10428
J. Phys. Chem. C 2008, 112, 10428–10434
Surface Tensions of Multicomponent Aqueous Electrolyte Solutions: Predictive Models Based on Binary Limits Tomi Raatikainen,*,† Ari Laaksonen,†,‡ Antti-Pekka Hyva¨rinen,† Joonas Vanhanen,† Kaisa Hautio,† Heikki Lihavainen,† Yrjo¨ Viisanen,† and Ismo Napari§ Finnish Meteorological Institute, Erik Palme´nin Aukio 1, P.O. Box 503, 00101 Helsinki, Finland, Department of Physics, UniVersity of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland, and Department of Physical Sciences, UniVersity of Helsinki, P.O. Box 64, 00014 Helsinki, Finland ReceiVed: December 13, 2007; ReVised Manuscript ReceiVed: March 27, 2008
Most simple inorganic acids and organic bases (for example amines) decrease surface tension in aqueous solutions, but common inorganic salts have the opposite effect. Therefore, the surface tension of an aqueous acid-base solution does not change linearly between acid and base binary limits. Surface tensions of two acids (hydrochloric and sulfuric acids), two bases (ammonia and dimethylamine), and their four salts were explained by surface activities of single ions and molecular bases. Estimates of surface activities are based on solute properties (charge, size, and structure), Gibbs adsorption equation and surface tensions, and published molecular dynamic studies. In addition to published surface tensions, new data were measured for aqueous dimethylammonium chloride and ammonia/dimethylamine-hydrochloric acid solutions. Surface tensions of the ternary acid-base solutions change quite linear between acid, base, and salt (neutral solution) binary limits. On the basis of this linearity, several simple models, which need only binary solution surface tensions, were tested by calculating model deviations from the experimental data. As a result, two simple surface tension models were suggested for aqueous acid-base mixtures. Introduction Surface tension is an important property of aqueous aerosols: it has impacts, for example, on hygroscopic properties of aerosols and on nucleation.1–5 In addition to the common inorganic ions (for example, H+, NH4+, Na+, SO42-, NO3-, and Cl-), aerosols contain several different classes of soluble organic compounds6–9 (for example, acids, amines, and compounds with several functional groups). Usually dissolved salts and inorganic bases (with the exception of ammonia) increase surface tension,10,11 but many organics can decrease surface tension even in small concentrations.4,12–14 From the atmospheric viewpoint, an interesting group of bases include ammonia and amines, which lower the surface tension in basic solutions.15,16 However, if acid is added, surface tension increases because of salt formation. Experimental surface tension data are available for pure liquids and common single solute solutions but only for some multicomponent mixtures. Therefore, surface tensions of mixtures are usually estimated by using binary solution data.17,18 The predictive power of such models is much enhanced if chemical properties of solutes are taken into account. Clearly, it is important to include the salt (neutral solution) limit when acid-base solutions surface tensions are estimated. Surface tensions of pure liquids and mixtures depend on the strength of intermolecular interactions (hydrogen bonding, van der Waals forces, ionic forces, etc.) and molecular arrangement in the bulk and surface (a few topmost layers of molecules and ions) phases. Ions have relatively strong and long-ranging * To whom correspondence should be addressed. Phone: +358 9 1929 5447. Fax: +358 9 1929 3503. E-mail:
[email protected]. † Finnish Meteorological Institute. ‡ University of Kuopio. § University of Helsinki.
