Published Papers

Papers Describing E-AIM

Here we list the papers, published in the peer-reviewed literature, that describe the science of the E-AIM models and recent applications to systems that include both inorganic and organic components. Please cite these papers in your work when you use results from E-AIM.

Contents of this page

1. Web site.
2. Activity coefficient equations.
3. Inorganic Model I.
4. Inorganic Model II.
5. Inorganic Model IIII.
6. Inorganic Model IV.
7. Models for mixed Inorganic/Organic Solutions.
8. The Zdanovskii-Stokes-Robinson model.
9. Applications to mixed inorganic/organic aqueous solutions.
10. Comparisons of organic vapour pressure estimators.
11. Evaluation of an air quality model.
12. Surface tensions of inorganic aqueous solutions.
13. Densities of inorganic aqueous solutions and solids.
14. Properties of atmospheric amines (organic bases).
15. Properties of aminium sulphate salts.

1. Web Site

This paper describes how the equilibrium state of the system is calculated, and summarises the development of the inorganic elements of the model.

A. S. Wexler and S. L. Clegg (2002) Atmospheric aerosol models for systems including the ions H⁺, NH4⁺, Na⁺, SO4²⁻, NO3⁻, Cl⁻, Br⁻ and H2O. J. Geophys. Res. 107, No. D14, art. no. 4207, 14 pages.

2. Activity Coefficient Equations

The equations for calculating solute and solvent activities in aqueous electrolyte solutions are fundamental to E-AIM, and the theory is presented in this paper. (The errata referenced below correct typographical errors.)

S. L. Clegg, K. S. Pitzer, and P. Brimblecombe (1992) Thermodynamics of multicomponent, miscible, ionic solutions. II. Mixtures including unsymmetrical electrolytes. J. Phys. Chem. 96, 9470-9479; and also (1994, 98, p1368); (1995, 99, p6755).

3. Inorganic Model I

This is the model for aqueous mixtures of acids present in the stratosphere. The Wexler and Clegg paper (the first reference on this page) adds a description of the treatment of gas/liquid equilibrium developed later for H2SO4. The Comment referenced below addresses uncertainties in model predictions at very low temperatures.

K. S. Carslaw, S. L. Clegg and P. Brimblecombe (1995) A thermodynamic model of the system HCl - HNO3 - H2SO4 - H2O, including solubilities of HBr, from <200 K to 328 K. J. Phys. Chem. 99, 11557-11574.
M. Massucci, S. L. Clegg and P. Brimblecombe (1999) Equilibrium partial pressures, thermodynamic properties of aqueous and solid phases, and Cl2 production from aqueous HCl and HNO3 and their mixtures. J. Phys. Chem. A 103, 4209-4226.
S. L. Clegg 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" by Knopf et al., J. Phys. Chem. A. 109, 2703-2706.

4. Inorganic Model II

This paper, plus those referenced above (for H2SO4 and HNO3 which are common to both models), describes Model II for acid nitrate/sulphate mixtures.

S. L. Clegg, P. Brimblecombe and A. S. Wexler (1998) A thermodynamic model of the system H⁺ - NH4⁺ - SO4²⁻ - NO3⁻ - H2O at tropospheric temperatures. J. Phys. Chem. A 102, 2137-2154.

5. Inorganic Model III

This model, which includes NaCl, is for 298.15 K only:

S. L. Clegg, P. Brimblecombe and A. S. Wexler (1998) A thermodynamic model of the system H⁺ - NH4⁺ - Na⁺ - SO4²⁻ - NO3⁻ - Cl⁻ - H2O at 298.15 K. J. Phys. Chem. A 102, 2155-2171.

6. Inorganic Model IV

This model includes NaCl and is for a wide range of temperatures. It includes elements of Models I and II, but has a few limitations regarding solutions supersaturated with respect to some salts, and the species that can be included in low temperature systems.

E. Friese and A. Ebel (2010) Temperature dependent thermodynamic model of the system H⁺ - NH₄⁺ - Na⁺ - SO₄²⁻ - NO₃⁻ - Cl⁻ - H2O. J. Phys. Chem. A, 114, 11595-11631.

7. Models for Mixed Inorganic/Organic Solutions

This paper describes the approximation used in E-AIM to obtain activity coefficients for water and solute species in aqueous solutions that contain both ions and undissociated organic species.

S. L. Clegg, J. H. Seinfeld and P. Brimblecombe (2001) Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds. J. Aerosol Sci. 32, 713-738.

8. The Zdanovskii-Stokes-Robinson Model

The ZSR relationship is used in E-AIM in its basic form, without either interaction parameters or corrections for unsymmetrical systems (those which contain ions of different charge magnitude). These additions, and methods of incorporating ZSR into a larger modelling scheme, are explored in these two papers.

S. L. Clegg and J. H. Seinfeld (2004) Improvement of the Zdanovskii- Stokes-Robinson model for mixtures containing solutes of different charge types. J. Phys. Chem. A 108 1008-1017.
S. L. Clegg, J. H. Seinfeld and E. O. Edney (2003) Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds. II. An extended Zdanovskii-Stokes-Robinson approach. J. Aerosol Sci. 34, 667-690.

