Improved AIOMFAC model parameterisation of the temperature dependence of activity coefficients for aqueous organic mixtures

This study presents a new, improved parameterisation of the temperature dependence of activity coefficients in the AIOMFAC (Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients) model applicable for aqueous as well as water-free organic solutions. For electrolyte-free organic and organic–water mixtures the AIOMFAC model uses a group-contribution approach based on UNIFAC (UNIversal quasi-chemical Functional-group Activity Coefficients). This group-contribution approach explicitly accounts for interactions among organic functional groups and between organic functional groups and water. The previous AIOMFAC version uses a simple parameterisation of the temperature dependence of activity coefficients, aimed to be applicable in the temperature range from ∼ 275 to ∼ 400 K. With the goal to improve the description of a wide variety of organic compounds found in atmospheric aerosols, we extend the AIOMFAC parameterisation for the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon to atmospherically relevant low temperatures. To this end we introduce a new parameterisation for the temperature dependence. The improved temperature dependence parameterisation is derived from classical thermodynamic theory by describing effects from changes in molar enthalpy and heat capacity of a multi-component system. Thermodynamic equilibrium data of aqueous organic and water-free organic mixtures from the literature are carefully assessed and complemented with new measurements to establish a comprehensive database, covering a wide temperature range (∼ 190 to ∼ 440 K) for many of the functional group combinations considered. Different experimental data types and their processing for the estimation of AIOMFAC model parameters are discussed. The new AIOMFAC parameterisation for the temperature dependence of activity coefficients from low to high temperatures shows an overall improvement of 28 % in comparison to the previous model version, when both versions are compared to our database of experimentally determined activity coefficients and related thermodynamic data. When comparing the previous and new AIOMFAC model parameterisations to the subsets of experimental data with all temperatures below 274 K or all temperatures above 322 K (i.e. outside a 25 K margin of the reference temperature of 298 K), applying the new parameterisation leads to 37 % improvement in each of the two temperature ranges considered. The new parameterisation of AIOMFAC agrees well with a large number of experimental data sets. Larger model–measurement discrepancies were found particularly for some of the systems containing multi-functional organic compounds. The affected systems were typically also poorly represented at room temperature and further improvements will be necessary to achieve better performance of AIOMFAC in these cases (assuming the experimental data are reliable). The performance of the AIOMFAC parameterisation is typically better for systems containing relatively small organic compounds and larger deviations may occur in mixtures where molecules of high structural complexity such as highly oxygenated compounds or molecules of high molecular mass (e.g. oligomers) prevail. Nevertheless, the new parameterisation enables the calculation of activity coefficients for a wide variety of different aqueous/water-free organic Published by Copernicus Publications on behalf of the European Geosciences Union. 448 G. Ganbavale et al.: Improved parameterisation of the AIOMFAC model solutions down to the low temperatures present in the upper troposphere.

∼ 400 K. With the goal to improve the description of a wide variety of organic compounds found in atmospheric aerosols, we extend the AIOMFAC parameterisation for the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon to atmospherically relevant low temperatures. To this end we introduce a new parameterisation for the temperature dependence. The improved temperature dependence parameterisation is derived from classical thermodynamic theory by describing effects from changes in molar enthalpy and heat capacity of a multi-component system. Thermodynamic equilibrium data of aqueous organic and water-free organic mixtures from the literature are carefully assessed and complemented with new measurements to establish a comprehensive database, covering a wide temperature range (∼ 190 to ∼ 440 K) for many of the functional group com-binations considered. Different experimental data types and their processing for the estimation of AIOMFAC model parameters are discussed. The new AIOMFAC parameterisation for the temperature dependence of activity coefficients from low to high temperatures shows an overall improvement of 28 % in comparison to the previous model version, when both versions are compared to our database of experimentally determined activity coefficients and related thermodynamic data. When comparing the previous and new AIOM-FAC model parameterisations to the subsets of experimental data with all temperatures below 274 K or all temperatures above 322 K (i.e. outside a 25 K margin of the reference temperature of 298 K), applying the new parameterisation leads to 37 % improvement in each of the two temperature ranges considered. The new parameterisation of AIOMFAC agrees well with a large number of experimental data sets. Larger model-measurement discrepancies were found particularly for some of the systems containing multi-functional organic compounds. The affected systems were typically also poorly represented at room temperature and further improvements will be necessary to achieve better performance of AIOM-FAC in these cases (assuming the experimental data are reliable). The performance of the AIOMFAC parameterisation is typically better for systems containing relatively small organic compounds and larger deviations may occur in mixtures where molecules of high structural complexity such as highly oxygenated compounds or molecules of high molecular mass (e.g. oligomers) prevail. Nevertheless, the new parameterisation enables the calculation of activity coefficients for a wide variety of different aqueous/water-free organic

Introduction
Atmospheric aerosols are complex mixtures of inorganic and organic components. A large variety of organic compounds account for a significant fraction of the tropospheric aerosol composition. Airborne and ground-based measurements suggest that the aerosols in the free troposphere are composed of ∼ 30 % up to about ∼ 80 % of carbonaceous material mostly in the form of organics (Murphy et al., 2006;Jacobson et al., 2000;Hallquist et al., 2009). Aerosol loading, size distribution, composition, morphology and physical states of particles affect the Earth's radiative budget through the direct effects of aerosols on climate and the indirect effects, in which aerosols act as cloud condensation (CCN) or ice nuclei (IN), affecting cloud particle number concentrations, precipitation, cloud albedo, and lifetime (Lohmann et al., 2005). Organic aerosols are expected to stay in a liquid, viscous semi-solid, or amorphous solid state, since the very large number of organic compounds depresses the temperature at which organic crystal formation takes place (Marcolli et al., 2004;Virtanen et al., 2010;Koop et al., 2011).
Non-ideal interactions between different organic and inorganic species in the particle phase influence water uptake and release (hygroscopicity), may induce liquid-liquid phase separation (LLPS) (e.g. Marcolli and Krieger, 2006;Zuend et al., 2010;Song et al., 2012), influence gas-particle partitioning of semivolatile compounds (e.g. Zuend et al., 2010;Zuend and Seinfeld, 2012), and alter efflorescence and deliquescence relative humidities (e.g. Krieger et al., 2012). Thermodynamic phase equilibrium calculations allow to determine whether the aerosol phase is a liquid (here liquid also refers to a homogeneous, yet potentially highly viscous amorphous phase), a crystalline solid, or a mixture of solid and liquid phases (when assumption of equilibrium is appropriate) and to what degree semivolatile species partition to the condensed phases (Pankow, 2003;Zuend et al., 2010;Zuend and Seinfeld, 2012;Shiraiwa et al., 2013). Furthermore, if the formation of crystalline phases is ignored intentionally in such calculations, metastable equilibria between the gas phase and supersaturated liquid solutions can be predicted. Phase equilibria calculations can be carried out by using composition dependent activity coefficients which account for the non-ideality of the liquid/amorphous phase (Gmehling, 1995;Raatikainen and Laaksonen, 2005;Zuend et al., 2010). The mole fraction based activity coefficient, γ Thermodynamic models for mixtures of organics and water in condensed phases are usually based on the UNIQUAC (UNIversal QUAsi Chemical) model (Abrams and Prausnitz, 1975) or its group contribution version UNIFAC (UNIquac Functional group Activity Coefficients) (Fredenslund et al., 1975). The original UNIFAC model was developed for vapour-liquid equilibria (VLE) calculations within a temperature range from ∼ 275 to ∼ 400 K. Using the UNIFAC model outside of its intended temperature range may result in poor predictions of real phase behaviour (Lohmann et al., 2001). For very dilute mixtures, UNIFAC thermodynamic model calculations for component activity coefficients at infinite dilution are sometimes not in agreement with the experimental data. This can be understood since most VLE measurements were performed for liquid mole fractions between 0.02 to 0.98 and, hence, do not provide specific information for the highly dilute regions (Compernolle and Müller, 2014). Inaccurate results were obtained for other types of thermodynamic data, e.g. molar enthalpies of mixing (h E ) or solid-liquid equilibrium (SLE) data. Following the Gibbs-Helmholtz relation, this leads to inaccurate description of activity coefficients as a function of temperature (Lohmann et al., 2001;Gmehling, 2003Gmehling, , 2009. With the original UNIFAC model, due to data insufficiency, inaccurate predictions were often obtained for asymmetric systems (systems containing molecules of different sizes and shapes) (Lohmann et al., 2001;Gmehling, 2003). Since then, the original UNIFAC model has been improved and in addition, modified UNIFAC versions such as modified UNIFAC (Dortmund) and modified UNIFAC (Lyngby) have been developed (Larsen et al., 1987;Hansen et al., 1991;Gmehling et al., , 2002Jakob et al., 2006), which amended some of the original weaknesses. For mixtures containing multifunctional components, both UNIFAC and modified UNI-FAC (Dortmund) sometimes show poor results since the functional group interaction parameters were mainly determined based on experimental data of mixtures of simple, monofunctional components (Weidlich and Gmehling, 1987;Gmehling et al., 2012).
One of the important differences between the UNIFAC model by Hansen et al. (1991), which we call here "standard UNIFAC", and the modified UNIFAC (Dortmund), is the use of a more elaborate parameterisation for the temperature dependence of activity coefficients in the modified UNI-FAC (Dortmund) model. However, the modified UNIFAC models still may not provide reliable predictions of activity coefficients at low temperatures relevant in the troposphere. Calculations of water activity (a w ) of atmospherically relevant aqueous organic solutions have shown that the performance of standard UNIFAC may be poor when the organic fraction consists of multi-functional molecules typically carrying several strong polar functional groups with enhanced hydrogen-bonding potential (Saxena and Hildemann, 1997;Peng et al., 2001). Marcolli and Peter (2005) have therefore proposed improved sets of interaction parameters for standard UNIFAC for alcohols and polyols. Peng et al. (2001) re-parameterised the interaction of the water (group) with the Atmos. Chem. Phys., 15, 447-493, 2015 www.atmos-chem-phys.net/15/447/2015/ carboxyl group and the hydroxyl group based on measured water activities of aqueous systems containing dicarboxylic acids and substituted dicarboxylic and tricarboxylic acids. For atmospheric applications, an accurate description of aqueous organic mixtures at atmospherically relevant temperatures is required. At low temperatures a w is a crucial parameter for homogeneous ice nucleation (Koop et al., 2000). Extrapolations of a w of different aqueous organic solutions measured in the temperature range from the ice melting curve to 313 K suggest that if the temperature dependence of the activity coefficients is neglected, errors on the order of 10 to 15 % result for a w at the homogeneous freezing temperature (Zobrist et al., 2008). The uncertainty in predicted homogeneous ice nucleation temperatures is stated as ±0.025 in a w (absolute uncertainties in a w ) in case of most of the data at higher temperature and ±0.05 in a w for all data collected at ice freezing temperatures (Koop et al., 2000;Koop, 2004). A small uncertainty in a w of about 0.025 can change the corresponding homogeneous nucleation rate coefficients by 6 orders of magnitude and may significantly affect predictions of the onset of ice crystal formation in cloud microphysical models (Knopf and Rigg, 2011;Alpert et al., 2011). This shows the need for an improved UNIFAC (and AIOMFAC) parameterisation at low temperatures. In addition, the new AIOMFAC parameterisation introduced in this work leads also to substantial improvements in activity coefficient calculations at temperatures significantly higher than room temperature, which is of interest for applications in other fields of science and engineering, such as distillation.