electrical interactions with water molecules and other ions. Therefore, most ions prefer bulk solutions and increase solution surface tension. On the other hand, most nonelectrolytes have weak intermolecular forces, so they prefer the surface phase and decrease solution surface tension. Surface active solutes have higher concentrations at solution surfaces than in bulk solutions. For small droplets, increased surface concentration means decreased bulk concentration, which has an effect on droplet surface tension, bulk concentrations, and equilibrium vapor pressures.19 Heterogeneous reactions such as reactions between gas and liquid phase species depend on solution surface concentrations. Evidently, increased surface concentrations of reactants speed up surface reactions, but inert compounds can prevent reactions by accumulating on the surface. Increased halide ion surface concentrations have been given as an explanation for high halide gas production rates in chamber studies.20,21 There are several ways to estimate surface activities, but in this paper we rely on the Gibbs adsorption equation22 and published molecular dynamics (MD) simulations.23–29 The Gibbs adsorption equation relates the surface tension gradient to the excess number of solutes at the surface, i.e. surface excess. Charge balance is expected, so surface activities cannot be predicted for individual ions. On the other hand, single ion surface activities have been estimated in several published MD studies. When the surface activity of, for example, a cation is known from MD studies, the anion surface activity can be estimated by using the adsorption equation and known surface tension. The first purpose of this paper is to explain the surface tension behavior of four aqueous acid-base solutions (hydrochloric and sulfuric acids, ammonia, and dimethylamine) by using single ion and molecule surface activities. These are estimated for eight binary solutions (acids, bases, and their four salts) by using
10.1021/jp7117136 CCC: $40.75 2008 American Chemical Society Published on Web 06/21/2008
Surface Tensions of Electrolyte Solutions
J. Phys. Chem. C, Vol. 112, No. 28, 2008 10429
TABLE 1: Descriptions of the Compounds Used in the Measurementsa
a
compound
formula
M (g/mol)
dimethylammonium chloride ammonium chloride dimethylamine ammonia hydrochloric acid
(CH3)2NH2Cl NH4Cl (CH3)2NH NH3 HCl
81.54 53.49 45.08 17.03 36.46
w (%)
purity (%)
manufacturer
99 99.5
Aldrich J.T. Baker Fluka J.T. Baker J.T. Baker
60 24-24.9 37-38
Concentrations of aqueous solutions (w) and purities of solid salts are given as weight percent.
published MD studies and surface tensions interpreted by the Gibbs adsorption equation. The second purpose is to find a practical method to estimate the surface tension of aqueous acid-base mixtures. Surface tension data are mainly from literature sources including our previous publications, but new data were measured for aqueous dimethylammonium chloride and dimethylamine/ammonia-hydrochloric acid solutions. The paper is organized as follows. First, experimental and theoretical methods for estimating surface activities are presented briefly. Then the surface tension measurements are presented. After that, surface tensions of the eight binary solutions and surface activities of ions and molecular bases are described. Then this view is extended to the ternary acid-base solutions by explaining their surface tensions. Simple surface tension models are also discussed in this section. Methods for Estimating Surface Activities There are several ways to estimate surface activities, but we rely on the Gibbs adsorption equation22 and surface tension data as well as on published results from molecular dynamics (MD) simulations.23–30 Molecular solutes are known to be surface active, so we will concentrate on electrolyte solutions and ion surface activities. Gibbs adsorption equation relates surface tension gradient to surface excess, Γ (mol/m2), which is the excess number of solute molecules at the surface divided by the surface area. The surface (Gibbs dividing surface) is selected here so that the solvent surface excess is zero. For aqueous single ideal solute solutions at constant temperature (T), the Gibbs adsorption equation is
Γ)-
1 ∂σ RT ∂(ln x)
(1)
where R [J/(mol K)] is the ideal gas constant, σ (N/m) is the solution surface tension, and x is the solute mole fraction. Activity coefficients have an effect on surface excess,31 but they were ignored due to the lack of activity data. In practice, decreasing surface tension means positive surface excess (surface active solute) and vice versa. On the basis of published surface tensions,10,11 most inorganic salts have negative surface excesses and simple acids have positive ones. Molecular dynamic (MD) simulations can be used to predict the average position and orientation of water molecules and ions. In a typical simulation, a liquid slab with two free surfaces is placed in an elongated simulation box with periodic boundaries and the system is allowed to equilibrate before the data are collected. In general, MD simulations show (e.g., Jungwirth29) that most inorganic ions, with the exception of hydrated proton and large anions (e.g., heavier halides), have decreased surface concentrations. Ion surface activity is related to hardness and softness: hard ions (cations, small and multiply charged ions) are depleted from surfaces, but soft ions (anions, large and polarizable ions) may have positive surface excesses. Also, counterions have a significant effect on total surface excess:
Figure 1. Experimental surface tension data (markers) and fitting (solid line) for dimethylammonium chloride as a function of solute mole fraction at 24.2 °C.
