References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-12-5429-2012

New representation of water activity based on a single solute specific constant to parameterize the hygroscopic growth of aerosols in atmospheric models

Metzger

¹ Steil

¹ Xu

² Penner

J. E.

² Lelieveld

¹ ³ ⁴

Max Planck Institute for Chemistry, Mainz, Germany

University of Michigan, Ann Arbor, Michigan, USA

The Cyprus Institute, Nicosia, Cyprus

King Saud University, Riyadh, Saudi Arabia

22 06 2012

12 12 5429 5446

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.

This article is available from http://www.atmos-chem-phys.net/12/5429/2012/acp-12-5429-2012.html

The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/5429/2012/acp-12-5429-2012.pdf

Water activity is a key factor in aerosol thermodynamics and hygroscopic growth. We introduce a new representation of water activity (aw), which is empirically related to the solute molality (μs) through a single solute specific constant, νi. Our approach is widely applicable, considers the Kelvin effect and covers ideal solutions at high relative humidity (RH), including cloud condensation nuclei (CCN) activation. It also encompasses concentrated solutions with high ionic strength at low RH such as the relative humidity of deliquescence (RHD). The constant νi can thus be used to parameterize the aerosol hygroscopic growth over a wide range of particle sizes, from nanometer nucleation mode to micrometer coarse mode particles. In contrast to other aw-representations, our νi factor corrects the solute molality both linearly and in exponent form x · ax. We present four representations of our basic aw-parameterization at different levels of complexity for different aw-ranges, e.g. up to 0.95, 0.98 or 1. νi is constant over the selected aw-range, and in its most comprehensive form, the parameterization describes the entire aw range (0–1). In this work we focus on single solute solutions. νi can be pre-determined with a root-finding method from our water activity representation using an aw−μs data pair, e.g. at solute saturation using RHD and solubility measurements. Our aw and supersaturation (Köhler-theory) results compare well with the thermodynamic reference model E-AIM for the key compounds NaCl and (NH4)2SO4 relevant for CCN modeling and calibration studies. Envisaged applications include regional and global atmospheric chemistry and climate modeling.

References 1

Biskos, G., Paulsen, D., Russell, L. M., Buseck, P. R., and Martin, S. T.: Prompt deliquescence and efflorescence of aerosol nanoparticles, Atmos. Chem. Phys., 6, 4633–4642, http://dx.doi.org/10.5194/acp-6-4633-2006doi:10.5194/acp-6-4633-2006, 2006a.

Biskos, G., Russell, L. M., Buseck, P. R., and Martin, S. T.: Nano-size effect on the hygroscopic growth factor of aerosol particles, Geophys. Res. Lett., 33, L07801, http://dx.doi.org/10.1029/2005GL025199doi:10.1029/2005GL025199, 2006b.

Brechtel, F. J. and Kreidenweis, S. M.: Predicting Particle Critical Supersaturation from Hygroscopic Growth Measurements in the Humidified TDMA. Part I: Theory and Sensitivity Studies, J. Atmos. Sci., 57, 1854–1871, 2000.

Charlson, R. J., Schwartz, S. E., Hales, J. M., Cess, R. D., Coakley, J. A., Jr., Hansen, J. E., and Hofmann D. J.: Climate forcing of anthropogenic aerosols, Science, 255, 423–430, 1992.

Charlson, R. J., Seinfeld, J. H., Nenes, A., Kulmala, M., Laaksonen, A., and Facchini, M. C.: Reshaping the theory of cloud formation, Science, 292, 2025–2026, 2001.

Clegg, S. L., Brimblecombe, P., and Wexler, A. S.: A thermodynamic model of the system \chemH^+-NH_4^+-SO_4^2-NO_3^–H_2O at tropospheric temperatures, J. Phys. Chem. A, 102, 2137–2154, 1998a.

Clegg, S. L., Brimblecombe, P., and Wexler, A. S.: A thermodynamic model of the system \chemH^+-NH_4^+-Na^+-SO_4^2-NO3^–Cl^–H_2O at 298.15~K, J. Phys. Chem. A, 102, 2155–2171, 1998b.

Clegg, S. L., Seinfeld, J. H., and Brimblecombe, P.: Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds, J. Aer. Sci., 32, 713–738, 2001.

Clegg, S. L. and Wexler, A. S.: Interactive comment on "Calibration and measurement uncertainties of a continuous-flow cloud condensation nuclei counter (DMT-CCNC): CCN activation of ammonium sulfate and sodium chloride aerosol particles in theory and experiment" by Rose, D., Gunthe, S. S., Mikhailov, E., Frank, G. P., Dusek, U., Andreae, M. O., and Pöschl, Atmos. Chem. Phys. Discuss., 7, S4180–S4183, 2007.

