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Determination of Activity Coefficients of Semi-Volatile Organic Aerosols Usingthe Integrated Volume MethodRawad Saleh a; Andrey Khlystov a

a Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA

First Published on: 01 August 2009

To cite this Article Saleh, Rawad and Khlystov, Andrey(2009)'Determination of Activity Coefficients of Semi-Volatile Organic AerosolsUsing the Integrated Volume Method',Aerosol Science and Technology,43:8,838 — 846

To link to this Article: DOI: 10.1080/02786820902959474

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Aerosol Science and Technology, 43:838–846, 2009Copyright © American Association for Aerosol ResearchISSN: 0278-6826 print / 1521-7388 onlineDOI: 10.1080/02786820902959474

Determination of Activity Coefficients of Semi-VolatileOrganic Aerosols Using the Integrated Volume Method

Rawad Saleh and Andrey KhlystovDepartment of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA

We demonstrate the use of the Integrated Volume Method(IVM) to estimate activity coefficients of semi-volatile organic com-pounds pertinent to ambient/atmospheric aerosols in binary mix-tures. We generate binary solution aerosols with different molefractions of individual components; for each mixture, we mea-sure total change in aerosol volume upon heating from 25◦C to35◦C, with the aerosols being at equilibrium in both states. Thechange in aerosol volume, or in other words, the partitioning be-tween the particle phase and the gas phase, is used to determineactivity coefficients of the compounds as a function of their molefraction in the mixture. We demonstrate this method using thefollowing four model systems. System 1: adipic acid–pimelic acid,which illustrates polar organic–polar organic interactions. Non-ideal behavior was observed with activity coefficients around threeat infinite dilution. System 2: adipic acid–dioctyl sebacate, whichillustrates polar organic–non-polar organic interactions. The com-pounds in this experiment did not form a solution. System 3: adipicacid–ammonium sulfate, which illustrates polar organic–inorganicinteractions. The compounds in this experiment did not form a so-lution. System 4: adipic acid–ambient extracts, which illustratesthe potential use of the method to study partitioning behavior ofindividual components in a complex matrix approximating that ofreal ambient aerosol. The measured activity coefficients of adipicacid were less than unity for the tested range of mixing ratios,indicating suppression of volatility of this compound in ambientorganic matrix.

1. INTRODUCTIONAtmospheric aerosols have a substantial effect on climate, as

they absorb or scatter solar radiation causing warming or cool-ing of the atmosphere (Chung and Seinfeld 2002). Moreover,there has been extensive evidence on ambient aerosols beingassociated with health hazards including respiratory diseases(Brunekreef et al. 1997), cardiopulmonary diseases, cancer, andadverse reproductive effects (Lewtas 2007).

Received 26 December 2008; accepted 6 April 2009.We appreciate the help of Ming-Yeng Lin in performing IVM ex-

periments for adipic acid–dioctyl sebacate mixtures.Address correspondence to Andrey Khlystov, Department of

Civil and Environmental Engineering, Box 90287, Duke University,Durham, NC, 27708, USA. E-mail: andrey@duke.edu

Ambient aerosols are complex mixtures of organics, inorgan-ics, and water (Saxena and Hildemann 1996; Ohta et al. 1990;Bardouki et al. 2002; Hueglen et al. 2005); a major portion ofthe organic fraction is comprised of semi volatiles (Andrae andCrutzen 1997; Saxena and Hildemann 1997; Seinfeld and Pandis1998). Partitioning of organic species between vapor and par-ticulate phases is an important determinant of ambient aerosolconcentrations and chemical composition (Seinfeld and Pankow2003; Robinson et al. 2007). Aerosol transport models, such asCMAQ, deal with partitioning by applying Raoult’s law, whichassumes ideal solution; the saturation pressures (or concentra-tions) of individual species are corrected by their correspondingmole (or mass) fractions. Bowman and Melton (2004) showeddiscrepancy up to 2 orders of magnitude between experimentaldata on SOA water uptake and models that assume ideal approx-imation; the discrepancy is significantly reduced—to the sameorder of magnitude—when non-ideal behavior is accounted forvia incorporating activity coefficients. The importance of in-clusion of activity coefficients in estimating particle/gas par-titioning for smog chamber aerosol was observed by Janget al. (1997). Seinfeld and Pankow (2003) estimated that ac-tivity coefficients in ambient aerosols are typically between 0.3and 3.