surface active ions can pull less surface active ions to the surface and vice versa. Surface Tension Measurements The surface tensions of dimethylammonium chloride were measured, because experimental data were not available. Also, a few points were measured for the aqueous dimethylaminehydrochloric acid and ammonia-hydrochloric acid solutions in order to test the performance of different simple surface tension models. The experimental method has already been described earlier by Hyva¨rinen et al.,32 and only an overview is given here. The surface tensions were measured with a thermostated tensiometer (Digital Tensiometer K 10ST, Kru¨ss, Gmbh, Germany) using the Wilhelmy plate method.33 The temperature control was performed with a circulation liquid path (Lauda RC6 CS). Descriptions of the compounds used in the measurements are given in Table 1. Purified water was used to prepare the solutions (Milli-Q, 18 MΩ). The preparation of samples and the actual surface tension measurements were made in a similar way as described by Hyva¨rinen et al.32 The measurements were made at about 25 °C with an estimated uncertainty of about 1.0%. The following equation was fitted to experimental dimethylammonium chloride surface tension data
σ ) σwpure(T) + ax + bx2 σwpure(T)
(2) water34
where (N/m) is the surface tension of pure at given temperature (0.072 N/m at 25 °C) and x is the mole fraction of the salt. Fitting parameters are a ) -0.029 N/m and b ) 0.010 N/m. The equation is valid up to mole fraction 0.35 and temperatures close to 25 °C. Experimental data and the fit are presented in Figure 1. Binary Solutions In order to explain the surface tension behavior of the four ternary acid-base solutions, we will first estimate surface
10430 J. Phys. Chem. C, Vol. 112, No. 28, 2008 activities for the ions and molecular solutes by examining binary solutions. The acids considered here are sulfuric (H2SO4) and hydrochloric (HCl) acids, and the bases are ammonia (NH3) and dimethylamine [(CH3)2NH]. Their four neutral salts are also included: ammonium sulfate [(NH4)2SO4], dimethylammonium sulfate [((CH3)2NH2)2SO4], ammonium chloride (NH4Cl), and dimethylammonium chloride [(CH3)2NH2Cl]. We will not give numerical values for the surface activities, because they depend on the concentration and because activity coefficients (needed in the Gibbs equation) are not available for all solutes. Instead, we estimate the surface activities in relation to the other ions. Bases. Weak bases ammonia and dimethylamine (DMA) are mostly in their molecular form in aqueous solutions. Therefore, they decrease surface tension much more than the electrolytes. Published ab initio calculations16 and studies based on the adsorption equation35 have shown that ammonia and DMA concentrate on the surfaces of aqueous solutions. There molecules are hydrogen bonded to dangling OH groups (that is, free water OH groups pointing out of the solution) so that nitrogen is the hydrogen-bond acceptor. DMA has a bigger effect on surface tension, because the methyl groups are more hydrophobic than the ammonia hydrogens. A decrease in surface tension with increasing number of methyl groups is seen from the series of ammonia and methylated amines.15,16 Acids. Hydrochloric and sulfuric acids are highly water soluble strong acids. Therefore, both HCl and H2SO4 are considered as completely dissociated. The second dissociation of H2SO4 is not complete, because bisulfate ion (HSO4-) is a weak acid. Just like other simple acids, also HCl decreases surface tension in aqueous solutions.36 According to the published MD simulation of HCl,26 both the cation and the anion have slightly increased surface concentrations. Even if chloride ions are not surface active, surface active hydronium cations (H3O+) pull anions closer to the surface. The surface tension of aqueous H2SO4 increases at low concentrations and decreases after a maximum value at acid mole fraction 0.136 at 25 °C.37 MD simulations of H2SO4 were not found from the literature, but the surface tension behavior can be explained by the partial dissociation of bisulfate ion (HSO4-) and ion surface activities. Doubly charged sulfate ion is depleted from the surface. Bisulfate is quite large and polarizable, so we expect its surface activity to be comparable to that of chloride ions. Sulfate ions dominate dilute sulfuric acid solutions (negative surface excess) and therefore surface tension increases. Bisulfate ions become more important as the concentration increases; thus, the negative surface excess approaches zero until it is zero at the acid mole fraction 0.136, where the maximum surface tension is reached. At