E-AIM Model News

June 2017: Models II to IV can now be used to calculate "Köhler curves" which represent the equilibrium saturation (or supersaturation) of water over liquid droplets of known size. The value of the saturation S can rise above 100% for very small droplets, i.e., the water vapour pressure becomes greater than the equilibrium value for a pure water plane surface, due to the Kelvin effect. Köhler curves are often plotted as % saturation of water against the logarithm of particle radius, and examples can be found in textbooks such as Pruppacher and Klett (2000).

There are links to the input pages for the Köhler calculations on the main page for each model. Particle composition can be entered in a number of ways: moles of ions, moles or masses of chemical components, and dry particle radius together with the volume fractions of the salts present. It is also possible to include a single organic compound in these calculations, which can be either non-dissociating or a mono- or di-carboxylic acid. The properties of the compound are entered on the Köhler calculation page. There is one further way of entering chemical composition: particle radius, volume fraction of solid(s), and kappa (κ) value(s). In this case the calculations are carried out using the κ–Köhler theory of Petters and Kreidenweis (2007).

Results are output both in column form (to the screen), and as a "comma separated value" (csv) file that can be directly opened by Excel or other spreadsheet programs. The results include hygroscopic growth factors, water activities and water saturations for the aqueous particle, particle radius, surface tension, density, and the partial molar volume of water. For calculations carried out by E-AIM the total κ value is also tabulated for all results for which the particle is entirely aqueous (i.e., no solids have formed). In the future we expect to add the ability to plot graphs.

In addition, calculated κ values for aqueous and liquid systems are now listed in the "verbose" standard output of models II-IV for all types of input ("Simple", "Comprehensive", "Parametric", etc.). This enables κ to be determined for systems that include one or more organic compounds whose properties and behaviour are defined in a more comprehensive and detailed way than is possible on the Köhler pages described above. Note that κ is only calculated for chemical systems in which no solids are formed at equilibrium, and for which no trace gases have been equilibrated with the vapour phase.

This work is the result of a collaboration with Markus Petters (North Carolina State University, USA) and Jonathan Reid (University of Bristol, UK), supported by the Natural Environment Research Council of the UK.


M. D. Petters and S. M. Kreidenweis (2007) A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys. 7, 1961-1971.
H. R. Pruppacher and J. D. Klett (2000) Microphysics of Clouds and Precipitation, 2nd. Edn., Kluwer Academic Publishers, pp. 954.

July 2016: Small changes have been made to the way 'Batch' calculations are entered for all of Models I-IV. These only affect the integer options for organic compounds. The new arrangement of options is described on the information pages for the inputs, for example this page for Model II.

The website has been moved to a new server. This has the same web address as the previous one. You should not notice any differences, except perhaps an increase in speed for large problems.

November 2014: Calculations can be carried out with Models I, II, and IV over ranges of temperature specified by the user (here, for example). Previously, the chemical systems either had to be at fixed relative humidities, contain a fixed total amount of water per m3 of atmosphere, or be in equilibrium with the water vapour pressure over ice.

This limitation on the behaviour of water also existed for calculations for variable inorganic chemical composition for all four models (here, for example).

The amount of water present in the liquid phase can now be fixed, so that the properties of aqueous solutions of specified solute concentrations can be calculated over ranges of temperature or inorganic composition. (To do this, first select the new radio button "Liquid water" on the appropriate problem input page. Next, enter 55.508681 as the number of moles of liquid water and the ion amounts will then be equivalent to molalities.) Using this option, volatile species such as NH3 and the acid gases are allowed to partition into the vapour phase, if desired, but not water.

June 2014: The E-AIM model has recently been compiled into dynamic link libraries (dlls), for machines running 32 and 64 bit Windows. Versions for Linux operating systems can also be prepared. All of Models I to IV can be called, as subroutines, from these libraries. Executable programs that call E-AIM from the dll are not restricted to being Fortran (like the model itself): the dll has been used successfully within Mathematica, and it is possible within other programming environments too.

If you are interested in obtaining a copy of a dll for a special project, please contact Simon Clegg and read the draft manual to see if it meets your needs.

