A thermodynamic model of mixed organic-inorganic aerosols to predict activity coefficients

Transcription

1 Atmos. Chem. Phys., 8, , 28 Author(s) 28. Ths work s dstrbuted under the Creatve Commons Attrbuton 3. Lcense. Atmospherc Chemstry and Physcs A thermodynamc model of mxed organc-norganc aerosols to predct actvty coeffcents A. Zuend, C. Marcoll, B. P. Luo, and T. Peter Insttute for Atmospherc and Clmate Scence, ETH Zurch, Swtzerland Receved: 2 February 28 Publshed n Atmos. Chem. Phys. Dscuss.: 26 March 28 Revsed: 2 June 28 Accepted: 8 July 28 Publshed: 6 August 28 Abstract. Tropospherc aerosols contan mxtures of norganc salts, acds, water, and a large varety of organc compounds. Interactons between these substances n lqud mxtures lead to dscrepances from deal thermodynamc behavour. By means of actvty coeffcents, non-deal behavour can be taken nto account. We present here a thermodynamc model named AIOMFAC (Aerosol Inorganc- Organc Mxtures Functonal groups Actvty Coeffcents) that s able to calculate actvty coeffcents coverng norganc, organc, and organc-norganc nteractons n aqueous solutons over a wde concentraton range. Ths model s based on the actvty coeffcent model LIFAC by Yan et al. (999) that we modfed and reparametrsed to better descrbe atmosphercally relevant condtons and mxture compostons. Focusng on atmospherc applcatons we consdered H +, L +, Na +, K +, NH +, Mg2+, Ca 2+, Cl, Br, NO 3, HSO, and SO2 as catons and anons and a wde range of alcohols/polyols composed of the functonal groups CH n and OH as organc compounds. Wth AIOMFAC, the actvtes of the components wthn an aqueous electrolyte soluton are well represented up to hgh onc strength. Most notably, a sem-emprcal mddle-range parametrsaton of drect organc-norganc nteractons n alcohol+water+salt solutons strongly mproves the agreement between expermental and modelled actvty coeffcents. At room temperature, ths novel thermodynamc model offers the possblty to compute equlbrum relatve humdtes, gas/partcle parttonng and lqud-lqud phase separatons wth hgh accuracy. In further studes, other organc functonal groups wll be ntroduced. The model framework s not restrcted to specfc ons or organc compounds and s therefore also applcable for other research topcs. Correspondence to: A. Zuend (andreas.zuend@env.ethz.ch) Introducton Tropospherc aerosols are composed of many dfferent organc and norganc substances orgnatng from drect emsson of partcles and from condensaton of gas phase speces (Kanakdou et al., 25). Feld measurements show that organcs are not just traces n ndvdual aerosol partcles, but rather that 3% to more than 8% of the aerosol mass n the free troposphere are carbonaceous materal. Most of ths carbonaceous materal s organc (Murphy et al., 26). The abundance of organcs n aerosols s comparable to the other well-known tropospherc aerosol components such as sulphurc acd and ammona. Sngle partcle measurements suggest that organc and norganc speces are mostly nternally mxed, especally far away from local sources (Murphy and Thomson, 997; Mddlebrook et al., 998; Lee et al., 22; Murphy et al., 26). Ths assumpton of aerosols as nternal mxtures of organcs and norgancs s also supported by gas phase dffuson consderatons of sem-volatle speces (Marcoll et al., 2). Whle the prevalent norganc aerosol consttuents are relatvely small n number, the organc fracton s hghly complex, contanng hundreds of compounds wth a large fracton stll undentfed (Rogge et al., 993). Such a wde varety of organc compounds n the lqud and sold aerosol phases requres some classfcaton. Ths s often done consderng dfferent functonal groups mplyng that sem-volatle, oxdsed organcs tend to contan a hgh degree of functonalty, ncludng hydroxyl, carboxyl, and carbonyl groups (Decesar et al., 2; Mara et al., 2). Whle the thermodynamcs of aqueous norganc systems at atmospherc temperatures s well establshed, lttle s known about the physcochemstry of mxed organcnorganc partcles. Saltng-out and saltng-n effects result from organc-norganc nteractons and are used to mprove ndustral separaton processes. In the atmosphere, they may nfluence the aerosol phases. Phase separatons nto a manly polar (aqueous) and a less polar organc phase Publshed by Coperncus Publcatons on behalf of the European Geoscences Unon.

2 56 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols as smulated by Erdakos and Pankow (2) and Chang and Pankow (26), may consderably nfluence the gas/partcle parttonng of sem-volatle substances compared to a sngle phase estmaton. Recent experments show that the nteractons between norganc ons and organc compounds n aerosol partcles may nduce a lqud-lqud phase separaton durng humdty cycles (Marcoll and Kreger, 26). Thus, a thermodynamc model s requred that predcts the phase parttonng of organc compounds between the gas and the condensed phases, as well as the compostons of the possble lqud and sold phases at thermodynamc equlbrum. Non-deal thermodynamc behavour n mxtures s usually descrbed by an expresson for the excess Gbbs energy G ex (p, T, n j ), as the characterstc state varables of experments are usually pressure p and temperature T. The correspondng actvty coeffcents γ j of the speces wth amount of moles n j n the mxture, are related to G ex by: ( G ex ) /RT ln γ j =. () n j T,p,n j =j For aqueous electrolyte solutons, Ptzer on-nteracton models are well-known for ther ablty to calculate actvty coeffcents n aqueous electrolyte solutons, rangng up to hgh concentratons (Ptzer, 99; Carslaw et al., 995; Clegg et al., 998a). For non-electrolyte lqud mxtures, the substance specfc UNIQUAC (UNIversal QUAs- Chemcal) model (Abrams and Prausntz, 975) and ts group-contrbuton verson UNIFAC (UNIquac Functonal group Actvty Coeffcents) (Fredenslund et al., 975) are wdely used for the predcton of lqud-phase actvty coeffcents of organc speces and water. The model LIQUAC (L et al., 99) and ts group-contrbuton verson LIFAC by Yan et al. (999) merge a Ptzer-lke approach wth a UNI- QUAC/UNIFAC model to calculate the actvty coeffcents of mxed organc-norganc systems. To resolve the problem of lqud-lqud equlbra (LLE) calculatons when usng varable reference states n mxed solutons, a modfed verson of LIQUAC/LIFAC