A curved multi-component aerosol hygroscopicity model framework: Part 1 Inorganic compounds

Abstract. A thermodynamic modelling framework to predict the equilibrium behaviour of mixed inorganic salt aerosols is developed, and then coupled with a technique for finding a solution to the Kohler equation in order to create a diameter dependent hygroscopic aerosol model (Aerosol Diameter Dependent Equilibrium Model – ADDEM). The model described here provides a robust and accurate inorganic basis using a mole fraction based activity coefficient model and adjusted energies of formation for treating solid precipitation. The model framework can accommodate organic components, though this added complexity is considered in a companion paper, this paper describes the development of the modelling architecture to be used and predictions of an inorganic model alone. The modelling framework has been developed to flexibly use a combination of mixing rules and other potentially more accurate techniques where available to calculate the water content. Comparisons with other state-of-the-art general equilibrium models and experimental data are presented and show excellent agreement. The Kelvin effect can be considered in this scheme using a variety of surface tension models. Comparison of predicted diameter dependent phenomena, such as the increased relative humidity for onset of deliquescence with decreasing diameter, with another diameter dependent model is very good despite the different approach used. The model is subject to various sensitivities. For the inorganic systems studied here, the model is sensitive to choice of surface tension scheme used, which decreases for larger aerosol. Large sensitivities are found for the value of dry density used. It is thus likely that the history of the aerosol studied in a hygroscopic tandem differential mobility analyser (HTDMA), specifically the nature of the drying process that will influence the final crystalline form, will create systematic uncertainties upon comparisons with theoretical predictions. However, the magnitudes of all of the above sensitivities are potentially less than those introduced when using a semi ideal growth factor analogue for certain conditions.

[1]  Y. Ming,et al.  Thermodynamic equilibrium of organic‐electrolyte mixtures in aerosol particles , 2002 .

[2]  J. Seinfeld,et al.  Atmospheric equilibrium model of sulfate and nitrate aerosols—II. Particle size analysis , 1984 .

[3]  K. Pitzer,et al.  Thermodynamics of electrolytes. VI. Weak electrolytes including H3PO4 , 1976 .

[4]  Kenneth S. Pitzer,et al.  Thermodynamics of electrolytes. V. effects of higher-order electrostatic terms , 1975 .

[5]  J. Seinfeld,et al.  A comparative review of inorganic aerosol thermodynamic equilibrium modules: similarities, differences, and their likely causes , 2000 .

[6]  J. Seinfeld,et al.  The distribution of ammonium salts among a size and composition dispersed aerosol , 1990 .

[7]  W. Malm,et al.  The effects of models of aerosol hygroscopicity on the apportionment of extinction , 1997 .

[8]  J. Seinfeld,et al.  Can chemical effects on cloud droplet number rival the first indirect effect? , 2002 .

[9]  John H. Seinfeld,et al.  Sensitivity of direct climate forcing by atmospheric aerosols to aerosol size and composition , 1995 .

[10]  S. Pandis,et al.  Deliquescence and Hygroscopic Growth of Mixed Inorganic−Organic Atmospheric Aerosol , 2000 .

[11]  R. Charlson,et al.  Modification of the Köhler Equation to Include Soluble Trace Gases and Slightly Soluble Substances , 1998 .

[12]  William H. Press,et al.  Numerical recipes in Fortran 77 : the art of scientificcomputing. , 1992 .

[13]  G. Wilemski.  The Kelvin equation and self‐consistent nucleation theory , 1995 .

[14]  I. Tang,et al.  Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance , 1994 .

[15]  Kenneth S. Pitzer,et al.  Thermodynamics of electrolytes. I. Theoretical basis and general equations , 1973 .

[16]  S. Kreidenweis,et al.  Predicting Particle Critical Supersaturation from Hygroscopic Growth Measurements in the Humidified TDMA. Part II: Laboratory and Ambient Studies , 2000 .

[17]  R. Turco,et al.  Simulating equilibrium within aerosols and nonequilibrium between gases and aerosols , 1996 .

[18]  Y. Ming,et al.  Deliquescence of small particles , 2002 .

[19]  J. Seinfeld,et al.  Studies of concentrated electrolyte solutions using the electrodynamic balance. 1. Water activities for single-electrolyte solutions , 1987 .

[20]  K. Denbigh,et al.  The principles of chemical equilibrium : with applications in chemistry and chemical engineering , 1981 .

[21]  Sonia M. Kreidenweis,et al.  Water activity and activation diameters from hygroscopicity data - Part I: Theory and application to inorganic salts , 2005 .

