How Well Does Water Activity Determine Homogeneous Ice Nucleation Temperature in Aqueous Sulfuric Acid and Ammonium Sulfate Droplets?

Brian D. Swanson Department of Earth and Space Sciences, University of Washington, Seattle, Washington

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Abstract

Frozen fraction measurements made using a droplet free-fall freezing tube apparatus are presented and used, along with other recent laboratory measurements, to evaluate how well both the water activity idea and the translated melting-point curve idea of Koop et al. predict homogeneous freezing-point temperatures for aqueous ammonium sulfate and sulfuric acid solution droplets. The new freezing-point temperature datasets agree with the previous lowest-temperature results for both solutes. The lowest measured freezing-point temperatures for aqueous ammonium sulfate solutions agree with a curve shaped like the translated melting-point curve. However, those for aqueous sulfuric acid solutions are significantly lower than predicted by the translated melting-point curve idea, and a single water activity freezing-point temperature curve does not represent the lowest-temperature freezing-point temperature data for both solutes. A linear extrapolation of the new aqueous sulfuric acid solution freezing data to low temperatures predicts that high critical supersaturations in cloud-free regions of the upper troposphere will occur when homogeneous ice nucleation in an aqueous sulfuric acid aerosol is the primary ice formation mechanism.

Corresponding author address: Brian D. Swanson, Laucks Foundation Inc., Bellevue, WA 98004. Email: brian@ess.washington.edu

Abstract

Frozen fraction measurements made using a droplet free-fall freezing tube apparatus are presented and used, along with other recent laboratory measurements, to evaluate how well both the water activity idea and the translated melting-point curve idea of Koop et al. predict homogeneous freezing-point temperatures for aqueous ammonium sulfate and sulfuric acid solution droplets. The new freezing-point temperature datasets agree with the previous lowest-temperature results for both solutes. The lowest measured freezing-point temperatures for aqueous ammonium sulfate solutions agree with a curve shaped like the translated melting-point curve. However, those for aqueous sulfuric acid solutions are significantly lower than predicted by the translated melting-point curve idea, and a single water activity freezing-point temperature curve does not represent the lowest-temperature freezing-point temperature data for both solutes. A linear extrapolation of the new aqueous sulfuric acid solution freezing data to low temperatures predicts that high critical supersaturations in cloud-free regions of the upper troposphere will occur when homogeneous ice nucleation in an aqueous sulfuric acid aerosol is the primary ice formation mechanism.

Corresponding author address: Brian D. Swanson, Laucks Foundation Inc., Bellevue, WA 98004. Email: brian@ess.washington.edu

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  • Abbatt, J. P. D., S. Benz, D. J. Cziczo, Z. Kanji, U. Lohmann, and O. Möhler, 2006: Solid ammonium sulfate aerosols as ice nuclei: A pathway for cirrus cloud formation. Science, 313 , 17701773.

    • Search Google Scholar
    • Export Citation
  • Baker, M. B., 1997: Cloud microphysics and climate. Science, 276 , 10721078.

  • Baker, M. B., and M. Baker, 2004: A new look at homogeneous freezing of water. Geophys. Res. Lett., 31 , L19102. doi:10.1029/2004GL020483.

    • Search Google Scholar
    • Export Citation
  • Beaver, M. R., M. J. Elrod, R. M. Garland, and M. A. Tolbert, 2006: Ice nucleation in sulfuric acid/organic aerosols: Implications for cirrus cloud formation. Atmos. Chem. Phys., 6 , 32313242.

    • Search Google Scholar
    • Export Citation
  • Bertram, A. K., D. D. Patterson, and J. J. Sloan, 1996: Mechanisms and temperatures for the freezing of sulfuric acid aerosols measured by FTIR extinction spectroscopy. J. Phys. Chem., 100 , 23762383.

    • Search Google Scholar
    • Export Citation
  • Bertram, A. K., T. Koop, L. T. Molina, and M. J. Molina, 2000: Ice formation in (NH4)2SO4-H2O particles. J. Phys. Chem., 104A , 584588.