AIOMFAC model
The AIOMFAC model (Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients) by Zuend et al. (2008Zuend et al. ( , 2011) is a thermodynamic group-contribution model specifically developed to meet the requirements of typical tropospheric aerosol compositions. The model enables calculations of activity coefficients covering inorganic (water, electrolytes), organic, and organic-inorganic interactions in multi-component solutions over a wide concentration range. AIOMFAC is based on the group-contribution model LIFAC by Yan et al. (1999) and, therefore, includes the standard UNIFAC model, yet also includes the modified parameter sets from Peng et al. (2001) and those from Marcolli and Peter (2005). In its short-range interaction part, the AIOM-FAC model shares the simple temperature dependence expressions of the original UNIFAC model and involves only one main group interaction term involving two adjustable parameters, a m,n and a n,m per binary interaction (of groups m and n). Throughout this article, we will refer to this (original) AIOMFAC model as "AIOMFAC-P1". The aim of this study is to improve the performance of AIOMFAC at low temperatures for multi-component organic + water systems. We will refer to the new AIOMFAC version, with an im-proved temperature dependence parameterisation with two additional main group interaction terms, as AIOMFAC-P3, indicating a three-term parameterisation in the short-range (modified UNIFAC) part. The focus is on a list of major organic functional groups that have been identified in tropospheric aerosols, namely hydroxyl, carboxyl, ketone, ether, ester, aldehyde, alkyl, and aromatic functionalities. Given the focus on organic + water systems, this work does not address the temperature dependence of interaction terms related to inorganic electrolyte/ionic components included in AIOMFAC. A few organic functional groups that have been considered explicitly in the AIOMFAC model development in the past are not included in this work. The excluded organic functionalities are the following: hydroperoxide, peroxy acid peroxide, peroxyacyl nitrate, and organonitrate, all introduced in the AIOMFAC model by Zuend and Seinfeld (2012) based on work by Compernolle et al. (2009). Note that these functional groups are available in AIOMFAC, but on the basis of the AIOMFAC-P1 model parameterisation only.
The thermodynamic group-contribution model AIOMFAC allows thermodynamically consistent calculations of activity coefficients at temperatures close to 298 K and covers multicomponent solutions containing water, inorganic ions, and organic compounds. For electrolyte-free systems of organic compounds and water, the applicable temperature range is ∼ 275 to ∼ 400 K, as for the original UNIFAC model. An estimate for the appropriate temperature range of AIOMFAC, when in addition to organic compounds and water also dissolved inorganic ions are included, is 298 ± 10 K. However, due to a rather weak temperature dependence of activity coefficients in aqueous electrolyte solutions, for many mixtures, the AIOMFAC model may also be applicable in a wider temperature range to good approximation (also relative to other uncertainties associated with a group-contribution model prediction). As mentioned above, the concept of AIOMFAC is based on the LIFAC model (Yan et al., 1999), which merges a Pitzer-like approach with a slightly modified version of the original UNIFAC model to calculate activity coefficients.
The non-ideality of a thermodynamic system is characterised by the excess Gibbs energy G ex p, T , n j , which in AIOMFAC is expressed as the sum of long range (LR), middle range (MR) and short range (SR) contributions: Here, p is the total pressure, T the absolute temperature, and n j (j = 1, . . ., k) the molar amounts of the k components in a system. Mole fraction based activity coefficients γ  (3) Electrolyte solutions, which may range from dilute to highly supersaturated concentrations are, aside from their SR contribution, considered in the Pitzer-like part, which combines LR and MR interactions. The LR interactions are described by an extended Debye-Hückel term and represents contributions by Coulomb electrostatic forces between permanently charged ions, moderated by the presence of the dielectric solvent medium (e.g. a homogeneous mixture of water + organic compounds act as the solvent medium). The MR part represents the effects of interactions involving ions and permanent or induced dipoles and contains most of the adjustable parameters to describe concentrated aqueous electrolyte solutions and organic-inorganic mixtures. The original AIOMFAC model by Zuend et al. (2008) has been extended and re-parameterised to include organic-inorganic interactions of most of the functional groups typically present in atmospheric organic compounds (carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon) (Zuend et al., 2011). In addition, based on the approach and UNIFAC parameters determined by Compernolle et al. (2009), Zuend and Seinfeld (2012) introduced in AIOMFAC the functional groups hydroperoxide, peroxy acid, and peroxide, including estimated interaction parameters with the inorganic ions of the model. For further details of the thermodynamic description of the LR and MR interactions within the Pitzer-like part of AIOMFAC we refer to Zuend et al. (2008Zuend et al. ( , 2011. The interactions among noncharged species (organic molecules and water) are calculated in the SR part of AIOMFAC, see Sect. 2.2.

Group-contribution method
A group-contribution concept similar to the one in UNIFAC has been adopted for the AIOMFAC model. According to the group-contribution concept, it is assumed that the system (and its organic constituents) are composed of combinations of functional groups instead of whole molecule entities. The advantage of applying the group-contribution method is that a very large number of organic compounds can be defined using the various combinations of a limited number of functional groups. In accordance to the UNIFAC model, the functional groups are further classified into so-called main groups and subgroups for their application in different model parts (Fredenslund et al., 1975;Marcolli and Peter, 2005;Zuend et al., 2008Zuend et al., , 2011. The main groups cover subgroups of the same functionality that only differ by the number of hydrogen atoms. The subgroup classification of a variety of organic compounds can be found in Table 1.

