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<front>
<journal-meta>
<journal-id journal-id-type="publisher">ACP</journal-id>
<journal-title-group>
<journal-title>Atmospheric Chemistry and Physics</journal-title>
<abbrev-journal-title abbrev-type="publisher">ACP</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1680-7324</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/acp-7-2371-2007</article-id>
<title-group>
<article-title>Surface tensions of multi-component mixed inorganic/organic aqueous systems of atmospheric significance: measurements, model predictions and importance for cloud activation predictions</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Topping</surname>
<given-names>D. O.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>McFiggans</surname>
<given-names>G. B.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kiss</surname>
<given-names>G.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Varga</surname>
<given-names>Z.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Facchini</surname>
<given-names>M. C.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Decesari</surname>
<given-names>S.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mircea</surname>
<given-names>M.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>School of Earth, Atmospheric and Environmental Sciences, The University of Manchester, The Sackville street building, Sackville street, Manchester, M60 1QD, UK</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Air Chemistry Group of the Hungarian Academy of Sciences, Univ. of Pannonia, 8201Veszprém, P.O. Box 158, Hungary</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Department of Earth and Environmental Sciences, University of Pannonia, 8201 Veszprém, P.O. Box 158, Hungary</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Instituto di Scienze dell Atmosfera e del Clima, Consiglio Nazionale delle Ricerche, Via Gobetti, Bologna, Italy</addr-line>
</aff>
<pub-date pub-type="epub">
<day>10</day>
<month>05</month>
<year>2007</year>
</pub-date>
<volume>7</volume>
<issue>9</issue>
<fpage>2371</fpage>
<lpage>2398</lpage>
<permissions>
<license xlink:type="simple">
<license-p>This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
</license>
</permissions>
<self-uri xlink:href="http://www.atmos-chem-phys.net/7/2371/2007/acp-7-2371-2007.html">This article is available from http://www.atmos-chem-phys.net/7/2371/2007/acp-7-2371-2007.html</self-uri>
<self-uri xlink:href="http://www.atmos-chem-phys.net/7/2371/2007/acp-7-2371-2007.pdf">The full text article is available as a PDF file from http://www.atmos-chem-phys.net/7/2371/2007/acp-7-2371-2007.pdf</self-uri>
<abstract>
<p>In order to predict the physical properties of aerosol particles, it is
necessary to adequately capture the behaviour of the ubiquitous complex
organic components. One of the key properties which may affect this
behaviour is the contribution of the organic components to the surface
tension of aqueous particles in the moist atmosphere. Whilst the qualitative
effect of organic compounds on solution surface tensions has been widely
reported, our quantitative understanding on mixed organic and mixed
inorganic/organic systems is limited. Furthermore, it is unclear whether
models that exist in the literature can reproduce the surface tension
variability for binary and higher order multi-component organic and mixed
inorganic/organic systems of atmospheric significance. The current study
aims to resolve both issues to some extent. Surface tensions of single and
multiple solute aqueous solutions were measured and compared with
predictions from a number of model treatments. On comparison with binary
organic systems, two predictive models found in the literature provided a
range of values resulting from sensitivity to calculations of pure component
surface tensions. Results indicate that a fitted model can capture the
variability of the measured data very well, producing the lowest average
percentage deviation for all compounds studied. The performance of the
other models varies with compound and choice of model parameters. The
behaviour of ternary mixed inorganic/organic systems was unreliably captured
by using a predictive scheme and this was dependent on the composition of
the solutes present. For more atmospherically representative higher order
systems, entirely predictive schemes performed poorly. It was found that use
of the binary data in a relatively simple mixing rule, or modification of an
existing thermodynamic model with parameters derived from binary data, was
able to accurately capture the surface tension variation with concentration.
Thus, it would appear that in order to model multi-component surface
tensions involving compounds used in this study one requires the use of
appropriate binary data. However, results indicate that the use of
theoretical frameworks which contain parameters derived from binary data may
predict unphysical behaviour when taken beyond the concentration ranges used
to fit such parameters. The effect of deviations between predicted and
measured surface tensions on predicted critical saturation ratios was
quantified, by incorporating the surface tension models into an existing
thermodynamic framework whilst firstly neglecting bulk to surface
partitioning. Critical saturation ratios as a function of dry size for all
of the multi-component systems were computed and it was found that
deviations between predictions increased with decreasing particle dry size.
