Journal of Atmospheric Chemistry

, Volume 74, Issue 3, pp 357–376 | Cite as

Modeling of hygroscopicity parameter kappa of organic aerosols using quantitative structure-property relationships

  • Jernej MarkeljEmail author
  • Sasha Madronich
  • Matevž Pompe


The hygroscopicity of organic aerosol in the atmosphere can be represented by a semi-empirical single parameter, κ. In this work we test possibilities for developing quantitative structure-property relationship (QSPR) models for κ based on chemical similarity. Models were developed in two ways: by manually assessing the suitability of several plausible physico-chemical descriptors; and by systematically evaluating hundreds of constitutional (e.g. number of particular atoms, bond types, molecular weight,...), topological, electrostatic, geometrical and quantum-chemical descriptors with the QSPR modelling software CODESSA (COmprehensive DEscriptors for Structural and Statistical Analysis). A set of 74 compounds with measured κ values was taken from the literature and prediction capabilities of the developed models were evaluated by leave-one-out cross-validation procedure. A 5-parameter linear regression model obtained with CODESSA was found to be the most suitable. Among the five descriptors, the two providing the highest contributions to the total variance were found to be (i) the final heat of formation divided by the number of atoms (69 %) and (ii) the ratio of molecular weight and molecular volume (16 %), although other topological and electrostatic descriptors were also of non-negligible importance for prediction of κ. The squared correlation coefficient and the root mean square error of a leave-one-out cross-validation procedure were 0.80 and 0.037, respectively. The results show that quantitative structure-property relationship approaches are useful for modeling κ.


κ parameter Aerosol water content Aerosol hygroscopicity CCN activity QSPR Modelling 

Supplementary material

10874_2016_9347_MOESM1_ESM.docx (36 kb)
ESM 1 (DOCX 35 kb)


