Henry ’ s law constants of polyols

Henry’s law constants (HLC) are derived for several polyols bearing between 2 and 6 hydroxyl groups, based on literature data for water activity, vapour pressure and/or solubility. While deriving HLC and depending on the case, also infinite dilution activity coefficients (IDACs), solid state vapour pressures or activity coefficient ratios are obtained as intermediate results. An error analysis on the intermediate quantities and the obtained HLC is included. For most compounds, these are the first values reported, while others compare favourably with literature data in most cases. Using these values and those from a previous work (Compernolle and Müller, 2014), an assessment is made on the partitioning of polyols, diacids and hydroxy acids to droplet and aqueous aerosol.


Introduction
Henry's law constant (HLC) describes the partitioning of a compound between the gas phase and a liquid, highly dilute solution.In the atmosphere, such dilute solutions, with water as the solvent, can be reached in cloud droplets.Aqueous aerosols are another example where liquid water is important, but in this case the solvent must be regarded as multicomponent, with significant inorganic and/or organic contributions.In a previous work (Compernolle and Müller, 2014) we determined additional HLC data for diacids and hydroxy polyacids, from water activities, solubilities and vapour pressures, employing thermodynamic relationships.We follow the same approach in this work, but with a focus on polyols: compounds with two or more hydroxyl groups, but no other functional group.Polyols such as 2-methyl tetrols were identified as important secondary organic aerosol (SOA) constituents (Claeys et al., 2004).HLC data on polyols are limited.Data are available e.g. in the often-cited compilation of Sander (1999).In this compilation however, most values are estimated by a group-contribution method, while only for three molecules are experimental values included, and some of the data were evaluated as unreliable.
In Sect.2, we first briefly review the thermodynamic relationships employed to derive HLC (k h ) and the associated enthalpy of dissolution of a gas phase species ( H ∞ g→aq ).In Sect. 3 we derive intermediate results, namely infinite dilution activity coefficients (IDACs), solid state vapour pressures and activity coefficient ratios, which are necessary components in deriving HLC but not as such available in the literature for all compounds.Next (Sect.4), we present k h and H ∞ g→aq using the data from the previous section and other literature data.An error analysis is presented in Appendix A. In Sect.5, we discuss the implications for partitioning to cloud droplets and aqueous ammonium sulfate aerosol, making use of the activity coefficient model AIOMFAC (Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients) (Zuend et al., 2011).We extend this also to dicarboxylic acids and hydroxy polyacids, making use of a model presented at the site E-AIM (Extended AIM Aerosol Thermodynamics Model), available at http://www.aim.env.uea.ac.uk/aim/aim.php,(see e.g.Clegg and Seinfeld, 2006;Friese and Ebel, 2010) to calculate the acid dissociation.
Note that in this work, non-IUPAC names are used for polyols with three or more hydroxyl groups.Their structures are presented in Table 1.

S. Compernolle and J.-F. Müller: Henry's law constants of polyols 2 Thermodynamic relationships between HLC and other quantities
For HLC, several definitions exist.We will follow here the convention used by Sander (1999): with c s the solute molar concentration of the solution and p s its partial pressure above it.Note that we assume ideal gas behaviour for the solute.With this convention, a larger k h means a higher partitioning of the solute to the solution.At some point, we will employ also another definition of HLC, following again the notation of Sander (1999), with x s the solute mole fraction.The px superscript specifies that vapour pressure p is used for the gas phase concentration, and mole fraction x for the aqueous phase concentration.
The relation between both quantities is with c sol the total molar concentration of the solution (or solvent, since we assume that the solute is infinitely diluted).
In the case that the solvent is pure water, we write c sol = c w (equal to 55.5 mol L −1 at 298.15 K).
If the solute is a liquid at the temperature of interest and the solvent is water, k h can be obtained by with γ ∞ the infinite dilution activity coefficient (IDAC) of the solute (mole fraction based and with the symmetric convention γ ∞ = 1 for pure liquid solute) and p 0 L its pure liquid state vapour pressure.The corresponding enthalpy of dissolution of an infinitesimal amount of gas phase species ( H ∞ g→aq ) can be derived from the van 't Hoff equation (see e.g.Atkins and de Paula, 2006) and (neglecting the small temperature dependence of c w ) related to the enthalpy of vaporization ( H vap ) and the enthalpy of solution of the liquid solute at infinite dilution ( H ∞ L→aq ) using Hess's law (Atkins and de Paula, 2006), since the dissolution of a gas in a solvent can be considered as first a condensation of the gas to the pure liquid (corresponding to − H vap ) followed by a dissolution of this liquid in the solvent (corresponding to H ∞ L→aq ).H vap and H ∞ L→aq can themselves be derived from the van 't Hoff equation or, for Eq. ( 7), from the Clausius-Clapeyron equation (Atkins and de Paula, 2006): If the solute is a solid at room temperature, as is generally the case for polyols with more than three hydroxyl groups, the following equation can be applied instead of Eq. (4) (see Compernolle and Müller, 2014, for the derivation): with x sat the solute mole fraction at the solubility limit and γ sat the corresponding activity coefficient.In the case that the solubility is small, γ ∞ /γ sat ≈ 1 and Eq. ( 8) reduces to The corresponding enthalpy of dissolution of gas phase species, derived from the van 't Hoff equation, can be related to (again neglecting the temperature dependence of c w ) the sublimation enthalpy ( H sub ) and the enthalpy of solution of the solid at infinite dilution ( H ∞ Cr→aq ) using Hess's law (Atkins and de Paula, 2006), with Equation ( 11) is the Clausius-Clapeyron equation for sublimation (Atkins and de Paula, 2006).Equation ( 12) can be derived by combining Eqs. ( 6) and ( 8) and the van 't Hoff relation for the activity of the solid a Cr s (see e.g.Nordström and Rasmuson, 2008): The data required for Eqs. ( 4), ( 5), ( 8) and ( 10) is not always available in the literature.In Sect.3, data for IDACs, solid state pressures and activity coefficient ratios are derived.