Extensive work has been done to obtain theoretical repre-sentation of activity coefficients of species in ambient aerosolmixtures. For organic-water interactions, the most widely usedmodel is UNIFAC, which is based on the group contribu-tion method introduced by Fredenslund et al. (1975). Severalresearchers have extended UNIFAC to include more organicspecies, as well as organic–inorganic (electrolyte) interactions(Erdakos et al. 2006a; Erdakos et al. 2006b; Clegg et al. 2001;Ming and Russell 2002; Raatikainen and Laaksonen 2005;Topping et al. 2004).

On the experimental front, most of the work has been doneon activity coefficients of water in solution with organic com-pounds. There are two widely used techniques, namely the Elec-trodynamic Balance (EDB) and the Hygroscopic Tandem Dif-ferential Mobility Analyzer (HTDMA). Single droplet levitationin EDB has been employed by Peng et al. (2001) to obtain wateractivity in the presence of water soluble organic compounds(WSOC). The mass fraction of solute was determined as a

838

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ACTIVITY COEFFICIENTS OF BINARY ORGANIC AEROSOLS 839

function of RH, and thus water activity. Choi and Chen (2002)employed the same principle, but using a scanning EDB, wherewater activity as a function of solute mass fraction was obtainedfrom the droplet evaporation rate as a response to a step changein RH. Moore and Raymond (2008) used the HTDMA tech-nique to estimate water activity present in solution with dicar-boxylic acids. The limitation of the EDB and HTDMA methodsis that the solute should be much less volatile than the solvent,because it is assumed that only the solvent—water in this case—undergoes partitioning with the gas phase. To our knowledge,the only investigation of activity coefficients in organic-organicmixtures relevant to atmospheric aerosol was reported by Cappaet al. (2008) who used Temperature-Programmed Desorption(TPD) to investigate evaporation behavior of an equimolar mix-ture of C3-C10 and C-12 dicarboxylic acids. Activity coeffi-cients of less than unity were observed for lower molecularmass diacids, while for heavier diacids activity coefficients werelarger than unity.

In this article, we present an experimental technique to es-timate activity coefficients of semi-volatile organic compoundsof atmospheric relevance in binary solutions. This techniquealso provides information on whether certain compounds formsolutions or not. Finally, we show how this technique can beused to estimate the activity coefficients of organic compoundswhen present in a complex matrix of ambient extracts. The

experimental method employed is an extension to the integratedvolume method (IVM) described in Saleh et al. (2008). To il-lustrate, experimental results are shown for the following mix-tures: adipic acid–pimelic acid, adipic acid–dioctyl sebacate,and adipic acid–ambient extracts.

2. EXPERIMENTAL SECTION

2.1. Experimental SetupThe experimental setup for IVM, shown in Figure 1, is de-

scribed in detail in Saleh et al. (2008); only a brief descriptionis given here.

Aerosol is produced by spraying aqueous (in de-ionized18 M� water) or ethanol solutions (for dioctyl-sebacate mix-tures) of pure compounds or binary mixtures using a TSI Con-stant Output Atomizer. The aerosol is sent to a 20 liter chamberto mix with dry particle free air at 40 SLPM for dilution anddrying. 2 SLPM are drawn through a diffusion-dryer to ensurethat the aerosol is dry, while the excess is sent to exhaust. Whenthe solvent used is ethanol, the diffusion dryer is replaced withan activated carbon denuder. The 2 SLPM dry aerosol are splitinto two 1 SLPM lines; one is sampled for reference measure-ments via the upstream SMPS, and the other is sent through a2.5 cm ID × 1 m long stainless steel heated tube (thermode-nuder) maintained at 35◦C, and is then sized via the downstream

FIG. 1. Schematic of experimental setup.