  1. Abraham M.H., McGowan J.C.: The use of characteristic volumes to measure cavity terms in reversed phase liquid-chromatography. Chromatographia. 23(4), 243–246 (1987)CrossRefGoogle Scholar
  2. Aumont B., Szopa S., Madronich S.: Modelling the evolution of organic carbon during its gas-phase tropospheric oxidation: development of an explicit model based on a self generating approach. Atmos. Chem. Phys. 5, 2497–2517 (2005)CrossRefGoogle Scholar
  3. Basak S.C., Magnuson V.R.: Molecular topology and narcosis - a quantitative structure-activity relationship (QSAR) study of alcohols using complementary information-content (CIC). Arzneimittel.-Forsch. 33-1(4), 501–503 (1983)Google Scholar
  4. Broekhuizen K., Kumar P.P., Abbatt J.P.D.: Partially soluble organics as cloud condensation nuclei: Role of trace soluble and surface active species. Geophys. Res. Lett. 31(1), (2004). doi: 10.1029/2003GL018203
  5. Carslaw K.S., Lee L.A., Reddington C.L., Pringle K.J., Rap A., Forster P.M., Mann G.W., Spracklen D.V., Woodhouse M.T., Regayre L.A., Pierce J.R.: Large contribution of natural aerosols to uncertainty in indirect forcing. Nature. 503(7474), 67 (2013)CrossRefGoogle Scholar
  6. Chang R.Y.W., Slowik J.G., Shantz N.C., Vlasenko A., Liggio J., Sjostedt S.J., Leaitch W.R., Abbatt J.P.D.: The hygroscopicity parameter (kappa) of ambient organic aerosol at a field site subject to biogenic and anthropogenic influences: relationship to degree of aerosol oxidation. Atmos. Chem. Phys. 10(11), 5047–5064 (2010)CrossRefGoogle Scholar
  7. Clegg S.L., Seinfeld J.H., Brimblecombe P.: Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds. J. Aerosol Sci. 32(6), 713–738 (2001)CrossRefGoogle Scholar
  8. Csizmadia, I.G.: Theory and Practice of MO Calculations on Organic Molecules, vol. 13. Elsevier Science Ltd, (1978)Google Scholar
  9. Dearden J.C., Rotureau P., Fayet G.: QSPR prediction of physico-chemical properties for REACH. SAR QSAR Environ. Res. 24(4), 545–584 (2013)CrossRefGoogle Scholar
  10. Dusek U., Frank G.P., Massling A., Zeromskiene K., Iinuma Y., Schmid O., Helas G., Hennig T., Wiedensohler A., Andreae M.O.: Water uptake by biomass burning aerosol at sub- and supersaturated conditions: closure studies and implications for the role of organics. Atmos. Chem. Phys. 11(18), 9519–9532 (2011)CrossRefGoogle Scholar
  11. Facchini M.C., Mircea M., Fuzzi S., Charlson R.J.: Cloud albedo enhancement by surface-active organic solutes in growing droplets. Nature. 401(6750), 257–259 (1999)CrossRefGoogle Scholar
  12. Farmer D.K., Cappa C.D., Kreidenweis S.M.: Atmospheric processes and their controlling influence on cloud condensation nuclei activity. Chem. Rev. 115(10), 4199–4217 (2015)CrossRefGoogle Scholar
  13. Fredenslund A., Jones R.L., Prausnitz J.M.: Group-contribution estimation of activity-coefficients in nonideal liquid-mixtures. AICHE J. 21(6), 1086–1099 (1975)CrossRefGoogle Scholar
  14. Gunthe S.S., King S.M., Rose D., Chen Q., Roldin P., Farmer D.K., Jimenez J.L., Artaxo P., Andreae M.O., Martin S.T., Poschl U.: Cloud condensation nuclei in pristine tropical rainforest air of Amazonia: size-resolved measurements and modeling of atmospheric aerosol composition and CCN activity. Atmos. Chem. Phys. 9(19), 7551–7575 (2009)CrossRefGoogle Scholar
  15. Hallquist M., Wenger J.C., Baltensperger U., Rudich Y., Simpson D., Claeys M., Dommen J., Donahue N.M., George C., Goldstein A.H., Hamilton J.F., Herrmann H., Hoffmann T., Iinuma Y., Jang M., Jenkin M.E., Jimenez J.L., Kiendler-Scharr A., Maenhaut W., McFiggans G., Mentel T.F., Monod A., Prevot A.S.H., Seinfeld J.H., Surratt J.D., Szmigielski R., Wildt J.: The formation, properties and impact of secondary organic aerosol: current and emerging issues. Atmos. Chem. Phys. 9(14), 5155–5236 (2009)CrossRefGoogle Scholar
  16. Hawkins D.M., Basak S.C., Mills D.: Assessing model fit by cross-validation. J. Chem. Inf. Comput. Sci. 43(2), 579–586 (2003)CrossRefGoogle Scholar
  17. Hodzic A., Aumont B., Knote C., Lee-Taylor J., Madronich S., Tyndall G.: Volatility dependence of Henry’s law constants of condensable organics: application to estimate depositional loss of secondary organic aerosols. Geophys. Res. Lett. 41(13), 4795–4804 (2014)CrossRefGoogle Scholar
