Iodine and carbonate species are important components in marine and dust aerosols, respectively. The non-ideal interactions between these species
and other inorganic and organic compounds within aqueous particle phases affect hygroscopicity, acidity, and gas–particle partitioning of
semivolatile components. In this work, we present an extended version of the Aerosol Inorganic–Organic Mixtures Functional groups Activity
Coefficients (AIOMFAC) model by incorporating the ions
The fitted AIOMFAC model performance for inorganic aqueous systems is considered excellent over the whole range of mixture compositions where
reference data are available. Moreover, the model provides physically meaningful predictions of water activity under highly concentrated
conditions. For organic–inorganic mixtures involving new species, the model–measurement agreement is found to be good in most cases, especially at
equilibrium relative humidities above
Atmospheric aerosols constitute a wide range of organic compounds, inorganic salts or acids, and water
Historically, a Pitzer-based approach has been shown to describe the thermodynamics in aqueous electrolyte solutions very well up to high ionic
strength (i.e., 10 mol kg
The abundance of iodine species in atmospheric aerosols is generally very small in the range from
Dust storms have various environmental impacts and are important sources of tropospheric aerosols
In previous work,
The degree of non-ideality in a multicomponent system is represented by the activity coefficients of all components within the system's (liquid)
phases. To describe the concentration of each constituent in a system, mole fraction,
The deviation from mixing ideality within a thermodynamic system is characterized by the Gibbs excess energy (
Physical properties of the new ions introduced in the study.
Here, the subscripts
To obtain the relevant parameters, an objective function is derived to allow the direct comparison between experimental data and model
calculations. The objective function, subject to minimization during the simultaneous fitting process concerning parameters for either a cation–anion
pair or ion–organic main group, is
Here,
As described previously by
For the mixture of inorganic iodide (
Experiment temperature (
Continued.
In terms of organic compounds and their interaction with iodides, several groups
Data summary of iodide salts mixed with organic compounds and thereby various organic main groups in aqueous solutions (unless specified otherwise).
In the past, measurements involving methanol were generally excluded from the AIOMFAC parameter optimization procedure. Being the shortest chain
alcohol, methanol tends to behave differently than a simple extrapolation from longer-chain alcohols would suggest (e.g., well known for saturation
vapor pressures
In the presence of carbonic acid, there are four relevant equilibria to consider:
Unlike aqueous sulfuric acid, whose first dissociation step is essentially complete
A thermodynamic equilibrium constant can be expressed as
Parameterization of the temperature-dependent equilibrium constants for the aqueous dissociation equilibria (Reactions
Constants
Here,
The
To ensure that a complete neutralization of the cumulative positive charges of cations is possible,
The equilibrium constant expressions for
In a system of
In the presence of both dissolved carbonic acid and sulfuric acid, the bisulfate ion needs to be accounted for when the maximum possible molar amount
of
One additional equilibrium relationship to account for the incomplete bisulfate dissociation is solved simultaneously with
Reactions (
After an equilibrium composition has been established for a given input of mixture components, the acidity (pH) of the solution can be calculated as
Some input compositions require additional considerations for meaningful calculations. For example, most computations outlined above are carried out
assuming that all components are mixed in a liquid phase and the potential precipitation of crystalline solids (e.g., salts) is ignored (i.e.,
metastable, supersaturated salt solutions allowed) unless specific solid–liquid equilibria are targeted. However, there is one exception: when
Summary of
The Extended Aerosol Inorganics Model (E-AIM) is a thermodynamic model that calculates various equilibria between water and inorganic species. The
specific E-AIM subset referenced in this study was developed by
The Simulating Composition of Atmospheric Particles at Equilibrium (SCAPE 2) model is an atmospheric gas–aerosol equilibrium model. It covers ions
Experiment temperature (
Continued.
Different data types, including measurements of water activity (
The electromotive force (EMF) method is used to determine the mean activity coefficients of an electrolyte at known concentration. By measuring the
electric potential difference between two different electrodes in an electrochemical cell, the mean activity coefficients are derived from the
modified Nernst equation and the use of a system-specific thermodynamic model
Coefficients for the Duhem–Margules excess Gibbs energy model
Coefficients and model expressions are as those of
We use a mixture-specific fit of a Duhem–Margules model
Finally, the SLE data report the liquid phase composition when in equilibrium with a specific solid (crystalline) phase. Under isothermal conditions, the solubility limit of the electrolyte or the organic compound is measured for different mixing compositions. At equilibrium, the liquid phase activity of the organic (if it is the solid) or the molal ion activity product of the electrolyte (for a salt as solid) should be at a constant value (for constant temperature), while the liquid phase concentration may vary (for ternary and higher mixtures). Therefore, the use of SLE data involves the comparison of the solution mass fractions predicted by AIOMFAC after solving for SLE with those from the measurements.