wth fxed reference states was proposed recently (Kepe et al., 26). Such models enable the computaton of chemcal potentals and the Gbbs energy of mxed systems, and therefore possble phase separatons. The orgnal LIFAC model was developed for chemcal engneerng purposes, whch dffer manly n the selecton of chemcal speces, the concentraton, and temperature ranges from the needs of aerosol scence. In ths study, we present a modfed LIFAC model to descrbe atmosphercally relevant aqueous solutons up to hgh onc concentratons at room temperature. Ths actvty coeffcent model named AIOMFAC (Aerosol Inorganc-Organc Mxtures Functonal groups Actvty Coeffcents) explctly accounts for molecular nteracton effects between soluton consttuents, both organc and norganc. In comparson, the ZSR mxng rule (Zdanovsk, 936, 98; Stokes and Robnson, 966) and models based on such rules do not explctly consder organc-norganc nteractons. The careful choce of reference and standard states (see below) for the neutral and onc speces allows to compute vapour-lqud (VLE), lqud-lqud (LLE) and sold-lqud (SLE) equlbra wthn one framework. In the atmosphere, the relatve humdty (RH) vares over a wde range and thus affects the concentratons and stable phases n aerosol partcles. Compared wth bulk solutons, n lqud aerosol droplets much hgher supersaturatons (metastabltes) wth respect to crystallne phases can be reached. For ths reason, AIOMFAC was parametrsed takng such hgh onc strengths nto account by usng also data from electrodynamc balance (EDB) measurements of sngle levtated partcles. Besdes choosng more approprate reference and standard states and accountng for hgh onc strength, other dfferences compared to the orgnal LI- FAC model concern the ntroducton of addtonal electrolyte speces such as sulphurc acd and ammonum bsulphate. Organc compounds used n ths study comprse a wde range of alcohols and polyols, represented by the functonal groups OH and CH n (n=,, 2, 3). The presented modular framework allows to nclude further functonal groups, e.g. carboxyl, carbonyl or aromatc groups, n future studes. 2 Model framework 2. General consderatons The lqud mxtures consdered n the present study are composed of dfferent norganc salts, norganc acds, organc compounds, and water at room temperature (298 K). Organcs are constraned to alcohols and polyols. As we are prmarly nterested n descrbng natural aerosols wth ther tendency to stay fully lqud despte supersaturatons wth respect to varous assocated crystallne states, the formaton of sold salts or hydrates s prevented on purpose, enablng the formaton of metastable solutons. The mxtures are treated as homogeneous bulk solutons excludng curvature effects, whch become only mportant for aerosol droplet rad smaller than 5 nm. Usng the termnology of Yan et al. (999), organc components and water are called solvents and the term solute refers to ons. All salts and acds n the lqud mxture are treated as completely dssocated nto ons, except for the second dssocaton stage of sulphurc acd (HSO H+ +SO 2 ) whch s explctly taken nto account. Strctly speakng, assumng complete dssocaton s vald only at very low solute concentratons because even strong electrolytes assocate to a certan amount at hgher concentratons (Heyrovska, 26). However, on assocaton effects on soluton thermodynamcs are taken nto account by the actvty coeffcents of the solutes and solvents, thereby justfyng the present approach. Atmos. Chem. Phys., 8, , 28

3 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols Group-contrbuton concept Followng the dea of UNIFAC, a group-contrbuton concept s used to descrbe nteracton effects of organc compounds and water n a soluton, thereby coverng a large number of organcs by means of just a few functonal groups. For the use n the dfferent model parts, the functonal groups of a chemcal speces are further dvded nto socalled (functonal) man groups and subgroups. For example, the alkyl groups CH 3, CH 2, CH and C are dfferent subgroups classfed nto the man group CH n. The hydroxyl group OH s the only subgroup of the man group OH. Therefore, -propanol (CH 3 CH 2 CH 2 OH) conssts of 3 CH n + OH n terms of man groups or when resolved nto subgroups of CH 3 +2 CH 2 + OH. The group-contrbuton concept can be extended to electrolyte solutons by the ncluson of ons as put forward by e.g., extended UNIFAC or the LIFAC models. AIOMFAC s based on LIFAC and uses the same group-contrbuton concept. In the cases of water and norganc ons, man groups, subgroups, and chemcal speces are dentcal and the terms are used accordng to the context. Consequently, the category solvent man groups of an aqueous organc-norganc soluton ncludes the dfferent man groups of organc solvents as well as water Reference states To avod problems when usng the AIOMFAC model to calculate lqud-lqud phase separatons, the reference and standard states of the solvents and solutes should be chosen approprately. The chemcal potental µ j (J mol ) of component j n the soluton s: µ j = µ j + RT ln a j, (2) where µ j s the chemcal potental of j wth respect to a standard state, R (J K mol ) the unversal gas constant, T (K) the temperature, and a j the actvty of speces j. Usng ndces for ons and s for solvent components, the mole fracton of j (j used for solvent or solute speces) n terms of number of moles n j s: n j x j = n +. (3) n s s s re- On the mole fracton scale the actvty coeffcent γ (x) j lated to a (x) j by: a (x) j = γ (x) x j j xj, () where the superscrpt (x) denotes the mole fracton bass and xj s the standard state mole fracton of j. For solvent components we choose the symmetrc conventon wth the standard state of the pure lqud (xs =) and the reference state of γ s (x) as x s. For ons a pure lqud (of catons or anons) s of course nconcevable. To use the symmetrc conventon for ons, one would therefore have to choose pure fused salts as the reference states (Erdakos et al., 26). However, havng more than one speces of both catons and anons n a mxture, the reference bass of pure fused salt becomes ambguous (Ptzer, 99). To avod such condtons (and to make use of an expermentally preferred scale), we chose the unsymmetrcal conventon on the molalty bass for the ons. Molalty m (mol kg ) of on n