Chemical Rubber Company (CRC): Handbook of Chemistry and Physics, 86th Edition, Taylor and Francis Group LLC, 2004–2005, CD-ROM version, 2006.

Dusek, U., Frank, G. P., Hildebrandt, L., Curtius, J., Schneider, J., Walter, S., Chand, D., Drewnick, F., Hings, S., Jung, D., Borrmann, S., and Andreae, M. O.: Size Matters More Than Chemistry for Cloud-Nucleating Ability of Aerosol Particles, Science, 312, 1375–1378, 2006.

Fountoukis, C. and Nenes, A.: ISORROPIA II: a computationally efficient thermodynamic equilibrium model for K$^+$-Ca$^2+$-Mg$^2+$-NH$_4^+$-Na$^+$-SO$_4^2-$-NO$_3^-$-Cl$^-$-H2O aerosols, Atmos. Chem. Phys., 7, 4639–4659, http://dx.doi.org/10.5194/acp-7-4639-2007doi:10.5194/acp-7-4639-2007, 2007.

Frank, G. P., Dusek, U., and Andreae, M. O.: Technical note: A method for measuring size-resolved CCN in the atmosphere, Atmos. Chem. Phys. Discuss., 6, 4879–4895, http://dx.doi.org/10.5194/acpd-6-4879-2006doi:10.5194/acpd-6-4879-2006, 2006.

Frank, G. P., Dusek, U., and Andreae, M. O.: Technical Note: Characterization of a static thermal-gradient CCN counter, Atmos. Chem. Phys., 7, 3071–3080, http://dx.doi.org/10.5194/acp-7-3071-2007doi:10.5194/acp-7-3071-2007, 2007.

Fredenslund, A., Jones, R. L., and Prausnitz, J. M.: Group contribution estimation of activity coefficients in non-ideal liquid mixtures (UNIFAC), American Institute of Chemical Engineers Journal (AIChE. J.), 21, 1086–1099, 1975.

Hanford, K. L., Mitchem, L. Reid, J. P., Clegg, S. L., Topping, D. O., and McFiggans, G. B., Comparative Thermodynamic Studies of Aqueous Glutaric Acid, Ammonium Sulfate and Sodium Chloride Aerosol at High Humidity, J. Phys. Chem., 112, 9413–9422, 2008.

Harmon, C. W., Ronald L. Grimm, T. M. McIntire, M. D. Peterson, B. Njegic, V. M. Angel, A. Alshawa, J. S. Underwood, D. J. Tobias, R. B. Gerber, M. S. Gordon, J. C. Hemminger, and S. A. Nizkorodov, Hygroscopic Growth and Deliquescence of NaCl Nanoparticles Mixed with Surfactant SD, J. Phys. Chem. B, 114, 2435–2449, 2010.

IPCC: Climate Change 2007: The Physical Science Basis: Sum- mary for Policymakers. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 2007.

Jacobson, M. Z.: Studying the effects of calcium and magnesium on size-distributed nitrate and ammonium with EQUISOLV II, Atmos. Environ., 33, 3635–3649, 1999.

Jacobson, M. Z., Tabazadeh, A., and Turco, R.: Simulating equilibrium within aerosols and non-equilibrium between gases and aerosols, J. Geophys. Res., 101, 9079–9091. 1996.

Konopka, P.: A re-examination of the derivation of the equilibrium supersaturation curve for soluble particles, J. Atmos. Sci., 53, 3157–3163, 1996.

Köhler, H.: The nucleus in and the growth of hygroscopic droplets, Trans. Faraday Soc., 32, 1152–1161, 1936.

Kreidenweis, S. M., Koehler, K., DeMott, P. J., Prenni, A. J., Carrico, C., and Ervens, B.: Water activity and activation diameters from hygroscopicity data – Part I: Theory and application to inorganic salts, Atmos. Chem. Phys., 5, 1357–1370, http://dx.doi.org/10.5194/acp-5-1357-2005doi:10.5194/acp-5-1357-2005, 2005.

Kreidenweis, S. M., Petters, M. D., and DeMott, P. J., Single parameter estimates of aerosol water content, Environ. Res. Lett., 3, 035002, http://dx.doi.org/10.1088/1748-9326/3/3/035002doi:10.1088/1748-9326/3/3/035002, 2008;

Künzli, N., Kaiser, R., Medina, S., Studnicka, M., Chanel, O., Filliger, P., Herry, M., Horak Jr., F., Puybonnieux-Texier, V., Quénel, P., Schneider, J., Seethaler, R., Vergnaud, J.-C., and Sommer, H.: Public-health impact of outdoor and traffic-related air pollution: a European assessment, The Lancet, 356, 795–801, 2000.