November 2013: We have recently developed a novel activity coefficient model for multicomponent solutions, based upon an adsorption isotherm (Dutcher et al., 2013). This model can be applied over the entire concentration range, to zero water activity (0% equilibrium relative humidity). Custom Excel executable files for some simple example systems at 25 °C can be made available to interested users, upon request to Cari Dutcher.


C. S. Dutcher, X. Ge, A. S. Wexler, and S. L. Clegg (2013) An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range. J. Phys. Chem. A 117, 3198-3213.

August 2013: Videos which demonstrate the most important elements of E-AIM, including the use of organic compounds in calculations, have been added to the website. All sixteen videos have captions which explain what is being shown, and there are sets of instructions to enable users to duplicate the demonstrations.

The videos are organised by subject:

  1. Introduction  [1 video].
  2. Different Types of Calculation (Normal Output)  [5 videos].
  3. Column and Graphical Output of Results, Using Deliquescence as an Example  [4 videos].
  4. Selecting and Creating Organic Compounds  [3 videos].
  5. Calculations that Include Organic Compounds  [2 videos].
  6. Website Help  [1 video].

The link to the videos is on the home page, under "Information". The videos complement the existing E-AIM tutorials, which show how to calculate the thermodynamic properties of inorganic systems under different conditions, and how to interpret the model results.

July 2013: Densities of aqueous solutions of five aminium sulphates (monomethyl, dimethyl, trimethyl, diethyl, and triethyl) have recently been measured at room temperature by Clegg, Qiu and Zhang (2013). These densities have been incorporated into E-AIM so that, in calculations involving solutions containing the aminium ion(s) and SO42− ions, they are used in the estimation of the density of the aqueous phase. This is stated, for each individual sulphate, in the notes that follow the printed results for the aqueous and/or other liquid phase in the verbose (i.e., not column) output of all of models I to IV.

For other aminium cations E-AIM now uses fixed estimates of the apparent molar volumes of the ions, obtained from a correlation of literature values (for 25 °C) of apparent molar volumes at infinite dilution in water against molar mass.

Comparisons of measured and calculated growth factors in the same paper have confirmed that (NH4)2SO4 is a good analogue for the aminium sulphates in the calculation of water activities (equilibrium relative humidities) and activity coefficients. Our recent (unpublished) results have also shown that:

We have added parameters for surface tensions of aqueous dimethyl aminium sulphate [((CH3)2NH2)2SO4] to the model, based upon measurements by Hyvarinen et al. at room temperature (J. Chem. Eng. Data 49, 917-922, 2004). This means that activities, volume properties, and surface tensions can now be calculated by the model for the important ((CH3)2)NH2)2SO4 – H2SO4 – H2O system (although users should be aware of the limited data on which the model is based, and the fact that it is likely to be most accurate close to 25 °C).

This work is part of a project supported by the Electric Power Research Institute.


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.
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.

December 2012: Volume properties of aqueous solutions (densities, and apparent and partial molar volumes) can now be calculated by entering solute concentrations as molarities (i.e., mol dm−3) in addition to molalities (mol per kg of water) or weight percentages.

This means that concentrations can be converted from volume-based units (molarities) to mole- and mass-based units (molalities and weight percentages), and vice versa.

March 2012: The model now includes the formation of solid aminium (i.e., amine cation) nitrate, sulphate, and chloride salts. Also, we have added vapour pressures, including their variation with temperature, to two of the dicarboxylic acids in the public database. Details are given below:


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.
F. D. Pope, H.-J. Tong, B. J. Dennis-Smither, P. T. Griffiths, S. L. Clegg, J. P. Reid, and R. A. Cox (2010) Studies of single aerosol particles containing malonic acid, glutaric acid, and their mixtures with sodium chloride. II. Liquid-state vapour pressures of the acids. J. Phys. Chem. A 114, 10156-10165.

November 2011: Several improvements and extensions have been made:


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.
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.