As expected, use of the surface tension of pure water, rather than calculate
the influence of the solutes explicitly, led to a consistently higher value
of the critical saturation ratio indicating that neglect of the
compositional effects will lead to significant differences in predicted
activation behaviour even at large particle dry sizes. Following this two
case studies were used to study the possible effect of bulk to surface
partitioning on critical saturation ratios. By employing various assumptions
it was possible to perform calculations not only for a binary system but
also for a mixed organic system. In both cases this effect lead to a
significant increase in the predicted critical supersaturation ratio
compared to the above treatment. Further analysis of this effect will form
the focus of future work.</p>
</abstract>
<counts><page-count count="28"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple"> Abdul-Razzak, H. and Ghan, S. J.: Parameterization of the influence of organic surfactants on aerosol activation, J. Geophys. Res. Atmos., 109(D3), D03205, doi:10.1029/2003JD004043, 2004. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple"> Alfarra, M. R., Paulsen, D., Gysel, M., Garforth, A. A., Dommen, J., Prévôt, A. S. H., Worsnop, D. R., Baltensperger, U., and Coe, H.: A mass spectrometric study of secondary organic aerosols formed from the photoxidation of anthropogenic and biogenic precursors in a reaction chamber, Atmos. Chem. Phys., 6, 5279&amp;ndash;5293, 2006. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple"> Amundson, N. R., Caboussat, A., He, J. W., Martynenko, A. V., Savarin, V. B., Seinfeld, J. H., and Yoo, K. Y.: A new inorganic atmospheric aerosol phase equilibrium model (UHAERO), Atmos. Chem. Phys., 6, 975&amp;ndash;992, 2006. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple"> Brooks, S. D., DeMott, P. J., and Kreidenweis, S. M.: Water uptake by particles containing humic materials and mixtures of humic materials with ammonium sulfate, Atmos. Environ., 38(13), 1859&amp;ndash;1868, 2004 </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple"> Chan, M. N., Choi, M. Y., Ng, N. L., and Chan, C. K.: Hygroscopicity of water-soluble organic compounds in atmospheric biomass burning derived organic species, Environ. Sci. Technol., 39, 1555&amp;ndash;1562, 2005. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple"> ChemSketch: Version 5.0. Advanced Chemistry Development, Inc., Toronto ON, Canada, www.acdlabs.com, 2003. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple"> Clegg, S. L. and Pitzer, K. S.: Thermodynamics of Multicomponent, Miscible, Ionic-Solutions &amp;ndash; Generalized Equations for Symmetrical Electrolytes, J. Phys. Chem., 96(8), 3513&amp;ndash;3520, 1992. </mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple"> Clegg, S. L. and Seinfeld, J. H.: Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15K. I. The acids as non-dissociating compounds, J. Phys. Chem. A, 110, 5692&amp;ndash;5717, 2006. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple"> Clegg, S. L., Seinfeld, J. H., and Brimblecombe, P.: Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds, J. Aero. Sci., 32(6), 713&amp;ndash;738, 2001. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple"> Escobedo, J. and Mansoori, G. A.: Surface tension prediction for pure fluids, AIChE J., 42(5), 1425&amp;ndash;1433, 1996. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple"> Facchini, M. C., Decesari, S., Mircea, M., Fuzzi, S., and Loglio, G.: Surface tension of atmospheric wet aerosol and cloud/fog droplets in relation to their organic carbon content and chemical composition, Atmos. Environ., 34(28), 4853&amp;ndash;4857, 2000. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple"> Fainerman, V. B., Miller, R., and Aksenenko, E. V.: Simple model for prediction of surface tension of mixed surfactant solutions, Adv. Col. Int. Sci., 96(1&amp;ndash;3), 339&amp;ndash;359, 2002. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple"> Fainerman, V. B. and Miller, R.: Simple method to Estimate Surface tension of Mixed Surfactant Solutions, J. Phys. Chem. B, 105, 11 432&amp;ndash;11 438, 2001. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple"> Fainerman, V. B., Wustneck, R., and Miller, R.: Surface tension of mixed surfactant solutions, Tenside Surfact Det., 38(4), 224&amp;ndash;229, 2001. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple"> Feingold, G.: Modeling of the first indirect effect: Analysis of measurement requirements, Geophys. Res. Lett., 30(19), ASC 7-1, 2003. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple"> Fredenslund, A., Jones, R. L., and Prausnitz, J. M.: Group-Contribution Estimation of Activity-Coefficients in Nonideal Liquid-Mixtures, AIChE J., 21(6), 1086&amp;ndash;1099, 1975. </mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple"> Fuzzi, S., Decesari, S., Facchini, M. C., Matta, E., Mircea, M., and Tagliavini, E.: A simplified model of the water soluble organic component of atmospheric aerosols, Geophys. Res. Lett., 28(21), 4079&amp;ndash;4082, 2001. </mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple"> Gaman, A. I., Kulmala, M., Vehkamaki, H., Napari, I., Mircea, M., Facchini, M. C., and Laaksonen, A.: Binary homogeneous nucleation in water-succinic acid and water-glutaric acid systems, J. Chem. Phys., 120(1), 282&amp;ndash;291, 2004. </mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple"> Goldsack, D. E. and White, B. R.: An Iterative Technique for Calculating Surface Tensions of Non Electrolyte Solutions, Canadian Journal of Chemistry-Revue Canadienne De Chimie, 61(8), 1725&amp;ndash;1729, 1983. </mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple"> Hansen, H. K., Rasmussen, P., Fredenslund, A., Schiller, M., and Gmehling, J.: Vapor-Liquid-Equilibria by Unifac Group Contribution, 5. Revision and Extension, Ind. Eng. Chem. Res., 30(10), 2352&amp;ndash;2355, 1991. </mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple"> Henning, S., Rosenorn, T., D&apos;Anna, B., Gola, A. A., Svenningsson, B., and Bilde, M.: Cloud droplet activation and surface tension of mixtures of slightly soluble organics and inorganic salt, Atmos. Chem. Phys., 5, 575&amp;ndash;582, 2005. </mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple"> Hori, M., Ohta, S., Murao, N., and Yamagata, S.: Activation capability of water solubile organic substances as CCN, Aerosol Sci., 34, 419&amp;ndash;448, 2003. </mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple"> Hu, Y. F. and Lee, H.: Prediction of the surface tension of mixed electrolyte solutions based on the equation of Patwardhan and Kumar and the fundamental Butler equations, J. Col. Int. Sci., 269(2), 442&amp;ndash;448, 2004. </mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple"> Jasper, J. J.: The Surface Tension of Pure Liquid Compounds, J. Phys. Chem. Ref. Data, 1, 841&amp;ndash;1010, 1972. </mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple"> Kiss, G., Tombacz, E., and Hansson, H. C.: Surface tension effects of humic-like substances in the aqueous extract of tropospheric fine aerosol, J. Atmos. Chem., 50(3), 279&amp;ndash;294, 2005. </mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple"> Kokkola, H., Sorjamaa, R., Peräniemi, A., Raatikainen, T., and Laaksonen, A.: Cloud formation of particles containing humic-like substances, Geophys. Res. Lett., 33, L10816, doi:10.1029/2006GL026107, 2006. </mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple"> Li, Z., Williams, A. L., and Rood, M. J.: Influence of soluble surfactant properties on the activation of aerosol particles containing inorganic solute, J. Atmos. Sci., 55, 1859&amp;ndash;1866, 1998. </mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple"> Li, Z. B. and Lu, B. C. Y.: Surface tension of aqueous electrolyte solutions at