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840 R. SALEH AND A. KHLYSTOV

TABLE 1Chemicals used in this study

Chemical Vendor Purity Molar mass (g/mol) Density (g/cm3)

Adipic acid Acros Organics 99% 146.14 1.36Pimelic acid Sigma-Aldrich 99% 160.17 1.28Dioctyl sebacate Acros Organics 97% 426.68 0.9Ammonium salufate Sigma-Aldrich 100% 132.14 1.77

SMPS. The cooling section downstream the thermodenuder isa 7 mm ID × 50 cm long copper tube. We do not use an ac-tivated carbon denuder in the cooling section, because its usecan produce larger errors than errors due to re-condensation oforganic vapor on the particles in the cooling section, which forthis configuration is negligible (Saleh et al. 2008).

We choose the set temperature to be 35◦C because it is highenough to obtain volume changes significantly greater than thenoise in the measurements, and is at the same time close toambient/atmospheric conditions.

The chemicals used in this study are given in Table 1.

2.2. Sample PreparationThe two compounds are dissolved in water or ethanol (for

dioctyl-sebacate mixtures). The solution is then atomized anddried, as described in section 2.1, to end up with a binary-mixtureaerosol. The experiments are repeated at several mole fractions,which is achieved by changing the relative concentrations of thecompounds in the solution.

For experiments with adipic–“ambient” mixtures, adipic acidwas mixed with an aqueous extract of ambient aerosol. Ambientair samples were collected on (20.3 cm × 25.4 cm) glass-fiberfilters for 3–4 days using a High-Volume air sampler installedon the roof of one of the buildings on Duke University campus.The filters were then extracted in water to form a solution ofthe soluble fraction of the ambient aerosol. The individual ex-tracts were combined and divided into 6 fractions. One fractionwas left unmodified (to test the volatility properties of the am-bient extract) and the remaining 5 were “doped” with differentamounts of adipic acid to obtain different mole fractions of thisacid in the resulting solution. The obtained solutions were thenatomized as described above.

3. DETERMINATION OF ACTIVITY COEFFICIENTS

3.1. Extension of the IVM to Multi-Component AerosolsFor detailed description of the IVM, the reader is referred to

Saleh et al. (2008); only a brief review is given here.Consider a control volume of volatile (or semi-volatile)

aerosol initially in equilibrium with its surrounding at tempera-ture T0 sent through a thermodenuder at temperature T1 > T0;the particles will evaporate to bring the system back to equi-librium at the new temperature T1. The total change of aerosol

volume can be expressed as:

�vp = M

ρpRT0(Psat,1 − Psat,0) [1]

Psat and �H can be linked by the Claussius-Clapeyron equa-tion, with the assumption that �H is constant over the temper-ature range:

ln(Psat,1) − ln(Psat,0) = −�H

R

(1

T1− 1

T0

)[2]

Combining Equations (1) and (2), the IVM equation reads:

�vp = Psat,0M

ρpRT0

[exp

(−�H

R

(1

T1− 1

T0

))− 1

][3]

For a multi-component aerosol, in a solution, the saturationpressure of component i is given by:

P ∗sat,i = xiγiPsat,i [4]

Where xi is the mole fraction of the component, γ i is the activ-ity coefficient, and Psat,i is the saturation pressure of the purecomponent.