43
a also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.
3 Intermediate results

Infinite dilution activity coefficients
In the case that the compound is a liquid at room temperature, Eq. ( 4) applies and the IDAC is required.Estimation methods to calculate activity coefficients exist (e.g.Fredenslund et al., 1975;Peng et al., 2001;Marcolli and Peter, 2005;Compernolle et al., 2009;Zuend et al., 2011) but experimental data are preferred.Suleiman and Eckert (1994) provide IDAC data for diols, but only for compounds with up to four carbon atoms.For many other polyols, the IDAC of the solute is not reported, but instead data are available on the water activity a w as a function of mixture composition.In that case, γ ∞ s can be obtained by the Gibbs-Duhem relation (here stated in its integral form) (Prausnitz et al., 1999;Mansoori, 1980), with γ w = a w /x w the activity coefficient of water and x w the water mole fraction.Note that we added the subscript "s" to γ ∞ to distinguish clearly the activity coefficient of the solute and the activity coefficient of water.
If sufficiently precise, fine-grained a w data over the whole composition range would be available, and numeric integration of the integral in Eq. ( 14) would be the most straightforward.If this is not the case, an alternative is to fit the ln γ w data with an activity coefficient expression f , e.g.Margules, Van Laar, Wilson or UNIQUAC (Prausnitz et al., 1999;Carlson and Colburn, 1942) -see Appendix A2 for the expressions.Marcolli and Peter (2005) provide a w data for 14 diols and two triols over a broad composition range (x w typically between 0.1 and 0.95.), but the data are rather coarse grained.This is especially critical in the dilute region; from Eq. ( 14) it can be concluded that a small change in ln γ w leads to a comparatively large change in ln γ s .Therefore, where possible, we included also more fine-grained data in the dilute region (Borghesani et al., 1989;Romero and Páez, 2006, x w typically between 0.93 and 0.996).In Table 2 the resulting γ ∞ s are presented.For eight diols we present also the γ ∞ s estimation without taking the available dilute region data into account, i.e. based on the Marcolli and Peter (2005) data only.This can then be compared with the γ ∞ s based on all data.In most cases, the difference in the resulting IDAC is rather small (see Appendix A2).This indicates that even in those cases where only the coarse-grained data of Marcolli and Peter (2005) are available, the derived γ ∞ s are still quite reliable.
Often, we were able to fit an activity expression to all ln γ w data.In other cases, where the broad-ranged but coarsegrained data of Marcolli and Peter (2005) was combined with the more fine-grained data in the dilute region, we had to split the integral in Eq. ( 14) into two parts.More details on the procedure to derive γ ∞ s are provided in Appendix A2.Also included in Appendix A2 is an uncertainty analysis in the derived γ ∞ s values by applying systematic and random shifts to the a w data, by testing alternative activity expressions and by comparing γ ∞ s derived with and without dilute region data.The γ ∞ s for pentane and hexane diols, derived from surface tension data, are reported by Romero et al. (2007) and Páez et al. (2011).These are considerably higher than the data presented in Table 2.However, as explained by Brocos et al. (2007), very accurate surface tension data are a prerequisite to derive γ ∞ s ; the γ ∞ s of diols, derived from surface  (1994).g The second value is obtained by applying Eq. ( 14) to the data of Marcolli and Peter (2005) only.
tension data, are all overestimated compared to the literature data in their analysis.Moreover, it is not clear to us whether the applied approximation (the Volmer surface equation of state, see Gracia-Fadrique et al., 2002) is valid in this case.

Solid state vapour pressures
The liquid state vapour pressure of organic compounds can be estimated (e.g.Pankow and Asher, 2008;Nannoolal et al., 2008;Compernolle et al., 2011), but for polyfunctional compounds the result is often not accurate.Solid state vapour pressure is even more difficult to estimate, as this depends on the molecular arrangement in the crystal structure which is compound specific.Therefore, experimental data are preferred.Solid state and/or liquid state vapour pressure data for polyols with four or more hydroxyl groups is available (Barone et al., 1990;Bradley and Cotson, 1953;Nitta et al., 1950Nitta et al., , 1951)), but obtained at temperatures considerably above room temperature.The solid state vapour pressure at If at the temperature of measurement T meas , the compound is a solid, the following temperature correction is applied In most cases, the high-temperature p 0 data are not measured at one temperature but in a temperature interval.T meas then corresponds to the centre of this interval.Fusion data were taken from Barone et al. (1990), Tong et al. (2007Tong et al. ( , 2008Tong et al. ( , 2010aTong et al. ( , 2009) ) and Badea et al. (2014).Experimental heat capacity data for solid and liquid were taken from Tong et al. (2007Tong et al. ( , 2008Tong et al. ( , 2009Tong et al. ( , 2010a, b), b), Zhang and Yang (1989) and Della Gatta et al. (1999), while for the gas it was calculated by the method of Benson (1976), available from the NIST Chemistry WebBook (Stein and Brown).In Table 3 the derived solid state vapour pressures and sublimation enthalpies at room temperature are presented.
Fusion data of Tong et al. (2007Tong et al. ( , 2008Tong et al. ( , 2010aTong et al. ( , 2009) ) on one hand and of Barone et al. (1990) on the other hand could be compared for erythritol, xylitol, adonitol, sorbitol and mannitol.There is generally a good agreement between both data sets: T fus was always within 6 K and H fus within 4 %, with the exception of xylitol where the deviation is 11 %.Interchanging both data sets had an impact of a factor 1.3 on p 0 Cr at room temperature at most.Where available, the more recent data set of Tong et al. was preferred over that of Barone et al. (1990).Tong et al. (2007Tong et al. ( , 2008Tong et al. ( , 2009Tong et al. ( , 2010b, a), a), i Góralski and Tkaczyk (2008), j Zhang and Yang (1989), k Della Gatta et al. (1999).l  No C p,Cr , C p,L data were found for arabinitol.The data for adonitol were taken instead.m No C p,L data were found for mannitol and dulcitol in the literature; the C p,L data for sorbitol were taken instead.n No C p,Cr data were found for dulcitol in the desired temperature range.Low-temperature (≤ 292.8 K) data (Parks and Huffman, 1926) are comparable to those of mannitol, therefore, C p,Cr of mannitol was taken instead.o No C p,L data for decane diol were found in the literature.It was estimated by the method of Domalski and Hearing (1993).
C p,L and C p,Cr were not always available.In that case, the data of a stereo-isomer were taken instead.In Appendix A5.2, it is shown that liquid phase heat capacities of polyol stereo-isomers are very close.This is in agreement with the similar S vap and H vap of stereo-isomers reported by Barone et al. (1990) and indicates similar thermodynamic properties of the liquid phase.Regarding C p,Cr , differences between stereo-isomers are larger (see Appendix A5.2) but still the approximation of using a stereo-isomer seems reasonable.
Neglecting the integrals involving the heat capacity differences in Eqs. ( 16) and ( 17) can lead to serious error: while for the tetrols the change is only minor, there is a factor of 5 to 7 increase in p 0 Cr (298.15K) for the pentols and most hexols, and a factor 40 increase for sorbitol.Estimating C p,g with the method of Joback and Reid (1987) instead of the method of Benson (1976) led to changes in p 0 Cr (298.15K) smaller than a factor of 2. Note that these two methods do not take the intramolecular hydrogen bonding into account.The group contribution C p,g estimation method of Paraskevas et al. (2013) and Sabbe et al. (2008), based on quantum chemical data, does include corrections for intramolecular hydrogen bonds.However, it is not clear how to apply these correction terms for species with three or more hydroxyl groups.Using one HOCCO term (NNI5 in the terminology of Paraskevas et al. (2013)) per hydroxyl group for the linear polyols, one obtains a factor of 2 to 3 higher p 0 Cr (298.15K) for the pentols and hexols, compared to the case when this term is neglected.
In most cases the high-temperature p 0 L or p 0 Cr data are obtained from a single reference (Barone et al., 1990); only for erythritol and pentaerythritol is a comparison possible between different data sources.The high-temperature p 0 L or p 0 Cr data of erythritol and pentaerythritol are roughly comparable among the different data sources (Barone et al., 1990;Bradley and Cotson, 1953;Nitta et al., 1951Nitta et al., , 1950)); if the p 0 parameterizations presented in these works are evaluated at mid-points between their respective T meas , differences ranging from 4 % up to 40 % are obtained.However, due to differences in H vap or H sub , the extrapolated p 0 Cr (298.15K) is a factor of 7 to 50 higher if the older data of Nitta et al. (1950Nitta et al. ( , 1951)); Bradley and Cotson (1953) are used, compared to when the more recent data of Barone et al. (1990) are used.In the older studies the enthalpy was determined using far fewer data points (6-11, compared to 25-30 for the data of Barone et al., 1990), and specifically for the data of Nitta et al. (1950Nitta et al. ( , 1951)), over a quite narrow temperature interval (∼ 12 K, compared to 30-40 K for the other studies).Therefore, we consider the p 0 Cr derived from the high-temperature data of Barone et al. (1990) as more reliable.(1961); Bower and Robinson (1963).
n For mannitol, only the a w data of Robinson and Stokes (1961) were used, as the data of Ninni et al. (2000) led to γ w > 1, which is probably wrong.o Due to the extrapolation involved (no a w data at x sat ), this value is more uncertain.
p No a w data were found.γ ∞ s /γ sat s = 1 was assumed because of the low solubility, i.e.Eq. ( 9) is considered valid.
Uncertainties in the derivation of p 0 Cr (T ref ) are analysed in Appendix A5.The largest uncertainties are encountered for the polyols with four or more hydroxyl groups; due to the large difference between T meas and T ref , relatively small changes in H vap or H sub lead to large changes in p 0 Cr (T ref ).Uncertainty in heat capacity becomes important for the hexols.Uncertainty in fusion data is relatively unimportant.

