess and inverse Langmuir adsorption coefficient from Szyszkowski equation for these three-dicarboxylic-acid solutions are listed in Table 4. Our surface tension measurements for these three-organic mixtures were compared in Fig. 7 with predictions made using the modified Szyszkowski equation (dashed line) and Henning’s model (dotted line). The modified Szyszkowski equation for mixtures overestimated the surface tension by up to 1.2 and 2.0%, while Henning’s prediction overestimated the surface tension by up to 1.1 and 2.0%, respectively, for the two mixtures. 3.5. Mixture of four dicarboxylic acids Fig. 8 shows the overall surface tension of equi-molar mixtures of four dicarboxylic acids: oxalic, malonic, succinic and glutaric acids (solid black line). As shown in Fig. 8, the surface tension of this

mixture falls between those of the succinic acid and glutaric acid solutions. The two parameters, Gmax and b, from the Szyszkowski equation are listed in Table 4. Again, we compared our measurements in Fig. 8 to the predictions made using the modified Szyszkowski equation (dashed line) and Henning’s model (dotted line). Our measurements are lower than the predictions, by up to 1.8% (for modified Szyszkowski eqn.) and 1.6% (Henning’s). Thus, for all dicarboxylic acid mixture measurements (shown in Figs. 4, 6 and 7) both the modified Szyszkowski eqn. and Henning’s model systematically overestimated the surface tensions, by around 1e2%.

3.6. Analysis with Köhler equation The Köhler equation (Köhler, 1936) is commonly used to model the activation of cloud droplets (e.g., Facchini et al., 1999; Petters and Kreidenweis, 2007; Tuckermann, 2007; Asa-Awuku et al., 2008; George et al., 2009; Aumann et al., 2010). The critical saturation (Sc), the minimum saturation level at which an aerosol can Table 4 Szyszkowski equation parameters measured from mixed organic solutions at 20  C. Compound name

Gmax (106 mol/m2)

Oxalic/Glutaric acids Malonic/Glutaric acids Malonic/Succinic acids Succinic/Glutaric acids Oxalic/Malonic/Succinic acids Malonic/Succinic/Glutaric acids Oxalic/Malonic/Succinic/Glutaric acids

1.19 1.46 1.00 1.65 0.93 1.11 1.13

      

0.05 0.05 0.06 0.06 0.05 0.05 0.05

b (103 mol/l) 67 94 99 104 93 46 64

      

10 12 19 12 18 7 10

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265

Fig. 6. Surface tension of two-dicarboxylic-acid solutions with three different molar mixing ratios. Each data point is the average of at least 3 replicate measurements. Standard deviations for all data points are less than 0.3 mN/m; error bars are depicted only for succinic and malonic acids, for simplicity.

activate and grow into a cloud droplet, can be derived from the Köhler equation as:

 3 12 4A Sc ¼ exp 27B

where A ¼

4MWw ssol 6ns MWw ; B ¼ prsol RT rsol

(5)

(6)

and where S ¼ saturation ratio (¼relative humidity/100); Dp ¼ droplet diameter (m); MWw ¼ molecular weight of water (kg/ mol); ssol ¼ surface tension of the solution (mN/m); R ¼ universal gas constant (mN m/mol K), T ¼ temperature (K); rsol ¼ density of the solution (kg/m3); ns ¼ moles of water soluble ions in solution. The lower the surface tension term (in Eq. (6)), the lower the critical saturation. Thus, when surface tension-lowering compounds are present, aerosols can be more easily activated into cloud droplets. This will lead to a larger number of smaller sized cloud droplets for a given water content in the atmosphere, thereby affecting cloud properties. Therefore, the reduction in critical saturation ratio due to surface tension lowering compounds is of high importance. The Köhler curves shown in Fig. 9 are for two solutions: one containing an oxalic/malonic/succinic acid mixture and the other, an oxalic/malonic/succinic/glutaric acid mixture. The dashed lines represent the Köhler curve assuming the surface tension is fixed at

72.7 mN/m (the surface tension of a pure water droplet at 20  C). The solid lines include the surface tension reduction measured in this study. As can be seen from Fig. 9, the critical (peak) saturation point for each organic mixture is lowered due to the surface tension reduction. However, the amount of reduction is small, especially for dry diameters of 0.1 mm and larger. The largest reduction in the critical saturation ratio, for the four organic mixture with a dry diameter of 0.05 mm, was from 1.0068 to 1.0063. 4. Discussion Our study shows that the surface tension reduction induced by an equi-molar dicarboxylic acid mixture is similar to that induced by the most surface-active acid alone especially at lower concentrations. This suggests that the amount of surface tension reduction induced by a dicarboxylic acid depends on what other surfaceactive acids are in the solution. In addition, the surface tension of a mixture depends on the mixing ratio at higher concentrations, but not at lower concentrations. This indicates that no linear combination of the individual components’ surface tensions (as in Henning’s model) can model such behavior of the mixture. To examine the behavior in more detail, we compared the maximum surface excess (Gmax) and the inverse Langmuir adsorption coefficient (b) parameters of the measured surface tensions of mixtures with estimates based on the modified Szyszkowski equation for mixtures (Eq. (2)). Fig. 10 shows the value of Gmax and b for various dicarboxylic acid mixtures. The measured