Due to the general lack of experimental data for mixtures of iodide, iodate, or carbonate electrolytes with organic compounds, alternative methods
were adopted for the determination of AIOMFAC interaction parameters between those ions and the organic main groups. A linear regression analysis is
chosen to have a broader coverage of the interaction parameters for
Because there is no thermodynamic data for the mixture of iodate electrolytes with organic compounds, we make the crude estimation of the interaction
parameters for
Since the main type of experimental data covering the mixture of carbonate salts
Revised AIOMFAC interaction matrix indicating available and missing binary interaction parameters. Parameters available based on regression analysis are depicted by symbol (
In short, methods like those described in this section can be adopted as a first-order estimation approach for interactions lacking support by
high-quality experimental data for a more sophisticated model parameter determination. The updated AIOMFAC group interaction matrix indicating all
available binary interactions in the model is shown in Fig
Using the outlined optimization procedure in Sect.
Determined middle-range interaction parameters between cation–anion pairs for iodide and iodate electrolytes
Water activities and mean molal activity coefficients of the electrolytes in binary aqueous iodide solutions near 298.15
Given the lack of reliable aqueous iodate solution data, especially at the concentrated range, aqueous
Water activities and mean molal ion activity coefficients of the electrolytes in binary aqueous iodate solutions at room temperature. Symbols: experimental data (see legend); solid blue and dashed red curves: fitted AIOMFAC model.
The resulting parameters of the model optimization for
Determined middle-range interaction parameters
Organic compounds such as carboxylic acids contribute a large fraction of the water-soluble organic aerosol mass, including in marine environments
Water activities of
Figure
Different types of experimental data (
The determination of interactions for
The complete set of middle-range interaction parameters involving carbonic acid and salts is listed in Table
Determined middle-range interaction parameters between cation–anion pairs in aqueous carbonate electrolytes
Experimental or reference model data (symbols) and AIOMFAC predictions (curves) of water activity and mean molal activity coefficients of the carbonate electrolytes
Analogous to the treatment of iodine salts, all carbonate salts are assumed to be completely dissociated (in the absence of significant amounts of
bicarbonate). As shown in Fig.
Figure
Experimental or reference (symbols) and AIOMFAC predictions (curves) of water activity and dissociation degree of
The agreement between AIOMFAC predictions and the experimental data from
Compared to the E-AIM online model for carbonate systems, which reports an error due to the exceedance of the supported input ion molalities, AIOMFAC
is still able to solve the system of equations using the constraints on the equilibria at higher input concentrations of electrolytes. However, unlike
the cases for other aqueous solutions of inorganic electrolytes for which AIOMFAC is able to perform well at very high ionic strengths, the validity
in systems involving bicarbonate electrolytes becomes numerically limited to some degree. This is the case because the three equilibria and the mass
balance equations have to be fulfilled simultaneously; it becomes numerically challenging to solve the system of equations reliably for highly
concentrated conditions. Furthermore, the high partial pressure of
Experimental or reference (symbols) and AIOMFAC predictions (curves) of water activity and degree of dissociation of
Figure
One might argue that the closed-system scenario is unlikely to occur in the real atmosphere when water activity or relative humidity is below a certain threshold; however, the consideration of such cases is to fit the AIOMFAC interaction parameters between cations and carbonate/bicarbonate ions following the same method as E-AIM and SCAPE 2 (i.e., a closed-system treatment).
We further performed a set of calculation scenarios for an open system, in which
Open-system scenario with constant partial pressure of
Unlike E-AIM, which makes the auto-dissociation of water a default equilibrium reaction to solve in the presence of carbonic acid, we implemented the
option of including/excluding it to accommodate solving a simpler set of equations for systems/cases in which this reaction can be neglected. When
consideration of the water dissociation process is switched off, there is one variable less (
Comparison of calculated pH for the same input solution compositions but with (
In the special occasion when both sulfuric and carbonic acids are present in a solution, the incomplete dissociation of the
E-AIM (symbols) and AIOMFAC predictions (curves) of water activity for an aqueous solution containing
Analogous to the treatment discussed in Sect.