    • Search Google Scholar
    • Export Citation
  • Bogdan, A., M. J. Molina, K. Sassen, and M. Kulmala, 2006: Formation of low-temperature cirrus from H2SO4/H2O aerosol droplets. J. Phys. Chem. Lett., 110 , 1254112542.

    • Search Google Scholar
    • Export Citation
  • Chelf, J. H., and S. T. Martin, 2001: Homogeneous ice nucleation in aqueous ammonium sulfate aerosol particles. J. Geophys. Res., 106 , 12151226.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., P. J. DeMott, S. M. Kreidenweis, D. C. Rogers, and D. E. Sherman, 2000: Ice formation by sulfate and sulfuric acid aerosol particles under upper-tropospheric conditions. J. Atmos. Sci., 57 , 37523766.

    • Search Google Scholar
    • Export Citation
  • Clegg, S. L., and P. Brimblecombe, 2005: Comment on the “Thermodynamic dissociation constant of the bisulfate ion from Raman and ion interaction modeling studies of aqueous sulfuric acid at low temperatures.”. J. Phys. Chem., 109A , 27032706.

    • Search Google Scholar
    • Export Citation
  • Clegg, S. L., S. Ho, C. Chan, and P. Brimblecombe, 1995: Thermodynamic properties of aqueous (NH4)2SO4 to high supersaturation as a function of temperature. J. Chem. Eng. Data, 40 , 10791090.

    • Search Google Scholar
    • Export Citation
  • Clegg, S. L., P. Brimblecombe, and A. S. Wexler, 1998: Thermodynamic model of the system H+ − NH4 + − SO4 2− − NO3 − H2O at tropospheric temperatures. J. Phys. Chem., 102A , 21372154. [Liquid solution model is available at http://www.aim.env.uea.ac.uk/aim/aim.htm.].

    • Search Google Scholar
    • Export Citation
  • Cziczo, D. J., and J. P. D. Abbatt, 1999: Deliquescence, efflorescence, and supercooling of ammonium sulfate aerosols at low temperature: Implications for cirrus cloud formation and aerosol phase in the atmosphere. J. Geophys. Res., 104 , 1378113790.

    • Search Google Scholar
    • Export Citation
  • Cziczo, D. J., and J. P. D. Abbatt, 2001: Ice nucleation in NH4HSO4, NH4NO3, and H2SO4 aqueous particles: Implications for cirrus cloud formation. Geophys. Res. Lett., 28 , 963966.

    • Search Google Scholar
    • Export Citation
  • DeMott, P. J., 2002: Laboratory studies of cirrus cloud processes. Cirrus, D. K. Lynch et al., Eds., Oxford University Press, 102–135.

    • Search Google Scholar
    • Export Citation
  • DeMott, P. J., and D. C. Rogers, 1990: Freezing nucleation rates of dilute solution droplets measured between −30° and −40°C in laboratory simulations of natural clouds. J. Atmos. Sci., 47 , 10561064.

    • Search Google Scholar
    • Export Citation
  • DeMott, P. J., M. P. Meyers, and W. R. Cotton, 1994: Parameterization and impact of ice initiation processes relevant to numerical model simulations of cirrus clouds. J. Atmos. Sci., 51 , 7790.

    • Search Google Scholar
    • Export Citation
  • DeMott, P. J., D. C. Rogers, and S. M. Kreidenweis, 1997: The susceptibility of ice formation in upper tropospheric clouds to insoluble aerosol components. J. Geophys. Res., 102 , 1957519584.

    • Search Google Scholar
    • Export Citation
  • DeMott, P. J., D. J. Cziczo, A. J. Prenni, D. M. Murphy, S. M. Kreidenweis, D. S. Thompson, R. Borys, and D. C. Rogers, 2003: Measurements of the concentration and composition of nuclei for cirrus formation. Proc. Natl. Acad. Sci. USA, 100 , 1465514660.

    • Search Google Scholar
    • Export Citation
  • Ettner, M., S. K. Mitra, and S. Borrmann, 2004a: Heterogeneous freezing of single sulfuric acid solution droplets: Laboratory experiments utilizing an acoustic levitator. Atmos. Chem. Phys., 4 , 19251932.