Fig. 7. Surface tension of three-dicarboxylic-acid solutions. (a) Equi-molar mixture of oxalic, malonic and succinic acids. (b) Equi-molar mixture of malonic, succinic and glutaric acids. Each data point is the average of at least 3 replicate measurements. Standard deviations for all data points are less than 0.3 mN/m; error bars are depicted only for oxalic acid and malonic acid, for simplicity.

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Fig. 8. Surface tension of the four-dicarboxylic-acid solution. Each data point is the average of at least 3 replicate measurements. Standard deviations for all data points are less than 0.3 mN/m; error bars are depicted only for oxalic acid, for simplicity.

values for both parameters (open circles) are consistently smaller than the predictions (solid triangles, calculated from Eqs. (3) and (4)), except for the succinic/glutaric mixture. The maximum surface excess, Gmax, is the total number of surface sites available for solute adsorption per unit area; it is a constant parameter for a given organic species. Our measured maximum surface excess is smaller than the one calculated via Eq. (3), suggesting that the total number of surface sites may be reduced when dicarboxylic acids with different chain lengths coexist at the surface. The inverse Langmuir adsorption coefficient, b, is the ratio of the desorption to the adsorption rate constants. A smaller b means the solute can adsorb to the surface more easily; that is, it is more surface active. Our measured b is smaller than the one calculated from Eq. (4), suggesting that the surface activity of dicarboxylic acids in solution may increase in the presence of other dicarboxylic acids. It should be noted that real atmospheric aerosols contain complex mixtures of organics and inorganics. This study has only considered simple mixtures of dicarboxylic acids. Nonetheless, our study shows that even a small amount of strongly surface-active dicarboxylic acid can exert the dominant influence on the overall surface tension of a solution containing a dicarboxylic acid mixture. The measured surface tensions of dicarboxylic acid mixtures are

Fig. 10. Comparison between the measured and calculated maximum surface excess (Gmax) and inverse Langmuir adsorption coefficients (b) from eqns. (3) and (4) for various multi-component dicarboxylic acid mixtures. Note: the label “O þ M þ S þ G” is used for the equi-molar mixture of oxalic, malonic, succinic and glutaric acids. Other mixtures are similarly labeled.

just w1e2% lower than what current models predict; however, the trends in the measured surface tensions with increasing concentration are much more complex than the weighted sum of the individual components. Thus, the results of this study may offer some helpful insights for beginning to better understand and model the behavior of much more complex atmospheric aerosols.

5. Summary We measured the surface tension of multi-component solutions containing up to four dicarboxylic acids using the Wilhelmy plate method. Our major findings are: 1) At lower solute concentrations, the surface tension of a solution with equi-molar dicarboxylic acids (from two- to fourcomponent mixtures) closely follows that of a single-

Fig. 9. Köhler activation curves for particles composed of (a) oxalic/malonic/succinic acid mixture and (b) oxalic/malonic/succinic/glutaric acid mixture, for dry diameters of 0.05, 0.1 and 0.5 mm.

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component solution with the most surface-active organic alone (the one with the longest carbon chain). 2) At higher dicarboxylic acid concentrations, the effect of the mixture composition, and the mixing ratio, on the surface tension becomes more pronounced and complex. 3) The estimated surface tensions for dicarboxylic acid mixtures, based on the modified Szyszkowski equation and Henning’s model, are systematically higher, by w1e2%, than actual measurements. 4) Only a slight reduction in the critical saturation ratio of multicomponent dicarboxylic acid solutions is seen due to their surface tension lowering effect. In summary, reductions in the surface tension of aerosols due to dicarboxylic acids are not large enough to lead to notable reductions in the critical saturation ratios. However, even for these simple solutions of mixed organics, both the concentration and mixing ratio of the solutes had a complex effect on the surface tension. Thus, this work highlights the need for future research to fundamentally elucidate how more complex, realistic mixtures of organic and inorganic solutes alter the properties and activation of atmospheric aerosols.

Acknowledgments Funding for this research came from National Science Foundation (grant ATM-0731451).

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