Activity coefficient ratios
The ratio γ ∞ s /γ sat s can be obtained from water activity data in the subsaturation range (Compernolle and Müller, 2014): The polyols with more than three hydroxyl groups considered here are solid at room temperature.Their water activity is only measured up to the solubility limit, if measured at all.Similarly to our previous work (Compernolle and Müller, 2014), activity coefficient expressions -Margules, Van Laar, Wilson (see e.g.Prausnitz et al., 1999;Carlson and Colburn, 1942) -were fitted to a w data in the subsaturation range, and the fitting parameters were used to obtain the solute activity coefficient ratio γ ∞ s /γ sat s .The precise procedure is described in Appendix A of Compernolle and Müller (2014), and the resulting parameters are shown in Fig. 1.This was done for erythritol, xylitol, sorbitol and mannitol (Fig. 1).The UNIFAC (UNIQUAC Functional-Group Activity Coefficient) method of Marcolli and Peter (2005) (UNIFAC-MP, identical to AIOMFAC for polyol-water systems) underestimates γ w of these polyol/water mixtures.
For adonitol and arabinitol, we calculated γ ∞ s /γ sat s from the one-parameter Margules fittings of Chirife et al. (1984) (see Appendix A4).The results are presented in Table 4.For nonane diol, decane diol, pentaerythritol and dulcitol, no a w data were found, but reasonable assumptions for γ ∞ s /γ sat s could be made (see Table 4).As expected, the polyols with a lower solubility (erythritol, mannitol) have γ ∞ s /γ sat s close to unity.We included estimations of the activity coefficient ratio by UNIFAC-MP.This method gave lower γ ∞ s /γ sat s as compared to our results.

Henry's law constants and enthalpies of gas dissolution
Using Eqs.(4, 5, 8, 10), the data provided in the previous tables, as well as literature data, the Henry's law constants and gas dissolution enthalpies can be derived.The values are given in Table 5.
The expected order hexols > pentols > tetrols > triol > diols in k h is generally followed.Diols have k h between 10 5 and 10 7 M atm −1 .The diols with longer hydrophobic chains have considerably lower k h than their α, ω counterparts (e.g. an order of magnitude difference between 1,2and 1,5-pentane diol).For the linear polyols, k h and H ∞ g→aq are roughly comparable among the different stereo-isomers.Clearly, the large differences in x sat and p 0 Cr of the hexols are mainly due to their different crystal structure, which does not affect k h .Although pentaerythritol has the same number of hydroxyl groups as erythritol, its k h is seven times larger.Probably the tetragonal arrangement of the hydroxyl groups of pentaerythritol facilitates bonding with the water molecules.

Impact on gas-particle partitioning
Similarly as for the diacids and hydroxy polyacids (Compernolle and Müller, 2014), we assess the importance of the partitioning to the particulate phase for polyols in clouds and aqueous aerosol, approximating the liquid phase as a dilute aqueous solvent.Moreover, we also perform a sensitivity test, aiming at determining the particulate fraction of polyols, diacids and hydroxy polyacids in the case of an aqueous ammonium sulfate aerosol.
We note that this discussion, based on Henry's law, is only applicable if the organic compound is present in a tiny amount, and this may not be justified for all situations encountered in the lower atmosphere.

Pure water as the solvent
For clouds, the liquid water content (LWC) varies between typically 0.1 and 1 g m −3 , and for aqueous aerosols between 10 −6 and 10 −4 g m −3 (Ervens et al., 2011).The particulate fraction of organic solute is equal to with n p,s , n g,s the moles of solute in particulate and gas phase respectively.Using the ideal gas law, Eq. ( 19) can be transformed into with V air a unit volume of air and V p the particle volume.If partitioning between gas and aqueous phase is governed solely by Henry's law (Eq.1), and the solvent is considered pure water, Eq. ( 20) becomes   Piacente et al. (1994Piacente et al. ( , 1993) ) (giving rise to the lower k h ) or Knauth and Sabbah (1990a) Bastos et al. (1988), i Jasra and Ahluwalia (1982).j Bone et al. (1983), value at 293 K. k Saxena and Hildemann (1996), value obtained from vapour-liquid equilibrium data.
with ρ w the density of pure water.From the LWC range given above, and fixing T to the reference temperature of 298.15 K, it follows that for clouds, k * varies between 4×10 4 and 4 × 10 5 M atm −1 .From Table 5, it can be deduced that all polyols with three or more hydroxyl groups will be almost completely partitioned to the aqueous phase.Diols will be completely or partially in the aqueous phase, depending on the case.For aqueous aerosol, if one (falsely) assumes the aerosol phase to be pure water, it is obtained from the LWC range given above that at the reference temperature k * varies between 4 × 10 8 and 4 × 10 10 M atm −1 .With this assumption, diols will not partition appreciably to the aqueous phase, glycerol will partition to some extent, and only at the highest water content, while all polyols with four or more hydroxy groups should reside almost completely in the particulate phase.