Short-range contribution
As in the UNIFAC model, in the SR part of AIOMFAC, activity coefficients of a mixture component j are in general expressed as the sum of contributions of a combinatorial part (denoted by superscript C), which accounts for the size and shape of the molecule, and the residual part (denoted by superscript R), which reflects the residual contribution from intermolecular (inter-group) interactions (Fredenslund et al., 1975;Marcolli and Peter, 2005;Zuend et al., 2008).
The expression for the combinatorial part of UNIFAC is (Fredenslund et al., 1975;Zuend et al., 2008): and In these equations, x j is the mole fraction of component j , and ν (j ) t denotes the number of subgroups of type t present in a formula unit of component j . The relative van der Waals subgroup volume and surface area are given by R t and Q t , respectively. The lattice coordinate number z is typically assumed to be a constant set to z = 10 (Fredenslund et al., 1975). Relative subgroup volume and surface area parameters published by Hansen et al. (1991) are used for the neutral species.
Enthalpic interaction contributions are considered in the residual part of UNIFAC. The residual part (γ R j ) of the activity coefficient of component j is given by the following: where t is the group residual activity coefficient in the mixture, while (j ) t represents the one in a reference liquid containing only compound j . ν (j ) t is the number of subgroups of type t in molecule j . The residual activity coefficient of subgroup t is as follows: In these expressions m is the relative surface area fraction of subgroup m, X m is the mole fraction of m in the mixture of subgroups (note: X m is different from the mole fraction x j that would refer to the mixture of components, not mixture of subgroups). The standard UNIFAC temperature-dependent interaction between the subgroups m and n is given by Fredenslund et al. (1975): where U n,m is a measure of change in the molar Gibbs free energy due to interaction between subgroups m and n. Eq. (12) is typically represented in the more compact form of Eq. (13).
ln n,m = − a n,m T Due to the formulation of Eq. (12), with equivalent differences for the interactions between subgroups m and n (with the difference U m,n − U m,m ), the main group interaction parameters a n,m are unsymmetrical, i.e. a n,m = a m,n . Note that all interaction parameters are only resolved on the main group level, i.e. all subgroups of a certain main group interacting with a subgroup of a different main group will share the same interaction parameter. Hence, we refer to the set of a n,m as main group interaction parameters. In standard UNIFAC, the a n,m interaction parameters of organic solutions were estimated using a large database of experimental vapour-liquid equilibrium (VLE) and a few liquid-liquid equilibrium (LLE) data sets. This approach leads to satisfying predictions for vapour-liquid equilibria, but reliable simultaneous description of VLE, LLE, solid-liquid equilibria (SLE), and molar enthalpies of mixing (h E ) can often not be obtained (Lohmann et al., 2001). In order to overcome these deficiencies of the standard UNIFAC, modified UNI-FAC (Dortmund) uses three main group interaction parameters in the residual part to improve predictions of activity coefficients over a wider range of temperatures and different types of phase equilibria (Gmehling et al., 1993;Lohmann et al., 2001;Jakob et al., 2006): ln n,m = − a n,m + b n,m T + c n,m T 2 T .
In modified UNIFAC (Dortmund) the relative van der Waals volume (R t ) and surface (Q t ) coefficients for the structural groups are not calculated from molecular parameters as in the standard UNIFAC approach; rather, they are fit together with the interaction parameters (a n,m , b n,m , c n,m ) to experimental data.
The AIOMFAC model is aimed for a wide range of applications, including the calculation of solid-liquid equilibria and other thermodynamic phase equilibria. The temperature dependence of these equilibria is related to the molecular interaction of the components in the liquid phase. Hence, the temperature dependence of chemical reaction equilibria and phase equilibria are described by the same thermodynamic functions and we can express them with parameterisations for the temperature dependence of reaction equilibria. According to Clarke and Glew (1966), if the equilibrium constant K p of a chemical reaction or exchange process is a function of temperature, the changes in the standard thermodynamic functions, i.e. change in molar Gibbs free energy g • , change in molar enthalpy h • and change in molar heat capacity c • p are directly related to K p (by definition) and are well-behaved functions of T . The relationship for the equilibrium constant K p and temperature T , when excluding higher order derivatives of the molar heat capacity change with temperature, are given by (Clarke and Glew, 1966): where T is a reference temperature at which the changes in g • , h • and c • p are determined or known. In order to better describe activity coefficients at low (and high) temperatures while preserving compatibility with the already estimated values of the interaction parameters a n,m at room temperature, we introduce a similar but slightly modified expression for n,m . We define the temperature dependent interaction potential in AIOMFAC as ln n,m = − a n,m T + b n,m with the reference temperature T = 298.15 K. The first term on the right hand side is exactly the same as in standard UNIFAC, but slightly different from the equivalent term in Eq. (15), due to the use of actual temperature T instead of reference temperature T for consistency with standard UNI-FAC/AIOMFAC. This term in Eq. (16) therefore includes both changes in g • T as well as a part of the changes related to h • T (note: this is obvious when considering a hypothetical, very high reference temperature for the second term on the right hand side of Eq. 16). The second term includes the change in enthalpy and in addition acts as a correction term for parameters a n,m at temperatures different from the reference temperature. The third term accounts for the contribution related to the heat capacity change of a main group interaction, whose importance increases for temperatures far away from the reference temperature.
We use a database of experimental thermodynamic equilibrium data for organic and organic-water systems (see Sects. 3 and 4), covering a wide temperature and concentration range, to determine simultaneously the AIOMFAC group interaction parameters b n,m and c n,m for pertaining organic functional groups. To preserve compatibility with the AIOMFAC model version of Zuend et al. (2011), and its fitted organic-inorganic interaction parameters at room temperature, all group-interaction parameters a m,n are kept the same, which implies that the performance of AIOMFAC at 298.15 K will not be altered by the improved three-parameter temperature-dependence parameterisation. With the goal to describe a wide variety of organic compounds at relevant atmospheric temperatures, we focus on the aqueous systems of oxidised organics at lower temperatures. The temperature dependence formulation given by Eq. (16) will at this point only be parameterised for interactions between the UNIFAC main groups alkyl (CH n ), specific variants of alkyl groups in alcohols (CH [alc] n ), (CH [alc−tail] n ), and (CH [OH] n ), hydroxyl (OH), carboxyl (COOH), ketone (CH n CO), aldehyde (CHO), ether (CH n O), ester (CCOO), alkenyl (C=C), aromatic carbon (ACH n ), aromatic carbon-alcohol (ACOH) (a phenol group), and water (H 2 O). For all other group interactions not considered, b n,m and c n,m are set to zero so that Eq. (16) reduces to Eq. (13). The rules for the use of specific alkyl groups are described below. With this approach, an improved description of activities for organic systems at low temperatures can be achieved, while maintaining compatibility with standard UNIFAC, hence, preserving the applicability of AIOMFAC to a wider range of functional groups.
The UNIFAC functional groups in AIOMFAC include some modifications with respect to standard UNIFAC to better describe the specific properties of organic aerosol constituents, which typically are molecules composed of several (polar) functional groups. Therefore a more detailed description of alcohol/polyol group interaction parameters published by Marcolli and Peter (2005) was implemented, where the relative positions of the OH functional group, as well as those of neighbouring alkyl groups are taken into account (Zuend et al., 2011). According to this approach, water-alkyl and water-hydroxyl group interaction parameters for alcohols/polyols are treated specifically, while keeping the alkyl-hydroxyl interaction parameter unchanged in order to maintain the performance of AIOMFAC in case of water free alkane/alcohol systems compatible with standard UNIFAC. Except for CH [OH] n groups directly bonded to an OH group, standard UNIFAC CH n groups are used for alkyl groups in multi-functional molecules that contain hydroxyl groups combined with different other functional groups. Another difference with respect to standard UNIFAC is that we use the parameters of Peng et al. (2001) for the interaction of the COOH group with the OH group and the H 2 O group. The use of these modified UNIFAC group interaction parameters leads to improvements for certain aqueous systems of alcohols, dicarboxylic and hydroxycarboxylic acids, while being compatible with the use of standard UNIFAC parameters for other group interactions, as described in more detail in Zuend et al. (2011).

Experimental data
A reliable estimation of group interaction parameters and temperature dependence relies on a comprehensive database covering a wide variety of compounds consisting of the targeted functional groups with consideration of a large temperature range. In order to establish such a database, an extensive literature search was carried out. The DETHERM databank (Gesellschaft für Chemische Technik und Biotechnologie e.V., http://www.dechema.de), which offers the world's largest collection of thermodynamic mixture data was used to check the completeness of the literature search and to directly purchase data for which the original publication was not easily accessible. Figure 1 provides an overview of the database collected in this study. The matrix lists the number of data sets at temperatures substantially different from 298 K available for each main group pair interaction. The green bars indicate the maximum number of overall data sets including all data types available for each main group interaction pair. For each interaction pair, the highest temperature (red shaded boxes) and lowest temperature (blue shaded boxes), for which data points are available, is indicated. In addition, listed are the median and arithmetic mean values of the assigned initial data set weighting values (w init d ) pertaining to each main group interaction pair. The combination of these values serves as an approximate measure of the data quality. A higher median value (median(w init d ) ≥∼ 1), paired with a large number of data sets and a wide temperature range covered, indicates the availability of reliable thermodynamic equilibrium data for the model parameterisation. For certain group interactions, the data coverage and reliability is clearly lacking, which was considered in the model parameterisation.
The database overall consists of 677 data sets covering different data types, for monofunctional and multi-functional organic molecules in aqueous and water-free mixtures of binary and ternary systems. Table 1 lists the data sets and the data types used for determining the main group interaction parameters (b n,m and c n,m ) in the SR part of the AIOM-FAC model. The table lists the mixture components, main groups, chemical formula (subgroups), data type, number of data points, temperature range, assigned initial weighting used in the model parameter fit, and the data source. Tables reporting new water activity measurements are provided in the Appendix (Tables A1 to A8). Different data types and their processing for use with the model parameterisation are described in the following.