higher concentrations, the surface excess is positive and surface tension decreases. Salts. The four salts considered here are products of a weak base and a strong acid, so complete dissociation is expected. Just like most inorganic salts, ammonium chloride38 and ammonium sulfate39 increase solution surface tension. According to the published MD simulations26,27 on aqueous (NH4)2SO4 and NH4Cl solutions, all ions are depleted from surfaces. Doubly charged sulfate ions have the smallest surface concentrations. Ammonium ions are not surface active due to the symmetrical structure and good hydrogen-bonding capabilities of the positively charged hydrogens. Because of the large size and polarizability, chloride ions are slightly depleted from surface. Neither surface tension data nor MD studies were found from the literature for dimethylammonium chloride (DMAC) or
Raatikainen et al. dimethylammonium sulfate (DMAS) solutions. To address this gap in the literature, the surface tension of DMAC was measured and eq 2 was fitted to the data. DMAS was not commercially available for surface tension measurements. Also, it was too difficult to make it from sulfuric acid and DMA because of the highly exothermic mixing reaction. The surface tension of DMAS could be estimated from the published waterDMA-H2SO4 fitting.40 However, there are only few measurements close to the salt (neutral solution) limit where the surface tension decreases rapidly when acidic solution turns into basic solution. It is possible that DMAS solution surface tensions are actually higher than those calculated from the fitting. Therefore, we estimated the salt solution surface tensions using the published experimental data40 on dilute acidic solutions only. Experimental values have been measured as a function of base mole fraction while the acid mole fraction was kept constant. We fitted linear equations (σ ) a + bxb) to the surface tensions measured at the constant acid mole fractions. Salt solution surface tensions were then extrapolated from the fits by using base mole fractions twice the constant acid mole fractions. Acid mole fractions were limited to 0.09, because the maximum base mole fraction is quite low in the more concentrated solutions. For example, the highest DMA mole fraction for the acid mole fraction 0.09 was also 0.09 when the mole fraction 0.18 was needed in the extrapolation. The corresponding salt solution mole fraction is 0.11. Finally, a linear equation was fitted to the estimated salt surface tensions and the calculated salt binary mole fractions (x):
σ ) a + bx
(3)
Fitted parameters are a ) 0.072 N/m (surface tension of pure water at 25 °C) and b ) -0.010 N/m. Because there are few data points close to the salt limit, uncertainty for parameter b is close to its magnitude. Compared with the published ternary fitting,40 eq 3 gives slightly higher surface tensions; for example, at salt mole fraction 0.25, the difference is 8 mN/m. Unlike most inorganic salts, both DMAC and DMAS decrease surface tension in aqueous solutions and thus they have positive surface excesses. Chloride and sulfate ions are usually depleted from the surface, but a positive total surface excess is possible if dimethylammonium cations (DMAH+) are surface active. In fact, on the basis of the surface tensions of aqueous DMAC and HCl, DMAH+ must have higher surface concentrations than the hydronium cations (H3O+). Mucha et al.26 explained the H3O+ surface activity based on the ion structure. The same idea can be applied to DMAH+: the ion has two relatively large hydrophobic methyl groups and two hydrophilic hydrogens. Surface ions can be oriented so that the hydrophobic methyl groups are toward the gas phase and the hydrogens are bonded to the liquid phase water molecules. DMAH+ has higher surface concentrations compared with those of H3O+ for the following reasons: the charge of DMAH+ is spread over a larger volume, its hydrophobic groups are bigger, and the ion has only two hydrophilic hydrogens. Because of different anion surface activities, DMAC solutions have slightly smaller surface tensions compared with those of DMAS solutions. Surface tensions of the eight considered binary solutions are presented in Figure 2 as four groups corresponding to the four acid-base solutions considered here. The two DMA-acid solutions have similar binary limit surface tensions; i.e., acid surface tensions are the highest, salt surface tensions are slightly smaller, and base surface tensions are much smaller. Also the two NH3-acid solutions have similar binary limit surface tensions, but in this case, salt solution surface tensions are the highest.