a soluton wth solvent components s s defned as: n m =, (5) n s M s s here n and n s are the number of moles of the onc and solvent components, respectvely, and M s (kg mol ) s the molar mass of compound s. Smlar to Eq. (), the relaton for the actvty coeffcent on the molalty bass (m) s: a (m) = γ (m) m m, (6) wth m beng the standard state molalty (conventonally defned as unt molalty,.e. m = kg mol ). For LLE calculatons t s very useful to have the same fxed standard state n all coexstng (lqud) phases of dfferent composton. For atmospherc aerosol systems t makes sense to choose water as the reference solvent. In the AIOMFAC model, the reference state of ons s therefore the nfntely dluted soluton of on n water: γ (m) as x w, s =w x s, and m, I, where I s the onc strength (Eq. ). In contrast to the symmetrc mole fracton conventon, where reference state and standard state are equal, n the unsymmetrc conventon the standard state s the hypothetcal deal aqueous soluton of unt molalty at standard pressure and temperature Non-deal thermodynamcs The excess Gbbs energy G ex (J ) characterses for the nondealty of a thermodynamc system. Dfferent types of nteractons nvolvng charged and non-charged soluton speces, nteractng over dfferent geometrc ranges, can be dentfed. The total excess Gbbs energy of a multcomponent mxture n the AIOMFAC model s expressed n terms of three contrbutons from long-range (LR), mddle-range (MR) and shortrange (SR) nteractons: G ex = G ex LR + Gex MR + Gex SR. (7) A detaled descrpton of typcal expressons for nteracton potentals, whch play a role n norganc mxtures or n organc-norganc mxtures has been gven by, e.g. Ptzer Atmos. Chem. Phys., 8, , 28

4 562 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols G ex = G ex LR + G ex MR + G ex SR AIOMFAC nteracton contrbutons Ionc strength n delectrc medum (e.g. water or solvent mxture) + - caton - anon on - dpole - on - nduced dpole + dpole - dpole dpole - nduced dpole dsperson Ptzer-lke UNIFAC Fg.. Three major terms represent dfferent types of molecular nteractons n a soluton and add up to the excess Gbbs energy (G ex ) of a certan system n the AIOMFAC model. Dsperson forces, also called London forces, are present n any mxture and denote nduced dpole-nduced dpole nteractons. Long-range forces between ons are descrbed by only takng the electrc charge nteractons nto account whle neglectng other on specfc propertes (e.g. the dfferent rad). (99) and L et al. (99), respectvely. Fgure schematcally shows the three nteracton ranges consdered n AIOM- FAC. Long-range and mddle-range nteractons are descrbed wthn a Ptzer-lke part, n whch the former are descrbed by an extended Debye-Hückel term. Short-range nteractons of non-charged components are calculated n the UNIFAC part. Note that when no electrolytes are n the mxture, AIOMFAC reduces to UNIFAC. In the followng sectons, the LR, MR, and SR model parts are explaned n more detal. 2.2 Long-range contrbuton The G ex LR term represents the LR nteracton contrbuton caused by Coulomb electrostatc forces between the permanently charged ons, moderated by the presence of the delectrc solvent medum. The Debye-Hückel theory was the frst approach to successfully descrbe the electrolyte effects n hghly dluted solutons (Debye and Hückel, 923). Ths theory treats the solutes as electrcal charges n a solvent medum of a specfc densty and delectrc constant and was shown to be correct n the lmt of nfnte dluton. In ths study, we use the extended Debye-Hückel theory modfed as by Fowler and Guggenhem (99). As a consequence of the choce of the reference solvent water for norganc ons, the Debye-Hückel expresson s dfferent from the one n orgnal LIFAC. Instead of usng mxng rules to estmate the densty and delectrc constant of the solvent mxture, we use water propertes for all solvent components. Smlar assumptons were made for the LR part of other mxed solvent models (Iluta et al., 2). Wth ths constrant, the correspondng LR actvty coeffcent expressons for the solvents γ LR,(x) s ln γ LR,(x) s ln γ LR,(x), and the ons γ LR,(x), are: = 2AM [ s + b I b 3 2 ln + b I ( + b I) ], (8) = z2 A I + b I. (9) Equaton (9) gves the actvty coeffcent of on n the mole fracton bass (x) wth the reference state of nfnte dluton Atmos. Chem. Phys., 8, , 28

5 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols 563 ons / man groups H + Na + + NH K + L + Mg 2+ Ca SO - HSO Cl - - NO 3 Br - CH n OH CH n -CO COOH CH n -O H 2 O H + Na + NH + K + L + Mg 2+ Ca 2+ SO 2- HSO - Cl - NO 3 - Br - CH n OH CH n -CO COOH CH n- O H2O caton anon, on funct. man group: parametrsed n MR caton caton: no MR parameters wth the excepton of NH + H + anon anon: no MR parameters funct. subgroup funct. subgroup: parametrsed n SR (UNIFAC) already same funct. group: no nteracton water as the reference solvent for ons: no drect MR parameters Fg. 2. Scheme of the currently parametrsed nteractons n the MR and SR part. Ft parameters for on-on and on-organc man group nteractons are all ncorporated n the MR part and set to zero n the SR (UNIFAC) part. CH n CO, COOH, and CH n O present further mportant organc man groups whose MR nteracton parameters are not estmated so far. n water, ndcated by superscrpt. M s s the molar mass of solvent s, z the number of elementary charges of on, and the onc strength I (mol kg ) s: I = m z 2 2. () The Debye-Hückel parameters A (kg /2 mol /2 ) and b (kg /2 mol /2 ), depend on temperature T (K), densty ρ w (kg m 3 ), and relatve statc permttvty ɛ w (dmensonless) of water, as calculated based on a dstance of closest approach of. nm between ons: A = ρw ρw, () (ɛ w T ) 3/2 b = ɛw T, (2) wth all varables expressed n SI unts as mentoned above. The smplfcaton to a water-propertes based expresson for LR actvty coeffcents mplcates the advantage of not havng to estmate unknown delectrc constants of certan organc compounds (Raatkanen and Laaksonen, 25) and mantans the thermodynamc consstency regardng the chosen reference states. In a real mxture solvents have denstes and delectrc propertes dfferent from those of pure water, whch was the reason for other authors to avod applyng ths smplfcaton. We compensate naccuraces stemmng from ths smplfcaton n the sem-emprcal MR part (see below). Also, snce the physcal valdty of the Debye-Hückel equaton s lmted to hghly dlute onc solutons, the man effect of the LR part and the nvolved approxmatons to descrbe a mxture s behavour holds only n that concentraton range (typcally<. mol kg ). 2.3 Mddle-range contrbuton The G ex MR term, as llustrated n Fg., s the contrbuton of the nteracton effects nvolvng ons and permanent or nduced dpoles. Moreover, the sem-emprcal character of the MR part, contanng most of the adjustable parameters, can be regarded as the model part, whch descrbes all the nteracton effects nvolvng ons not consdered by the LR and SR contrbutons. Ths ncludes correctons to assumptons made n the LR and SR parts wth respect to approxmatons Atmos. Chem. Phys., 8, , 28