Solid-liquid equilibrium data
Most low temperature data available for the model parameterisation are binary SLE data with water and an organic component. SLE data can be obtained by measuring the melting point depression of solutes as a function of solution aw ( aw ( aw ( aw ( Leu et al. (1989) a Derived water activity data from differential scanning calorimetry (DSC) measurements at homogeneous freezing temperatures. b M5 is a mixture of dicarboxylic acids consisting of the following: malic acid (2) + malonic acid (3) + maleic acid (4) + glutaric acid (5) + methylsuccinic acid (6). c The chemical subgroup formulas of the M5 components are given in the table for the individual components, except for maleic acid, for which the subgroup formula is as follows: (CH=CH)(COOH) 2 . d SLE data where the equilibrium is with respect to an organic compound in a solid (crystalline) state. e Derived water activity data from total pressure measurements, for more information we refer to Ganbavale et al. (2014). f Derived water activity data from electrodynamic balance (EDB) measurements, for more information we refer to Ganbavale et al. (2014). composition. Consequently, at maximum two data points for each temperature level can be acquired for binary systems, corresponding to the points on the melting curves of the two components. However, most data sets collected provide only data for one component forming a solid in equilibrium with the remaining liquid solution. In many of these cases, hexagonal water ice is the solid phase. Since the temperature dependence of water activity (a w ) of aqueous solutions in equilibrium with ice is well known, an accurate determination of the activity coefficients (γ (x) w = a w x w ) of water as a function of solution composition and temperature using SLE data is possible. At SLE, the activity of water in a solution with organic mole fraction x org at thermodynamic equilibrium with ice, a SLE w (T , p), is given by (Koop et al., 2000): where µ S w (T ) and µ •,L w (T ) are the pressure and temperature dependent chemical potentials of ice (superscript S) and pure liquid water (superscript •, L), respectively. At ambient pressures, neglecting the pressure dependence of the liquids and solids is well justified. The parameterisation in Eq. (18) represents the thermodynamically consistent function for use with Eq. (17) valid at low (ambient) pressure in the temperature range 150 < T < 273 K (Koop et al., 2000). The activity of a dissolved organic component in equilibrium with its pure crystalline solid can be calculated using the following relationship (Prausnitz et al., 1986;Dománska et al., 2009): where h m,i is the molar enthalpy of fusion (melting, subscript m), h tr,i is the molar enthalpy of a certain solid-solid phase transition, c p,m,i is the molar heat capacity change upon fusion at constant pressure, T tr is the solid-solid phase transition temperature and T m,i the melting temperature of pure component i. The second term is only of significance ACHn a(i, j ): −1.1120 ×10 1 3.4460 ×10 0 0.0 9.0380 ×10 2 1.3290 ×10 3 2.5770 ×10 1 3.4730 ×10 2 5.9940 ×10 0 b(i, j ):     Marcolli and Peter (2005). The a i,j values for COOH ↔ H 2 O group interactions are taken from Peng et al. (2001). For all other functional groups the a i,j values from the revised parameter set of Hansen et al. (1991) are used. b Main group interaction parameters b i,j and c i,j are set to zero since appropriate data to determine these interactions are missing. c Interaction parameters between different types of alkyl main groups (CH n , CH [alc] n , CH [ (Domalski and Hearing, 1996;Dean, 1999). We note that for certain organic compounds rather large uncertainties in the physicochemical property values used in Eq. (19) will translate into large uncertainties in the calculated SLE activity values, particularly when the target temperature is far from the melting point temperature at standard pressure. In this work, such uncertainties were assessed based on the comparison of derived activity values with activity values from other data types for the same system, and by means of preliminary model fits of AIOMFAC-P3. Affected data sets were either assigned a much lower weighting or zero weighting (removing the data set from the fit).

Water activity measurements
Water activity measurements were conducted for aqueous organic solutions with an Aqualab dew point water activity meter (Model 3TE, Decagon Devices, USA), which enables water activity measurements within the temperature range from 289-313 K for several concentrations at each temperature level. Water activity data for measured binary aqueous organic bulk solutions are tabulated in Tables A1-A8. Additional measurements of aqueous multi-functional organic solutions are provided in Ganbavale et al. (2014). Measured water activities were then used directly for the AIOMFAC-P3 parameter determination -with the exception of data within ±10 K from 298 K.

Liquid-liquid equilibria data
The equilibrium state between coexisting liquid phases is known as liquid-liquid equilibrium (LLE). Liquid-liquid equilibria are useful as a source of data for systems containing relatively hydrophobic organic compounds and water, with a miscibility gap that depends on temperature and mixture composition. In general, multi-component systems may form more than two phases (in binary systems at maximum two liquid phases may coexist). For salt-free aqueous organic systems with two coexisting liquid phases, usually one phase is an aqueous (water-rich) phase while the other is an organic-rich phase. Most available experimental LLE data has been measured relatively close to room temperature and is useful for a better description of the phase behaviour. However, for the purpose of our new parameterisation of AIOMFAC with regard to low temperatures far from room temperature, the LLE data tend to be less useful than, e.g. SLE data. We use the tie-line data from LLE measurements, which represents the composition of the two liquid phases in equilibrium at a certain temperature. A direct calculation and comparison of activities in coexisting phases is possible at experimental LLE compositions, i.e. measured mole fractions x α j and x β j of the two liquid phases α and β at equilibrium. According to the reference state definitions of AIOM-FAC, different independent components j should have the same activities in coexisting phases, i.e. a (x),α j = a (x),β j . This data type can therefore be implemented in the model fit by minimising the relative differences between the activities of the components in the two liquid phases. We use the method introduced by Zuend et al. (2011) for the comparison of calculated relative activity deviations between the activities of components j present in the two phases.
Furthermore, we also performed AIOMFAC-based predictions of the phase compositions at LLE using the method of Zuend and Seinfeld (2013), particularly for the graphical comparison of measured and predicted tie-line LLE data. To perform such predictions, an initial composition point is required from which a liquid-liquid equilibrium calculation is performed in order to determine whether the initial mixture composition is stable as a single homogeneous phase or whether two coexisting liquid phases represent the stable equilibrium state (according to the model) and what the compositions of the two phases are in the LLE case. An initial mixture composition with mole fraction x init j of component j on a unstable / metastable point of an experimental tie-line can be generated by the following: Such LLE predictions from an initial composition are computationally more expensive than the relative activity difference calculations used in the model fit, yet offer a different view on the performance of the model for applications of phase separation / phase composition computations. For more details about the LLE computations with AIOM-FAC we refer to Zuend et al. (2010) and Zuend and Seinfeld (2013); the specific method used for fitting LLE data based on relative activity deviations is described in more detail in Zuend et al. (2011).

Vapour-liquid equilibria
VLE data represent the temperature and pressure conditions where a liquid (mixture) and its vapour(s) (gas phase) are in equilibrium with each other. The VLE data are usually obtained by performing measurements either at isobaric or isothermal conditions. VLE data considered in the model include binary water + organic systems and binary  Figure 1. Database distribution for the water ↔ organic and organic ↔ organic interaction parameters. The table lists for each main group interaction pair at temperatures substantially different from the reference temperature, T = 298.15 K, i.e. per data set d: T d,low < 289 K or T d,high > 307 K, the following information. Top boxes: the total number of data sets available, visualised by the green bars. Middle boxes: the lowest temperature (T low ) and the highest temperature (T high ) (units of K) of the data points using a percentile-wise colour scale. Bottom boxes: the median and arithmetic mean of the assigned initial data set weighting values (w init d ) of the data sets involved.
data for water-free organic (1) + organic (2) systems. Since isobaric measurements are usually conducted at 1 atm (= 101.325 kPa) pressure by measuring the boiling point temperature, they typically provide data at relatively high temperatures. In order to be used for the model parameterisation, the composition of the liquid in terms of mole fraction x j of each component j , the composition of the gas phase in terms of mole fraction y j and the total pressure p of the gas phase have to be stated or need to be derived from the data source. VLE data provide the composition dependence of activity coefficients. Assuming that the gas phase can be treated as an ideal gas mixture, activity coefficients of the components in the solution can be calculated by modified Raoult's law: Here, p j is the partial pressure of component j , and p • j (T ) is the pure liquid component saturation vapour pressure calculated at the measurement temperatures using the Antoine equation with coefficients from the Landolt-Börnstein database (Dykyj et al., 2000), from Yaws et al. (2005) or, in some cases, the p • j (T ) are directly available from the reference of the experimental VLE data. Except for monocarboxylic acids such as formic, acetic, and propionic acid, which exhibit significant gas phase association (dimers, trimers), assuming an ideal gas mixture for the total pressure and temperature ranges of the data is acceptable. Other ex-ceptions include certain diols and triols, e.g. glycerol, which show moderate non-ideality in the gas phase, requiring fugacity corrections. For mono-alcohols, fugacity corrections of the gas phase did not lead to substantial changes in activity coefficients, due to the form of Eq. (21) (where the ratio of partial pressure and saturation vapour pressure, both similarly affected by association effects, cancel most of the non-ideality effects), and were typically ignored. For glycerol, fugacity corrections were not applied; instead, given the large amount of data sets covering functional groups of alcohols, the glycerol VLE data sets were assigned a very small weighting, essentially excluding their influence on the parameter fit. To account for the gas-phase dimerisation of carboxylic acids we obtain the monomer partial pressures using the dimerisation equilibrium coefficients from Tsonopoulos and Prausnitz (1970). The procedure for calculating experimental activity coefficients using this dimerization correction is described in more detail in Zuend et al. (2011).