Surface Tensions of Electrolyte Solutions
J. Phys. Chem. C, Vol. 112, No. 28, 2008 10431
Figure 2. Surface tensions of aqueous acids (hydrochloric36 and sulfuric37 acids), bases (DMA40 and ammonia41), and their salts [DMAC, DMAS, NH4Cl,38 and (NH4)2SO439] as a function of solute mole fraction at 25 °C. Surface tensions of DMAC and DMAS are calculated using eqs 2 and 3, respectively. Some of surface tensions are extrapolated beyond the experimental data range.
Ternary Solutions Surface tensions of aqueous DMA-H2SO4 and NH3H2SO441 were measured and parametrizations were fitted to data in two previous studies. A few data points were measured for aqueous NH3-HCl and DMA-HCl solutions. These ternary solution surface tensions can be explained on the basis of the estimated molecular base and single ion surface activities: SO42– < NH4+ < Cl- ≈ HSO4– < H+ < DMAH+ , NH3 < DMA. According to the experimental data, the surface tensions of the four ternary solutions vary nearly linearly between their three binary solution limits (see Figures 3–6). When an acid is added to an aqueous base, surface tension increases rapidly as the surface active molecular base is ionized. Because neutral NH3-H2SO4 and NH3-HCl solutions include only the less surface active ions, surface tension reaches its maximum. On the other hand, due to the surface active DMAH+ ions, surface tension is slightly decreased in neutral DMA-H2SO4 and DMA-HCl solutions. When more acid is added, surface active H+ and slightly depleted Cl- and HSO4- ions become more important and thus surface tension increases in the DMA solutions and decreases in the NH3 solutions. Simple Models. On the basis of the observed linear behavior of surface tensions, it should be possible to estimate surface tensions of aqueous acidsbase solutions using surface tensions of the binary limits (acid, base, and salt). Previously, surface tensions have been estimated by calculating weighted averages of binary solution surface tensions.17,18,41 In addition to different weights, different binary solution concentrations, which are calculated from ternary concentrations, have been used. Van Dingenen and Raes17 used mass percents as weights, and binary solution surface tensions were calculated using total solute mass percents. The salt limit was not used because the model was 40
designed for sulfuric acid-methanesulfonic acid solutions. In contrast, the ammonia-hydrochloric acid surface tension model of Arstila et al.18 includes the salt limit. They calculated binary solution surface tensions by using single solute-water mole fractions, where the other solutes are ignored. Surface tension of the mixture is a (unnormalized) sum of the three binary limits each multiplied by the single solute-water mole fractions. Hyva¨rinen et al.41 presented a surface tension parametrization for NH3-H2SO4. The parametrization is sum of a fitted polynomial correction term and weighted average of the three binary solution surface tensions. Both weights and binary solution concentrations are quaternary (aqueous acid-salt-base) solution mole fractions, which are calculated from ternary solution mole fractions so that ion concentrations are equal. In practice, this means that, for example, acidic ternary solutions are described using acid and salt quaternary mole fractions while the base quaternary mole fraction is zero. Several different weights and binary solution concentrations were tested in calculating differences between the model predictions and the four experimental ternary data sets. Model deviations are much smaller when the salt limit is included and quaternary solution mole fractions are used as weights. It is not that easy to select the best binary solution mole fraction (e.g., single solute-water, total solute, or quaternary solution mole fraction), because it seems to depend on the base. Therefore, two simple models with different binary solution mole fractions were selected; one for the ammonia and one for the DMA solutions. The first model is the ideal part of the above-mentioned NH3-H2SO4 parametrization,41 and it is accurate for the ammonia solutions:
10432 J. Phys. Chem. C, Vol. 112, No. 28, 2008
σ)
xaσa(xa) + xbσb(xb) + xsσs(xs) xa + xb + xs
Raatikainen et al.