Laaksonen, A., Korhonen, P., Kulmala, M., and Charlson, R. J., Modification of the Köhler equation to include soluble trace gases and slightly soluble substances, J. Atmos. Sci., 55, 853–862, 1998.

Low, R. D. H.: A generalized equation for the solution effect in droplet growth, Atmos. Sci., 26, 608–611, 1969.

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., and Weingartner, E.: The effect of physical and chemical aerosol properties on warm cloud droplet activation, Atmos. Chem. Phys., 6, 2593–2649, http://dx.doi.org/10.5194/acp-6-2593-2006doi:10.5194/acp-6-2593-2006, 2006.

Metzger, S. and Lelieveld, J.: Reformulating atmospheric aerosol thermodynamics and hygroscopic growth into fog, haze and clouds, Atmos. Chem. Phys., 7, 3163–3193, http://dx.doi.org/10.5194/acp-7-3163-2007doi:10.5194/acp-7-3163-2007, 2007.

Metzger, S., Steil, B., Penner, J. E., Xu, L., and Lelieveld, J.: Derivation of the stoichiometric coefficient of water ($\nu_\rm w$) to account for water uptake by atmospheric aerosols, Atmos. Chem. Phys. Discuss., 10, 8165–8188, http://dx.doi.org/10.5194/acpd-10-8165-2010doi:10.5194/acpd-10-8165-2010, 2010.

Metzger, S., Steil, B., Xu, L., Penner, J. E., and Lelieveld, J.: Description of EQSAM4: gas-liquid-solid partitioning model for global simulations, Geosci. Model Dev. Discuss., 4, 2791–2847, http://dx.doi.org/10.5194/gmdd-4-2791-2011doi:10.5194/gmdd-4-2791-2011, 2011.

Mikhailov, E., Vlasenko, S., Niessner, R., and Pöschl, U.: Interaction of aerosol particles composed of protein and saltswith water vapor: hygroscopic growth and microstructural rearrangement, Atmos. Chem. Phys., 4, 323–350, http://dx.doi.org/10.5194/acp-4-323-2004doi:10.5194/acp-4-323-2004, 2004.

Mikhailov, E., Vlasenko, S., Martin, S. T., Koop, T., and Pöschl, U.: Amorphous and crystalline aerosol particles interacting with water vapor: conceptual framework and experimental evidence for restructuring, phase transitions and kinetic limitations, Atmos. Chem. Phys., 9, 9491–9522, http://dx.doi.org/10.5194/acp-9-9491-2009doi:10.5194/acp-9-9491-2009, 2009.

Naono M. and Nakuman C.: Analysis of adsorption isotherms of water vapor for nonporous and porous adsorbents, J. Colloid Interface Sci., 145, 405–412, 1991.

Numerical Recipes (http://www.nr.com/) in Fortran 90, Second Edition, 1996.

Petters, M. D. and Kreidenweis, S. M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity, Atmos. Chem. Phys., 7, 1961–1971, http://dx.doi.org/10.5194/acp-7-1961-2007doi:10.5194/acp-7-1961-2007, 2007.

Pilinis, C., Pandis, S. N., and Seinfeld, J. H.: Sensitivity of direct climate forcing by atmospheric aerosols to aerosol size and composition, J. Geophys. Res., 100, 18739–18754, 1995.

Pitzer, K. S. and Mayorga, G.: Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent, J. Phys. Chem., 77, 2300–2308, 1973.

Pringle, K. J., Tost, H., Message, S., Steil, B., Giannadaki, D., Nenes, A., Fountoukis, C., Stier, P., Vignati, E., and Lelieveld, J.: Description and evaluation of GMXe: a new aerosol submodel for global simulations (v1), Geosci. Model Dev., 3, 391–412, http://dx.doi.org/10.5194/gmd-3-391-2010doi:10.5194/gmd-3-391-2010, 2010.

Pruppacher, H. R. and Klett, J. D.: Microphysics of clouds and precipitation, Dordrecht, Kluwer Academic Publishers, 1997.

Raoult, F. M.: Über die Dampfdrucke ätherischer Lösungen, Z. Phys. Chem., 2, 353–373, 1888.

Reiss, H.: The kinetics of phase transitions in binary systems, J. Chem. Phys., 18, 840–848, 1950.

