Atmospheric Chemistry and Physics
www.atmos-chem-phys.net
1680-7316
1680-7324
7
12
2007
10.5194/acp-7-3163-2007
http://www.atmos-chem-phys.net/7/3163/2007/
http://www.atmos-chem-phys.net/7/3163/2007/acp-7-3163-2007.html
http://www.atmos-chem-phys.net/7/3163/2007/acp-7-3163-2007.pdf
3163
3193
2007-06-20
Reformulating atmospheric aerosol thermodynamics and hygroscopic growth into fog, haze and clouds
S. Metzger
metzger@mpch-mainz.mpg.de
J. Lelieveld
Max Planck Institute for Chemistry, Mainz, Germany
Modeling atmospheric aerosol and cloud microphysics is rather complex, even
if chemical and thermodynamical equilibrium is assumed. We show, however,
that the thermodynamics can be considerably simplified by reformulating
equilibrium to consistently include water, and transform laboratory-based
concepts to atmospheric conditions. We generalize the thermodynamic principles
that explain hydration and osmosis – merely based on solute solubilities –
to explicitly account for the water mass consumed by hydration. As a result,
in chemical and thermodynamical equilibrium the relative humidity (RH) suffices
to determine the saturation molality, including solute and solvent activities
(and activity coefficients), since the water content is fixed by RH for a
given aerosol concentration and type. As a consequence, gas/liquid/solid
aerosol equilibrium partitioning can be solved analytically and
non-iteratively. Our new concept enables an efficient and accurate
calculation of the aerosol water mass and directly links the aerosol
hygroscopic growth to fog, haze and cloud formation.
<br><br>
We apply our new concept in the 3rd Equilibrium Simplified Aerosol
Model (EQSAM3) for use in regional and global chemistry-transport and
climate models. Its input is limited to the species' solubilities from which
a newly introduced stoichiometric coefficient for water is derived.
Analogously, we introduce effective stoichiometric coefficients for the
solutes to account for complete or incomplete dissociation. We show that
these coefficients can be assumed constant over the entire activity range
and calculated for various inorganic, organic and non-electrolyte compounds,
including alcohols, sugars and dissolved gases. EQSAM3 calculates the
aerosol composition and gas/liquid/solid partitioning of mixed
inorganic/organic multicomponent solutions and the associated water uptake
for almost 100 major compounds. It explicitly accounts for particle
hygroscopic growth by computing aerosol properties such as single solute
molalities, molal based activities, including activity coefficients for
volatile compounds, efflorescence and deliquescence relative humidities of
single solute and mixed solutions.
Various applications and a model inter-comparison indicate that a) the
application is not limited to dilute binary solutions, b) sensitive aerosol
properties such as hygroscopic growth and the pH of binary and mixed inorganic/organic salt
solutions up to saturation can be computed accurately, and c) aerosol water
is central in modeling atmospheric chemistry, visibility, weather and climate.
Arrhenius, S.: Z. Phys. Chem., 1, 631, 1887.
Chan, C. K., Flagan, R. C., and Seinfeld, J. H., Water activities of NH<sub>4</sub>NO<sub>3</sub>/(NH$_4)_2$SO<sub>4</sub> solutions, Atmos. Environ., 26A, 1661–1673, 1992.
Cohen, M. D., Flagan, R. C., and Seinfeld, J. H. Studies of concentrated electrolyte solutions using the electrodynamic balance. 1. Water activities for single electrolyte solutions, J. Phys. Chem., 91, 4563–4574, 1987a.
Cohen, M. D., Flagan, R. C., and Seinfeld, J. H. Studies of concentrated electrolyte solutions using the electrodynamic balance. 2. Water activities for mixed electrolyte solutions, J. Phys. Chem., 91, 4575–4582, 1987b.
Chemical Rubber Company (CRC): Handbook of Chemistry and Physics, 86th Edition, Taylor and Francis Group LLC, 2004–2005, CD-ROM version 2006.
Clegg, S. L., Milioto, S., and Palmer, D. A.: Osmotic and Activity Coefficients of Aqueous (NH4)2SO4 as a Function of Temperature, and Aqueous (NH4)2SO4-H2SO4 Mixtures at 298.15 K and 323.15 K J. Chem. Eng. Data, 41, 3, 455–467, 1996.
Clegg, S. L. and Seinfeld, J. H.: Thermodynamic Models of Aqueous Solutions Containing Inorganic Electrolytes and Dicarboxylic Acids at 298.15 K. 2. Systems Including Dissociation Equilibria, J. Phys. Chem. A, 110, 17, 5718–5734, 2006.