(4)
The second model is a modification of the van Dingenen and Raes17 model (mole fractions are used instead of mass fractions and the salt limit is included), and it gives better results for the DMA solutions:
σ)
xaσa(1 - xw) + xbσb(1 - xw) + xsσs(1 - xw) xa + xb + xs
(5)
All the mole fractions (acid, xa; base, xb; salt, xs; and water, xw), including mole fractions used to calculate binary solution surface tensions, are quaternary solution mole fractions. For ternary acid (A) and base (B) solution with ternary mole fractions xA and xB and neutral salt BβAR, unnormalized quaternary solution mole fractions are
xs ) MIN(xB/β, xA/R )
xi ) xa + xb + xs ) 1 - xw (10) xi xi + x xa + xb + xs w
Previously published fitted models have average absolute deviations (AAD) of 1.0 mN/m (average error is 1.5%) and 0.8 mN/m (1.3%) for aqueous NH3-H2SO441 and DMA-H2SO440 solutions, respectively. Corresponding deviations for eq 4 are 1.2 mN/m (1.7%) and 1.6 mN/m (2.7%), and for the eq 5 they are 1.4 mN/m (2.0%) and 1.3 mN/m (2.2%). The model AAD’s are equal to those of surface tension changes (σ - σw). Figures 3, 4, 5, and 6 show experimental data and surface tension prediction from the two simple models for the NH3-H2SO4,41 DMA-H2SO4,40 NH3-HCl, and DMA-HCl solutions, respectively. Both data and model predictions are shown as a function of base mole fraction with constant acid mole fractions. The importance of the salt limit can be seen in these figures.
(6)
β xb ) MAX 0, xB - xA, R R xa ) MAX 0, xA - xB , β xw ) 1 - xA - xB
( (
xibin )
) )
Discussion
(7) (8) (9)
These mole fractions must be normalized so that their sum is one. The binary solution mole fractions (xbin i ) in the second model, 1 - xw, are the results of the idea that water is associated with solutes in proportion to their mole fractions:
Surface activities were estimated for ions and molecular solutes from eight binary solutions based on solute properties (charge, ion/molecular geometry and size), surface tension data interpreted by the Gibbs adsorption equation, and publications on molecular dynamic simulations. The binary solutions are binary limits in four acid-salt-base solutions. The surface activities of the ions and molecular bases increases in the order SO42– < NH4+ < Cl- ≈ HSO4– < H3O+ < DMAH+ , NH3 < DMA. Doubly charged sulfate is the least surface active ion. Ammonium ion prefers bulk solutions due to its symmetrical structure and good hydrogen-bonding capabilities. Chloride and
Figure 3. Experimental NH 3-H2SO4 surface tensions41 (markers) and predictions from the two ideal models [solid (eq 4) and dashed (eq 5) lines]. Surface tensions are shown as a function of base mole fraction for constant acid mole fraction.
Surface Tensions of Electrolyte Solutions
J. Phys. Chem. C, Vol. 112, No. 28, 2008 10433
Figure 4. Experimental DMA-H2SO4 surface tensions40 (markers) and predictions from the two ideal models [solid (eq 4) and dashed (eq 5) lines]. Surface tensions are shown as a function of base mole fraction for constant acid mole fraction.
Figure 5. Experimental surface tension data and prediction from the two ideal models (solid and dashed lines) for aqueous NH3-HCl.
Figure 6. Experimental surface tension data and prediction from the two ideal models (solid and dashed lines) for aqueous DMA-HCl.