July 2011: The thermodynamic model of H+ - NH4+ - Na+ - SO42− - NO3 - Cl - H2O mixtures developed by Friese and Ebel (2010) has been added to the website as Model IV. It can be used from 180 to 330 K for mixtures of the same compositions as for Models I and II, and is valid from 263.15 K to 330 K for mixtures that also contain Na+, or both NH4+ and Cl. See the model description (and the help associated with each problem input page) for details.

The set of data input pages, and the types of calculation that can be carried out with Model IV, are the same as those for the other models. We are grateful for Elmar Friese's help in implementing and checking the model.


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.

December 2010: A revision has been made to the vapour pressure prediction method of Moller et al. (2008), which is used on this site. The changes affect molecules that contain multiple polar functional groups, and the interactions between these groups, and improve predictions of vapour pressure. A letter describing these changes will be submitted to the Journal of Molecular Liquids.


B. Moller, J. Rarey, and D. Ramjugernath (2008) Estimation of the vapour pressure of non-electrolyte organic compounds via group contributions and group interactions. J. Molecular Liquids 143, 53-63.

October 2010: Several improvements and extensions have been made:


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.

June 2010: Density models for the following systems have been added to the site:

These models yield apparent and partial molar volumes of the solution components as well as density. They combine high accuracy in the normal liquid range (and for temperatures above 273.15 K) with reasonable extrapolations to highly supersaturated and/or supercooled conditions. They will be integrated into the main equilibrium partitioning models (Models I to III) during 2010. See the density pages for details of the papers describing these models.

January 2010: An activity model of the system H+ - NH4+ - Na+ - K+ - Ca2+ - Mg2+ - SO42− - NO3 - Cl - CO32− - OH - H2O  at 298.15 K has been added to the site, and can be accessed from a link on the home page. This model can be used to calculate aqueous phase dissociation equilibria (including those of the carbonate system), equilibrium partial pressures of the gases HNO3, HCl, CO2, H2SO4 and NH3, and degrees of saturation of aqueous solutions with respect to over 50 solids.

The model is based on that described by Harvie, Moller, and Weare (Geochim. et. Cosmochim. Acta 48, 723-751, 1984), with the ions NH4+ and NO3 added by us. It has been developed with the support of the ACCENT project (an EC 6th Framework Programme).

October 2009: The E-AIM vapour pressure calculator page now includes predictions made by both the Moller et al. equation (J. Molecular Liquids 143, 53-63, 2008) and the earlier work of Nannoolal et al. from the same group (Fluid Phase Equilibria 269, 117-133, 2008). The latter method is recommended in a critical review of prediction methods, published in Atmospheric Chemistry and Physics. Inconsistencies in the method of Moller et al. that were identified in the critical review have now been rectified.

March 2009: On the E-AIM vapour pressure calculator page users can now enter the boiling point of the organic compound, as an alternative to the two estimation methods provided. (A value of the boiling point is required for predicting vapour pressures of the compound at other temperatures.) This facility is useful for carrying out sensitivity studies, and for compounds with known boiling points. We have noted, for example, that the methods for estimating boiling points yield values for some dicarboxylic acids that are too high. Improved predictions of the vapour pressures can now be obtained by entering measured boiling points.

February 2009: We have added to the E-AIM home page a description of how to implement web interfaces for Fortran computer models. This explains – with a couple of very simple and easy-to-code examples – how E-AIM is called from the web pages, and how it writes results to the user's browser. We provide this information, and other guidance, to encourage others to make their own applications available on the web in the same way.

December 2008: Several improvements have been made this month:

July 2008: Both Batch and Parametric calculations (in which T, RH and chemical composition are varied across a range of values) can now include organic compounds in addition to inorganic ions. The organic compounds can either be chosen from a small library that is provided, or users can create their own compounds, in the same way as for the other types of calculations.

The graph-plotting capabilities of the site have been revised, and 'column output' of results has been improved.

March 2008: The three models on this site can now include organic compounds in addition to inorganic ions. The organic compounds can either be chosen from a small library that is provided, or users can create their own compounds and define their thermodynamic properties. Users can register with the site, and save their compounds (on the E-AIM servers) for later use.