6 56 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols Table. Relatve van der Waals subgroup volume (R H t ) and surface area. (Q H t ) parameters for catons and anons consderng dynamc hydraton. Ion r c (pm) a N ADH b R t Q t R H t H L Na K NH Mg Ca Cl Br NO HSO SO a The unhydrated (crystal) rad taken from Krukhn and Collns (22) and for NO 3 and Br from Achard et al. (99). The radus of bsulphate (HSO ) was assumed to be the same as the one for sulphate (SO 2 ). b The apparent dynamc hydraton numbers (N ADH ) at 33.5 K and. M taken from Krukhn and Collns (22). Values of N ADH = are assgned to the ons, whch act as chaotropes (where dynamc hydraton s not sgnfcant). c Calculated usng Eqs. (26) and (27), respectvely. of physcal parameters. MR nteractons of solvent compounds (organcs and water) wth ons are calculated usng functonal man groups. The expresson for G ex MR of a mxture contanng n k moles of solvent man groups k (man groups of organcs and water), wth molar masses M k, and n moles of ons s: RT = B k, (I)n k n n k M k G ex MR k k + B c,a (I)n c n a n k M k k c a n z + C c,a (I)n c n a n k M k n k M k k c + R c,c n c n c n k M k k c a c c + ( ) 2 Q c,c,an c n c n a. (3) c c n k M c a k k n c and n c are moles of catons, n a are moles of anons, and I s the onc strength (Eq. ). B k, (I) (kg mol ) and B c,a (I) k c Q H t c Table 2. Relatve van der Waals subgroup volume (R t ) and surface area (Q t ) parameters for solvent subgroups (Hansen et al., 99). Man group k Subgroup t R t Q t CH n (n =,, 2, 3) CH CH CH C.295 OH OH.2 H 2 O H 2 O.92. (kg mol ) are bnary nteracton coeffcents between solvent man groups and ons, and between catons and anons, respectvely. C c,a (I) (kg 2 mol 2 ) are nteracton coeffcents between caton-anon pars wth respect to the total charge concentraton. The coeffcents R c,c (kg mol ) and Q c,c,a (kg 2 mol 2 ) descrbe bnary and ternary nteractons nvolvng two dfferent catons. These latter two nteracton coeffcents were ntroduced to mprove the descrpton of systems contanng the on combnatons NH +, H+ or NH +, H+, SO 2 (e.g., sulphurc acd-ammonum sulphate solutons), especally at very hgh onc strength. Hence, the last two terms of Eq. (3) vansh n other cases. Equaton (3) could be extended by terms accountng for nteractons between two dfferent anons, two dfferent anons and a caton, and so on. We found that t s not necessary to ntroduce such hgher order nteracton terms for the solutons studed. The frst three nteracton coeffcents are parametrsed as functons of onc strength I. In contrast to LIFAC, n AIOMFAC we use expressons, whch are smlar to the ones used for the Ptzer model of Knopf et al. (23): B k, (I) = b () k, + b(2) k, e b(3) k, I, () B c,a (I) = b c,a () c,a + I b(2) c,a e b(3), (5) C c,a (I) = c c,a () c,a I e c(2), (6) where b () k,, b(2) k,, b() c,a, b c,a, (2) b c,a, (3) c c,a, () and c c,a (2) are adjustable parameters, whch are determned by fttng AIOMFAC actvty coeffcents to expermental data sets. The parameter b c,a (3) was found to descrbe most aqueous salt solutons when assumng a fxed value of.8 kg /2 mol /2. In cases where ths value dd not result n a satsfactory data ft, b c,a (3) was allowed to vary. The parameter b (3) k, was fxed for all mxed organc-norganc solutons assumng a value of.2 kg /2 mol /2. All nteracton coeffcents n the MR part are symmetrc,.e. B c,a (I)=B a,c (I). The MR actvty coeffcents are obtaned by dfferentatng Eq. (3) wth respect to the number of moles of solvent man groups, catons, and anons respectvely. For a specfc solvent man group k the related expresson s: Atmos. Chem. Phys., 8, , 28

7 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols 565 Table 3. Contnued. Table 3. Data types, number of data ponts (N), and references of aqueous norganc soluton data. Bnary data was used to ft and ternary to valdate the AIOMFAC model at room temperature. Inorganc solutes Data type a N b Reference bnary mxtures ( salt/acd + water) HCl γ ± 29 Robnson and Stokes (22) a w 23 Robnson and Stokes (22) HBr γ ± 22 Robnson and Stokes (22) a w 7 Robnson and Stokes (22) HNO 3 γ ± 7 Robnson and Stokes (22) a w 7 Robnson and Stokes (22) H 2 SO α HSO Knopf et al. (23) α HSO Myhre et al. (23) a w 8 Staples (98) a w 6 Robnson and Stokes (22) LCl γ ± 3 Hamer and Wu (972) γ ± 37 Robnson and Stokes (22) a w 3 Hamer and Wu (972) a w 37 Robnson and Stokes (22) LBr γ ± 37 Robnson and Stokes (22) γ ± 3 Hamer and Wu (972) a w 37 Robnson and Stokes (22) a w 3 Hamer and Wu (972) LNO 3 γ ± 3 Robnson and Stokes (22) γ ± 3 Hamer and Wu (972) a w 3 Robnson and Stokes (22) a w 3 Hamer and Wu (972) LSO γ ± 7 Robnson and Stokes (22) a w 7 Robnson and Stokes (22) NaCl γ ± 3 Hamer and Wu (972) a w 35 Robnson and Stokes (22) a w 3 Hamer and Wu (972) a w 26 Tang (997) a w Ha et al. (2) NaBr γ ± 32 Hamer and Wu (972) γ ± 9 Robnson and Stokes (22) a w 32 Hamer and Wu (972) a w 9 Robnson and Stokes (22) NaNO 3 γ ± 3 Hamer and Wu (972) a w 23 Robnson and Stokes (22) a w 99 Tang and Munkelwtz (99) a w 9 Ha et al. (2) Na 2 SO γ ± 9 Robnson and Stokes (22) a w 9 Robnson and Stokes (22) a w 68 Tang and Munkelwtz (99) KCl γ ± 27 Hamer and Wu (972) γ ± 2 Robnson and Stokes (22) a w 27 Hamer and Wu (972) a w 2 Robnson and Stokes (22) a w 2 Tang (997) KBr γ ± 28 Hamer and Wu (972) γ ± 22 Robnson and Stokes (22) a w 28 Hamer and Wu (972) a w 22 Robnson and Stokes (22) KNO 3 γ ± 2 Hamer and Wu (972) a w 2 Hamer and Wu (972) a w 8 Robnson and Stokes (22) Inorganc solutes Data