The change in volume of component i can be obtained bysubstituting Equation (4) in Equation (1):

�v∗p,i = Mi

ρp,iRT0(xi,1γi,1Psat,i,1 − xi,0γi,0Psat,i,0) [5]

The change in total volume of the multi-component aerosolis written as:

�vp,tot =∑

�v∗p,i [6]

3.2. Algorithm to Calculate Activity CoefficientsThe following iterative algorithm is used to calculate activity

coefficients of the individual components in the mixture. Themain steps of the algorithm involve estimating mole fractionof the components (section 3.2.1), then estimating the activ-ity coefficients (3.2.2), after which the procedure is repeateduntil convergence. Since the molecular weight of organics in

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ACTIVITY COEFFICIENTS OF BINARY ORGANIC AEROSOLS 841

ambient extracts is not known, calculations for the adipic acid–“ambient” mixtures involve estimation of the activity-weighedaverage molecular weight of the ambient extracts (section 3.2.3).Individual stages of the algorithm are described below.

3.2.1. Mole Fraction CalculationThe mole fractions of the components in the mixture change

upon evaporation because the more volatile species evaporatesmore than the less volatile. The final equilibrium mole fractionscan be estimated as follows.

Assume that we have an aerosol composed of a binary mix-ture of species A and species B initially at equilibrium at T0

(state “0”); the aerosol is then brought to equilibrium at a highertemperature T1 (state “1”). Conservation of mass requires:

CA,0 + γAxA,0Csat,A,0 = CA,1 + γAxA,1Csat,A,1 [7]

CB,0 + γB(1 − xA,0)Csat,B,0 = CB,1 + γB(1 − xA,1)Csat,B,1

[8]

where C is the molar concentration in the aerosol phase, andCsat is the saturation molar concentration. For this stage ofcalculations, γ is assumed to be constant over the range ofmole fractions.

Knowing that CB = 1−xA

xACA (since xA = CA

CA+CBand

xB = CB

CA+CB), Equation (7) and Equation (8) can be combined

to obtain the following quadratic equation in the final molefractions:

[γBCsat,B,1 − γACsat,A,1]x2A,1

+ [CA,0 + CB,0 + γAxA,0Csat,A,0 + γB(1 − xB,0)Csat,B,0

+ γACsat,A,1 − γBCsat,B,1]xA,1

+ [−CA,0 − γAxA,0Csat,A,0] = 0 [9]

3.2.2. Activity CoefficientsTo estimate activity coefficients in binary mixtures, we use

the empirical Van Laar equation (Smith and Van Ness 1987):

ln γ1 = A[1 + Ax1

Bx2

]2 and ln γ2 = B[1 + Bx2

Ax1

]2 [10]

where A and B are experimentally obtained fit parameters.Equation (10) is substituted in Equation (6), which is used as

a model fit for the experimental data—� vp,tot vs x—to obtainthe parameters A and B; activity coefficients are then calculatedusing Equation (10). Finally, Equation (9) is used to update thevalues of the mole fractions.

This procedure constitutes one iteration, and is repeated untilconvergence.

3.2.3. Estimation of Molecular Weight of Organic Compo-nents in Ambient Extracts

A recent field study on the chemical composition ofPM2.5 in the Research Triangle Park area performed by EPA(Lewandowski et al. 2007) reported 41% organic matter, 2%elemental carbon, 12% ammonium, 37% sulfate, and 1% ni-trate and oxalate. 50% of the organics were found to be water-soluble (WSOC); other field studies have also reported WSOCconcentrations of 30–70% of the total organics (Sempere andKawamura 1994; Mader et al. 2004).

For the purpose of this study, we assume that 50% of theambient extracts are inorganic salts and 25% are WSOC, withdensities of 1.8 g/cm3 and 1.3 g/cm3, respectively. Thus, WSOCconstitutes 40% of the total aerosol volume in the aqueous ex-tract. Adipic acid is assumed to interact only with the organicfraction of the ambient extracts to form solution. We base thisassumption on our experimental findings which show that adipicacid does not form solution with ammonium sulfate in a binarymixture; discussion on the validity of this assumption is givenin section 4.2. The organic fraction is lumped together, andis assigned a molar mass of Mamb, which is estimated in thefollowing fashion.