The organic compounds can be included in the following types of problem, for Models I-III: "simple", "comprehensive", and "aqueous solution and liquid mixture". Please note: for "batch" and "parametric" calculations the models currently treat inorganic systems only, using the previous version of AIM. Read the quick start guide for details of the E-AIM models and how to use them.

The original version of the model is still available, at the following address: http://www.aim.env.uea.ac.uk/aim-old/aim.htm.

Tabulations of thermodynamic data for aqueous solutions containing H2SO4, (NH4)2SO4, and NH4NO3 have been added to the website and are accessible from the home page. These data, on which the inorganic component of the E-AIM model is based, have been compiled with the support of the ACCENT project (an EC 6th Framework Programme). Data for other inorganic electrolytes will follow in the future.

March 2006: Tabulations of thermodynamic data for aqueous solutions containing dicarboxylic acids, and an online activity coefficient calculator, are now accessible from the AIM home page. Data were compiled for the following acids and their mixtures with salts: oxalic, malonic, succinic, glutaric, malic, maleic and methylsuccinic. This work was supported by the ACCENT project (an EC 6th Framework Programme).

March 2005: Both Comment and Response regarding the paper of Knopf et al. (February 2004 news, below) have now been published. See J. Phys. Chem. A 109, 2703-2709 (DOI: 10.1021/jp0401170 and 10.1021/jp040300t).

February 2005: The thermodynamic data for aqueous solution mixtures that form the basis of the AIM models have been tabulated, and are accessible from the AIM home page. This compilation of data, for ternary aqueous mixtures of the inorganic ions in AIM models I, II, and III, has been supported by the ACCENT project (an EC 6th Framework Programme).

February 2004: Recently, D. A. Knopf et al. have measured degrees of dissociation of H2SO4 in aqueous solution at low temperature, and developed a thermodynamic model of the system (J. Phys. Chem. A 107, 4322-4332 (2003)). The authors compare predicted water activities and H2SO4 activity coefficients with results from the AIM model, and find large differences. In a Comment submitted to the Journal of Physical Chemistry we compare both models with the best available thermodynamic information. The results (i) confirm the accuracy of AIM for activity and phase equilibrium calculations; (ii) show that for applications in which the degree of dissociation of the bisulphate ion is of interest then the experimental data should be consulted directly.

View the submitted Comment as a Word document, or as a pdf file. (March 2005: both Comment and Response have now been published.)

February 2003: The thermodynamic basis of the AIM models, their capabilities, and the way they are solved to determine equilibrium, is described in the following published paper: A. S. Wexler and S. L. Clegg (2002), Atmospheric aerosol models for systems including the ions H, NH4, Na, SO4, NO3, Cl, Br, and H2O, J. Geophys. Res. 107, No. D14, art. no. 4207, 14 pages.

July 2001: A set of nine tutorials has been added to the AIM web site in order to teach the use of the model and the interpretation of results. Subjects covered include an explanation of the output of the model, the properties (activities, water uptake) of single salt and mixed solutions, deliquescence behaviour, and gas/aerosol partitioning of volatile compounds.

February 2001: The treatment of HBr solubility in water and H2SO4 solutions in Model I has been revised. The parameterisation given in the paper of Massucci et al. (1999) fits satisfactorily the available equilibrium partial pressure and HBr uptake data for aqueous HBr/H2SO4 and H2SO4 solutions (see their Figures 25 and 26). This is the parameterisation that has been used in the model since July 1998. However, it was recently found that the trend in effective Henry's law constant (H*, equal to mBr/pHBr) with HBr molality was incorrectly predicted by the model. Calculated values of H* for trace HBr concentrations in less than about 60 wt% H2SO4 were too low because of this. The error has now been rectified, and we have taken the opportunity to include the recent measurements of Kleffmann et al. (2000) in the data set used for parameterisation. The updated model, now implemented on this web site, is primarily intended for applications at temperatures less than or equal to 298.15 K and HBr molalities of up to a few mol kg-1.

The change in the calculated solubility of HBr in pure water is due to a revision to the heat capacity change for the Henry's law reaction (terms a and b in equation (19) of Carslaw et al. (1995)). This adjustment was made in order to obtain better agreement with the available data for HBr/H2SO4/H2O solutions, and is only significant at low temperatures.