Aqueous ammonium sulfate aerosol as the solvent
An aqueous aerosol is not a dilute aqueous solution, but is instead a concentrated mixture of organics and/or inorganics.HLC determined for a pure water solvent are less applicable to such mixtures.We present here a sensitivity test for a simple aerosol mixture of water and ammonium sulfate ((NH 4 ) 2 SO 4 , AS).
Note however that this test is only applicable to a situation with a tiny amount of organics.If e.g. a separate organic phase is present, less hydrophilic compounds may partition substantially to the particles, even if the HLC-based analysis suggests otherwise.It is more convenient to use here the alternative HLC definition k px h instead (Eq.2).Let us define n g,s and n p,s as the number of moles of solute in gas and particulate phase respectively, and n p,tot as the total number of moles of the solution.As the particulate solute mole fraction is equal to n p,s /n p,tot , and using the ideal gas law, Eq. ( 2) can be transformed into

Atmos
In the last step Eq. ( 19) was used.Eq. ( 22) can be rearranged to Note that in the particular case of the AS-water system as each molecule of AS dissociates into three ions, and the amount of organic solute is infinitesimally small.The organic solutes considered are the polyols discussed in this work, and the diacids and hydroxy polyacids treated in our previous work (Compernolle and Müller, 2014).The k px h of a solute for a solvent consisting of water and a mole fraction x AS of dissolved AS can be calculated from with γ * s the activity coefficient of the organic solute using the asymmetric convention (i.e.γ * = 1 if the solute is infinitely diluted in pure water).The k px h (x AS = 0) was taken from Table 5 or Table 3 ) and γ ∞ s (x AS = 0) were calculated with the model AIOMFAC (Zuend et al., 2011), available online (http://www.aiomfac.caltech.edu).This model calculates activity coefficients taking interactions between water, organics and inorganics into account.A very small organic mole fraction (x org = 10 −10 ) was chosen to ensure that γ ∞ s (x AS ) and γ ∞ s (x AS = 0) represent IDACs.As a consequence, the impact of the organic solute on the activities of water and the ions is negligible.Although the activities are estimated and not measured, we note that activity data sets of several AS-water-organic mixtures (organic being a polyol, diacid or hydroxy polyacid) are used to determine AIOMFAC's parameters (Zuend et al., 2011).
Given a particular x AS , the water activity and hence the relative humidity (RH) are fixed by the AIOMFAC model.
x AS was varied between 0.43 and 0, corresponding to a RH range between 30 and 100 %.Note that pure AS particles have a deliquescence RH (DRH) of 79.5 % and an efflorescence RH (ERH) of ∼ 35 % (Martin, 2000).The DRH is the equilibrium point below which solid AS is the thermodynamically stable phase and this corresponds to the solubility limit of AS in water.However, depending on the RH history of the particle, a metastable supersaturated solution may instead be present below the DRH.Below the ERH, only solid AS is present in the particulate phase.
The particulate fraction f p,s of the organic solute depends on the amount of solvent (water + AS) per volume of air.A fixed AS mass concentration of 4 µg m −3 was chosen, typical for inorganic aerosols at mid-latitudes over continents (http://vista.cira.colostate.edu/improve/).As a consequence, upon increasing RH from the ERH to 90 %, the LWC varies between 10 −6 and 10 −5 g m −3 , a typical range for aqueous aerosol.
Polyols.Due to their low k h , diols do not partition significantly to aqueous aerosol and hence are not included in this analysis.Stereo isomers of xylitol and sorbitol were also not included, given their similar k h and the fact that AIOMFAC does not distinguish between stereo isomers.For the polyols, AIOMFAC predicts an activity increase with lowering RH (or equivalently increasing the salt concentration) (Fig. 2a).The effect increases with the number of hydroxyl groups.However, this is more than compensated by the concomitant increase in k h (x AS = 0) (Table 5).The particulate fraction of polyols decreases with decreasing RH both due to the increase in solute activity, and the decrease of total absorbing mass.At RH = 90 % glycerol, with three hydroxyl groups, is 95 % in the gas phase while sorbitol, with six hydroxyl groups, is still 50 % in the particulate phase at RH = 44 %.This is due to the large difference (8 orders of magnitude) of their k h values.
Linear diacids.Diacids with two (oxalic) up to 10 (sebacic) carbon atoms are considered.Let us neglect acid dissociation for the moment.AIOMFAC's interaction parameters are negative (stabilizing) between the carboxylic acid group COOH on the one hand, and the ions NH + 4 and SO 2− 4 on the other hand.For the group CH 2 , these interaction parameters are positive (destabilizing).As a consequence, the activity of the linear diacids with four carbon atoms or more increases with decreasing RH.The activity of oxalic acid, on the other hand, decreases with decreasing RH, while the activity of malonic acid stays roughly constant.Even without taking acid dissociation into account, it is clear that these diacids partition appreciably to the particulate phase (Fig. 2b).Note that for malonic acid, we chose the lower of the recommended k h values from Table 3 of Compernolle and Müller (2014); the higher value would lead to f p near unity even without acid dissociation.Hydroxy polyacids.Citric and tartaric acid exhibit a modest activity increase upon decrease of the RH.On the other hand, they have extremely high k h (x AS = 0) values (Compernolle and Müller, 2014).Therefore, they will reside almost with x H 2 A , x HA − and x A 2− the mole fractions of the undissociated acid, monodissociated acid and twice dissociated acid respectively.Acid dissociation is governed by the acid dissociation constants with K a,i mole fraction based acid dissociation constants, and γ * mole fraction based activity coefficients, with the asymmetric convention (i.e.becoming unity at infinite dilu-tion in pure water).Combining Eqs. ( 26) and ( 27) leads to AIOMFAC does not calculate activity coefficients of ionized organic acids.To describe the ionization in the water-ASdiacid system, we used the models provided at the site of E-AIM (http://www.aim.env.uea.ac.uk/aim/aim.php).Specifically, model IV was used, which is an implementation of the parameterizations of Friese and Ebel (2010) and (for the diacids) of Clegg and Seinfeld (2006).Solid formation was prevented, and the dissociation equilibria H 2 O/OH − , NH + 4 /NH 3 , HSO − 4 /SO 2− 4 were taken into account.At the vanishingly small acid concentration used, E-AIM calculates the same γ H 2 A * , γ HA − * and γ A 2− * regardless of the identity of the diacid.This is not realistic; one expects a larger γ * value for a diacid with more CH 2 groups.Therefore, γ H 2 A * , equal to γ * s in Eq. ( 25), is still calculated by AIOMFAC, to take into account the destabilizing CH 2 -ion interaction.The 28) are determined by the E-AIM calculation.Note that due to the vanishingly small acid concentration, γ H + * x H + is determined by the amounts of water and AS only.Acid dissociation constants were taken from E-AIM or Apelblat (2002).are predicted to be completely in the aqueous phase from RH = 100 % to the ERH, while the particulate fraction of the other diacids are clearly enhanced (Fig. 2c), compared to the calculation without acid dissociation (Fig. 2b).