  18. Hudson J.G., Da X.Y.: Volatility and size of cloud condensation nuclei. J. Geophys. Res. 101(D2), 4435–4442 (1996)CrossRefGoogle Scholar
  19. IPCC: Climate Change 2014: Synthesis report. contribution of working groups i, ii and iii to the fifth assessment report of the intergovernmental panel on climate change. Geneva (2014).Google Scholar
  20. Jimenez J.L., Canagaratna M.R., Donahue N.M., Prevot A.S.H., Zhang Q., Kroll J.H., DeCarlo P.F., Allan J.D., Coe H., Ng N.L., Aiken A.C., Docherty K.S., Ulbrich I.M., Grieshop A.P., Robinson A.L., Duplissy J., Smith J.D., Wilson K.R., Lanz V.A., Hueglin C., Sun Y.L., Tian J., Laaksonen A., Raatikainen T., Rautiainen J., Vaattovaara P., Ehn M., Kulmala M., Tomlinson J.M., Collins D.R., Cubison M.J., Dunlea E.J., Huffman J.A., Onasch T.B., Alfarra M.R., Williams P.I., Bower K., Kondo Y., Schneider J., Drewnick F., Borrmann S., Weimer S., Demerjian K., Salcedo D., Cottrell L., Griffin R., Takami A., Miyoshi T., Hatakeyama S., Shimono A., Sun J.Y., Zhang Y.M., Dzepina K., Kimmel J.R., Sueper D., Jayne J.T., Herndon S.C., Trimborn A.M., Williams L.R., Wood E.C., Middlebrook A.M., Kolb C.E., Baltensperger U., Worsnop D.R.: Evolution of Organic Aerosols in the Atmosphere. Science. 326(5959), 1525–1529 (2009)CrossRefGoogle Scholar
  21. Kanakidou M., Seinfeld J.H., Pandis S.N., Barnes I., Dentener F.J., Facchini M.C., Van Dingenen R., Ervens B., Nenes A., Nielsen C.J., Swietlicki E., Putaud J.P., Balkanski Y., Fuzzi S., Horth J., Moortgat G.K., Winterhalter R., Myhre C.E.L., Tsigaridis K., Vignati E., Stephanou E.G., Wilson J.: Organic aerosol and global climate modelling: a review. Atmos. Chem. Phys. 5, 1053–1123 (2005)CrossRefGoogle Scholar
  22. Karelson M., Lobanov V.S., Katritzky A.R.: Quantum-chemical descriptors in QSAR/QSPR studies. Chem. Rev. 96(3), 1027–1043 (1996)CrossRefGoogle Scholar
  23. Katritzky, A.R., Lobadov, V.S., Karelson, M.: CODESSA PRO User’s Manual. Gainesville (2005).Google Scholar
  24. Katritzky A.R., Kuanar M., Slavov S., Hall C.D., Karelson M., Kahn I., Dobchev D.A.: Quantitative correlation of physical and chemical properties with chemical structure: utility for prediction. Chem. Rev. 110(10), 5714–5789 (2010)CrossRefGoogle Scholar
  25. Kirpichenok M.A., Zefirov N.S.: Electronegativity and geometry of molecules. 1. principles of developed approach and analysis of the effect of nearest electrostatic interactions on the bond length in organic-molecules. Zh. Org. Chim. 23(4), 673–691 (1987)Google Scholar
  26. Köhler H.: The nucleus in and the growth of hygroscopic droplets. Trans. Faraday Soc. 32(2), 1152–1161 (1936)CrossRefGoogle Scholar
  27. Kroll J.H., Seinfeld J.H.: Chemistry of secondary organic aerosol: formation and evolution of low-volatility organics in the atmosphere. Atmos. Environ. 42(16), 3593–3624 (2008)CrossRefGoogle Scholar
  28. Lambe A.T., Ahern A.T., Wright J.P., Croasdale D.R., Davidovits P., Onasch T.B.: Oxidative aging and cloud condensation nuclei activation of laboratory combustion soot. J. Aerosol Sci. 79, 31–39 (2015)CrossRefGoogle Scholar
  29. Lee-Taylor J., Hodzic A., Madronich S., Aumont B., Camredon M., Valorso R.: Multiday production of condensing organic aerosol mass in urban and forest outflow. Atmos. Chem. Phys. 15(2), 595–615 (2015)CrossRefGoogle Scholar
  30. Levin E.J.T., Prenni A.J., Palm B.B., Day D.A., Campuzano-Jost P., Winkler P.M., Kreidenweis S.M., DeMott P.J., Jimenez J.L., Smith J.N.: Size-resolved aerosol composition and its link to hygroscopicity at a forested site in Colorado. Atmos. Chem. Phys. 14(5), 2657–2667 (2014)CrossRefGoogle Scholar
  31. Massoli P., Lambe A.T., Ahern A.T., Williams L.R., Ehn M., Mikkila J., Canagaratna M.R., Brune W.H., Onasch T.B., Jayne J.T., Petaja T., Kulmala M., Laaksonen A., Kolb C.E., Davidovits P., Worsnop D.R.: Relationship between aerosol oxidation level and hygroscopic properties of laboratory generated secondary organic aerosol (SOA) particles. Geophys. Res. Lett. 37, (2010). doi: 10.1029/2010GL045258