Objective function and model parameter estimation
Organic-organic and organic-water main group interactions are parameterised in the SR part of AIOMFAC. The model parameter determination procedure involves simultaneous fitting of the various group interaction parameters to available thermodynamic phase equilibria data (see the database overview in Fig. 1). In order to ensure inter-comparability of different thermodynamic quantities and with due consideration of the various aspects of uncertainty in measurements and the group-contribution concept of the model, we use the following general objective function (F obj ), subject to minimisation (Zuend et al., 2011): Here, w d,u is the weighting value of a data point and the sums cover all data points u in all data sets d considered. Q ref d,u is a reference quantity, directly determined from experiments (e.g. a measured water activity value at a certain T and x w ) or derived from measurements by means of thermodynamic relations, e.g. SLE water activity on the ice melting curve at a specific temperature. Q calc d,u represents the corresponding quantity calculated with the model at the given conditions. Q tol d,u is a tolerance quantity (> 0) which represents the measurement uncertainty or model sensitivity and has the same units as Q ref d,u . During the iterative fitting of the model parameters, we use the AIOMFAC model (with the so far fitted parameter set at that iteration step) to calculate the model activity sensitivity with respect to an assumed representative uncertainty in absolute mixture composition, a mole fraction tolerance set to x tol = 0.01. We refer to Zuend et al. (2011) (their Sect. 3.3) for a detailed description of how the model sensitivity is calculated. We use the AIOMFAC model to calculate the effect of a tiny change in composition on the activity coefficients of the different mixture components by means of a total molar derivative. Technically, this is done by scaling and summation of the partial derivatives of the activity coefficients at a given solution composition by means of finite differences in molar composition (Eq. 10 of Zuend et al., 2011).

Data set weighting and temperature range
Both experimental uncertainties and model deficiencies need to be considered while determining the main group interaction parameters. The measured experimental quantities have some level of random and systematic errors, which may also depend on mixture composition, rendering some data points more reliable than others. This is considered during the parameter estimation procedure by giving appropriate weighting to the data sets and by data point-specific tolerance quantities computed in parallel from the model sensitivities as the iterative model fit progresses. With the aim of reducing a disproportionate influence of data sets with a large number of data points, as well as preventing an immoderate high weighting of data sets with a small number of data points, Zuend et al. (2011) propose a simplified procedure of assigning individual weighting to data sets on the basis of data type and number of data points N d in a data set: where w init d is an initial weighting of data set d on the basis of its temperature range, data type, and, in certain cases, additional expert judgement of its reliability. η is a characteristic number of data points per data set. The weighting of individual data points that are part of large data sets can be reduced by multiplication with η/N d . In this work, we keep η = 10 as in Zuend et al. (2011). Initial weightings assigned to data sets for the model fit are given in Table 1.
With the goal of fitting the AIOMFAC model parameters for a better description of activities at (low/high) temperatures far from room temperature, a set of rules was applied to assign initial weightings based on data type and the temperature range covered. Low temperature a w data were assigned an initial weighting w init d = 5.0 while the SLE organic activity (SLE(org)) data sets (i.e. SLE data where an organic compound forms the solid in equilibrium with the liquid solution) are given an initial weighting of w init d = 0.2 because of the lower reliability of deriving solute activities using Eq. (19) compared to calculating water activities with Eq. (17). Relying on the water activity parameterisation of homogeneous freezing temperatures in aqueous solutions (Koop and Zobrist, 2009), freezing point depressions were also used as data source for parameter fitting. The a w from differential scanning calorimetry (DSC) measurements at homogeneous freezing temperatures (T hom ) are assigned w init d = 1.0 (considering some uncertainties associated with the T hom determination from DSC measurements). The weighting of all types of data sets close to room temperature (289-307 K) are set to zero to keep AIOMFAC unchanged around room temperature and guarantee consistency with functional groups that were not included in the new three-parameter temperature-dependence parameterisation. The LLE and VLE data sets are assigned an initial weighting of w init d = 1.0. However, data sets showing large scatter or inconsistencies with other comparable data (direct comparison of measurements or comparable via the thermodynamic relations underpinning AIOMFAC) were given lower or even zero weightings. To obtain parameters representing the best simultaneous description of all phase equilibria, thermodynamically inconsistent data have been excluded from the parameter fitting process (but only after test runs and a careful data quality review).
For determining the set of main group interaction parameters, i.e. the set of b m,n and c m,n values, where m, n represent all combinations of different main groups, we use a set of selective criteria by considering the temperature range of available experimental data. These criteria are separately applied to each group interaction pair as follows: the b m,n values are determined only if: T low = |T low − T | or T high = T high − T > 40 K and T = T low − T high > Atmos. Chem. Phys., 15, 447-493, 2015 www.atmos-chem-phys.net/15/447/2015/ 40 K, where T low and T high are the lowest and highest temperatures covered by the data points involved (see Fig. 1) and T = 298.15 K is the reference temperature. Similarly, the c m,n parameters for the main groups are determined only if T low > 80 K or T high > 80 K and if T > 80 K. In addition, we set numeric bounds on the values of the fitted parameters, described below. The three terms on the right hand side of Eq. (16) contain parameters of different thermodynamical meaning (see Eq. 15) and different magnitude. The terms containing a m,n and b m,n are associated with changes of molar enthalpy over a certain temperature difference, while c m,n is related to changes in the molar heat capacity at constant pressure (hence, accounting for the change of the change of enthalpy with temperature). These thermodynamic quantities tend to be of different magnitude. In the temperature range of interest here, molar heat capacity changes (units of J mol −1 K −1 ) are roughly 2 to 3 orders of magnitude smaller in value than changes in molar enthalpy (units of J mol −1 ). Hence, the expected values and set numeric bounds on the parameters b m,n and c m,n are quite different for these reasons. Symmetric parameter bounds for permissible values of b m,n are set to ±max[a m,n , 200], while the numerical limits on c m,n are set to ±max[4 × 10 −3 × max(a m,n , 200)]. With the implementation of these parameter bounds and based on the reduced set of experimental data fulfilling the selection criteria, 150 new short-range interaction parameters were determined simultaneously for 14 functional main groups. As described in Zuend et al. (2011), due to the high dimensionality, and nonlinear coupling of the fit parameters, the minimisation problem is a challenging task for any global optimisation method. For the parameter optimisation, it is sufficient to find a "good" local minimum, which may not be the global minimum. As a part of data quality control and to avoid that a few data sets dominate the parameter optimisation due to potential numerical issues or other reasons, such as inconsistent data sets and outliers, a large number of trial parameter optimisation runs were carried out. To solve the parameter optimisation problem, we use the formulation introduced by Zuend et al. (2011) by using a combination of algorithms to solve the parameter optimisation problem. First, a best-of-random differential evolution (BoRDE) algorithm (Lin et al., 2011) is used to explore the parameter space and to broadly locate a minimum of F obj . Second, the global trust region method BOBYQA (Bound Optimization BY Quadratic Approximation) of Powell (2009) is applied to further refine the solution. Finally, the downhill simplex algorithm by Nelder and Mead (1965) is used to fully converge to the minimum. More details are given in Zuend et al. (2011).
During trial runs, the contributions of the individual data sets to the objective function value (Eq. 22) were used to identify potential inconsistencies among data sets, errors in data calculations and conversion or the implementation in the model. This allowed us to establish a high level of data quality, correct mistakes (e.g. typing errors) and compare thermo-dynamic data from different types of experiments and references for general consistency. Table 2 provides the final values of the determined organic main group interaction parameters. For comparison and completeness, the values of a m,n parameters, which were preserved in the new AIOMFAC parameterisation are listed as well. All main group interaction parameters b m,n and c m,n , for which the database does not satisfy our criteria concerning temperature range and data availability, are set to zero.