[22]  Kenneth S. Pitzer,et al.  Thermodynamics of multicomponent, miscible, ionic solutions: generalized equations for symmetrical electrolytes , 1992 .

[23]  J. Hemminger,et al.  Effect of Water on the HNO3 Pressure Dependence of the Reaction between Gas-Phase HNO3 and NaCl Surfaces , 1999 .

[24]  G. Wilemski.  Composition of the critical nucleus in multicomponent vapor nucleation , 1984 .

[25]  Jos Lelieveld,et al.  Gas/aerosol partitioning: 1. A computationally efficient model , 2002 .

[26]  H. Reiss,et al.  The Kelvin Relation: Stability, Fluctuation, and Factors Involved in Measurement , 1995 .

[27]  R. Harrison,et al.  Physico-chemical speciation and transformation reactions of particulate atmospheric nitrogen and sulphur compounds , 1984 .

[28]  B. Svenningsson,et al.  CCN activation of slightly soluble organics: the importance of small amounts of inorganic salt and particle phase , 2004 .

[29]  S. Kreidenweis,et al.  Predicting Particle Critical Supersaturation from Hygroscopic Growth Measurements in the Humidified TDMA. Part I: Theory and Sensitivity Studies , 2000 .

[30]  C. Corrigan,et al.  Cloud condensation nucleus activity of organic compounds : a laboratory study , 1999 .

[31]  I. Tang.  Thermodynamic and optical properties of mixed‐salt aerosols of atmospheric importance , 1997 .

[32]  Application of osmolality for the determination of water activity and the modelling of cloud formation , 2004 .

[33]  A. Wexler,et al.  Thermodynamic Model of the System H+−NH4+−Na+−SO42-−NO3-−Cl-−H2O at 298.15 K , 1998 .

[34]  Mian Chin,et al.  Effects of the physical state of tropospheric ammonium-sulfate-nitrate particles on global aerosol direct radiative forcing , 2003 .

[35]  R. Synovec,et al.  Dissolution behavior and surface tension effects of organic compounds in nucleating cloud droplets , 1996 .

[36]  A. Nenes,et al.  ISORROPIA: A New Thermodynamic Equilibrium Model for Multiphase Multicomponent Inorganic Aerosols , 1998 .

[37]  G. Ewing,et al.  Water Content and Morphology of Sodium Chloride Aerosol Particles , 1999 .

[38]  J. Israelachvili,et al.  Direct experimental verification of the Kelvin equation for capillary condensation , 1979, Nature.

[39]  Huen Lee,et al.  Prediction of the surface tension of mixed electrolyte solutions based on the equation of Patwardhan and Kumar and the fundamental Butler equations. , 2004, Journal of colloid and interface science.

[40]  C. Chan,et al.  Study of water activities of supersaturated aerosols of sodium and ammonium salts , 2000 .

[41]  L. Crocker,et al.  Two methods for the measurement of the dissociation pressure of a crystalline hydrate. , 1997, Journal of pharmaceutical and biomedical analysis.

[42]  J. Seinfeld,et al.  Atmospheric Gas-Aerosol Equilibrium I. Thermodynamic Model , 1993 .

[43]  J. Hemminger,et al.  Physical Chemistry of Airborne Sea Salt Particles and Their Components , 2000 .

[44]  D. Topping,et al.  A curved multi-component aerosol hygroscopicity model framework : 2 – Including organics , 2004 .

[45]  Jen‐Ping Chen.  Theory of deliquescence and modified Köhler curves , 1994 .

[46]  Erik Swietlicki,et al.  A closure study of sub-micrometer aerosol particle hygroscopic behaviour , 1999 .

[47]  Peter Brimblecombe,et al.  Thermodynamics of multicomponent, miscible, ionic solutions. Mixtures including unsymmetrical electrolytes , 1992 .

[48]  J. Seinfeld,et al.  A comparative study of equilibrium approaches to the chemical characterization of secondary aerosols , 1986 .

[49]  J. Seinfeld,et al.  Atmospheric Gas-Aerosol Equilibrium: IV. Thermodynamics of Carbonates , 1995 .

[50]  H. Hansson,et al.  Hygroscopic growth of ultrafine ammonium sulphate aerosol measured using an ultrafine tandem differential mobility analyzer , 2000 .

[51]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[52]  S. Solberg,et al.  Atmospheric Chemistry and Physics , 2002 .

[53]  J. Seinfeld,et al.  Atmospheric Gas–Aerosol Equilibrium: III. Thermodynamics of Crustal Elements Ca2+, K+, and Mg2+ , 1995 .

[54]  J. Seinfeld,et al.  Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds. II. An extended Zdanovskii–Stokes–Robinson approach , 2003 .