    • Search Google Scholar
    • Export Citation
  • Ettner, M., S. K. Mitra, and S. Borrmann, 2004b: Heterogeneous freezing of single sulfuric acid droplets: Laboratory experiments utilizing an acoustic levitator. Atmos. Chem. Phys. Discuss., 4 , 18871909.

    • Search Google Scholar
    • Export Citation
  • Gao, R. S., and Coauthors, 2004: Evidence that nitric acid increases relative humidity in low-temperature cirrus clouds. Science, 303 , 516520.

    • Search Google Scholar
    • Export Citation
  • Gayet, J., and Coauthors, 2006: Microphysical and optical properties of midlatitude cirrus clouds observed in the Southern Hemisphere during INCA. Quart. J. Roy. Meteor. Soc., 132 , 27192748.

    • Search Google Scholar
    • Export Citation
  • Gettleman, A., E. J. Fetzer, A. Eldering, and F. W. Irion, 2006: The global distribution of supersaturation in the upper troposphere from the atmospheric infrared sounder. J. Climate, 19 , 60896103.

    • Search Google Scholar
    • Export Citation
  • Haag, W., B. Kärcher, J. Strom, A. Minikin, U. Lohmann, J. Ovarlez, and A. Stohl, 2003: Freezing thresholds and cirrus cloud formation mechanisms inferred from in-situ measurements of relative humidity. Atmos. Chem. Phys., 3 , 17911806.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and R. M. Sabin, 1989: Cirrus crystal nucleation by homogeneous freezing of solution droplets. J. Atmos. Sci., 46 , 22522264.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and L. M. Miloshevich, 1993: Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds. J. Atmos. Sci., 50 , 23352353.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., L. M. Miloshevich, C. Twohy, G. Sachse, and S. Oltmans, 1998: Upper-tropospheric relative humidity observations and implications for cirrus ice nucleation. Geophys. Res. Lett., 25 , 13431346.

    • Search Google Scholar
    • Export Citation
  • Hung, H-M., and S. T. Martin, 2001: Apparent freezing temperatures modeled for several experimental apparatus. J. Geophys. Res., 106 , 2037920394.

    • Search Google Scholar
    • Export Citation
  • Hung, H-M., and S. T. Martin, 2002: Infrared spectroscopic evidence for the ice formation mechanisms active in aerosol flow tubes. Appl. Spectrosc., 56 , 10671081.

    • Search Google Scholar
    • Export Citation
  • Hung, H-M., A. Malinowski, and S. T. Martin, 2002: Ice nucleation kinetics of aerosols containing aqueous and solid ammonium sulfate particles. J. Phys. Chem., 106A , 293306.

    • Search Google Scholar
    • Export Citation
  • Jeffery, C. A., and P. H. Austin, 1997: Homogeneous nucleation of supercooled water: Results from a new equation of state. J. Geophys. Res., 102 , 2526925279.

    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., and O. B. Toon, 1997: The potential impact of soot particles from aircraft exhaust on cirrus clouds. Geophys. Res. Lett., 24 , 249252.

    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., O. B. Toon, D. L. Westphal, S. Kinne, and A. J. Heymsfield, 1994: Microphysical modeling of cirrus. 1. Comparison with 1986 FIRE IFO measurements. J. Geophys. Res., 99 , 1042110442.

    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., and Coauthors, 1998: Ice nucleation processes in upper tropospheric wave-clouds observed during SUCCESS. Geophys. Res. Lett., 25 , 13631366.

    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., L. Pfister, A. S. Ackerman, A. Tabazadeh, and O. B. Toon, 2001: A conceptual model of the dehydration of air due to freeze-drying by optically thin, laminar cirrus rising slowly across the tropical tropopause. J. Geophys. Res., 106 , 1723717252.

    • Search Google Scholar
    • Export Citation
  • Jensen, E. J., and Coauthors, 2005: Ice supersaturations exceeding 100% at the cold tropical tropopause: Implications for cirrus formation and dehydration. Atmos. Chem. Phys., 5 , 851862.