Assuming volume additivity, the mole fraction of adipic acidin the mixture can be expressed as:

xa = na

na + namb

=ρaVa

/Ma

ρaVa/Ma

+ ρambVamb/Mamb

[11]

where, Va and Vamb are the volumes of adipic acid and organicambient extract in the aerosol, Ma and Mamb are the molarmasses, and ρa and ρamb are the densities. The molar mass ofthe organic ambient extract can be isolated from Equation (11):

Mamb = ρamb

ρa

Vamb

Va

Ma

(1

xa

− 1

)−1

[12]

Equation (12) is incorporated in the iteration scheme to esti-mate Mamb.

3.3. Uncertainty AnalysisThe parameter measured in our experiments is the total

change in aerosol volume, � vp,tot . The error in the measure-ments is random, and is assumed to be normally distributedwith a standard deviation of σ �v . To estimate the effect of errorpropagation in our model, we perform 100 model runs, eachwith a perturbed � vp,tot defined as:

�vperturbedp,tot = �vp,tot + φσ�v [13]

where φ is a vector of random variables with elements–1 < φ i < +1.

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842 R. SALEH AND A. KHLYSTOV

Results from the 100 model runs are used to calculate meansand standard deviations of the activity coefficients.

4. RESULTS AND DISCUSSION

4.1. Adipic Acid–Pimelic AcidFigure 2a shows the total change in aerosol volume of adipic

acid–pimelic acid mixtures versus adipic acid mole fraction;also shown is the theoretical fit based on the model describedin section 3.2, and the envelopes obtained by the uncertaintyanalysis as outlined in section 3.3.

FIG. 2. (a) Change in total aerosol volume for aidpic acid – pimelic acidmixtures between 25◦C and 35◦C. The solid line is the fit based on the modeldescribed in section 3.2. The dotted lines are uncertainty envelopes, based onthe analysis in section 3.3. (b) Activity coefficients for adipic acid and pimelicacid when present in a binary solution, based on the model described in section3.2. The dotted lines are uncertainty envelopes, based on the analysis in section3.3.

The points where adipic acid mole fraction is equal to 1 and 0represent the change in saturation vapor pressure (as expressedin terms of aerosol volume change) of pure adipic acid andpimelic acid, respectively. Although it might be expected thatpimelic acid (a C-7 diacid) should be less volatile than thesmaller (C-6) adipic acid, the odd-number acids tend to havehigher vapor pressures (Bilde et al. 2003). It should be notedthat vapor pressures of pimelic acid and adipic acid measuredwith the IVM agree very well with other studies (Saleh et al.2008). For example, the saturation vapor pressure of pimelicacid measured with the IVM is 0.76 × 10–4 Pa at 25◦C and 5.1× 10–4 Pa at 35◦C, as compared to 0.72 × 10–4 Pa at 25◦C and5.2 × 10–4 Pa at 35◦C based on Bilde et al. (2003) data.

Observing the change in aerosol volume at different adipicacid mole fractions makes it clear that the adipic acid and pimelicacid interact with each other in the mixture, i.e., form a “solu-tion,” because the volume change (�v) of the mixtures liesbelow the sum of the volume changes of the pure components.If the substances were not interacting, the resulting change inaerosol volume would have been the sum of those of pure com-pounds (around 110 µg/m3) for all mole fractions, since therewould be no decrease in equilibrium vapor pressure.

The evaporation of this binary mixture aerosol cannot bedescribed by Raoult’s law. If the mixture were ideal, the resultingchange in volume would have been the molar fraction—weighed�v of the pure compounds (as implied by Equations [5] and [6]),and the data points would lie on a straight line connecting thepoints representing pure substances. To account for the non-ideal behavior, activity coefficients for both compounds needto be incorporated in the analysis using the model given insection 3.2.2. Values of the activity coefficients as a functionof adipic acid mole fraction are shown in Figure 2b, alongwith the envelopes defined by the uncertainty analysis. For bothacids, the maximum uncertainties occur at infinite dilution, withnumerical values of 22% and 17% for pimelic acid and adipicacid, respectively.