bisulfate are nearly surface active ions because of their bigger size and polarizability. H3O+ and DMAH+ ions are surface active due to their hydrophobic and hydrophilic parts. As usual, molecular solutes have the highest surface activities. Due to the electric attraction between cations and anions, the total surface excess depends on both ions. For example, two DMAH+ ions can pull one doubly charged sulfate anion to the surface, but the surface excess is bigger if chloride is the anion. These ion surface activities interpreted by the Gibbs adsorption equation can be used to explain the surface tension behavior of the binary and ternary solutions. Different approximations have been used in estimating surface tensions for multicomponent solutions. One common method is to calculate weighted averages of surface tensions of the binary limits. Several different weights and binary solution concentrations were tested by calculating model deviations from
four ternary solution data sets. As a result two simple surface tension models were suggested (eqs 4 and 5) for aqueous acid-base solutions. Fitting parameters are not needed but only the surface tensions of aqueous acid, base, and neutral salt solutions. Model deviations decreased significantly when the salt limit was included. The same weights (quaternary solution mole fractions) were used in the both models, but binary limit surface tensions were calculated using different mole fractions. This has quite a small effect on deviations between models and data, but at least in this case, the first model is better for ammonia solutions and the second model is better for dimethylamine solutions. If mixtures contain weak acids or bases, which can be surface active in molecular forms, surface tension may be sensitive to solution acidity. Because aerosols are commonly acidic, dissolved amines and other weak bases are in their ionized forms. Therefore, the surface tension is rather high and not sensitive
10434 J. Phys. Chem. C, Vol. 112, No. 28, 2008 on acidity changes (as long as the solution remains acidic). However, weak organic acids, which constitute a major fraction of the aerosol organic matter, cause the biggest reduction to surface tension in acidic solutions, where they are in their molecular forms. This means that the surface tension increases rapidly as acidity decreases. In principle, the simple models should be applicable for these solutions, but this should be tested in further studies. Conclusions Surface activities were estimated for eight ions and molecules from eight binary or four ternary acid-base solutions based on new (aqueous dimethylammonium chloride) and published surface tension data, the Gibbs adsorption equation, and published theoretical studies. Estimated surface activities can explain the surface tension behavior of the binary and ternary solutions. When the salt (neutral solution) limit is taken into account, surface tensions of the acid-base solutions change quite linearly between the binary limits. On the basis of this linearity, several different simple models were tested by calculating deviations from new (dimethylamine/ammoniahydrochloric acid) and published (dimethylamine/ ammonia-sulfuric acid) experimental data. As a result, two simple models based on the weighted average of binary solution surface tensions were selected, one for the ammonia and one for the dimethylamine solutions. Model deviations are significantly smaller than those of, for example, constant surface tension approximation or models including only the acid-water and base-water binary limits. Acknowledgment. We thank Maj and Tor Nessling foundation for support (grants 2007083 and 2008095) and Dr. Tatu Anttila for useful discussions. References and Notes (1) Brimblecombe, P.; Latif, M. T. EnViron. Chem. 2004, 1, 11–12. (2) Topping, D. O.; McFiggans, G. B.; Coe, H. Atmos. Chem. Phys. 2005, 5, 1205–1222. (3) Topping, D. O.; McFiggans, G. B.; Coe, H. Atmos. Chem. Phys. 2005, 5, 1223–1242. (4) Mircea, M.; Facchini, M. C.; Decesari, S.; Cavalli, F.; Emblico, L.; Fuzzi, S.; Vestin, A.; Rissler, J.; Swietlicki, E.; Frank, G.; Andreae, M. O.; Maenhaut, W.; Rudich, Y.; Artaxo, P. Atmos. Chem. Phys. 2005, 5, 3111–3126. (5) Shulman, M. L.; Jacobson, M. C.; Carlson, R. J.; Synovec, R. E.; Young, T. E. Geophys. Res. Lett. 1996, 23, 277–280. (6) Saxena, P.; Hildemann, L. M. J. Atmos. Chem. 1996, 24, 57–109. (7) Chow, J. C.; Watson, J. G.; Fujita, E. M.; Lu, Z.; Lawson, D. R.; Ashbaugh, L. L. Atmos. EnViron. 1994, 28, 2061–2080. (8) Makar, P. A. Atmos. EnViron. 2001, 35, 961–974.