As discussed in Sect.
Comparison of experimental data (
The correlation coefficients
Comparison of AIOMFAC predictions of water activity and mean molal activity coefficients at 298.15
Since no experimental data are available to determine the interaction parameters for iodate and main organic groups, aqueous solutions with different
anions were compared to those with iodate to find the best substitution anion of iodate. Figure
For the same reason, aqueous
Experimental (
Based on the analogy approach, the parameters for organic main groups interacting with
The hygroscopic growth behavior and cloud droplet activation ability of aerosol particles are two (among many) important composition-dependent
properties of ambient particles. These properties are directly dependent on the mixing and gas/liquid/solid phase equilibrium thermodynamics of
aerosols
With the newly implemented parameters describing the interactions between aqueous iodine or carbonate electrolytes and organic compounds, the AIOMFAC
model is capable of predicting the mixing behavior within aerosol phases containing these species (among many others). Furthermore, while the
uncertainty of parameters determined using the substitution method might be relatively large, such method adoption allows for the completion of
AIOMFAC's interaction parameter matrix (Fig.
Recent measurements have shown different soluble iodine speciation in fine-mode and coarse-mode aerosol particles
We also show that if an aerosol particle is composed of both bicarbonate and bisulfate, at equilibrium, the effects of sulfate are mostly dominating
over carbonate as shown in Fig.
A key atmospheric impact of fine- and ultrafine-mode aerosol particles stems from their ability to act as cloud condensation nuclei. The number–size
distribution and hygroscopic properties of sufficiently large aerosol particles impact cloud droplet number concentrations during cloud formation,
ensuing cloud microphysics and aerosol–cloud–radiation effects
Based on the introduced AIOMFAC model extension, thermodynamic CCN activation calculations for systems containing iodine or carbonate species are now
possible. This includes computations of Köhler curves and associated CCN activation properties for sodium iodide or sodium carbonate particles
mixed/coated with suberic acid at 293
AIOMFAC predictions of the critical supersaturation for CCN activation,
Comparison of critical supersaturation (
As stated previously, the parameters for
Notwithstanding the remaining challenges in modeling CCN activation properties of rather peculiar systems (such as those of Fig.
The latest extension of the AIOMFAC model, developed and introduced in this work, adds the ions
During the simultaneous fitting of AIOMFAC cation–anion and ion–organic main group interaction parameters, numerous experimental datasets were
accessed and compared with the model predictions. The agreement between AIOMFAC calculations and the majority of experiments ranges from satisfactory
to excellent. Relatively large deviation exists in some cases, for which we discussed potential reasons related to the use of a group-contribution
method. Due to the lack of experimental data covering certain aqueous cation–iodate systems, as well as the interactions of the newly introduced ions
with several organic functional groups, alternative approaches for parameter estimation were explored. Among those approaches are the use of linear
regression to determine iodide ion interactions with certain organic functional groups based on the interaction coefficients of a set of other ions
with those groups. Adoption of such methods in practice means that we were able to provide estimates for model parameters describing most of the
possible binary interactions involving the new species. This is considered very useful to close otherwise existing gaps in the model's interaction
matrix (Fig.
As an example of an application of AIOMFAC using the newly determined interaction parameters, we computed the critical supersaturation as a function
of dry particle size and organic fraction for suberic-acid-coated salt particles. The AIOMFAC predictions of
The source code of AIOMFAC is available as part of the AIOMFAC-web model code repository (version 3.00) on GitHub (
The supplement related to this article is available online at:
AZ conceptualized the project. HY and AZ developed the methodology, evaluated the data, and wrote the software. HY carried out a part of the water activity measurements at McGill University with the assistance of AB, BJW, and TCP. JD, LK, and UKK performed the EDB and water activity measurements at ETH Zurich. HY analyzed the data and created the visualizations. HY wrote the manuscript with contributions from all co-authors.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This project was undertaken with the financial support of the Government of Canada through the federal Department of Environment and Climate Change (ECCC). Liviana Klein acknowledges funding support by the Swiss National Science Foundation (SNSF).
This research has been supported by the Fonds de recherche du Québec – Nature et technologies (grant no. PR-286433), the Natural Sciences and Engineering Research Council of Canada (grant nos. RGPIN-2014-04315 and RGPIN-2021-02688), the Government of Canada through the federal Department of Environment and Climate Change (grant no. GCXE20S049), and the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. CRSII5-189939).
This paper was edited by James Allan and reviewed by two anonymous referees.