It should be noted that in this study we had no means to deter-mine whether the compounds are in a solid or a subcooled liquidsolution. Therefore, we can not attribute the observed values ofthe activity coefficients to one or the other state. However, themixtures were most probably in a solid state, because the melt-ing point depression for any of the two compounds is expectedto be not more than about 10◦C for the range of molar frac-tions tested in our experiments. Because the melting points ofadipic acid and pimelic acid are, respectively, 152◦C and 104◦C(Linstrom and Mallard 2009), the mixture should remain solidat the temperature of our experiments (35◦C).

The condition of the particles (solid or liquid) can affectthe calculation of the activity coefficients. If the particles aresolid, diffusion limitations may cause a radial gradient of chem-ical composition within the particles. The solid-state diffusioncoefficients of the acids are of the order of 10–14 m2/s (Lide2007). The corresponding mixing time scale for 100 nm par-ticles, the VMD of our aerosol distribution, can be estimated

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ACTIVITY COEFFICIENTS OF BINARY ORGANIC AEROSOLS 843

using τ ≈ r2/D (in which τ is the characteristic time, r is theparticle radius and D is the diffusion coefficient) to be of the or-der of 1 s. Therefore, it is reasonable to assume that the averageresidence time in our thermodenuder (22 s) is long enough tohave a fairly uniform composition within the particles and, thus,to assume that the diffusion limitation within particles have anegligible effect on the calculated values of activity coefficients.

The non-uniform distribution of points along the x-axis inFig. 2a is explained by the difficulty of producing aerosol witha high mole fraction of pimelic acid. The reason is that for thetemperature change in this experiment (25◦C to 35◦C), pimelicacid undergoes a larger relative increase of Psat than adipic acid(in terms of aerosol volume change: � v is 90 µm3/cm3 for purepimelic acid versus 20 µm3/cm3 for pure adipic acid). Therefore,more pimelic acid is evaporated from the particles relatively tothe less volatile adipic acid, decreasing its mole fraction in theparticle phase. At high aerosol concentrations (relative to thechange in vapor pressure concentrations) the change in aerosolcomposition after the re-equilibration is small. However, to keepthe concentrations such that the CPCs in the SMPS systems arenot overloaded, we had to work at concentration levels whichcause an appreciable change in aerosol composition, especiallyat the high mixing ratios of the more volatile compound. Thismakes it difficult to obtain data points for low adipic acid molefractions, which is the reason for the non-uniform distributionof experimental data points. This problem can be alleviatedby installing a dilution system in front of the SMPS to avoidoverloading at high concentration.

We have compared the measured activity coefficients with theUNIFAC group contribution method (Fredenslund et al. 1975)predictions. The activity coefficients predicted by the UNIFACwere 1.02 or lower, significantly below the values observedin this study. Although it would be expected that mixtures ofdicarboxylic acids should exhibit activity coefficients close tounity given the similarity in structure, activity coefficients muchdifferent than one were also observed in multi-component di-carboxylic acid mixtures (Cappa et al. 2008).

4.2. Adipic Acid–Dioctyl Sebacate and AdipicAcid–Ammonium Sulfate

Pure dioctyl sebacate did not exhibit measurable volumechange when heated from 25◦C to 35◦C, and it can thus beassumed to be non-volatile in this temperature range; conse-quently dioctyl sebacate is not expected to partition to the gasphase. Adipic acid on the other hand is expected to partition,but, as depicted in Figure 3, partitioning of adipic acid (changein total aerosol volume) is not affected by the presence of dioctylsebacate. This leads to the conclusion that the two species donot form a solution, which is expected since adipic acid is po-lar while dioctyl sebacate is non-polar. This was confirmed byattempting to dissolve adipic acid crystals in pure dioctyl seba-cate oil: the crystals did not dissolve even at ratios higher thanused in this study. It should be noted, that the sebacate/adipic

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

12

14

16

18

20

22

24

26

adipic acid mole fraction

V (

m3 /c

m3 )

FIG. 3. Change in total aerosol volume for aidpic acid–dioctyl sebacate mix-tures between 25◦C and 35◦C.

acid aerosol was produced by nebulizing and drying an ethanolsolution of these compounds as described in section 2.2. Bothcompounds formed a uniform mixture with ethanol (i.e., nosuspension or physical separation of phases was observed).Therefore, the aerosol produced by atomizing this solution isinternally mixed, i.e., both compounds are present in each par-ticle. The fact that no interaction between the compounds wasobserved means that the oil and the acid were in separate phasesin each particle.