Assessing main uncertainties
HLC of polyols with 2-6 hydroxy groups are derived in this work, using experimental data and thermodynamic relationships.This study complements a previous work (Compernolle and Müller, 2014) where the focus was on diacids and hydroxy polyacids.
An error analysis is performed in Appendix A. The compounds that are liquid at room temperature (most diols and glycerol) have a relatively low uncertainty in k h (relative standard error 6-28 %, see Table 7).For some compounds, further improvement is possible with more precise p 0 L data and/or more fine-grained and precise a w data in the dilute region.b-h The same references as for Table 3 apply.
The compounds that are solid at room temperature, especially the polyols with four or more hydroxy groups, bear a much larger uncertainty in k h (relative standard error 34-82 %, see Table 8).This is mainly due to the use of hightemperature liquid or solid state vapour pressures.More specifically, it is due to the uncertainty in H vap or H sub in combination with the extrapolation over a large temperature interval.For the hexols, also the uncertainty in heat capacity becomes important, although we note that the error in C p,g is speculative as this property is estimated.Measuring the (solid or liquid state) vapour pressure closer to room temperature will lower these uncertainties.
As noted above, the C p,g values are estimated.Improvement here is possible by using C p,g derived from experiment or from ab initio calculations rather than using a group contribution method.For nonane diol and decane diol, only solubilities from a secondary reference (Merck Millipore) could be retrieved, for which it is difficult to estimate the reliability.New solubility measurements are desirable to obtain a more reliable k h estimate.

Comparison with literature
HLC compilations of polyols are provided by e.g.Sander (1999) and Saxena and Hildemann (1996).However, most values in these studies are estimated.Bone et al. (1983) provide HLC measurements for 1,2-ethane diol and 1,3-propane diol (Table 5).Their values are lower but reasonably close (within a factor of 2) to ours.While the majority of HLC values of polyols provided by Saxena and Hildemann (1996) are estimated, a few are derived from vapour-liquid equilibrium data.For 1,2-propane diol, 2,3-butane diol and glycerol, their HLC values are within a factor 3, but for 1,4-butane diol the difference is more than an order of magnitude.In conclusion, for five out of six HLC values, we have a reasonable agreement with the literature values.
The estimated values presented by Saxena and Hildemann (1996) are obtained by a group-contribution method (Suzuki et al., 1992) (values not reproduced in Table 5).For the diols, overestimations by ∼ 1 order of magnitude compared to our values are common.For the compounds with three or more hydroxyl groups, the overestimation ranges between 3 (glycerol) and 8 (mannitol) orders of magnitude, showing the limitations of such an estimation method.

Atmospheric implications
According to the HLC derived in this and the previous work (Compernolle and Müller, 2014), diols will be partially (e.g.1,2 hexane diol, depending on the droplet size) or completely (e.g.1,4-butane diol) in the aqueous phase in clouds, while polyols with three or more hydroxyl groups, diacids and hydroxy polyacids will be completely in the aqueous phase.Regarding aqueous aerosol, the sensitivity test performed here using aqueous AS aerosol indicates that polyols with four or more hydroxyl groups are significantly or totally in the particulate phase, depending on the RH.The same holds for the longer linear diacids (succinic and higher).The shorter linear diacids (oxalic and malonic) and the hydroxy polyacids (citric and tartaric) are completely in the particu-Table 9. p 0 L calculations for erythritol, xylitol and sorbitol, with three vapour pressure estimation methods (Nannoolal et al., 2008;Moller et al., 2008;Myrdal and Yalkowsky, 1997) available at http://www.aim.env.uea.ac.uk/aim/aim.php.a Hypothetical boiling point, adjusted such that the experimental p 0 L at T meas (Barone et al., 1990) is reproduced.These experimental (T meas /K, p 0 L /Pa) data points are (412, 8.6), (433, 5.5) and (477, 6.8) for erythritol, xylitol and sorbitol respectively.
late phase both at lower and higher RH, due to (i) their relatively high acid dissociation constants and/or (ii) stabilizing or only mildly destabilizing interactions with AS and/or (iii) very high k h values.
Note that this analysis is only applicable for aqueous AS aerosol in the limiting case of a small concentration of organics.If e.g. a separate organic phase is present in the aerosol, partitioning to this phase should be taken into account as well.Bao et al. (2012) measured gas particle partitioning of diacids at a site in Japan in different seasons.According to this study, both particulate and gaseous fractions are significant, and RH influences the partitioning.Xie et al. (2014) measured gas particle partitioning of 2-methyl tetrols at a site in Denver and found about equal particulate and gaseous fractions.Our sensitivity test, based on a simple AS-water aerosol system, cannot be quantitatively compared with these studies, but does show that partitioning to the particulate phase is important for diacids and tetrols.