Results and discussion
The new temperature dependence parameterisation is applied to aqueous organic and water-free organic solutions covering a wide concentration and temperature range. As discussed in Sect. 4.1, the database and therefore the values of F obj (Eq. 22) evaluated with both AIOMFAC-P3 and AIOMFAC-P1 for comparison, do not include data sets with data points exclusively near room temperature (298 ± 10 K). In this section, we compare the model performance of the new AIOMFAC-P3 version, with AIOMFAC-P1 (original AIOMFAC version) based on overall quantitative measures followed by a discussion of a selection of aqueous organic mixtures and water-free organic mixtures.
The new AIOMFAC-P3 parameterisation for the temperature dependence of activity coefficients shows an overall improvement of 28 % in terms of F obj in comparison to AIOMFAC-P1 (542 data sets involved). As stated earlier, AIOMFAC-P1 uses the temperature-dependence expression of standard UNIFAC and represents the AIOMFAC performance using only a m,n interaction parameters. The AIOMFAC-P3 model version uses all the three parameters i.e. a m,n , b m,n and c m,n , where applicable, with our new expression for the temperature dependence of group interactions.
For the purpose of evaluating the improvement of the new parameterisation it is of interest to compare the performance of the two AIOMFAC model versions for different subsets of the database covering separately low and high temperature ranges and certain aspects of the complexity of molecular structures involved ("monofunctional" vs. "multi-functional" organic components). We define the value F obj, low-T calculated as the objective function value based on Eq. (22) when exclusively considering data sets with T high < 274 K. That is, the subset of the database including only data sets containing data points with a maximum temperature below 274 K (at least 25 K below the reference temperature of 298 K). This serves to represent the low-temperature range in our comparison. Analogously, to represent the high-temperature range (at least 25 K above 298 K), we define F obj, high-T by exclusively considering the data sets with T low > 322 K. The minimum distance of 25 K from the reference temperature was chosen such that there is (i) a clear difference between the low and high temperature ranges considered, yet that (ii) still  Panels (b, e) show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Ott et al. (1972) and Gmehling and Onken (2003a). many data sets are included in the comparison (especially given that low-temperature SLE-derived water activity data usually starts at the melting point temperature of pure waterice). Based on this distinction into low and high temperature ranges and from the evaluation of F obj, low-T and F obj, high-T with both AIOMFAC versions, it is found that AIOMFAC-P3 improves similarly in both temperature ranges relative to AIOMFAC-P1. For the low-temperature range the improvement of AIOMFAC-P3 is 37 % (152 data sets involved; F obj, low-T (AIOMFAC-P3) = 10.207), while for the hightemperature range the improvement is 37 % (223 data sets involved; F obj, high-T (AIOMFAC-P3) = 37.554). The better improvement in the lower and higher temperature ranges compared to the overall improvement (of 28 %) is not surprising. This is simply because the two additional fit parameters in AIOMFAC-P3 have a relatively small effect on the model performance in the ±25 K range around the reference temperature. Therefore, the AIOMFAC-P3 improvement relative to AIOMFAC-P1 is better when the data sets covering the temperature range close to room temperature are excluded from the comparison (to clarify: these data are not excluded from the AIOMFAC-P3 fit -except for data sets within the 10 K margin around 298 K, which are also not considered in the overall model performance comparison).
We further differentiate the low and high temperature subsets of the database each into two classes of (i) data sets containing monofunctional organic compounds only and (ii) data sets containing at least one multi-functional organic compound. The terminology applied here is to call an organic compound "monofunctional" when its molecular structure contains only one oxygen-bearing subgroup (e.g. phenol, 2-butanol, or palmitic acid), while glycerol, sucrose, 2-ethoxyethanol, glutaric acid, vanillylmandelic acid, and resorcinol are examples for multi-functional compounds included in our database (see Table 1). Despite this terminology, in AIOMFAC/UNIFAC the compounds termed monofunctional here are typically also composed of several types of subgroups (e.g. different CH n and ACH n groups in addition to an oxygen-bearing subgroup). Multifunctional oxygenated compounds are often found as major contributors to the total mass of the organic aerosol fraction (e.g. Hallquist et al., 2009 Panels (b, e) show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Faucon (1910) and Narayana et al. (1985). the evaluation with these subclasses in terms of average improvement of AIOMFAC-P3 compared to AIOMFAC-P1 for the low-temperature range are as follows: 55 % (46 data sets; F obj, low-T ,mono (AIOMFAC-P3) = 5.197) for the subset of data sets with monofunctional compounds and −7 % (106 data sets; F obj, low-T ,multi (AIOMFAC-P3) = 5.010), i.e. a decline in agreement, in the case of data sets with multi-functional compounds. For the hightemperature range the average improvement is as follows: 35 % (162 data sets; F obj, high-T ,mono (AIOMFAC-P3) = 31.237) for monofunctional and 43 % (61 data sets; F obj, high-T ,multi (AIOMFAC-P3) = 6.317) for the data sets involving multi-functional compounds. Note that these percentages reflect a weighted average improvement of AIOMFAC-P3 (weighting depends on the w init d values). There are some data sets for which the AIOMFAC-P3 parameterisation shows an improvement over AIOMFAC-P1 and in return there are some data sets for which the AIOMFAC-P1 parameterisation shows better agreement. In the case of the low-temperature range comparisons for the subset of data sets containing monofunctional compounds, AIOMFAC-P3 leads to improvement in the case of 34 data sets vs. a decline in the case of 12 data sets. For the low-temperature range subset of data sets containing multi-functional compounds, AIOMFAC-P3 leads to improvement in case of 50 data sets but to decline in case of 56 data sets.
Thus, while this evaluation shows that AIOMFAC-P3 leads to improvement with the experimental data considering the whole database, as well as for the subsets of low and high temperature ranges, the new parameterisation does also lead to a decline in agreement for a number of data sets with respect to the performance of the original AIOMFAC-P1 parameterisation. This is is partly due to the nature of applying a global parameter optimisation aiming at the simultaneous improvement of the weighted model-measurement deviations based on Eq. (22), which entails the possibility for reduced agreement for some systems as long as the overall model-measurement agreement increases. Moreover, the AIOMFAC-P1 parameterisation shows already good agreement with a part of the experimental data sets at low and high temperatures. For this fraction of data sets any changes in model prediction due to a new parameterisation may eas-  show analogous SLE data for the malonic acid melting curve. The error bars represent the model sensitivity to a composition variation by x tol = 0.01. The dashed line represents the hypothetical water activity of an ideal mixture. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Braban et al. (2003) and Apelblat and Manzurola (1987). ily lead to a decline rather than an improved agreement with experimental data. However, as long as the changes in the model predictions are small for these systems, a decline in agreement relative to AIOMFAC-P1 could still mean that AIOMFAC-P3 performs well. Nevertheless, there are also data sets for which both AIOMFAC parameterisations show relatively large discrepancies (e.g. the water + 2-butoxyethanol system further discussed below). For such systems, additional improvements of the AIOMFAC model are conceivable -either by a new fit of certain a m,n interaction parameters (kept untouched in this work) or by introduction of additional (special) subgroups that help to account for the effects of certain intra-and inter-molecular subgroupsubgroup interactions (e.g. intramolecular hydrogen-bonding among oxygenated functional groups in close proximity). A thorough evaluation of these options and improvement of AIOMFAC in this direction is the topic of future work.
In the following, the two AIOMFAC parameterisations are compared for a selection of aqueous organic mixtures and water-free organic mixtures. Again, it should be noted that the model was not just fitted to the selection of data sets shown; rather the figures show a few examples, and the AIOMFAC-P3 model is, of course, based on the simultaneous optimisation of all fit parameters to the complete database. For each individual system, a specific fit of either AIOMFAC-P1 or -P3 (to that data set only) would represent those data better, but is not the goal of a versatile groupcontribution model. Figure 2 shows the comparison of aqueous 1,2-ethanediol solutions using the AIOMFAC-P1 and AIOMFAC-P3 models. Panels (a-c) represent the AIOMFAC-P1 performance while panels (d-f) represent the corresponding AIOMFAC-P3 results. The low-temperature SLE data (a and d) are well represented by both AIOMFAC-P1 and AIOMFAC-P3. The hightemperature VLE data are better represented by AIOMFAC-P3 in comparison to AIOMFAC-P1 even though both models show deviations from the experimental VLE-derived activity coefficients at low and high mole fraction of water. Panels (c) and (f) show predicted water activities covering the full concentration space from pure water to pure organic for 12 different temperature levels between 150 K and 480 K. In  show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Lohmann et al. (1997) and Gmehling et al. (1981). comparison to AIOMFAC-P1, the resulting temperature dependence from low to high x org is slightly smaller in the case of the AIOMFAC-P3 parameterisation (f). Figure 3 compares the model performance of AIOMFAC-P1 and AIOMFAC-P3 for SLE and VLE experimental data of aqueous acetic acid systems. The SLE data are well represented by both AIOMFAC-P1 and AIOMFAC-P3 ( Fig. 3a and d). At higher temperatures, covered by VLE data, the AIOMFAC-P3 prediction is clearly in better agreement with the experimental data than the AIOMFAC-P1 calculation. The AIOMFAC-P1 parameterisation tends to underestimate the activity coefficients of water and acetic acid, particularly at high and low mole fractions of water. The extended description of the temperature dependence of activity coefficients in AIOMFAC-P3 allows a relatively good representation of observations at low and high temperatures, while AIOMFAC-P1 shows quite large deviations at higher temperatures. The temperature dependence predictions for the temperature range 150-480 K are given in panels (c, f). AIOMFAC-P1 predicts less pronounced temperature dependence at higher temperatures in the range 330-480 K.