Ammonium sulfate is also non volatile in the temperaturerange of our experiments. Similar to dioctyl sebacate, our datasuggest that ammonium sulfate did not form a solution withadipic acid. As shown in Figure 4, there is no suppression orenhancement of the evaporation of adipic acid. It is interesting

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 112

14

16

18

20

22

24

26

28

adipic acid mole fraction

V (

m3 /c

m3 )

FIG. 4. Change in total aerosol volume for aidpic acid–ammonium sulfatemixtures between 25◦C and 35◦C.

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844 R. SALEH AND A. KHLYSTOV

to note that Cappa et al. (2008) observed mutual dissolution ofsodium nitrate and several dicarboxylic acids. One reason forthis discrepancy can be that in our binary aerosol ammoniumsulfate and adipic acid were present in the same particles, but,apparently, in separate crystalline phases, while in the Cappaet al. (2008) study the multi-component mixture was in sub-cooled liquid state, which may have promoted dissolution andinteraction of sodium nitrate in the mixture. Another possiblereason for discrepancy is that different inorganic salts behavedifferently; consequently, interaction between organic and in-organic fractions in ambient aerosols could be particle size de-pendent: ammonium sulfate is a dominant inorganic componentin fine aerosol, while sodium nitrate is found mostly in coarseparticles.

These experiments indicate that compounds present in am-bient or smog chamber aerosols might not form solution. Theimplication is that when estimating partitioning of individualcompounds, or classes of compounds, activities need to be cal-culated with respect to the solutions they are part of, and notthe whole mass of the aerosol. However, these findings are notconclusive because compounds that do not dissolve each otherin a binary mixture might still form solution in a more complexmatrix.

4.3. Adipic Acid–Ambient ExtractsFigure 5a shows the total change in aerosol volume of adipic

acid–ambient matrix mixtures versus adipic acid mole fraction.The volume change of the pure ambient extract (0.7 µm3/cm3)is not shown on the figure in order to emphasize the regionwhere most of the measurements were performed (adipic acidmole fractions higher than 0.7). The reason why there are nodata points for adipic acid mole fraction of less than 0.7 is thatthe concentration of ambient extract was too low to producemore points. Our experimental setup requires about 150 ml ofsolution per experiment. The solution should be concentratedenough to produce an aerosol concentration that would be suffi-cient to saturate the gas stream at the temperature of our exper-iments. Because the ambient extract concentration was ratherlow, we could not dilute the extract to produce enough aerosolvolume for experiments at lower adipic acid fractions. This is alimitation of the method, which can be solved by collecting alarger ambient aerosol sample (i.e., by sampling higher ambientaerosol concentrations and/or for longer period of time).

Figure 5a also shows the theoretical fit based on the modeldescribed in section 3.2, and the envelopes defined by the un-certainty analysis as outlined in section 3.3. Though the point ofpure ambient extract is not included in Figure 5a, it was used incalculating the fit and the uncertainty bounds. It is clear that thebehavior of adipic acid in the ambient aerosol matrix is highlynon-ideal, with activity coefficients significantly lower than 1(Figure 5b).

Using the analysis described in section 3.2.3, we obtainedan effective ambient WSOC molar mass of 176 ± 26 g/mol.