A2 Infinite dilution activity coefficient
The infinite dilution activity coefficient is calculated from a w data using Eq. ( 14).If these data were sufficiently finegrained, precise and cover the entire x w range from 0 to 1, a numerical integration of the integral in Eq. ( 14) would be appropriate.However, if this is not the case, it might be better to fit the a w data with a reasonable model.The following models for ln γ w were considered in this work: Margules, Van Laar, Wilson and UNIQUAC (Carlson and Colburn, 1942;Prausnitz et al., 1999), as they were derived from physical considerations.These models are reproduced below: +θ 2 e −A 21 /T − e −A 12 /T θ 2 + θ 1 e −A 12 /T with x 1 the mole fraction of the first component (here water), x 2 = 1 − x 1 the mole fraction of the second component (here the solute), and A 12 , A 21 the parameters to fit.To determine A 12 , A 21 , a least square regression was performed, minimizing the difference between experimental and modelled ln γ w .For a detailed overview of the quantities used in the UNIQUAC equation, see Prausnitz et al. (1999).Errors in γ ∞ s arise from uncertainty and sparsity in the a w data, but also from a suboptimal model choice.This is especially important if no data in the highly dilute concentration range are available.
All the γ ∞ s derived in this work are based -partially or totally -on the a w from Marcolli and Peter (2005).This work presents a w data, relatively coarse-grained, with a x w range typically between 0.1 and 0.95.The main limitation of this data source is that no data in the highly dilute range are available.We present here first an error analysis for all the 14 diols from Table 2, but using the data of Marcolli and Peter (2005) only.The four activity coefficient expressions were all tested, and the one that fitted the data best was chosen.The results are presented in Table 6.Marcolli and Peter (2005) report that the a w data are "accurate within ±0.015", as specified by the employed instrument, but this does not make clear whether the error is ran-dom and/or systematic, or whether this range corresponds to e.g. one or two standard deviations.If we assume that the selected fitting model is correct and any systematic error in a w is absorbed in the fitting parameters, then any remaining deviation between modelled and experimental values should be due to the random error in the experiment (Bevington, 2003).Standard deviations between modelled and observed a w vary between 0.003 and 0.009 (Table 6).We drew repeatedly random errors from a normal distribution with a standard deviation of 0.0075 (corresponding to 2σ = 0.015), using the python scipy.statsmodule (Jones et al., 2001) and applied these to the a w data.This resulted in a distribution of γ ∞ s values.A relative standard error between 2 % and 14 % on γ ∞ s is obtained in this way.We note however, that this error depends also on the selected model, i.e. γ ∞ s based on Margules models tend to be the least sensitive to the random shifts, while γ ∞ s based on Van Laar and Wilson models are the most sensitive.
Systematic errors in a w can be estimated by comparing with other data sources (Romero and Páez, 2006;Borghesani et al., 1989).The a w data of Marcolli and Peter (2005) are typically higher than from the other data sources, with a MD of 0.005.We applied systematic shifts of ±0.005 on the a w data of Marcolli and Peter (2005).This had a minor impact on γ ∞ s , between 2 and 6 %.We note that we had expected that the largest γ ∞ s (from 1,7-heptane diol and 1,2-hexane diol) would exhibit the largest sensitivity on these random and systematic shifts.This turned out not to be true, however.
Errors due to a suboptimal model choice are more difficult to quantify.Per compound, the other three activity coefficient models (apart from the "best" one) were also considered.If the fitting was considerably worse, the model was rejected because it was probably not appropriate.If the fitting gave essentially the same γ ∞ s result, it was also not retained, because in that particular case the models were not truly different.In this way, for seven diols γ ∞ s from an alternative model were selected (presented in Table 6).The RMSRD between γ ∞ s of the "best" model and "alternative" model was 12 %.The most important reason for the discrepancy between the activity coefficient models was their behaviour at the highly dilute region, where no data were used to constrain them.
For eight diols in Table 2, also data from two other sources (Borghesani et al., 1989;Romero and Páez, 2006) were available.Note that Borghesani et al. (1989) do not provide the data points but only fitted expressions.These two data sources are very precise; e.g.Romero and Páez (2006) report a relative uncertainty in a w of 0.005 % or less.They are also in good agreement with each other; the difference in a w is typically 0.001 or less.These data cover the highly dilute region (x w typically in the range between 0.93 and 0.996) and therefore enable us to largely correct for the error due to a suboptimal model choice.Using these data as well, more accurate estimations of γ ∞ s were made (  (2005) data, a RMSRD of 13 % was obtained, in good agreement with our above estimate of the error due to a suboptimal model choice.Therefore, we assign to all γ ∞ s where only data from Marcolli and Peter (2005) are used, a standard error of 13 %.
Practically, the derivation of γ ∞ s when multiple data sources are available was done in the following way.The integral in Eq. ( 14) was split into two parts: where x w marks the start of the highly dilute region for which data of Borghesani et al. (1989) and Romero and Páez (2006) are available.For the region [0, x w ] we employed for ln γ w the corresponding activity coefficient expression from Table 6.For the region [ x w , 1], the data from Borghesani et al. (1989) and Romero and Páez (2006) were integrated.This was attained either by a numeric integration, or by fitting an activity coefficient expression over this small region, or -if only data of Borghesani et al. (1989) were available -the analytic expression given in this study was used.We assign to these more accurate estimations of γ ∞ s a small standard error of 5 %.
For the two triols in Table 2, the data of Marcolli and Peter (2005) and of Ninni et al. (2000) and Scatchard et al. (1938) were combined.There is a good agreement between the data; e.g.Ninni et al. (2000) report that for glycerol, there is only 0.1 % relative deviation between their a w data and those of Scatchard et al. (1938).Also here we assign a small standard error of 5 % on γ ∞ s .

A3 Solubility
As some solubility data of the polyols are from literature compilations, uncertainties are not always available.But when reported, they are typically very low.For xylitol, Wang et al. (2013) reported an error of no more than 0.5 % on x sat s .For pentaerythritol, a 0.3 % error can be derived from the study of Cheon et al. (2005) and 0.15 % from the study of Chianese et al. (1995).Higher errors are found when comparing different studies.For erythritol, Hao et al. (2005) report a 4 % uncertainty by comparing with literature data.For pentaerythritol, we found by comparing data of Cheon et al. (2005), Chianese et al. (1995) and Mullin (2001) that the RMSRD on room temperature x sat s is 5 %.Compared to the estimated errors on solid state pressure (see Sect.A5), these errors are very minor.We assign a standard error of 5 % to all solubility values, except for those of 1,9-nonane diol and 1,10-decane diol.For these latter two compounds, there are two issues.First, the data are from a secondary reference (Merck Millipore; http://www.merckmillipore.com/)from which it is difficult to assess the reliability.Second, the solubility is not reported at the reference temperature of 298.15K but at 293.15 K instead.The temperature dependence of solubility can be described by a van 't Hoff relation (Atkins and de Paula, 2006): The H vH Cr→aq is not known for these two diols.For monoalcohols it can be either positive or negative and is (in absolute value) in the range 0-30 kJ mol −1 (based on data from Mackay et al., 2006).Based on this, we estimate roughly the standard error on x sat s at 298.15 K as 15 %.