Aqueous organic mixtures
This steeper slope of changes in water activity with temperature seems to be necessary to reproduce both VLE and SLE data for this system and other systems containing compounds with functional groups in common with the acetic acid + water system. Figure 4 shows measured SLE data for the malonic acid + water system and its comparison with the predictions from AIOMFAC-P1 and AIOMFAC-P3. In the panels a and c, water is the component in equilibrium with ice (hence the data describes the ice melting curve at different T and mixture composition), while panels (b) and (e) show analogous data for the malonic acid melting curve. The temperature ranges are slightly different, with the highest temperature in the plots referring to the melting temperatures of the pure component or the SLE at the highest concentration of the organic component, respectively. The predicted a w shows slight deviations from the experimental data towards lower water activities for both AIOMFAC-P1 and AIOMFAC-P3 (a, d). The predicted a org (in a range close to and above room temperature) is well represented in both AIOMFAC-P1 and AIOMFAC-P3 (b, e  Figure 6. SLE and VLE measurements for 2-butoxyethanol + water solutions and corresponding calculations of AIOMFAC-P1 (a-c) or AIOMFAC-P3 (d-f). Panels (c, f) show the temperature dependence of water activities predicted for the range 150-480 K. (a, d) Low temperature experimental SLE data (crosses) are compared with the predictions for water activity at the same compositions and temperatures (blue circles). Predictions of the corresponding organic activities are shown as well (green triangles). The error bars represent the model sensitivity to a composition variation by x tol = 0.01. The dashed line represents the hypothetical water activity of an ideal mixture. Panels (b, e) show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Koga et al. (1994) and Schneider and Wilhelm (1959). malonic acid at higher temperatures and hence could not be compared. AIOMFAC-P3 predicts a larger temperature dependence in comparison to AIOMFAC-P1, the latter shows a relatively small temperature dependence of water activity at higher temperatures (c, f). Figure 5 shows an example of a binary system consisting of water and 2-butanone with a miscibility gap present over a large temperature and composition range. Both model parameterisations show deviations from the SLE data (a, d). However, the AIOMFAC-P3 parameterisation clearly reduces the deviations from the experimental data in comparison to AIOMFAC-P1, the latter showing deviations up to > 0.3 in a w at low water contents. On the other hand, at the higher temperatures covered by VLE data, both AIOMFAC-P1 (b) and AIOMFAC-P3 (e) are in good agreement with the experimental data. A miscibility gap is also predicted by both AIOMFAC parameterisations, although the width and temperature range of the predicted phase separations differ between the model results. According to the AIOMFAC-P3 prediction, a phase separation occurs in the temperature range 150 to ∼ 390 K. The composition space where a liquid-liquid phase separation occurs is indicated in such diagrams by drawing a horizontal line (parallel to the abscissa) from one of the local minima of a w to the point where it intersects with the a w curve at a different x org value. For example, for the green a w curve at T = 180 K, liquid-liquid phase separation is predicted at a w = 0.98 in the composition range between x org (2-butanone) = 0.05 and x org (2-butanone) = 0.61. A miscibility gap is also found in the experiments and is the reason why in panels (a, b, d, e) there are no data points in the mole fraction range 0.35 < x (H 2 O) < 0.85. Figure 6 shows the model-measurement comparison for aqueous 2-butoxyethanol. AIOMFAC-P1 and AIOMFAC-P3 show similar performance. Both models are not in good agreement with the experimental data. Contrary to the experimental data, both AIOMFAC-P1 and AIOMFAC-P3 predict a w > 1 in a certain composition range and both models predict a liquid-liquid phase separation over a wide range of temperatures, explaining the reason for deviations in predicted water activity shown in (a) and (d) (see also local minima in a w curves of panels c, f). Note that the model   predictions in these figures do not include phase separation computations on purpose, since the experimental data are for a homogeneous single phase (no phase separation found experimentally) so are the model calculations here. Also, at higher temperatures the activity coefficients of both water and 2-butoxyethanol show deviation from experimental data (b, e). AIOMFAC-P3 shows a larger temperature dependence over the entire temperature range in comparison to AIOMFAC-P1 (c, f). The observed disagreement between both models and the experimental data is mainly due to the fact that there is already a clear discrepancy between AIOM-FAC (both versions) and the experimental data near room temperature. Since there is already disagreement at the reference temperature (298.15 K), the new model parameters for improved temperature dependence (b m,n and c m,n ) cannot (and should not) remove this model-measurement discrepancy. This system illustrates that a re-parameterisation of certain a m,n group interaction parameters may be necessary to improve AIOMFAC for this and similar systems. Figure 7 shows the model-measurement comparison for SLE data of the water-free mixture of cyclohexanol + adipic acid. The AIOMFAC-P3 prediction is in better agreement with the experimental data than AIOMFAC-P1, which shows a positive deviation at lower mole fractions of component 1 (cyclohexanol). In this binary system, the AIOMFAC-P3 parameterisation leads to a relatively large temperature dependence of the activity of cyclohexanol, a org (1), (panel d). In addition, with that parameterisation a phase separation occurs at lower x org (2) values for temperatures below ∼ 180 K. However, no phase separation is expected at higher temperatures, more relevant in the troposphere. AIOMFAC-P1 on the other hand shows a much smaller temperature dependence (b) and does not predict a phase separation in the range shown.

Binary organic mixtures
Measurements for water-free binary organic mixtures of ethanol + acetone are shown in Fig. 8 Panels (b, e) show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. Experimental data: Sapgir (1929) and Amer et al. (1956). agreement with the experimental SLE-derived data (d), while AIOMFAC-P1 shows larger deviations from the experimental data at these low temperatures (a). At high temperatures, the VLE data for both AIOMFAC-P1 and AIOMFAC-P3 show similar results (b, e), with slightly larger deviations of γ (x) org 2 (activity coefficient of component 2, i.e. acetone) in the predictions of AIOMFAC-P1. At temperatures higher than 300 K both AIOMFAC-P1 and AIOMFAC-P3 show a much smaller temperature dependence than for the range below room temperature. Figure 9 shows a similar example for ethanol + 3heptanone mixtures. The prediction from AIOMFAC-P3 is in relatively good agreement with the experimental SLE data, showing less deviations in 3-heptanone activities than the results from the AIOMFAC-P1 calculations. Achieving better agreement with the new (AIOMFAC-P3) parameterisation requires a larger temperature dependence of the organic activities, particularly towards lower temperatures (d). Figure 10 shows the binary ethanol + diethyl ether system, where experimental data are available for a temperature range spanning more than 200 K: from 149 K up to 378 K. Of course, additional data from other systems of our database are also affecting the main group interaction parameters that are necessary to describe this system with AIOMFAC-P3. Both models describe the diethyl ether activity derived from SLE at low temperatures quite well (a and d). AIOMFAC-P3 shows slight overprediction of the diethyl ether activity in the range 0.15 < x(ethanol) < 0.6, while AIOMFAC-P1 tends to underpredict the experimental data. In contrast, at higher temperatures (∼ 350 to 380 K) covered by experimental VLE data (b and e), the predicted activity coefficients γ (x) org (diethyl ether) at high mole fractions of ethanol (component 1) both by AIOMFAC-P1 and AIOMFAC-P3 are not in good agreement with the VLE experimental data. The main reason for the observed deviations is due to inaccurately predicted activity coefficients at infinite dilution (i.e. when one of the compounds is present only as a tiny mole fraction in the solution) of the two organic compounds at these temperatures. At infinite dilution conditions the activity coefficients are dominated by subgroup volume and surface area properties in the UNIFAC/AIOMFAC model, so that the activity coefficient values are largely unaffected by the new main  group interaction parameterisation of AIOMFAC-P3 in comparison to AIOMFAC-P1. As is visible from panels (c) and (f), particularly at x(diethyl ether) > 0.4, the temperature dependence of ethanol activities predicted by AIOMFAC-P3 is larger than the original one in AIOMFAC-P1. The example of this system shows that it is not always possible to achieve good model predictions for the full temperature range with the new treatment of temperature dependence in AIOMFAC. For further improvements, other model parts, such as the lattice constant (z), which is not really a constant, may need to be considered for the introduction of additional, physically meaningful temperature dependent parameterisations.