9. Applications to Mixed Inorganic/Organic Aqueous Solutions

These two papers test the E-AIM modelling methods against data for aqueous solutions of dicarboxylic acids and electrolytes. The first paper also contains a critical assessment of the available activity data for aqueous solutions of the dicarboxylic acids.

S. L. Clegg and J. H. Seinfeld (2006) Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. I. The acids as non-dissociating components. J. Phys. Chem. A 110, 5692-5717.
S. L. Clegg and J. H. Seinfeld (2006) Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. II. Systems including dissociation equilibria. J. Phys. Chem. A 110, 5718-5734.

10. Comparisons of Organic Vapour Pressure Estimators

The vapour pressure estimator for organic compounds that we provide on this site (courtesy of DDBST GmbH) is one of a number of methods compared in the paper below.

S. L. Clegg, M. J. Kleeman, R. J. Griffin, and J. H. Seinfeld (2008) Effects of uncertainties in the thermodynamic properties of aerosol components in an air quality model – Part II: Predictions of the vapour pressures of organic compounds. Atmos. Chem. and Phys. 8, 1087-1103.

11. Evaluation of an Air Quality Model

Here E-AIM is used to assess the thermodynamic treatment of aerosols and gas/aerosol equilibria in an air quality model.

S. L. Clegg, M. J. Kleeman, R. J. Griffin, and J. H. Seinfeld (2008) Effects of uncertainties in the thermodynamic properties of aerosol components in an air quality model – Part I: Treatment of inorganic electrolytes and organic compounds in the condensed phase. Atmos. Chem. and Phys. 8, 1057-1085.

12. Surface Tensions

This paper describes a new model for the calculation of surface tensions of pure (single solute) aqueous solutions and mixtures that is used in both E-AIM and the stand-alone surface tension calculator on the web site.

C. S. Dutcher, A. S. Wexler and S. L. Clegg (2010) Surface tensions of inorganic multicomponent aqueous electrolyte solutions and melts. J. Phys. Chem. A 114, 12216-12230.

13. Densities and Other Volume Properties

These papers describe studies of the volume properties (densities and partial and apparent molar volumes) of inorganic aqueous solutions, giving the fitted equations that are used in E-AIM and the density calculator on the web site. The first paper also summarises the E-AIM treatment of the densities of inorganic solids.

S. L. Clegg and A. S. Wexler (2011) Densities and apparent molar volumes of atmospherically important electrolyte solutions. I. The solutes H₂SO₄, HNO₃, HCl, Na₂SO₄, NaNO₃, NaCl, (NH₄)₂SO₄, NH₄NO₃, and NH₄Cl from 0 to 50 °C, including extrapolations to very low temperature and to the pure liquid state, and NaHSO₄, NaOH and NH₃ at 25 °C. J. Phys. Chem. A 115, 3393-3460.
S. L. Clegg and A. S. Wexler (2011) Densities and apparent molar volumes of atmospherically important electrolyte solutions. II. The system H⁺ - HSO₄⁻ - SO₄²⁻ - H₂O from 0 - 3 mol kg⁻¹ as a function of temperature and H⁺ - NH₄⁺ - HSO₄⁻ - SO₄²⁻ - H₂O from 0 - 6 mol kg⁻¹ at 25 °C using a Pitzer ion interation model, and NH₄HSO₄ - H₂O and (NH₄)₃H(SO₄)₂ - H₂O over the entire concentration range. J. Phys. Chem. A 115, 3461-3474.

14. Properties of Atmospheric Amines (Organic Bases)

The first paper below reviews the current state of knowledge of amines that have been detected in the atmosphere (over 150 individual compounds), and the second one describes the thermodynamic properties that control their gas/particle partitioning. Methods of predicting vapour pressures, dissociation constants and solubilities are assessed in the second paper, and values – both measured and predicted – are compiled for key amines and presented in the Supplementary Information to that paper. This compilation is the source of the values for the amines included in E-AIM.

X. Ge, A. S. Wexler, and S. L. Clegg (2011a) Atmospheric amines - Part I. A review. Atmos. Environ. 45, 524-546.
X. Ge, A. S. Wexler, and S. L. Clegg (2011b) Atmospheric amines - Part II. Thermodynamic properties and gas/particle partitioning. Atmos. Environ. 45, 561-577.

15. Properties of Aminium Sulphate Salts

This paper presents experimental measurements of densities of solutions of five aminium sulphate salts, and fitted equations for their apparent molar volumes over the entire concentration range. Measured and calculated growth factors of aminium sulphate aerosols (over a wide range of relative humidities) are compared, and found to agree well. The treatment of aminium sulphate salts in E-AIM is described.

S. L. Clegg, C. Qiu, and R. Zhang (2013) The deliquescence behaviour, solubilities, and densities of aqueous solutions of five methyl- and ethyl-aminium sulphate salts. Atmos. Environ. 73, 145-158.