[55]  I. Tang,et al.  Water activity measurements with single suspended droplets: The NaCl-H2O and KCl-H2O systems☆ , 1986 .

[56]  Mark D. Cohen.  Studies of Concentrated Electrolyte Solutions Using the Electrodynamic Balance , 1987 .

[57]  A. Wexler,et al.  Atmospheric aerosol models for systems including the ions H+, NH4+, Na+, SO42−, NO3−, Cl−, Br−, and H2O , 2002 .

[58]  P. Brimblecombe,et al.  Equilibrium partial pressures of strong acids over concentrated saline solutions—II. HCl , 1988 .

[59]  H. Hansson,et al.  Hygroscopic properties of mixed ammonium sulfate and carboxylic acids particles , 2002 .

[60]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[61]  J. Seinfeld,et al.  Water content of atmospheric aerosols , 1989 .

[62]  J. Seinfeld,et al.  Continued development of a general equilibrium model for inorganic multicomponent atmospheric aerosols , 1987 .

[63]  J. Seinfeld,et al.  Water activities of NH4NO3/(NH4)2SO4 solutions , 1992 .

[64]  R. Robinson,et al.  Interactions in Aqueous Nonelectrolyte Solutions. I. Solute-Solvent Equilibria , 1966 .

[65]  Peter Brimblecombe,et al.  Thermodynamic Model of the System H+−NH4+−SO42-−NO3-−H2O at Tropospheric Temperatures , 1998 .

[66]  M. Jacobson.  Studying the effects of calcium and magnesium on size-distributed nitrate and ammonium with EQUISOLV II , 1999 .

[67]  M. Pitchford,et al.  Relationship between measured water vapor growth and chemistry of atmospheric aerosol for Grand Canyon, Arizona, in winter 1990 , 1994 .

[68]  J. Seinfeld,et al.  Atmospheric equilibrium model of sulfate and nitrate aerosols , 1983 .

[69]  P. Chylek,et al.  Erroneous Use of the Modified Kohler Equation in Cloud and Aerosol Physics Applications , 1998 .

[70]  J. Seinfeld,et al.  Second-generation inorganic aerosol model , 1991 .

[71]  F. Binkowski,et al.  The Regional Particulate Matter Model 1. Model description and preliminary results , 1995 .

[72]  J. Lelieveld,et al.  Gas/aerosol partitioning 2. Global modeling results , 2002 .

[73]  H. Reiss,et al.  A theory for the deliquescence of small particles , 2000 .

[74]  P. Reilly,et al.  Prediction of the properties of mixed electrolytes from measurements on common ion mixtures , 1969 .

[75]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[76]  A. Nenes,et al.  Continued development and testing of a new thermodynamic aerosol module for urban and regional air quality models , 1999 .

[77]  S. Pandis,et al.  Prediction of multicomponent inorganic atmospheric aerosol behavior , 1999 .

[78]  Yigui Li,et al.  Surface Tension Model for Concentrated Electrolyte Aqueous Solutions by the Pitzer Equation , 1999 .

[79]  J. Klett,et al.  Microphysics of Clouds and Precipitation , 1978, Nature.

[80]  Y. Ming,et al.  Predicted hygroscopic growth of sea salt aerosol , 2001 .

[81]  John H. Seinfeld,et al.  Relative humidity and temperature dependence of the ammonium nitrate dissociation constant , 1982 .

[82]  C. Chan,et al.  Study of water activities of aerosols of mixtures of sodium and magnesium salts , 2000 .

[83]  Zhibao Li,et al.  Surface tension of aqueous electrolyte solutions at high concentrations — representation and prediction , 2001 .

[84]  K. Pitzer,et al.  Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent , 1973 .

[85]  M. Facchini,et al.  The influence of the organic aerosol component on CCN supersaturation spectra for different aerosol types , 2002 .

[86]  J. Seinfeld,et al.  Atmospheric gas−aerosol equilibrium. II: Analysis of common approximations and activity coefficient calculation methods , 1993 .

[87]  Reinhard Niessner,et al.  Interaction of aerosol particles composed of protein and salts with water vapor: hygroscopic growth and microstructural rearrangement , 2003 .

[88]  S. Girshick,et al.  Kinetic nucleation theory: A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor , 1990 .

[89]  A. Tits,et al.  User's Guide for FSQP Version 2.0 A Fortran Code for Solving Optimization Problems, Possibly Minimax, with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates , 1990 .

[90]  Peter Brimblecombe,et al.  Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds , 2001 .

[91]  P. Rasmussen,et al.  Prediction of surface tensions of nonelectrolyte solutions , 1989 .