Scope and limitations of the new parameterisation
The thermodynamic model AIOMFAC has been developed based on modified versions of UNIFAC and LIFAC, with the aim to establish a versatile activity coefficient model for atmospheric applications. The new parameterisation of the model aims at improving AIOMFAC predictions particularly at lower temperatures of atmospheric relevance. Deviations between the experimental data and model predictions from the new AIOMFAC-P3 version are associated with either the inaccuracy of the measurements, the lack of data to better cover and parameterise the model for a wide composition and temperature range, or limitations of the AIOMFAC expressions and the group contribution method. Own measurements were performed for selected aqueous organic systems at low temperatures and at temperatures around room temperature, which were used together with experimental data from the literature for parameterising the model over a wider temperature range.
While an extensive database was compiled to allow for an improvement of the AIOMFAC model with respect to its performance at temperatures substantially lower and higher than room temperature, there are still limitations present in the general coverage of the extended temperature range by experimental data. The complexity of organic molecules   Panels (b, e) show the model predictions of the activity coefficients compared to VLE data covering temperatures significantly higher than room temperature. The temperatures of the individual data points are given in the boxes below the main panels. The error bars represent the model sensitivity to a composition variation by x tol = 0.01. Experimental data: Lalande (1934) and Moeller et al. (1951). in terms of their physical and chemical properties such as size, shape and combinations of functional groups, particularly the number and proximity of oxygen-bearing functionalities, are important factors that influence the quality of AIOMFAC predictions. Of interest for atmospheric aerosol systems are data sets containing multi-functional organic compounds, such as sugar-like compounds, di-and polycarboxylic acids, hydroxylated ketones and functionalized aromatic compounds. We have added many experimental thermodynamic equilibrium data sets that cover systems containing such compounds (e.g. sorbitol, 1,2,7,8octanetetrol, sucrose, raffinose, citric acid, malonic acid, 2isopropoxyethanol, vanillylmandelic acid, etc.; see Table 1 for a complete list), yet overall the database remains dominated by small, monofunctional organic compounds. This possibly limits the accuracy of AIOMFAC-P3 for predicting activity coefficients in multi-component systems containing multi-functional, high-molecular mass species. This is a disadvantage not just for AIOMFAC-P3 or this work, but generally rooted in the very limited amount of experimental data covering such systems (especially at temperatures much lower/higher than 298 K). Due to this, the accuracy of AIOMFAC predictions is expected to decrease with increasing complexity of organic compounds. As discussed in more detail at the beginning of Sect. 5, it is found that the new temperature dependence parameterisation shows particular improvement for the majority of systems containing monofunctional compounds both in the low and high temperature ranges (the temperature ranges at least 25 K above/below 298 K). In case of the mixtures containing multi-functional compounds present in our database, the improvement for the low-temperature range in comparison to AIOMFAC-P1 is more diverse: for about half of the data sets a small improvement is found while for the other half a reduced agreement is the result of the parameter optimisation. For some systems containing multi-functional compounds, the model-measurement agreement is not good with either AIOMFAC version (e.g. in case of the aqueous 2butoxyethanol system shown in Fig. 6). For such systems and corresponding main group interactions, further improvement of AIOMFAC may only be achieved by a refitting of certain a m,n interaction parameters involved.
It is known that the standard UNIFAC parameterisation and model expressions need to be modified for aque-Atmos. Chem. Phys., 15, 447-493, 2015 www.atmos-chem-phys.net/15/447/2015/ ous oligomer/polymer solutions to achieve good modelmeasurement agreement (e.g. Ninni et al., 1999). This has been done in previous work targeting specific types of polymers, including the introduction of specific UNIFAC groups fitted to experimental data exclusively of such polymer systems (e.g. Ninni et al., 1999). The introduced AIOMFAC-P3 parameterisation has as purpose general applicability, as is the case for AIOMFAC-P1. Therefore, it is expected that the AIOMFAC model may perform rather poorly when used for predicting activity coefficients in oligomer/polymer solutions. For such systems, the application of specifically fitted models is recommended. However, the new AIOMFAC parameterisation provides a tool to predict activity coefficients with better overall accuracy than the previous version and offers the versatility of a group-contribution method for the prediction of activity coefficients in complex mixtures containing many tens to thousands of individual components.

Conclusions
An improved temperature dependence parameterisation of aqueous organic and water-free organic mixtures is presented for the thermodynamic group contribution model AIOM-FAC. A comprehensive database of experimental thermodynamic equilibria data is established by collecting and carefully validating different data types covering a wide temperature and concentration range. In addition, new measurements that have been performed for selected aqueous organic systems, at room temperature and below, were also included in the database. The database is used to determine new AIOMFAC group interaction parameters for organic main groups of atmospheric relevance: carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkyl, aromatic carbonalcohol, and aromatic hydrocarbons. The parameter fitting procedure involved the simultaneous determination of 150 interaction parameters for the 14 main groups. Thus, the new temperature dependence parameterisation allows to calculate activity coefficients and their temperature dependence for a wide variety of organic and water-free mixtures. In general, the new AIOMFAC parameterisation achieves good agreement with a large number of experimental data sets. In the case of some organic systems, lack of experimental data to constrain the activity coefficients is a major limitation. Further improvements of the AIOMFAC model description of these systems and by that, the interactions of the functional groups involved, will require additional measurements over a wide temperature and concentration range. In addition, larger discrepancies in model-measurement agreement were found in particular for some of the systems containing multi-functional organic compounds. The affected systems were typically also poorly represented at room temperature. Further investigations will be needed to thoroughly address these issues and achieve better performance of AIOM-FAC in such cases over the full temperature range of interest.
The performance of the AIOMFAC parameterisation is typically better for systems containing relatively small organic compounds and substantial deviations may occur in mixtures when molecules of high structural complexity such as highly oxygenated compounds or molecules of high molecular mass (e.g. oligomers and polymers) prevail. The improved AIOM-FAC model can be used to better account for the temperature dependence of activity coefficients relevant in predictions related to atmospheric ice nucleation and gas-particle partitioning in multi-component systems.

Appendix A
Bulk water activities, a w , were measured for aqueous organic solutions using an AquaLab water activity meter (Model 3TE, Decagon devices, USA). The instrument applies the chilled mirror technology to determine the dewpoint temperature of air equilibrated with the aqueous solution being measured which is then translated to water activity. The instrument's infrared thermometry indicates the sample temperature, which is then considered in the determination of water activity. So, accurate measurements are not dependent on precise thermal equilibrium at a set temperature level. The internal temperature control allows to perform measurements under stable temperature from 289-313 K. The standard sample block with a specified error of ±0.003 in a w (absolute range) was used for most experiments. For the more volatile polyols (2,5-hexanediol, 1,2,6hexanetriol, and glycerol) the volatile sample block available using a hygroscopic polymer sensor to detect the equilibrium relative humidity of air in the headspace above the sample was used to perform measurements. The stated error for the volatile sample block is ±0.015 in a w (absolute range). Instrument offset is frequently corrected and the performance of the sample block was controlled and readjusted with reference samples. All measurements were performed at 289-313 K. The substances were purchased from Sigma-Aldrich in the best available purity. The following solutes were investigated: glycerol (Sigma, > 99 %), 2,5-hexanediol (Fluka, > 97 %), 1,2,6-hexanetriol (Fluka, > 95 %), 1,2,7,8-octanetetrol (Fluka, > 97 %), 2,2,6,6tetrakis(hydroxymethyl)cyclohexanol (Aldrich, 97 %), DL-4-hydroxy-3-methoxy mandelic acid ("vanillylmandelic acid"; Sigma, > 95 %), raffinose (Sigma, > 98 %). The substances were used without further purification. The water/polyol mixtures were prepared by mass percent with MilliQ water using an analytical balance. Each solution was measured at least three times at each temperature. Water activity data for these aqueous solutions are tabulated in Appendix Tables A1-A8.    Table A5. Bulk water activity (a w ) measurements a of water (1) + 2,2,6,6-tetrakis(hydroxymethyl)-cyclohexanol (2) solutions at three different temperatures. Solution compositions are given in mole fraction of the organic component (2), x 2 .
x 2 a w a w a w (T = 289.15 K) (T = 298.15 K) (T = 313.15 K)