Clegg, S. L., Brimblecombe, P., and Wexler, A. S.: Thermodynamic Model of the System H+-NH4+-Na+-SO42–NO3–Cl–H2O at 298.15 K J. Phys. Chem. A, 102, 12, 2155–2171, 1998.
Denbigh, K.: The Principles of Chemical Equilibrium, 4th ed., Cambridge Univ. Press, New York, 1981.
Dufour, L. and Defay, R.: Thermodynamics of Clouds, Academic Press, New York, 1963, 1427–1434, 1998.
Environmental Protection Agency (EPA): Air quality criteria for particulate matter, EPA/600/P-95/001cF, 1996.
Gibbs, J. W.: On the equilibrium of heterogeneous substances (1876), in: Collected Works, Vol 1, Longmans, Green, and Co., 1928.
Hamer, W. J. and Wu, Y. C.: Osmotic coefficients and mean activity coefficients of uni-valent electrolytes in water at 25\degree C, J. Phys. Chem. Ref. Data, 1, 1047–1099, 1972.
Hänel, G.: The size of atmospheric aerosol particles as a function of the relative humidity, Beitr. Phys. Atmos., 43, 119–132, 1970.
Hänel, G.: The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air, Adv. Geophys. Res., 19, 73–188, 1976.
Heyrovska, R.: A Reappraisal of Arrhenius' Theory of Partial Dissociation of Electrolytes, American Chem. Soc., 1989.
Hofmeister, F.: Zur Lehre von der Wirkung der Salze, Arch. Exp. Pathol. Pharmakol, (Leipzig) 24 (1888) 247–260; translated in: Zur Lehre von der Wirkung der Salze (about the science of the effect of salts: Franz Hofmeister's historical papers, edited by: Kunz, W., Henle, J., and Ninham, B. W., Curr. Opin. Coll. Interface Sci., 9, 19–37, 2004.
Holgate, S. T., Samet, J. M., Koren, H. S., and Maynard, R. L.: Air pollution and health, Academic Press, San Diego, 1999.
Intergovernmental Panel on Climate Change (IPCC): Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., and Miller, H. L., Cambridge University Press, Cambridge, UK and New York, NY, USA, 2007.
IUPAC Solubility Data Series, International Union of Pure and Applied Chemistry, Vol 1 to 53 were published by Pergamon Press, Oxford, from 1979 to 1994; subsequent volumes were published by Oxford University Press, Oxford.
Jöckel, P., Tost, H., Pozzer, A., Brühl, C., Buchholz, J., Ganzeveld, L., Hoor, P., Kerkweg, A., Lawrence, M. G., Sander, R., Steil, B., Stiller, G., Tanarhte, M., Taraborrelli, D., van Aardenne, J., and Lelieveld, J.: The atmospheric chemistry general circulation model ECHAM5/MESSy1: consistent simulation of ozone from the surface to the mesosphere, Atmos. Chem. Phys., 6, 5067–5104, 2006.
Kim, Y. P., Seinfeld, J. H., and Saxena, P.: Atmospheric gas/aerosol equilibrium I. Thermodynamic model, Aerosol Sci. Technol., 19, 157–181, 1993a.
Kim, Y. P., Seinfeld, J. H., and Saxena, P.: Atmospheric gas/aerosol equilibrium II. Analysis of common approximations and activity coefficient calculation methods, Aerosol Sci. Technol., 19, 182–198, 1993b.
Kim, Y. P. and Seinfeld, J. H.: Atmospheric gas/aerosol equilibrium III. Thermodynamics of crustal elements Ca$^2+$, K$^+$, and Mg$^2+$, Aerosol Sci. Technol., 22, 93–110, 1995.
Köhler, H.: The nucleus in and the growth of hygroscopic droplets, Trans. Faraday Soc., 32, 1152–1162, 1936.
Lelieveld, J., Berresheim, H., Borrmann, S., Crutzen, P. J., Dentener, F. J., Fischer, H., Feichter, J., Flatau, P. J., Heland, J., Holzinger, R., Korrmann, R., Lawrence, M. G., Levin, Z., Markowicz, K. M., Mihalopoulos, N., Minikin, A., Ramanathan, V., de Reus, M., Roelofs, G. J., Scheeren, H. A., Sciare, J., Schlager, H., Schultz, M., Siegmund, P., Steil, B., Stephanou, E. G., Stier, P., Traub, M., Warneke, C., Williams, J., and Ziereis, H.: Global Air Pollution Crossroads over the Mediterranean, Science, 298, 794–799, 2002.