high concentrations &amp;ndash; representation and prediction, Chem. Eng. Sci., 56(8), 2879&amp;ndash;2888, 2001. </mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple"> Loglio, G., Pandolfini, P., Miller, R., Makievski, A. V., Ravera, F., Ferrari, M., and Liggieri, L.: Drop and Bubble Shape Analysis as a Tool for Dilational Rheology Studies of Interfacial Layers, in: Novel Methods to Study Interfacial Layers, Studies in Interface Science, edited by: Miller, D. M. a. R., Elsevier, Amsterdam, pp 439&amp;ndash;485, 2001. </mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple"> Marcolli, C., Luo, B. P., and Peter, T.: Mixing of the organic aerosol fractions: Liquids as the thermodynamically stable phases, J. Phys. Chem. A, 108(12), 2216&amp;ndash;2224, 2004. </mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple"> Marrero, J. and Gani, R.: Group-contribution based estimation of pure component properties, Fluid Phase Equilib., 183, 183&amp;ndash;208, 2001. </mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple"> McFiggans, G., Artaxo, P., Baltensperger, U., Coe, H., Facchini, M. C., Feingold, G., Fuzzi, S., Gysel, M., Laaksonen, A., Lohmann, U., Mentel, M., Murphy, D. M., O&apos;Dowd, C. D., Snider, J. R., and Weingartner, E.: The effect of physical and chemical aerosol properties on warm cloud droplet activation, Atmos. Chem. Phys., 6, 2593&amp;ndash;2649, 2006. </mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple"> Metzger, S., Dentener, F., Pandis, S., and Lelieveld, J.: Gas/aerosol partitioning: 1. A computationally efficient model, J. Geophys. Res. Atmos., 107(D16), 4312, doi:10.1029/2001JD001102, 2002. </mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple"> Ming, Y. and Russell, L. M.: Thermodynamic equilibrium of organic-electrolyte mixtures in aerosol particles, AICHe J., 48(6), 1331&amp;ndash;1348, 2002. </mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple"> Needham, D.E., Wei, I.C. and Seybold, P.G,. Molecular Modeling of the Physical-Properties of the Alkanes. J Am Chem Soc, 110(13): 4186-4194. 1988 </mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple"> Peng, C., Chan, M. N., and Chan, C. K. The hygroscopic properties of dicarboxylic and multifunctional acids: Measurements and UNIFAC predictions, Environ. Sci. Technol., 35(22), 4495&amp;ndash;4501, 2001. </mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple"> Perry, R. H. and Green, D. W.: Perry&apos;s Chemical Engineers Handbook (7th edition), McGraw-Hill, 1997. </mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple"> Poling, B. E., Prausnitz, J. M., and O&apos;Connell, J. P.: The Properties of Gases and Liquids, McGraw-Hill Professional, 2000. </mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple"> Quayle, O. R.: The parachors of organic compounds, Chem. Rev., 53, 439&amp;ndash;591, 1953. </mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple"> Reinhard, M. and Drefahl, A.: Handbook for Estimating Physicochemical Properties of Organic Compounds, John Wiley &amp; Sons, 1999. </mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple"> Riddick, J. A., Bunger, W. B., and Sakano, T. K.: Techniques of Chemistry, Organic Solvents, J. Wiley and Sons, New York, pp 553, 1986. </mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple"> Rissman, T. A., Nenes, A., and Seinfeld, J. H.: Chemical amplification (or dampening) of the Twomey effect: Conditions derived from droplet activation theory, J. Atmos. Sci., 61(8), 919&amp;ndash;930, 2004. </mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple"> Rowlinson, J. S., Widom, B., Abraham, D. B., Evans, R., Sullivan, D. E.,,, Schofield, P., Henderson, J. R., Percus, J. K., Sluckin, T. J., Richmond, P., Findenegg, G. H., Rowlinson, J. S., Schofield, P., Pethica, B. A., Mclure, I. A., Rice, S. A., Smith, E. B., Mazo, R. M., Vassilieff, C. S., Whittington, S. G., Sluckin, T. J., Rasaiah, J. C., Develyn, M. P., Stepto, R. F. T., Croxton, C. A., Lal, M., Oxtoby, D. W., Vincent, B., Everett, D. H., Parsons, R., Parsonage, N. G., Blum, L., Nicholson, D., Torrie, G., Outhwaite, C. W., Levine, S., Bushnellwye, G., and