    • Search Google Scholar
    • Export Citation
  • Johari, G. P., G. Fleissner, A. Hallbrucker, and E. Mayer, 1994: Thermodynamic continuity between glassy and normal water. J. Phys. Chem., 98 , 47194725.

    • Search Google Scholar
    • Export Citation
  • Kanno, H., M. Soga, and K. Kajiwara, 2007: Linear relation between TH (homogeneous ice nucleation temperature) and Tm (melting temperature) for aqueous solutions of sucrose, trehalose, and maltose. Chem. Phys. Lett., 443 , 280283.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and U. Lohmann, 2002: A parameterization of cirrus cloud formation: Homogeneous freezing of supercooled aerosols. J. Geophys. Res., 107 , 4010. doi:10.1029/2001JD000470.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., and U. Lohmann, 2003: A parameterization of cirrus cloud formation: Heterogeneous freezing. J. Geophys. Res., 108 , 4402. doi:10.1029/2002JD003220.

    • Search Google Scholar
    • Export Citation
  • Kärcher, B., J. Hendricks, and U. Lohmann, 2006: Physically based parameterization of cirrus cloud formation for use in global atmospheric models. J. Geophys. Res., 111 , D01205. doi:10.1029/2005JD006219.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., V. Tsemekhman, B. Larson, M. B. Baker, and B. D. Swanson, 2003: Comment on evidence for surface-initiated homogeneous nucleation. Atmos. Chem. Phys., 3 , 14391443.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., M. B. Baker, and D. Hegg, 2006: Microphysical and dynamical controls on cirrus cloud optical depth distributions. J. Geophys. Res., 111 , D24205. doi:10.1029/2005JD006916.

    • Search Google Scholar
    • Export Citation
  • Keith, D., 2000: Stratosphere-troposphere exchange: Inferences from the isotopic composition of water vapor. J. Geophys. Res., 105 , 1516715174.

    • Search Google Scholar
    • Export Citation
  • Khalizov, A. F., M. E. Earle, W. J. W. Johnson, G. D. Stubley, and J. J. Sloan, 2006a: Development and characterization of a laminar aerosol flow tube. Rev. Sci. Instrum., 77 , 033102. doi:10.1063/1.2175958.

    • Search Google Scholar
    • Export Citation
  • Khalizov, A. F., M. E. Earle, W. J. W. Johnson, G. D. Stubley, and J. J. Sloan, 2006b: Modeling of flow dynamics in laminar aerosol flow tubes. J. Aerosol Sci., 37 , 11741187.

    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V. I., and K. Sassen, 1998: Toward the theory of homogeneous nucleation and its parameterization for cloud models. Geophys. Res. Lett., 25 , 31553158.

    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V. I., and J. A. Curry, 2004: Thermodynamic theory of freezing and melting of water and aqueous solutions. J. Phys. Chem., 108A , 1107311085.

    • Search Google Scholar
    • Export Citation
  • Knopf, D. A., B. P. Luo, U. K. Krieger, and T. Koop, 2003: Thermodynamic dissociation constant of the bisulfate ion from raman and ion interaction modeling studies of aqueous sulfuric acid at low temperatures. J. Phys. Chem., 107A , 43224332.

    • Search Google Scholar
    • Export Citation
  • Knopf, D. A., B. P. Luo, U. K. Krieger, and T. Koop, 2005: Reply to “Comment on the ‘Thermodynamic dissociation constant of the bisulfate ion from raman and interaction modeling studies of aqueous sulfuric acid at low temperatures.’”. J. Phys. Chem., 109A , 27072709.

    • Search Google Scholar
    • Export Citation
  • Koop, T., 2004: Homogeneous ice nucleation in water and aqueous solutions. Z. Phys. Chem., 218 , 12311258.

  • Koop, T., H. P. Ng, L. T. Molina, and M. J. Molina, 1998: A new optical technique to study aerosol phase transitions: The nucleation of ice from H2SO4 aerosols. J. Phys. Chem., 102A , 89248931.