  32. McFiggans G., Artaxo P., Baltensperger U., Coe H., Facchini M.C., Feingold G., Fuzzi S., Gysel M., Laaksonen A., Lohmann U., Mentel T.F., Murphy D.M., O’Dowd C.D., Snider J.R., Weingartner E.: The effect of physical and chemical aerosol properties on warm cloud droplet activation. Atmos. Chem. Phys. 6, 2593–2649 (2006)CrossRefGoogle Scholar
  33. Mei F., Setyan A., Zhang Q., Wang J.: CCN activity of organic aerosols observed downwind of urban emissions during CARES. Atmos. Chem. Phys. 13(24), 12155–12169 (2013)CrossRefGoogle Scholar
  34. Nannoolal Y., Rarey J., Ramjugernath D., Cordes W.: Estimation of pure component properties pPart 1. Estimation of the normal boiling point of non-electrolyte organic compounds via group contributions and group interactions. Fluid Phase Equilib. 226, 45–63 (2004)CrossRefGoogle Scholar
  35. Nannoolal Y., Rarey J., Ramjugernath D.: Estimation of pure component properties - pPart 3. Estimation of the vapor pressure of non-electrolyte organic compounds via group contributions and group interactions. Fluid Phase Equilib. 269(1–2), 117–133 (2008)CrossRefGoogle Scholar
  36. Pankow J.F., Asher W.E.: SIMPOL.1: a simple group contribution method for predicting vapor pressures and enthalpies of vaporization of multifunctional organic compounds. Atmos. Chem. Phys. 8(10), 2773–2796 (2008)CrossRefGoogle Scholar
  37. Petters M.D., Kreidenweis S.M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys. 7(8), 1961–1971 (2007)CrossRefGoogle Scholar
  38. Petters M.D., Kreidenweis S.M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity - part 2: including solubility. Atmos. Chem. Phys. 8(20), 6273–6279 (2008)CrossRefGoogle Scholar
  39. Petters M.D., Kreidenweis S.M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity - part 3: including surfactant partitioning. Atmos. Chem. Phys. 13(2), 1081–1091 (2013)CrossRefGoogle Scholar
  40. Petters M.D., Kreidenweis S.M., Prenni A.J., Sullivan R.C., Carrico C.M., Koehler K.A., Ziemann P.J.: Role of molecular size in cloud droplet activation. Geophys. Res. Lett. 36, (2009). doi: 10.1029/2009GL040131
  41. Petters M.D., Kreidenweis S.M., Ziemann P.J.: Prediction of cloud condensation nuclei activity for organic compounds using functional group contribution methods. Geosci. Model Dev. 9(1), 111–124 (2016)CrossRefGoogle Scholar
  42. Pringle K.J., Tost H., Pozzer A., Poschl U., Lelieveld J.: Global distribution of the effective aerosol hygroscopicity parameter for CCN activation. Atmos. Chem. Phys. 10(12), 5241–5255 (2010)CrossRefGoogle Scholar
  43. Prisle N.L., Dal Maso M., Kokkola H.: A simple representation of surface active organic aerosol in cloud droplet formation. Atmos. Chem. Phys. 11(9), 4073–4083 (2011)CrossRefGoogle Scholar
  44. Randic M.: High quality structure-property regressions. Boiling points of smaller alkanes. New J. Chem. 24(3), 165–171 (2000)CrossRefGoogle Scholar
  45. Randic M.: The connectivity index 25 years after. J. Mol. Graph. Model. 20(1), 19–35 (2001)CrossRefGoogle Scholar
  46. Randic M., Pompe M.: Retro-regression - a way to resolve multivariate regression ambiguities. Acta Chim. Slov. 52(4), 408–416 (2005)Google Scholar
  47. Raventos-Duran T., Camredon M., Valorso R., Mouchel-Vallon C., Aumont B.: Structure-activity relationships to estimate the effective Henry’s law constants of organics of atmospheric interest. Atmos. Chem. Phys. 10(16), 7643–7654 (2010)CrossRefGoogle Scholar
  48. Rickards A.M.J., Miles R.E.H., Davies J.F., Marshall F.H., Reid J.P.: Measurements of the sensitivity of aerosol hygroscopicity and the kappa parameter to the O/C ratio. J. Phys. Chem. A. 117(51), 14120–14131 (2013)CrossRefGoogle Scholar
  49. Rissler J., Vestin A., Swietlicki E., Fisch G., Zhou J., Artaxo P., Andreae M.O.: Size distribution and hygroscopic properties of aerosol particles from dry-season biomass burning in Amazonia. Atmos. Chem. Phys. 6, 471–491 (2006)CrossRefGoogle Scholar
  50. Rissman T.A., Varutbangkul V., Surratt J.D., Topping D.O., McFiggans G., Flagan R.C., Seinfeld J.H.: Cloud condensation nucleus (CCN) behavior of organic aerosol particles generated by atomization of water and methanol solutions. Atmos. Chem. Phys. 7(11), 2949–2971 (2007)CrossRefGoogle Scholar