A4 Activity coefficient ratio
The activity coefficient ratio γ ∞ s /γ sat s is calculated from a w data.The error on γ ∞ s /γ sat s depends on the solubility.If the solubility is very low, γ ∞ s /γ sat s will necessarily be very close to unity and the uncertainty on γ ∞ s /γ sat s will vanish (see Eq. 18).For all compounds with x sat s < 0.1 we neglect the error.Xylitol, adonitol, arabinitol and sorbitol have relatively high solubilities (x sat s ≈ 0.2) and γ ∞ s /γ sat s considerably deviating from 1 (Table 4).For xylitol and sorbitol, precise a w data are available (Ninni et al., 2000;Comesaña et al., 2001;Bower and Robinson, 1963); e.g.Ninni et al. (2000) report a reproducibility of ±0.001 a w units.There is a good agreement between the data sources.For sorbitol, there is a near perfect agreement between the data sets of Comesaña et al. (2001) and Bower and Robinson (1963) (no significant MD, and a RMSD of 0.0005).The RMSD between the a w data of Ninni et al. (2000) on the one hand, and the data of Comesaña et al. (2001) and Bower and Robinson (1963) on the other hand, for both xylitol and sorbitol, is 0.003.This is similar to the standard deviation between modelled a w and experimental a w (0.0015 for sorbitol, 0.003 for xylitol).Therefore, we applied random shifts from a normal distribution with a standard deviation of 0.003 to the a w data.This resulted in a 5 % uncertainty on γ ∞ s /γ sat s for sorbitol and a 2.5 % uncertainty for xylitol.We adopted 5 % as a relative standard error for the γ ∞ s /γ sat s of xylitol and sorbitol (Table 8).Chirife et al. (1984) presented one-parameter fittings of the form ln γ w = exp (−Ax s ), from which γ ∞ /γ sat can be derived.Using Eq. ( 18), one has For adonitol and arabinitol, these are the only data available.γ ∞ s /γ sat s values derived in this way are likely more uncertain than the values given above for sorbitol and xylitol.For these two compounds, we compared our own γ ∞ s /γ sat s values (in Table 4) with the values obtained using the one-parameter fittings of Chirife et al. (1984) and found a RMSRD of 16 %.Therefore, we assign a relative standard error of 16 % to the γ ∞ s /γ sat s of adonitol and arabinitol (Table 8).

A5 Derivation of sublimation data
Starting from high-temperature solid state pressure data, and heat capacity data, the solid state pressure p 0 Cr at T ref = 298.15K is given by ln In the case that the high-temperature data corresponds to liquid vapour pressure p 0 L , the relation is Uncertainties on terms A (involving high temperature vapour pressure data), B (involving heat capacity data) and, depending on the case, C (involving fusion data) will contribute to the error on ln p 0 Cr (T ref ): In the next sections these three uncertainties are analysed.

A5.1 High-temperature p 0 Cr and p 0 L data
To simplify the discussion, in this section, p 0 , S and H stand for either p 0 Cr , S sub and H sub or p 0 L , S vap and H vap respectively, depending on whether the compound is a solid or a liquid at T meas .Term A is then given by The standard error of A, from the error propagation rule (Bevington, 2003) (neglecting the uncertainty in T meas ), is equal to In the study of Knauth and Sabbah (1990a), p 0 (T meas ) and H (T meas ) are measured separately and at one fixed temperature.In the other studies, however (Nitta et al., 1951;Bradley and Cotson, 1953;Barone et al., 1990;Nitta et al., 1950;Piacente et al., 1993Piacente et al., , 1994)), H was derived from a linear regression of ln p 0 vs. 1/T .Over the relatively small temperature interval, the temperature dependence of H can be neglected (Clausius-Clapeyron relation, see e.g.Atkins and de Paula, 2006).Eq. () still applies, if p 0 L is taken at the centre of the measurement interval (Ramsey and Shafer, 1997).T meas then corresponds to the centre of the temperature interval (see Table 3) and is presented in Table 8.Most high-temperature p 0 data are from Piacente and co-workers, covering both diols and polyols with four or more hydroxyl groups (Piacente et al., 1993(Piacente et al., , 1994;;Barone et al., 1990).
As before (see Sect.A1), we estimate SE p 0 (T meas ) p 0 (T meas ) as 0.25 for the data of Knauth and Sabbah (1990a) and Piacente et al. (1993Piacente et al. ( , 1994)).By comparing H data on diols from Knauth and Sabbah (1990a) and Piacente et al. (1994), we find a RMSD of 3.5 kJ mol −1 , which we adopt as SE [ H (T meas )] for both data sources.As is often the case when comparing different data sources, this error is higher than the errors reported in the individual studies themselves (typically 1-2 kJ mol −1 ).For large differences between T ref and T meas , SE(A) is determined mainly by uncertainty in the enthalpy term.This is the case for the polyols with four or more hydroxyl groups.The largest SE(A), about 0.6, is obtained for the hexols (Table 8).
Most data on polyols with four or more hydroxyl groups is from Piacente and co-workers (Barone et al., 1990).There are a few other, much older studies (Nitta et al., 1950(Nitta et al., , 1951;;Bradley and Cotson, 1953) on erythritol and pentaerythritol, with H values strongly deviating (15-30 kJ mol −1 lower) from the data of Barone et al. (1990).These large discrepancies cannot be understood from the reported precisions, or from the error of 3.5 kJ mol −1 adopted above.We think that this points to problems with one or more of the experimental studies, rather than to a typical experimental uncertainty.We judge the data of Piacente and co-workers as the more reliable, for the following reasons.(i) A relatively good agreement in H of diols with Knauth and Sabbah (1990a) (Piacente et al., 1993(Piacente et al., , 1994)).(ii) Piacente and co-workers also present p 0 L measurements on diols using another technique, and with comparable results (Piacente et al., 1993).(iii) Consistency, in the sense that the high-temperature p 0 L data of stereo-isomers of polyols are comparable, as one would expect (Barone et al., 1990).(iv) Compared to the older studies, S. Compernolle and J.-F.Müller: Henry's law constants of polyols those of Piacente and co-workers employ more data points and a larger temperature interval.Obviously, more p 0 measurements on polyols with four or more hydroxyl groups are desirable.