We would like to thank Leah R. Williams for bringing the problem to our attention.


K. S. Carslaw, S. L. Clegg and P. Brimblecombe (1995) J. Phys. Chem. 99, 11557-11574.
M. Massucci, S. L. Clegg and P. Brimblecombe (1999) J. Phys. Chem. A 103, 4209-4226.
J. Kleffmann, K. H. Becker, R. Broske, D. Rothe and P. Wiesen (2000) J. Phys. Chem. A 104, 8489-8495.

September 2000: Graph plotting for "batch" and "parametric" calculations has now been added. Graphs are displayed on the screen (your browser needs to be able to display frames), and are also downloadable as encapsulated postscript files.

The web site has also been moved to a faster machine, so response times should improve. For now, users will be redirected to the new site automatically, but should note the new URL: http://www.aim.env.uea.ac.uk/aim.html.

April 2000: A facility to carry out parametric calculations has been added for all models. This enables multiple calculations to be carried out over user-specified ranges of conditions. The following properties can be varied: (1) relative humidity or total atmospheric water content; (2) temperature; (3) ionic composition; (4) atmospheric pressure, assuming adiabatic movement of the air parcel containing the aerosol.

Although the option to plot graphs of results has been added to many of the input pages, this has not been enabled yet. We will add this capability over the coming months.

August 1999(a): The formation of solids is now enabled in the "Aqueous Solution" type calculations for all models. (It can also be switched off for each solid individually, in the usual way, to investigate the properties of supersaturated solutions.) The solid HNO3 · 2H2O is now included in models I and II for "Aqueous Solution" calculations (see news for October 1998 below).

August 1999(b): A facility to carry out batch calculations, for up to 100 problems at a time, has been added for all models. Data should be prepared according to the instructions given, and then pasted into the text boxes on the input pages for the models.

October 1998: Models I and II have been updated to include the formation of the solid nitric acid dihydrate (HNO3 · 2H2O), based upon data yielding the saturation curve in aqueous HNO3, and the vapour pressure product of HNO3 and H2O over the solid at very low temperatures. Note that the solid has so far been enabled only for the "Simple" and "Comprehensive" type calculations, pending further improvements to the web site. Results from the following papers were used:


L. E. Fox, D. R. Worsnop, M. S. Zahniser, S. C. Wofsy (1995) Science 267, 351-355.
D. R. Hanson, A. R. Ravishankara (1993) J. Geophys. Res. 98, 22931-22936.
K. Ji, J. C. Petit, P. Negrier, Y. Haget (1993) C. R. Acad. Sci. 316, Ser. II, 1743-1748.
D. R. Worsnop, L. E. Fox, M. S. Zahniser, S. C. Wofsy (1993) Science 259, 71-74.

July 1998(a): Facilities for comprehensive calculations have been added for models I - III, and can be accessed from the main page for each model. Using this new method of calculation it is now possible to equilibrate a chemical system within a fixed volume (1 m3) of atmosphere, including the partitioning of water and trace gases between condensed and vapour phases.

July 1998(b): Model I has been updated for HBr, based on recent data for HBr solubility in aqueous H2SO4. The measurements from the different groups agree well, and the model represents the combined data essentially to within the experimental uncertainty. Results from the following papers were used:


J. P. D. Abbatt (1995) J. Geophys. Res. 100, 14009-14017.
J. P. D. Abbatt, J. B. Nowak (1997) J. Phys. Chem. 101, 2131-2137.
W. Gestrich, C. Kottek, D. van Velzen, H. Langenkamp (1984) Chem. Ing. Tech. 56, Nr. 3, 252-253.
J. K. Klassen, Z. Hu, L. R. Williams (1998) J. Geophys. Res. 103, 16197-16202.
C. E. L. Myhre, C. J. Nielsen, O. W. Saastad (1998) J. Chem. Eng. Data 43, 617-622.
L. R. Williams, D. M. Golden, D. L. Huestis (1995) J. Geophys. Res. 100, 7329-7335.
L. R. Williams, F. S. Long (1995) J. Phys. Chem. 99, 3748-3751.