Low, R. D. H.: A generalized equation for the solution effect in droplet growth, Atmos. Sci., 26, 608–611, 1969.
Meng, Z., Seinfeld, J. H., Saxena, P., and Kim, Y. P.: Atmospheric gas/aerosol equilibrium. IV: Thermodynamics of carbonates, Aerosol Sci. Technol., 131–154, 1995.
Metzger, S. M.: Gas/Aerosol Partitioning: A simplified Method for Global Modeling, Ph.D. Thesis, University Utrecht, The Netherlands, ISBN:90-393-2510-3, http://igitur-archive.library.uu.nl/dissertations/1930853/inhoud.htm, 2000.
Metzger, S. M., Dentener, F. J., Lelieveld, J., and Pandis, S. N.: Gas/aerosol partitioning I: A computationally efficient model, J. Geophys. Res., 107(D16), ACH 16-1-24, doi:10.1029/2001JD001102, 2002.
Metzger, S., Mihalopoulos, N., and Lelieveld, J.: Importance of mineral cations and organics in gas-aerosol partitioning of reactive nitrogen compounds: case study based on MINOS results, Atmos. Chem. Phys., 6, 2549–2567, 2006.
Mozurkewich M.: The dissociation constant of ammonium nitrate and its dependence on temperature, relative humidity and particle size, Atmos. Environ., 27A, 261–270, 1993.
Nenes, A., Pilinis, C., and Pandis, S. N.: Isorropia: A new thermodynamic model for multiphase multicomponent inorganic aerosols, Aquat. Geochem., 4, 123–152, 1998.
Nernst, W.: Z. Phys. Chem., 4, 129, 1889.
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, 18 739–18 754, 1995.
Pfeffer, W.: Pflanzenphysiologie, Leipzig, Verlag von W. Engelmann, 1881.
Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation, Dordrecht, Holland, D. Reidel Publ. Co., 950~p., 1997.
Raoult, F. M.: Z. Phys. Chem., 2, 353, 1888.
Robinson, R. A. and Stokes, R. H.: Electrolyte solutions, 2nd Ed., Butterworths, London, 1965.
Röckner, E., Bäuml, G., Bonaventura, L., Brokopf, R., Esch, M., Giorgetta, M., Hagemann, S., Kirchner, I., Kornblueh, L., Manzini, E., Rhodin, A., Schlese, U., Schulzweida, U., and Tompkins, A.: The atmospheric general circulation model ECHAM5. PART I: Model description, Max Planck Institute for Meteorology, MPI-Report 349, http://www.mpimet.mpg. de/fileadmin/publikationen/Reports/max scirep 349.pdf, 2003.
Seinfeld, J. H. and Pandis, S. N.: Atmospheric chemistry and physics, J. Wiley and Sons, Inc., New York, 1998.
Stokes, R. H. and Robinson, R. A.: Interactions in aqueous nonelectrolyte solutions. I. Solute solvent equilibria, J. Phys. Chem., 70, 2126–2130, 1966.
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, 18 801–18 808, 1994.
ten Brink, H. M., Veefkind, J. P., Waijers-Ijpelaan, A., and van der Hage, J. C.: Aerosol light-scattering in The Netherlands, Atmos. Environ., 30, 4251–4261, 1996.
van't Hoff, J. H.: Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen, Z. Phys. Chem., 1, 481, 1887.
Vignati E., Wilson, J., and Stier, P.: M7: An efficient size-resolved aerosol microphysics module for large-scale aerosol transport models, J. Geophys. Res., 109, D22202, doi:10.1029/2003JD004485, 2004.
Warneck, P.: Chemistry of the Natural Atmosphere, Internat. Geophys. Series, 41, Academic Press. Inc., 1988.
Winkler, P.: The growth of atmospheric aerosol particles as a function of the relative humidity – II. An Improved concept of mixed nucleii, Aerosol Sci., 4, 373–387, 1973.
Winkler, P.: The growth of aerosol particles with relative humidity, Physica Scripta, 37, 223–230, 1988.
Wexler, A. S. and Potukuchi, S.: Kinetics and Thermodynamics of Tropospheric Aerosols, Atmospheric Particles, John Wiley & Sons Ltd., 1998.
Zadanovskii, A. B.: New methods of calculating solubilities of electrolytes in multicomponent systems, Zhu. Fiz. Khim., 22, 1475–1485, 1948.
Zaveri, R. A., Easter, R. C., and Wexler, A. S.: A new method for multicomponent activity coefficients of electrolytes in aqueous atmospheric aerosols, J. Geophys. Res.-Atmos., 110, D02201, doi:10.1029/2004JD004681, 2005.