    • Search Google Scholar
    • Export Citation
  • Koop, T., B. Luo, A. Tsias, and T. Peter, 2000: Water activity as the determinant for homogeneous ice nucleation in aqueous solutions. Nature, 406 , 611614.

    • Search Google Scholar
    • Export Citation
  • Krämer, B., 1998: Freezing of single levitated micro-droplets of water, sulfuric acid and ternary H2SO4/HNO3/H2O solutions. Ph.D. thesis, Frie University of Berlin, 184 pp.

    • Search Google Scholar
    • Export Citation
  • Larson, B. H., 2004: Experimental investigations of ammonium sulfate-water solution droplet nucleation temperatures. M.S. thesis, ESS Department, University of Washington, 64 pp.

  • Larson, B. H., and B. D. Swanson, 2006: Experimental investigation of the homogeneous freezing of aqueous ammonium sulfate droplets. J. Phys. Chem., 110A , 19071916.

    • Search Google Scholar
    • Export Citation
  • Mangold, A., R. Wagner, H. Saathoff, U. Schurath, C. Giesemann, B. Ebert, M. Krämer, and O. Möhler, 2005: Experimental investigation of ice nucleation by different types of aerosols in the aerosol chamber AIDA: Implications to microphysics of cirrus clouds. Meteor. Z., 14 , 485497.

    • Search Google Scholar
    • Export Citation
  • Möhler, O., and Coauthors, 2003: Experimental investigation of homogeneous freezing of sulphuric acid particles in the aerosol chamber AIDA. Atmos. Chem. Phys., 3 , 211223.

    • Search Google Scholar
    • Export Citation
  • Murphy, D. M., and T. Koop, 2005: Review of the vapour pressures of ice and supercooled water for atmospheric applications. Quart. J. Roy. Meteor. Soc., 131 , 15391565.

    • Search Google Scholar
    • Export Citation
  • Murray, B. J., D. A. Knopf, and A. K. Bertram, 2005: The formation of cubic ice under conditions relevant to earth’s atmosphere. Nature, 434 , 202205.

    • Search Google Scholar
    • Export Citation
  • Peter, T., C. Marcolli, P. Spichtinger, T. Corti, M. B. Baker, and T. Koop, 2006: When dry air is too humid. Science, 314 , 13991402.

  • Prenni, A. J., P. J. DeMott, S. M. Kreidenweis, D. E. Sherman, L. M. Russell, and Y. Ming, 2001a: The effects of low molecular weight dicarboxylic acids on cloud formation. J. Phys. Chem., 105A , 1124011248.

    • Search Google Scholar
    • Export Citation
  • Prenni, A. J., M. E. Wise, S. D. Brooks, and M. A. Tolbert, 2001b: Ice nucleation in sulfuric acid and ammonium sulfate particles. J. Geophys. Res., 106 , 30373044.

    • Search Google Scholar
    • Export Citation
  • Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Kluwer, 954 pp.

  • Rasmussen, D. H., and A. P. MacKenzie, 1972: Effect of solute on ice-solution interfacial free energy: Calculation from measured homogeneous nucleation temperatures. Water Structure at the Water Polymer Interface, H. H. G. Jellinek, Ed., Plenum Press, 126–145.

    • Search Google Scholar
    • Export Citation
  • Sassen, K., and G. Dodd, 1988: Homogeneous nucleation rate for highly supercooled cirrus cloud droplets. J. Atmos. Sci., 45 , 13571369.

    • Search Google Scholar
    • Export Citation
  • Seeley, L. H., and G. T. Seidler, 2001: Two-dimensional nucleation of ice from supercooled water. Phys. Rev. Lett., 87 , 055702. doi:10.1103/PhysRevLett.87.055702.

    • Search Google Scholar
    • Export Citation
  • Shilling, J. E., T. J. Fortin, and M. A. Tolbert, 2006a: Depositional ice nucleation on crystalline organic and inorganic solids. J. Geophys. Res., 111 , D12204. doi:10.1029/2005JD006664.