Toxvaerd, S.: Structure of the Interfacial Region &amp;ndash; General Discussion. Faraday Symp. Chem. S, 16, 205&amp;ndash;256, 1981. </mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple"> Seidl, W.: Model for a surface film of fatty acids on rain water and aerosol particles, Atmos. Environ., 34(28), 4917&amp;ndash;4932, 2000. </mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple"> Seinfeld, J. H. and Pandis, S. N.: Atmospheric Chemistry and Physics, Wiley-Interscience Publication, 1998. </mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple"> Shulman, M. L., Jacobson, M. C., Charlson, R. J., Synovec, R. E., and Young, T. E.: Dissolution behavior and surface tension effects of organic compounds in nucleating cloud droplets (Vol 23, p 277, 1996), Geophys. Res. Lett., 23(5), 603&amp;ndash;603, 1996. </mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple"> Sorjamaa, R., Svenningsson, B., Raatikainen, T., Henning, S., Bilde, M., and Laaksonen, A.: The role of surfactants in Kohler theory reconsidered, Atmos. Chem. Phys., 4, 2107&amp;ndash;2117, 2004. </mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple"> Sorjamaa, R. and Laaksonen, A.: The influence of surfactant properties on critical supersaturations of cloud condensation nuclei, J. Aerosol Sci., 37, 12, 1730&amp;ndash;1736, 2006. </mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple"> Sprow, F. B. and Prausnitz, J. M.: Surface Tensions of Simple Liquid Mixtures, Transactions of the Faraday Society, 62(521P), 1105&amp;ndash;1111, 1966a. </mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple"> Sprow, F. B. and Prausnitz, J. M.: Surface Tensions of Simple Liquids. Transactions of the Faraday Society, 62(521P), 1097&amp;ndash;1104, 1966b. </mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple"> Stanton, D. T. and Jurs, P. C.: Development and Use of Charged Partial Surface-Area Structural Descriptors in Computer-Assisted Quantitative Structure Property Relationship Studies, Anal. Chem., 62(21), 2323&amp;ndash;2329, 1990. </mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple"> Suarez, J. T., Torres-Marchal, C., and Rasmussen, P: Prediction of surface tension of nonelectrolyte solutions, Chem. Eng. Sci., 44(3), 782&amp;ndash;786, 1989. </mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple"> Svenningsson, B., Rissler, J., Swietlicki, E., Mircea, M., Bilde, M., Facchini, M. C., Decesari, S., Fuzzi, S., Zhou, J., Monster, J., and Rosenorn, T.: Hygroscopic growth and critical supersaturations for mixed aerosol particles of inorganic and organic compounds of atmospheric relevance, Atmos. Chem. Phys., 6, 1937&amp;ndash;1952, 2006. </mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple"> Tamura, M., Kurata, M., and Odani, H.: Practical Method for Estimating Surface Tensions of Solutions, Bulletin of the Chemical Society of Japan, 28(1), 83&amp;ndash;88, 1955. </mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple"> Topping, D. O., McFiggans, G. B., and Coe, H.: A curved multi-component aerosol hygroscopicity model framework: Part 1 &amp;ndash; Inorganic compounds, Atmos. Chem. Phys., 5, 1205&amp;ndash;1222, 2005a. </mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple"> Topping, D. O., McFiggans, G. B., and Coe, H.: A curved multi-component aerosol hygroscopicity model framework: Part 2 &amp;ndash; Including organic compounds, Atmos. Chem. Phys., 5, 1223&amp;ndash;1242, 2005b. </mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple"> Tuckermann, R. and Cammenga, H. K.: The surface tension of aqueous solutions of some atmospheric water-soluble organic compounds, Atmos. Environ., 38(36), 6135&amp;ndash;6138, 2004. </mixed-citation>
</ref>
</ref-list>
</back>
</article>