Raatikainen et al. (9) Sellegri, K.; Hanke, M.; Umann, B.; Arnold, F.; Kulmala, M. Atmos. Chem. Phys. 2005, 5, 373–384. (10) Weissenborn, P. K.; Pugh, R. J. Langmuir 1995, 11, 1422–1426. (11) Weissenborn, P. K.; Pugh, R. J. J. Colloid Interface Sci. 1996, 184, 550–563. (12) Facchini, M. C.; Decesari, S.; Mircea, M.; Fuzzi, S.; Loglio, G. Atmos. EnViron. 2000, 34, 4853–4857. (13) Abdul-Razzak, H.; Ghan, S. J. J. Geophys. Res. 2004, 109, D03205. (14) Henning, S.; Rosenørn, T.; D’Anna, B.; Gola, A. A.; Svenningsson, B.; Bilde, M. Atmos. Chem. Phys. 2005, 5, 575–582. (15) Mmereki, B. T.; Hicks, J. M.; Donaldson, D. J. J. Phys. Chem. A 2000, 104, 10789–10793. (16) Donaldson, D. J. J. Phys. Chem. A 1999, 103, 62–70. (17) van Dingenen, R.; Raes, F. J. Aerosol Sci. 1993, 24, 1–17. (18) Arstila, H.; Korhonen, P.; Kulmala, M. J. Aerosol Sci. 1999, 30, 131–138. (19) Sorjamaa, R.; Svenningsson, B.; Raatikainen, T.; Henning, S.; Bilde, M.; Laaksonen, A. Atmos. Chem. Phys. 2004, 4, 2107–2117. (20) Knipping, E. M.; Lakin, M. J.; Foster, K. L.; Jungwirth, P.; Tobias, D. J.; Gerber, R. B.; Dabdub, D.; Finlayson-Pitts, B. J. Science 2000, 288, 301–306. (21) Clifford, D.; Donaldson, D. J. Phys. Chem. A 2007, 111, 9809– 9814. (22) Gibbs, J. W. The Collected Works of J. Willard Gibbs; Longmans Green and Co.: New York, 1928; Vol. 1. (23) Jungwirth, P.; Tobias, D. J. J. Phys. Chem. B 2001, 105, 10468– 10472. (24) Vrbka, L.; Mucha, M.; Minofar, B.; Jungwirth, P.; Brown, E. C.; Tobias, D. J. Curr. Opin. Colloid Interface Sci. 2004, 9, 67–73. (25) Petersen, M. K.; Iyengar, S. S.; Day, T. J. F.; Voth, G. A. J. Phys. Chem. B 2004, 108, 14804–14806. (26) Mucha, M.; Frigato, T.; Levering, L. M.; Allen, H. C.; Tobias, D. J.; Dang, L. X.; Jungwirth, P. J. Phys. Chem. B 2005, 109, 7617–7623. (27) Gopalakrishnan, S.; Jungwirth, P.; Tobias, D. J.; Allen, H. C. J. Phys. Chem. B 2005, 109, 8861–8872. (28) Chang, T.-M.; Dang, L. Chem. ReV. 2006, 106, 1305–1322. (29) Jungwirth, P.; Tobias, D. Chem. ReV. 2006, 106, 1259–1281. (30) Petersen, P. B.; Saykally, R. J. Annu. ReV. Phys. Chem. 2006, 57, 333–364. (31) Strey, R.; Viisanen, Y.; Aratono, M.; Kratohvil, J.; Yin, Q.; Friberg, S. J. Phys. Chem. B 1999, 103, 9112–9116. (32) Hyva¨rinen, A.-P.; Lihavainen, H.; Gaman, A.; Vairila, L.; Ojala, H.; Kulmala, M.; Viisanen, Y. J. Chem. Eng. Data 2006, 51, 255–260. (33) Wilhelmy, L. Ann. Phys. 1863, 119, 177–179. (34) Surface Tension of Ordinary Water Substance; Technical Report, IAPWS, 1994. (35) McDuffie, N. G. Langmuir 2001, 17, 5711–5713. (36) Surface tension of aqueous HCl is obtained from the fitting to the data presented by Landolt-Bo¨rnstein: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik; Springer-Verlag: Berlin, 1960; Vol. 2. (37) Myhre, C. E. L.; Nielsen, C. J.; Saastad, O. W. J. Chem. Eng. Data 1998, 43, 617–622. (38) Korhonen, P.; Kulmala, M.; Viisanen, Y. J. Aerosol Sci. 1997, 28, 901–917. (39) Ha¨meri, K.; Va¨keva¨, M.; Hansson, H.-C.; Laaksonen, A. J. Geophys. Res. 2000, 105, 22231–22242. (40) Hyva¨rinen, A.-P.; Lihavainen, H.; Hautio, K.; Raatikainen, T.; Viisanen, Y.; Laaksonen, A. J. Chem. Eng. Data 2004, 49, 917–922. (41) Hyva¨rinen, A.-P.; Raatikainen, T.; Laaksonen, A.; Viisanen, Y.; Lihavainen, H. Geophys. Res. Lett. 2005, 32, L16806.
JP7117136