    • Search Google Scholar
    • Export Citation
  • Shilling, J. E., M. A. Tolbert, O. B. Toon, E. J. Jensen, B. J. Murray, and A. K. Bertram, 2006b: Measurements of the vapor pressure of cubic ice and their implications for atmospheric ice clouds. Geophys. Res. Lett., 33 , L17801. doi:10.1029/2006GL026671.

    • Search Google Scholar
    • Export Citation
  • Speedy, R. J., P. G. Debenedetti, R. S. Smith, C. Huang, and B. D. Kay, 1996: The evaporation rate, free energy, and entropy of amorphous water at 150 K. J. Chem. Phys., 105 , 240244.

    • Search Google Scholar
    • Export Citation
  • Spichtinger, P., K. Gierens, and W. Read, 2002: The statistical distribution law of relative humidity in the global tropopause region. Meteor. Z., 11 , 8388.

    • Search Google Scholar
    • Export Citation
  • Tabazadeh, A., E. J. Jensen, and O. B. Toon, 1997: A model description for cirrus cloud nucleation from homogeneous freezing of sulfate aerosols. J. Geophys. Res., 102 , 2384523850.

    • Search Google Scholar
    • Export Citation
  • Tabazadeh, A., and Coauthors, 1998: Nitric acid scavenging by mineral and biomass burning aerosols. Geophys. Res. Lett., 25 , 41854188.

    • Search Google Scholar
    • Export Citation
  • Tabazadeh, A., Y. S. Djikaev, P. Hamill, and H. Reiss, 2002a: Laboratory evidence for surface nucleation of solid polar stratospheric cloud particles. J. Phys. Chem. A, 106 , 1023810246.

    • Search Google Scholar
    • Export Citation
  • Tabazadeh, A., Y. S. Djikaev, and H. Reiss, 2002b: Surface crystallization of supercooled water in clouds. Proc. Natl. Acad. Sci. USA, 99 , 1587315878.

    • Search Google Scholar
    • Export Citation
  • Treffeisen, R., R. Krejci, J. Ström, A. C. Engvaill, A. Herber, and L. Thomason, 2007: Humidity observations in the arctic troposphere over Ny-Ålesund, Svalbard based on 15 years of radiosonde data. Atmos. Chem. Phys., 7 , 27212732.

    • Search Google Scholar
    • Export Citation
  • Vortisch, H., B. Krämer, I. Weidinger, L. Wöste, T. Leisner, M. Schwell, H. Baumgärtel, and E. Rühl, 2000: Homogeneous freezing nucleation rates and crystallization dynamics of single levitated sulfuric acid solution droplets. Phys. Chem. Chem. Phys., 2 , 14071413.

    • Search Google Scholar
    • Export Citation
  • Wise, M. E., R. M. Garland, and M. A. Tolbert, 2004: Ice nucleation in internally mixed ammonium sulfate/dicarboxylic acid particles. J. Geophys. Res., 109 , D19203. doi:10.1029/2003JD004313.

    • Search Google Scholar
    • Export Citation
  • Wood, S. E., M. B. Baker, and B. D. Swanson, 2002: Instrument for studies of homogeneous and heterogeneous ice nucleation in free-falling supercooled water droplets. Rev. Sci. Instrum., 73 , 39883996.

    • Search Google Scholar
    • Export Citation
  • Zobrist, B., U. Weers, and T. Koop, 2003: Ice nucleation in aqueous solutions of poly[ethylene glycol] with different molar mass. J. Chem. Phys., 118 , 1025410261.

    • Search Google Scholar
    • Export Citation
  • Zobrist, B., and Coauthors, 2006: Oxalic acid as a heterogeneous ice nucleus in the upper troposphere and its indirect aerosol effect. Atmos. Chem. Phys., 6 , 31153129.

    • Search Google Scholar
    • Export Citation
  • Zuberi, B., A. K. Bertram, T. Koop, L. T. Molina, and M. J. Molina, 2001: Heterogeneous freezing of aqueous particles induced by crystallized (NH4)2SO4, ice, and letovicite. J. Phys. Chem. A, 105 , 64586464.

    • Search Google Scholar
    • Export Citation
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