Robinson, R. A. and Stokes, R. H.: Electrolyte Solutions, (revised), London: Butterworth, 1959.

Robinson, R. A. and Stokes, R. H.: Electrolyte Solutions, 2nd ed. (revised); Butterworths: London, 1965.

Rose, D., Gunthe, S. S., Mikhailov, E., Frank, G. P., Dusek, U., Andreae, M. O., and Pöschl, U.: Calibration and measurement uncertainties of a continuous-flow cloud condensation nuclei counter (DMT-CCNC): CCN activation of ammonium sulfate and sodium chloride aerosol particles in theory and experiment, Atmos. Chem. Phys., 8, 1153–1179, http://dx.doi.org/10.5194/acp-8-1153-2008doi:10.5194/acp-8-1153-2008, 2008.

Ruehl, C. R., Chuang, P. Y., and Nenes, A.: Aerosol hygroscopicity at high (99 to 100%) relative humidities, Atmos. Chem. Phys., 10, 1329–1344, http://dx.doi.org/10.5194/acp-10-1329-2010doi:10.5194/acp-10-1329-2010, 2010.

Russell, L. M. and Ming, Y.: Deliquescence of small particles, J. Chem. Phys., 116, 311–321, 2002.

Seinfeld, J. H. and Pandis, S. N.: Atmospheric chemistry and physics, J. Wiley and Sons, Inc., New York, 1998.

Seinfeld, J. H. and Pandis, S. N.: Atmospheric chemistry and physics, J. Wiley and Sons, Inc., New York, 2006.

Stokes, R. H. and Robinson, R. A.: Interactions in aqueous non-electrolyte solutions, I. Solute-solvent equilibria, J. Phys. Chem., 70, 2126–2130, 1966.

Shulman, M. L., Jacobson, M. C., Carlson, R. J., Synovec, R. E., and Young, T. E.: Dissolution behavior and surface tension ef-fects of organic compounds in nucleating cloud droplets, Geophys. Res. Lett., 23, 277–280, 1996.

Tang, I. N.: Chemical and size effects of hygroscopic aerosols on light scattering coefficients, J. Geophys. Res., 101, 19245–19250, 1996.

Tang, I. N. and Munkelwitz, H. R.: Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance, J. Geophys. Res., 99, 18801–18808, 1994.

van't Hoff, J. H.: Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen, Z. Phys. Chem., 1, 481, 1887.

Wang, Z., King, S. M., Freney, E., Rosenoern, T., Smith, M. L., Chen, Q., Kuwata, M., Lewis, E. R., Pöschl, U., Wang, W., Buseck, P. R., and Martin S. T.: The Dynamic Shape Factor of Sodium Chloride Nanoparticles as Regulated by Drying Rate, Aerosol Sci. Technol., 44, 939–953, 2010.

Warneck, P.: Chemistry of the Natural Atmosphere, Internat, Geophys. Series, 41, Academic Press. Inc., 1988.

Wexler, A. S. and Clegg, S. L.: Atmospheric aerosol models for systems including the ions H$^+$, NH$_4^+$, Na$^+$, SO$_4^2-$, NO$_3^-$, Cl$^-$, Br$^-$ and H2O, J. Geophys. Res., 107, 4207, http://dx.doi.org/10.1029/2001JD000451doi:10.1029/2001JD000451, 2002.

Wexler, A. S. and Potukuchi, S.: Kinetics and Thermodynamics of Tropospheric Aerosols, Atmospheric Particles, John Wiley & Sons Ltd., 1998.

Wexler, A. S. and Seinfeld, J. H.: Second-generation inorganic aerosol model, Atmos. Environ., 25A, 2731–2748, 1991.

Xu, L., Penner, J. E., Metzger, S., and Lelieveld, J.: A comparison of water uptake by aerosols using two thermodynamic models, Atmos. Chem. Phys. Discuss., 9, 9551–9595, http://dx.doi.org/10.5194/acpd-9-9551-2009doi:10.5194/acpd-9-9551-2009, 2009.

Xu, L.: Global simulation of nitrate and ammonium aerosols and their radiative effects and comparison of satellite-based and modeled aerosol indirect forcing, Dissertation, University of Michigan, 2011.

Young, K. C. and Warren, A. J.: A reexamination of the derivation of the equilibrium supersaturation curve for soluble particles, J. Atmos. Sci., 49, 1138–1143, 1992.

Zdanovskii, A. B.: New methods of calculating solubilities of electrolytes in multicomponent systems, Zhu. Fiz. Khim., 22, 1475–1485, 1948.