A5.2 Heat capacity data
Assuming that the error on heat capacity is temperature independent, one derives from Eq. () for the standard error on term B (if no fusion point is involved) Most C p,L and C p,Cr data we use is from Tong and coworkers (Tong et al., 2007(Tong et al., , 2008(Tong et al., , 2009(Tong et al., , 2010b, a), a), as it covers a wide range of polyols and temperatures.Quoted errors on the experimental values of C p,L and C p,Cr are very low, e.g.0.2 % for those of Tong and co-workers.This corresponds to about 0.5 J/(Kmol) error on the heat capacity value.However, the discrepancy between data of different groups is much larger.We compared the data of Tong and co-workers with other data where possible: for erythritol (Lopes Jesus et al., 2005;Spaght et al., 1931), sorbitol (Lian et al., 1982) and mannitol (Lian et al., 1982;Spaght et al., 1931).Based on the RMSD of the data, we assign SE C p,L = SE C p,Cr = 20 J/(Kmol), much larger than the reported errors.By taking identical errors for C p,L and C p,Cr (there are not enough data to treat them separately), Eq. (A24) simplifies to Eq. (A23).
In a few cases (arabinitol, dulcitol, liquid state mannitol) we did not found heat capacity data in the appropriate temperature range and we took heat capacity data of a stereoisomer instead (see Table 3).To test the validity of this assumption, we compared heat capacity data at or above room temperature of stereo-isomers from the same research group.Regarding the liquid state, C p,L data of the stereo-isomers erythritol and threitol (Lopes Jesus et al., 2005), and of the stereo-isomers xylitol and adonitol (Tong et al., 2007(Tong et al., , 2010b) ) differ by less than 2 J/(Kmol).This justifies the approximations C p,L (arabinitol) ≈ C p,L (xylitol), C p,L (dulcitol) ≈ C p,L (sorbitol) and C p,L (mannitol) ≈ C p,L (sorbitol) applied in this work.Regarding the solid state, we compared C p,Cr of stereo-isomers erythritol and threitol (Lopes Jesus et al., 2005), xylitol and adonitol (Tong et al., 2007(Tong et al., , 2010b)), mannitol and sorbitol (Tong et al., 2010a(Tong et al., , 2008;;Lian et al., 1982), only taking into account the data at T ≥ T ref (as this is the most relevant for our work) and found a RMSD of 9 J/(Kmol).This is larger than for the liquid state but still smaller than the discrepancies between different works on the same molecule.Moreover, for the low-temperature (88-291 K) C p,Cr data for the stereo-isomers dulcitol and mannitol (Parks and Huffman, 1926;Parks and Anderson, 1926), the RMSD was only 2 J/(Kmol).Therefore, also the approximations C p,Cr (arabinitol) ≈ C p,Cr (xylitol) and C p,Cr (dulcitol) ≈ C p,Cr (mannitol) seem to be justified.
Regarding C p,g , the error is difficult to quantify as this value is not measured but obtained by the Benson group contribution method.Poling et al. (2001) quote a relative error of 1 % for this method, but as polyols are under-represented in the fitting set of this method, this is probably not realistic.The method of Domalski and Hearing (1993) is a very close relative to the Benson group contribution method (although limited to room temperature), yielding very similar results for C p,g .Importantly, this method also estimates C p,L and C p,Cr .Comparing C p,Cr for erythritol, xylitol and sorbitol from Tong and co-workers with estimations by the method of Domalski and Hearing (1993) yields a RMSD of 20 J/(Kmol).We make now the assumption that this error is applicable to C p,g as well.Hence we assign SE C p,g = 20 J/(Kmol).
For the diols, where T meas is relatively close to T ref , SE [B] is small (1-7 %), but for the compounds with four or more hydroxyl groups it becomes more important -over 40 % for the hexols (see Table 8).

A5.3 Fusion data
In this section the error due to the term H fus (T fus ) in Eq. (A17) is estimated.From the error propagation rule the standard error can be derived as Fusion data were collected from Tong et al. (2007Tong et al. ( , 2008Tong et al. ( , 2009Tong et al. ( , 2010b, a), a), Barone et al. (1990), Badea et al. (2014) and Knauth and Sabbah (1990a).The selected T fus are presented in Table 8.Reported errors in these works are typically 0.1 K for T fus and 0.1-0.3kJ mol −1 for H fus .However, comparing the data between the different references reveals larger uncertainties: a standard deviation of 2.8 K for T fus and 2.2 kJ mol −1 for H fus .Using these errors, SE(C) ranges from 0.13 for nonane diol to 0.33 for dulcitol (see Table 8).

A6 Overall discussion of errors
Table 7 gives an overview of the estimated relative standard errors on p 0 L , γ ∞ s and the derived relative standard error on k h .This applies to the compounds which are liquid at room temperature, i.e. most diols discussed in this work and glycerol.The relative standard error on k h ranges between 6 % and 30 %.
Table 8 gives the different error contributions when the compound is solid at room temperature, and the resulting relative standard error on k h .In all cases, SE (A) is the dominant error contribution.For all polyols with four or more hydroxyl groups, this is caused by the large difference between T meas and T ref and the uncertainty on H fus .The estimated relative standard error on k h ranges between 30 and 80 %.

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also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 arabinitol b, c 5 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43erythritol 4 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 sorbitol 6 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 pentaerythritol 4 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 mannitol e 6 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 xylitol 5 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 dulcitol d, e 6 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.43 adonitol a, c 5 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .Figure 1 .
Figure1.The ln γ w data for erythritol, xylitol, mannitol and sorbitol, compared with the fitting using the Margules formula, and UNIFAC-MP results.Note that the data ofComesaña et al. (2001) is at 20 • C rather than 25 • C, but from their data at 35 • C, it can be deduced that the temperature dependence of ln γ w is small.

Figure 2 .Figure 2 .
Figure 2. (a) Activity coefficient correction (log 10 γ * s ) of the organic solute vs. RH for an AS-water particle, as calculated by AIOMFAC.(b) Particulate fraction of the organic solute vs. RH.Acid dissociation is not taken into account.Tartaric and citric acid have f p = 1 over the entire presented range.(c), as (b), but taking acid dissociation into account using the on-line model of E-AIM (see text for more details).Oxalic, malonic, tartaric and citric acid have f p = 1 over the entire presented range.

Table 1 .
Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 1 .
Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.

Table 1 .
Molecular structures of polyols with three or more hydroxyl groups, discussed in this work using non-IUPAC names.
a also named ribitol, b also named arabitol, c stereo isomer of xylitol, d also named galacticol, e stereo isomer of sorbitol.

Table 2 .
Infinite dilution activity coefficients derived in this work, the sources of water activity they are based on, and comparison with the literature.

Table 3 .
Solid state pressure and enthalpy of sublimation of polyols, obtained from Eqs. (15), (16) and/or (17), at T ref = 298.15K,andreference to the data used to obtain them.C p,g is estimated by the method ofBenson (1976).

Table 5 .
Henry's law constants and gas dissolution enthalpies at 298.15 K for the polyols considered in this work, from Eqs. (4, 5, 8, 10).γ ∞ s is taken from Table 2, p 0 Cr , H sub from Table 3 and γ ∞ s /γ sat s from Table 4.

Table 6 .
Marcolli and Peter (2005)ods that best fit the data ofMarcolli and Peter (2005).For seven compounds, an alternative fitting is presented.
a Optimized parameters to use in the activity coefficient expression for ln γ w .bStandarddeviation between modelled and observed ln γ w .cStandarddeviation between modelled and observed a w .dRangefor ln γ ∞ s , obtained by applying systematic shifts of ±0.005 to the a w data.eStandarddeviation on ln γ ∞ s , obtained by applying random shifts from a normal distribution with σ = 0.0075 to the a w data.completely in the particulate phase from RH = 100 % to the ERH.Impact of acid dissociation.The effective HLC, k

Table 7 .
Estimated relative standard errors on p 0 L , γ ∞ s and the resulting relative standard error on k h .See Sects.A1 and A2.

Table 8 .
Estimated relative standard errors on x sat s , a Fusion point and SE (C) not relevant here as T fus > T meas .