type a N b Reference bnary mxtures ( salt/acd + water) K 2 SO γ ± 7 Robnson and Stokes (22) a w 7 Robnson and Stokes (22) NH Cl γ ± 23 Robnson and Stokes (22) γ ± 3 Hamer and Wu (972) a w 23 Robnson and Stokes (22) a w 3 Hamer and Wu (972) a w 5 Ha et al. (2) NH Br γ ± 23 Covngton and Irsh (972) a w 23 Covngton and Irsh (972) NH NO 3 γ ± 37 Robnson and Stokes (22) γ ± 9 Hamer and Wu (972) a w 37 Robnson and Stokes (22) a w 9 Hamer and Wu (972) a w 7 Chan et al. (992) (NH ) 2 SO γ ± 9 Robnson and Stokes (22) a w 22 Robnson and Stokes (22) a w 5 Clegg et al. (995) a w 8 Tang and Munkelwtz (99) MgCl 2 γ ± 2 Robnson and Stokes (22) a w 2 Robnson and Stokes (22) a w 6 Ha and Chan (999) Mg(NO 3 ) 2 γ ± 2 Robnson and Stokes (22) a w 2 Robnson and Stokes (22) a w 6 Ha and Chan (999) MgSO γ ± 7 Robnson and Stokes (22) a w 6 Guendouz et al. (23) a w 7 Robnson and Stokes (22) a w 62 Ha and Chan (999) ln γ MR,(x) k = B k,(i)m M k [ Bk, (I) + IB k, M (I)] x k m av k [ M k Bc,a (I) + IB c,a (I)] m c m a c a ( ) [ M k m z 2 Cc,a (I) + IC c,a (I)] m c m a M k R c,c m c m c c c c c a M k 2 Q c,c,a m c m c m a, (7) c c c a where m, m c, m a are the molaltes of ons, catons, and anons respectvely, x k are the salt-free mole fractons of solvent man groups k, and M av = s x s M s s the average molar mass of the solvent mxture. Mk s the molar mass of man group k, calculated from the molar masses of the correspondng subgroups and ther partal Atmos. Chem. Phys., 8, , 28

8 566 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols Table 3. Contnued. Inorganc solutes Data type a N b Reference CaCl 2 γ ± 23 Robnson and Stokes (22) a w 3 Robnson and Stokes (22) a w Guendouz et al. (2) Ca(NO 3 ) 2 γ ± 23 Robnson and Stokes (22) a w 23 Robnson and Stokes (22) ternary and hgher multcomponent mxtures c NaHSO ( ˆ= Na 2 SO + H 2 SO [ : ]) a w 32 Tang and Munkelwtz (99) NH HSO α HSO 5 Irsh and Chen (97) ( ˆ= (NH ) 2 SO + H 2 SO [ : ]) α HSO 9 Young et al. (959) α HSO 7 Dawson et al. (986) a w 2 Tang and Munkelwtz (977) a w Spann (98) a w 23 Km et al. (99) (NH ) 2 SO + H 2 SO [ : 2] a w 33 Km et al. (99) (NH ) 2 SO + H 2 SO [2 : ] a w 2 ths study (bulk) a w 33 ths study (EDB) (NH ) 3 H(SO ) 2 [3 : ] a w 9 Tang and Munkelwtz (99) (NH ) 2 SO + H 2 SO [.82 : ] a w 36 Clegg et al. (996) (NH ) 2 SO + H 2 SO [.97 : ] a w 35 Clegg et al. (996) Mg(NO 3 ) 2 + MgSO [ : ] a w 57 Ha and Chan (999) MgCl 2 + MgSO [ : ] a w 62 Ha and Chan (999) MgCl 2 + Mg(NO 3 ) 2 [ : ] a w 29 Ha and Chan (999) MgCl 2 + Mg(NO 3 ) 2 [3 : ] a w 26 Ha and Chan (999) MgCl 2 + Mg(NO 3 ) 2 [ : 3] a w 27 Ha and Chan (999) MgCl 2 + Mg(NO 3 ) 2 + MgSO [ : : ] a w 62 Ha and Chan (999) MgCl 2 + Mg(NO 3 ) 2 + MgSO [ : : 5] a w 62 Ha and Chan (999) NH Cl + (NH ) 2 SO [ : ] a w 6 Ha et al. (2) NH Cl + NH NO 3 [ : ] a w 58 Ha et al. (2) NaCl + NH Cl [ : ] a w 73 Ha et al. (2) NaCl + NH Cl [3 : ] a w 73 Ha et al. (2) NaCl + NH NO 3 [ : ] a w 62 Ha et al. (2) a w 3 ths study (bulk) NaCl + NH NO 3 [3 : ] a w 62 Ha et al. (2) NaNO 3 + (NH ) 2 SO [ : ] a w 62 Ha et al. (2) NaNO 3 + (NH ) 2 SO [3 : ] a w 6 Ha et al. (2) NaNO 3 + NH NO 3 [ : ] a w 6 Ha et al. (2) NaNO 3 + NH NO 3 [3 : ] a w 9 Ha et al. (2) NaNO 3 + Na 2 SO [ : ] a w 26 Ha et al. (2) NaNO 3 + Na 2 SO [3 : ] a w 26 Ha et al. (2) NaCl + KCl + LCl [ : : ] a w 9 Dnane (27) NaCl + KCl + LCl [2 : : ] a w 6 Dnane (27) NaCl + KCl + LCl [ : 2 : 2] a w 6 Dnane (27) NaCl + Na 2 SO + MgCl 2 [.82 : :.89] a w ths study (bulk) Na 2 SO + MgCl 2 + MgSO [.9 : :.26] a w 9 ths study (bulk) NaCl + MgSO [ : ] a w 8 ths study (bulk) a w 68 Chan et al. (2) a Water actvty (a w ) data was calculated from lsted osmotc coeffcents and solute molaltes when not gven n the lterature. b Data ponts by Tang and Munkelwtz (99) were generated by usng the gven polynomals to ther measurements. c In brackets the molar rato of the salts or alternatvely the rato of ammonum sulphate to sulphurc acd. Atmos. Chem. Phys., 8, , 28

9 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols 567 contrbutons to k. B k, (I), B c,a (I) (kg2 mol 2 ), and C c,a (I) (kg3 mol 3 ) are the partal dervatves wth respect to I, e.g. B c,a (I)= B c,a (I)/ I. The actvty coeffcent of solvent compound s s then obtaned from the man group contrbutons by: ln γ MR,(x) s = k ν (s) k ln γ MR,(x) k (8) where ν (s) k refers to the stochometrc number of man groups k n the solvent molecule s, e.g. ν (,2 butanedol) CH n = and ν (,2 butanedol) OH =2. In analogy to Eq. (7) the expressons for a specfc caton c are: ln γ MR,(x), c = B k,c (I)x k M av + z2 c B k, 2M (I)x k m av k k + B c,a(i)m a + z2 c B c,a a 2 (I)m cm a c a + C c,a(i)m a m z a + [ C c,a (I) z c c a ] +C c,a (I)z2 c m z m c m a 2 + R c,c m c + Q c,c,a m c m a, (9) c c a and for anon a : ln γ MR,(x), a = B k,a (I)x k M av + z2 a B k, 2M (I)x k m av k k + B c,a (I)m c + z2 a B c,a c 2 (I)m cm a c a + C c,a (I)m c m z c + [ C c,a (I) z a c a ] +C c,a (I)z2 a m z m c m a 2 + Q c,c,a m cm c. (2) c c c Specfc nteracton coeffcents (and the correspondng ft parameters) between the reference solvent,.e. water, and the norganc ons are set to zero (B k=w, (I)=). Therefore, the unsymmetrcal reference state condton for nfnte dluton of ons n water (γ MR ) s ndeed fulflled and we wrte ln γ MR,(x), MR,(x) c (normalsed) nstead of ln γc. As a consequence of ths defnton, aqueous electrolyte solutons are descrbed n a smlar manner as n a conventonal Ptzer model. All bnary and ternary coeffcents concernng nteractons between catons and anons actually descrbe nteractons of catons and anons dssolved n water, thus, ncludng onc nteractons wth water. Consequently, specfc nteracton coeffcents between organc functonal man groups and ons, the B k, (I), actually descrbe the devatons from the nteractons of the ons wth water. In prncple, a dfferent reference solvent could be defned, as dscussed n Kepe et al. (26), but most tabulated data, e.g. standard chemcal potentals, are stated wth respect to water as the reference solvent. 