  51. Rosenfeld D., Sherwood S., Wood R., Donner L.: Climate Effects of Aerosol-Cloud Interactions. Science. 343(6169), 379–380 (2014)CrossRefGoogle Scholar
  52. Ruehl C.R., Wilson K.R.: Surface organic mono layers control the hygroscopic growth of Submicrometer particles at high relative humidity. J. Phys. Chem. A. 118(22), 3952–3966 (2014)CrossRefGoogle Scholar
  53. Ruehl C.R., Davies J.F., Wilson K.R.: An interfacial mechanism for cloud droplet formation on organic aerosols. Science. 351(6280), 1447–1450 (2016)CrossRefGoogle Scholar
  54. Seinfeld J.H., Pandis S.N.: Atmospheric chemistry and physics: from air pollution to climate change 2nd edition. Wiley (2006)Google Scholar
  55. Sihto S.L., Mikkila J., Vanhanen J., Ehn M., Liao L., Lehtipalo K., Aalto P.P., Duplissy J., Petaja T., Kerminen V.M., Boy M., Kulmala M.: Seasonal variation of CCN concentrations and aerosol activation properties in boreal forest. Atmos. Chem. Phys. 11(24), 13269–13285 (2011)CrossRefGoogle Scholar
  56. Sorjamaa R., Svenningsson B., Raatikainen T., Henning S., Bilde M., Laaksonen A.: The role of surfactants in Kohler theory reconsidered. Atmos. Chem. Phys. 4, 2107–2117 (2004)CrossRefGoogle Scholar
  57. Stewart J.J.P.: MOPAC: a semiempirical molecular orbital program. J. Comput.-Aided Mater. 4(1), 1–45 (1990)CrossRefGoogle Scholar
  58. Suda S.R., Petters M.D., Yeh G.K., Strollo C., Matsunaga A., Faulhaber A., Ziemann P.J., Prenni A.J., Carrico C.M., Sullivan R.C., Kreidenweis S.M.: Influence of functional groups on organic aerosol cloud condensation nucleus activity. Environ. Sci. Technol. 48(17), 10182–10190 (2014)CrossRefGoogle Scholar
  59. Sullivan R.C., Moore M.J.K., Petters M.D., Kreidenweis S.M., Roberts G.C., Prather K.A.: Effect of chemical mixing state on the hygroscopicity and cloud nucleation properties of calcium mineral dust particles. Atmos. Chem. Phys. 9(10), 3303–3316 (2009)CrossRefGoogle Scholar
  60. Topping D.O., McFiggans G.B., Coe H.: A curved multi-component aerosol hygroscopicity model framework: part 2 – including organic compounds. Atmos. Chem. Phys. 5(5), 1223–1242 (2005)CrossRefGoogle Scholar
  61. Tuckermann R.: Surface tension of aqueous solutions of water-soluble organic and inorganic compounds. Atmos. Environ. 41(29), 6265–6275 (2007)CrossRefGoogle Scholar
  62. Wex H., Hennig T., Salma I., Ocskay R., Kiselev A., Henning S., Massling A., Wiedensohler A., Stratmann F.: Hygroscopic growth and measured and modeled critical super-saturations of an atmospheric HULIS sample. Geophys. Res. Lett. 34(2), (2007). doi: 10.1029/2006GL028260
  63. Zefirov N.S., Kirpichenok M.A., Ismailov F.F., Trofimov M.I.: Calculation schemes for atomic electronegativities in molecular graphs within the framework of sanderson principle. Dokl. Akad. Nauk SSSR. 296(4), 883–887 (1987)Google Scholar
  64. Zhao D.F., Buchholz A., Kortner B., Schlag P., Rubach F., Fuchs H., Kiendler-Scharr A., Tillmann R., Wahner A., Watne A.K., Hallquist M., Flores J.M., Rudich Y., Kristensen K., Hansen A.M.K., Glasius M., Kourtchev I., Kalberer M., Mentel T.F.: Cloud condensation nuclei activity, droplet growth kinetics, and hygroscopicity of biogenic and anthropogenic secondary organic aerosol (SOA). Atmos. Chem. Phys. 16(2), 1105–1121 (2016)CrossRefGoogle Scholar
  65. Ziemann P.J., Atkinson R.: Kinetics, products, and mechanisms of secondary organic aerosol formation. Chem. Soc. Rev. 41(19), 6582–6605 (2012)CrossRefGoogle Scholar
  66. Zuend A., Marcolli C., Booth A.M., Lienhard D.M., Soonsin V., Krieger U.K., Topping D.O., McFiggans G., Peter T., Seinfeld J.H.: New and extended parameterization of the thermodynamic model AIOMFAC: calculation of activity coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups. Atmos. Chem. Phys. 11(17), 9155–9206 (2011)CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Faculty of Chemistry and Chemical TechnologyUniversity of LjubljanaLjubljanaSlovenia
  2. 2.National Center for Atmospheric ResearchBoulderUSA

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