2. Short-range contrbuton The SR contrbuton G ex SR to the total Gbbs excess energy s represented by the group-contrbuton method UNIFAC (Fredenslund et al., 975). The UNIFAC parametrsatons n AIOMFAC nclude some modfcatons to better meet the specfc propertes of atmospherc sem-volatle organcs, whch typcally contan molecules carryng several strongly polar functonal groups. Therefore, we mplemented the more detaled descrptons of alcohol/polyol group nteracton parameters publshed by Marcoll and Peter (25). Ths UNIFAC parametrsaton of alcohols/polyols dstngushes between three types of alkyl groups: () CH n (n=,, 2) wth a hydroxyl group, accountng for the nduced polarty of alkyl groups drectly connected to the electronegatve hydroxyl group, () CH n (n=,, 2, 3) n hydrophobc tals, accountng for the non-polar nature of alkyl chans that easly agglomerate and form mcelles n water, and () CH n (n=,, 2, 3) n alcohols, whch consttutes the general type of alkyl group that apples when the specal condtons for the other two types are not fulflled. In UNIFAC the actvty coeffcent γ j of mxture component j (j used for solute or solvent) s n general expressed as the contrbutons of a combnatoral part (C), accountng for the geometrcal propertes of the molecule, and a resdual part (R), whch reflects nter-molecular nteractons: ln γ SR j = ln γ C j + ln γ R j. (2) The expresson for the combnatoral part of UNIFAC s (Fredenslund et al., 975): ln γ C j where j = = ln j x j + z 2 q j ln j j + l j j x j j x j l j, (22) r j x j ; j = q j x j, (23) r j x j q j x j j j Atmos. Chem. Phys., 8, , 28

10 568 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols wth r j = t and ν (j) t R t ; q j = t ν (j) t Q t, (2) l j = z 2 (r j q j ) (r j ). (25) Here, j and j denote mxture speces (solvents or ons), x j s the mole fracton of component j, and ν t (j) s the number of subgroups of type t n component j. R t and Q t are the relatve van der Waals subgroup volume and surface area parameters, respectvely. The lattce coordnaton number z, a constant, s set equal to (Fredenslund et al., 975). The relatve van der Waals subgroup volume and surface area parameters, R t and Q t, account for pure component propertes. R t and Q t values for the ons can be estmated from the onc rad. However, as Yan et al. (999) pont out, the very small rad of the catons sgnfcantly reduce the fttng capabltes of the SR contrbuton. Therefore we estmated R t and Q t values for the ons, takng hydraton effects nto account, whch are especally promnent for the small catons havng a hgh surface charge densty. Usng an emprcal parametrsaton, the hydrated group volume and surface area parameters Rt H and Q H t are calculated by (Achard et al., 99): R H t Q H t = R t + Nt ADH R w, (26) = Q t + Nt ADH Q w, (27) where R w and Q w refer to the values of the water molecule and Nt ADH are measured apparent dynamc hydraton numbers at 33.5 K (Krukhn and Collns, 22). Rt H and Q H t values calculated wth ths assumptons are lsted n Table. They are used as constant, on-specfc values over the whole concentraton range. In the case of an onc component, n Eq. (2), R t and Q t are replaced by Rt H and Q H t, respectvely. The resultng SR contrbutons were found to be much better suted for an overall model ft compared to unhydrated parameters. For neutral substances we took the relatve subgroup volume and surface area parameters publshed by Hansen et al. (99), lsted n Table 2. The terms for the resdual part of the actvty coeffcent of j are: ln γj R = [ ] ν t (j) ln Ɣ t ln Ɣ t (j), (28) t where Ɣ t and Ɣ t (j) are the group resdual actvty coeffcents n the mxture and n a reference soluton contanng only compound j, a (hypothetcal) pure lqud of j, respectvely. The expresson for the resdual actvty coeffcent of subgroup t s: ( ) ln Ɣ t =Q t ln m m,t m t,m (29) m m n n,m Atmos. Chem. Phys., 8, , 28 n wth m = Q mx m ; Q n X n m,n = e am,n/t, (3) n where m s the relatve surface area fracton of subgroup m, X m s the mole fracton of m n the mxture, and m,n s the temperature dependent functon of the subgroup nteracton parameter a m,n. Note that the subgroup nteracton parameters are unsymmetrcal,.e. a m,n =a n,m. The sums are over all dfferent subgroups. For a more detaled UNIFAC descrpton, we refer to Fredenslund et al. (975). The subgroup nteracton parameters of non-electrolyte solutons have to be estmated usng large data sets of bnary and hgher order mxtures, to dstngush the effectve contrbutons of the dfferent subgroups. In ths study, we took the values of a m,n for the alcohol groups and water from the UNIFAC parametrsaton of Marcoll and Peter (25). For LIFAC, Yan et al. (999) showed, that the model senstvty to SR nteracton parameters a m,n between ons and between ons and organc subgroups s rather small. Thus, n AIOMFAC we set all SR nteracton parameters whch nvolve ons to zero, as t s done n LIFAC. Ths also reduces the number of AIOMFAC ft parameters to those used n the MR part. Snce ons are treated lke solvent components n the SR terms, resultng actvty coeffcents (Eq. 2) are wth respect to the symmetrcal conventon on mole fracton bass. For ons, the unsymmetrcal normalsed actvty coeffcent s determned from: ln γ SR,(x), = ln γ SR,(x) ln γ SR,(x),ref. (3) The symmetrcally normalsed value at the reference state s computed from Eqs. (22) and (28) by ntroducng the reference state condtons of the ons (settng x w =, s x s= for s =w, and x =): ln γ SR,(x),ref = ln r r w + r + r q w r w q [ ( rw q ln ) + z r w 2 q r q w ] ( ) + q ln w,,w (32) where subscrpt w stands for the reference solvent (water). The last term on the rght-hand sde of Eq. (32), reflectng the resdual part reference contrbuton, becomes zero as we defned the SR on-solvent nteractons to be zero. 2.5 AIOMFAC actvty coeffcents Fnally, accordng to Eqs. () and (7), the complete expresson for the actvty coeffcent of solvent speces s s: ln γ (x) s = ln γ LR,(x) s + ln γ MR,(x) s + ln γ SR,(x) s (33) wth the specfc contrbutons computed from Eqs. (8), (8), and (2). For the ons, the complete expresson wth regard to the unsymmetrcal conventon on molalty bass s:

11 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols 569 a) b) water actvty a w mean actvty coeff water actvty a w Fg.. Three major terms represent dfferent types of molecular nteractons n a soluton and add up to the excess Gbbs energy (G ex ) of a certan system n the 2.AIOMFAC model. Dsperson forces, also called London HCl forces, are present n any mxture and denote nduced dpole nduced dpole nteractons. LBr Long-range forces.5.5 KCl Fgure Captons NaCl LCl KCl NH Cl NH Cl LCl HCl NaCl CaCl 2 MgCl 2 between ons are descrbed by only takng the electrc charge nteractons nto account whle neglectng other on specfc propertes (e.g. the dfferent rad). CaCl 2 MgCl mean actvty coeff..5 Fg. 2. Scheme of the currently parametrsed nteractons n the MR and SR part. Ft parameters for on on and on organc man group nteractons are all ncorporated n the MR part and set to zero n the SR (UNIFAC) part Fg. 3. Expermental (symbols) and modelled (sold lnes) water actvtes and mean actvty coeffcents of the ons nx w bnary (salts, aqueous acds dssocated) salt (or acd) solutons at 298 K. Thex w x-axs (salts, scale acds s dssocated) the mole fracton of H 2 O n the Fg. 3. Expermental soluton (symbols) wth and respect modelled to completely (sold lnes) water dssocated actvtes salts and mean and actvty acds. coeffcents a) Cl electrolytes, of the ons n b) bnary Br aqueous electrolytes; salt data (or acd) solutons from: at 298Robnson K. The x-axs andscale Stokes s the(22) mole fracton ( ), Hamer of H 2 Oand n the Wu soluton (972) wth (+), respect Ha et to completely al. (2) dssocated ( ), Tang salts (997) and ( ), Ha acds. (a) Cl -electrolytes, (b) Br -electrolytes; data from: Robnson and Stokes (22) ( ), Hamer and Wu (972) (+), Ha et al. (2) ( ), Tang (997) and ( ), Chan Ha and(999) Chan (999) ( ), Guendouz ( ), et et al. al. (2) (b), ( and Covngton and and Irsh Irsh (972) (972) ( ). The ( ). dagonal, The dagonal, dashed dashed lne n the upper panels shows the water actvty of an deal mxture. At very hgh concentratons, beyond the efflorescence of supersaturated solutons, the curves lneare nmodel the upper predctons panels wthout shows drect theexpermental water actvty support. of an deal mxture. At very hgh concentratons, beyond the efflorescence of supersaturated solutons, the curves are model predctons wthout drect expermental support. the actvty coeffcent on molalty bass and nfntely dluted (n water) reference state. Ths term can be derved [ ] ln γ (m) = ln γ LR,(x), + ln γ MR,(x), + ln γ SR,(x), usng the conventon-ndependence of the chemcal potentals (µ (m) w Fg.. Expermental (symbols) and modelled (sold lnes) water actvtes and mean actvty coeffcents of ln M (p, T, n j )=µ (x) (p, T, n j )) and the defntons of the ons x s M + M w m, (3) the chosen reference states. Whle a model provdes actvty n s bnary aqueous salt (or acd) solutons at 298 K. a) NO 3 electrolytes, b) SO2 electrolytes; data s coeffcents of catons and anons, n experments one cannot where M s s the from: molar Robnson mass of solvent and Stokes component (22) s, ( ), x s ts Hamer dstngush and Wu (972) between (+), the Ha ndvdual et al. (2) nteracton ( ), Tang contrbutons and Munkelwtz salt-free mole fracton, and m (99) ( ), Ha s the molalty of on and Chan (999) ( ), of the ons n the mxture. Therefore the mean actvty coeffcentetγ al. (23) (b), Chan et al. (992) ( ), and Clegg et al.. The Guendouz contrbutons are from Eq. (9) for the LR, Eq. (9) or (2) ± of a salt M ν +X ν, s defned as: for the MR (dependng (995) ( ). on whether The dagonal, s a caton dashed or an lne anon), n the upper panels shows the water actvty of an deal mxture. and Eq. (3) for the SR part. The last term on the rght-hand sde of Eq. (3) converts the actvty coeffcent ln γ (x), (nfntely dluted Fg. reference 5. Expermental state on the mole (symbols) fractonand bass) modelled to γ ± = ν [γ + ν (sold + γ ] /(ν + +ν ) lnes) water (35) actvtes of aqueous sulphurc acd, ammonum sulphate, and mxtures of both, ndcated by the molar rato of (NH ) 2 SO : H 2 SO. The correspondng Atmos. Chem. Phys., 8, , 28 degrees of bsulphate dssocaton, α HSO, are plotted n the lower panels. In b) x w on the x-axs s takng the modelled partal dssocaton of bsulphate nto account, whle n a) complete dssocaton s assumed. a) up- KBr NaBr NH Br KBr HBr HBr NaBr NH Br LBr

12 57 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols a) Fgure Captons b) Na 2 SO.8.8 water actvty a w mean actvty coeff Fg.. Three major terms represent dfferent types of molecular nteractons n a soluton and add up to the Fgure Mg(NOCaptons 3 ) excess Gbbs energy (G ex ) of a certan system n the 2 AIOMFAC model. Dsperson forces, also called London water actvty a w forces,. NH NO are 3 present n any mxture and denote nduced dpole nduced dpole nteractons. Long-range forces LNO MgSO 3 Ca(NO 3 ) L 2 SO between ons are descrbed by only takng the 2 electrc charge nteractons nto account whle neglectng other NaNO 3 on specfc propertes (e.g. the dfferent rad)..2 K 2 SO HNO 3 Fg. 2. Scheme of the currently parametrsed nteractons n the MR and SR part. Ft parameters for on on and on organc man group nteractons are all ncorporated n the MR part and set to zero n the SR (UNIFAC) part. Mg(NO 3 ) KNO 3 LNO 3.8 Fg. 3. Expermental (symbols) and modelled MgSO on HNOspecfc (sold 3 propertes lnes) water (e.g. actvtes theand dfferent mean actvty rad). coeffcents of the ons n bnary aqueous salt (or acd) solutons at 298 K. The x-axs scale s the mole fracton of H 2 O n the.6 soluton wth respect to completely Ca(NO 3 ) 2 dssocated salts and acds. a) Cl electrolytes, b) Br electrolytes; L 2 SO data from: Robnson and Stokes (22) ( ), Hamer and Wu (972) (+), Ha et al. (2) ( ), Tang (997) ( ), Ha. and Chan (999) ( ), Guendouz NaNO 3 et al. (2) (b), and Covngton and Irsh (972) ( ). The dagonal, dashed lne n the upper NHpanels NO 3 shows the water part. actvty of an deal mxture. At very hgh concentratons, beyond the.2 efflorescence of supersaturated solutons, the curves are model predctons wthout drectna expermental K 2 SO 2 SO support. (NH KNO ) 2 SO Fg.. Expermental x w (salts, acds (symbols) dssocated) and modelled (sold lnes) water actvtes x and w (salts, meanacds actvtydssocated) coeffcents of the ons n bnary aqueous salt (or acd) solutons at 298 K. a) NO 3 electrolytes, b) SO2 electrolytes; data Fg.. Expermental from: (symbols) Robnson andmodelled Stokes (22) (sold( ), lnes) Hamer waterand actvtes Wu (972) and mean (+), actvty Ha et al. coeffcents (2) ( ), oftang the ons andn Munkelwtz bnary aqueous salt (or acd) solutons at 298 K. (a) NO 3 -electrolytes, (b) SO2 -electrolytes; data from: Robnson and Stokes (22) ( ), Hamer and Wu (972) (99) ( ), Ha and Chan (999) ( ), Guendouz et al. (23) (b), Chan et al. (992) ( ), and Clegg et al. (+), Ha et al. (2) ( ), Tang and Munkelwtz (99) ( ), Ha and Chan (999) ( ), Guendouz et al. (23) ( ), Chan et al. (992) ( ), and Clegg et al. (995) ( ). ( The dagonal, dashed lne n the upper panels shows the water actvty of ofan andeal mxture. mean actvty coeff. (NH ) 2 SO Fg.. Three major terms represent dfferent types of molecular nteractons n excess Gbbs energy (G ex ) of a certan system n the AIOMFAC model. Dsperso forces, are present n any mxture and denote nduced dpole nduced dpole nte between ons are descrbed by only takng the electrc charge nteractons nto acc Fg. 2. Scheme of the currently parametrsed nteractons n the MR and SR part and on organc man group nteractons are all ncorporated n the MR part and set Fg. 3. Expermental (symbols) and modelled (sold lnes) water actvtes and mea ons n bnary aqueous salt (or acd) solutons at 298 K. The x-axs scale s the soluton wth respect to completely dssocated salts and acds. a) Cl electrolyte from: Robnson and Stokes (22) ( ), Hamer and Wu (972) (+), Ha et al. (2 and Chan (999) ( ), Guendouz et al. (2) (b), and Covngton and Irsh (972 lne n the upper panels shows the water actvty of an deal mxture. At very hgh efflorescence of supersaturated solutons, the curves are model predctons wthout where ν + and Fg. ν [, 5. areexpermental the stochometrc (symbols) numbers and modelled of catons (sold lnes) water actvtes ν of aqueous sulphurc acd, ammonum ( ) sulphate, respectvely, and mxtures assumng of both, complete ndcated dssoc- by the molar rato of (NH ) 2 SO : H 2 SO. The correspondng m ± = m + ν + m ] /(ν + +ν ). (37) (+) and anons aton of the salt. Lkewse, usng the geometrcal mean, the degrees of bsulphate dssocaton, α HSO, are plotted n the lower panels. In b) x w on the x-axs s takng the mean molal actvty s obtaned: 2.6 Estmaton of model parameters modelled partal dssocaton of bsulphate nto account, whle n a) complete dssocaton s assumed. a) upper panel data from: Robnson and Stokes (22) ( ), Staples (98) ( ), Km et al. (99) ( ), Tang and ( ) the ons n bnary aqueous salt (or acd) solutons at 298 K. a) NO 3 Fg.. Expermental (symbols) and modelled (sold lnes) water actvtes and m [ a Munkelwtz (977) ( ), Clegg et al. (995) ( ), Spann (98) (b), Tang and Munkelwtz (99) ( ), ths electrolytes ± (m) = a (m) ν + ( ) ] The sem-emprcal expressons of the MR part contan adjustable parameters, descrbng nteractons between ons, or- + a (m) ν /(ν + +ν ) ganc functonal groups and water. The Debye-Hückel (LR) study (bulk) ( ), ths study (EDB) (+). from: Lower Robnson panel data and from: Stokes Knopf (22) et al. (23) ( ), Hamer ( ), Myhre andetwu al. (23) (972) (+), Ha et al. (2 [ (m+ ) = ( ), Young et al. (959) ( ), Dawson(99) et al. (986) ( ),( ), HaIrsh and and Chan Chen (999) (97) ( ), (b). Guendouz et al. (23) (b), Chan et al. m γ (m) ν + ( m ) ] part and the UNIFAC (SR) part contan no freely adjustable + m γ (m) ν /(ν + +ν ) parameters for ons. Organc-organc and organc-water subgroup nteractons are parametrzed n the SR part. The UNI- (995) ( ). The dagonal, dashed lne n the upper panels shows the water actvty = m FAC parameters used here are taken from Marcoll and Peter (25). Due to the many modfcatons n the MR part, ± Fg. 6. Predctons and measurements of mult-salt mxtures. a) salt mxture contanng the four ons Na +, m γ ± (m) (36) NH +, Cl, and NO 3. Symbols: ( ) EDB measurements all pertnent (Ha et al., nteracton 2), ( ) bulk parameters a had to be recalculated by w measurements (ths wth fttng the model to expermental data. In a frst step, measurements of water actvty and mean actvty coeffcents, Fg. 5. Expermental (symbols) and modelled (sold lnes) water actvtes of aqu num sulphate, 5and mxtures of both, ndcated by the molar rato of (NH ) 2 SO : Atmos. Chem. Phys., 8, , 28 degrees of bsulphate dssocaton, α HSO, are plotted n the lower panels. In b) x modelled partal dssocaton of bsulphate nto account, whle n a) complete ds per panel data from: Robnson and Stokes (22) ( ), Staples (98) ( ), Km

13 A. Zuend et al.: Thermodynamc model of mxed organc-norganc aerosols 57 Table. Data types, number of data ponts (N), temperature range, and references of organc-norganc-water mxtures used to ft or valdate the AIOMFAC model. Salt + alcohol n mxture a Data type b N T (K) c Reference LCl + 2-propanol VLE Sada et al. (975) VLE Ln et al. (993) LBr + ethanol VLE Rudakoff et al. (972) LBr + 2-propanol VLE Sada et al. (975) VLE Ln et al. (993) NaCl + ethanol γ ± Lopes et al. (2) γ ± Esteso et al. (989) SLE Pnho and Macedo (996) VLE Meyer et al. (99) VLE Meyer et al. (99) VLE Johnson and Furter (965) NaCl + KCl + ethanol γ ± Farelo et al. (22) NaCl + -propanol VLE Morrson et al. (99) VLE Johnson and Furter (965) VLE Ln et al. (993) LLE 298 De Sants et al. (976) LLE Chou et al. (998) LLE Goms et al. (99) NaCl + 2-propanol VLE Rajendran et al. (99) LLE De Sants et al. (976) LLE Goms et al. (99) NaCl + -butanol LLE De Sants et al. (976) LLE 298 L et al. (995) LLE De Sants et al. (976) NaCl + 2-butanol LLE De Sants et al. (976) LLE Goms et al. (996) NaCl + sobutanol LLE Goms et al. (996) LLE De Sants et al. (976) NaCl + tert-butanol LLE 298 De Sants et al. (976) LLE Goms et al. (996) NaCl + glycerol a w 298 Marcoll and Kreger (26) NaCl +,-butanedol a w 298 Marcoll and Kreger (26) NaCl +,2-hexanedol a w Marcoll and Kreger (26) NaBr + -propanol VLE Morrson et al. (99) LLE 298 Chou et al. (998) NaBr + 2-propanol VLE Morrson et al. (99) NaNO 3 + ethanol VLE Pena et al. (996) SLE 33.5 Taylor (897) Na 2 SO +,2-ethanedol SLE Vener and Thompson (99) Na 2 SO + -propanol SLE Brenner et al. (992) LLE Brenner et al. (992) Na 2 SO + 2-propanol SLE Brenner et al. (992) SLE 298 Brenner et al. (992) LLE Brenner et al. (992) LLE Lynn et al. (996) Na 2 SO + tert-butanol SLE Brenner et al. (992) LLE Lynn et al. (996) LLE Brenner et al. (992) KCl + ethanol VLE Johnson and Furter (965) γ ± Lopes et al. (999) KCl + -propanol VLE Johnson and Furter (965) VLE Ln et al. (993) LLE 298 Goms et al. (996) LLE Chou et al. (998) Atmos. Chem. Phys., 8, , 28