FIG. 5. (a) Change in total aerosol volume for aidpic acid–ambient extractsmixtures between 25◦C and 35◦C. The solid line is the fit based on the modeldescribed in section 3.2. The dotted lines are uncertainty envelopes, based onthe analysis in section 3.3. The volume change of the pure ambient extract(0.7 µm3/cm3) is not shown, but was taken into account when calculating thefit and the uncertainty envelopes. (b) Activity coefficients for adipic acid whenpresent in a solution with ambient extracts, based on the model described insection 3.2. The dotted lines are uncertainty envelopes, based on the analysis insection 3.3.

This value depends on the assumption that the volume frac-tion of WSOC in the aerosol is 40%. Assuming WSOC volumefractions of 30% and 50% gives molar masses of 149 ± 10g/mol and 212 ± 40 g/mol, respectively. These values are notmeant to be quantitative estimates; however, they might sug-gest that the compounds constituting WSOC in our samples aremostly high molar mass multifunctional compounds. The esti-mated molecular weight is within the range reported for watersoluble organic aerosol. Ambient samples from K-pustza and

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ACTIVITY COEFFICIENTS OF BINARY ORGANIC AEROSOLS 845

Jungfraujoch were reported to have average molecular weightsin the range 200–300 g/mol (Kiss et al. 2003, Krivacsy et al.2001).

Saxena and Hildemann (1996) reported that the major con-stituents of WSOC in atmospheric aerosols are C2 to C7 mul-tifunctional compounds. The compounds suggested by Saxenaand Hildemann have saturation pressures at 25◦C comparable tothose of adipic and pimelic acid or (up to several orders of mag-nitude) higher. Their selection of compounds seems to contradictour observations: the aerosol generated from the ambient aque-ous extract has very low volatility compared to pure adipic acidand pimelic acid. The total volume change of the ambient mat-rix at thermodenuder set-temperature of 35◦C is 0.7 µm3/cm3

versus 18 µm3/cm3 for adipic acid and 90 µm3/cm3 for pimelicacid. Since the change in volume observed in our experimentsis the average volatility of all the components in the mixture,the measurements show that the WSOC portion of the ambi-ent aerosol is less volatile than the components proposed bySaxena and Hildemann. Our results (both the volatility andmolecular weight) are more consistent with longer chain di-carboxilic acids (such as azelaic acid) or C8–C10 polyols.On the other hand, the compounds selected by Saxena andHildemann have been observed in ambient aerosols (Grosjeanet al. 1978; Kawamura and Kaplan 1987; Sempere and Kawa-mura 1994; Rogge et al. 1993). The behavior of adipic acid whenin mixture with the WSOC ambient matrix observed in thisstudy shows activity coefficients significantly lower than one(Figure 5b), which agrees with the findings of Cappa et al. (2008)for lab generated multicomponent dicarboxylic acid mixtures.This suggests that evaporation of adipic acid is strongly reducedin the ambient matrix, which would shift its partitioning to theaerosol phase. Whether such behavior is observed for other di-craboxylic acids and other ambient aerosol matrices was beyondthe scope of this study and needs to be investigated.

5. CONCLUSIONSThis work demonstrates the application of the integrated

volume method to estimate activity coefficients of binary or-ganic mixtures pertinent to ambient/atmospheric aerosols. Themethod is applied to adipic acid–pimelic acid as an example forpolar–polar organic mixtures, adipic acid–dioctyl-sebacate as anexample for polar–non-polar mixtures, adpic acid–ammoniumsulfate as an example of polar organic–inorganic mixtures, andadipic acid–ambient extracts to illustrate application to realisticambient systems. Adipic acid–pimelic acid mixture exhibitedhighly non-ideal behavior with activity coefficients of about 3at infinite dilution, which stresses the importance of activitycoefficients in partioning of semi-volatile organics in ambientaerosols. On the other hand, adipic acid–dioctyl sebacate andadipic acid–ammonium sulfate mixtures did not form a solution;adipic acid partitioned to the gas phase in the same manner asin the pure case. Care needs to be taken when calculating molefractions of compounds in ambient or smog chamber aerosols

to estimate their activities, since an aerosol particle might becomprised of multiple phases/solutions depending on the affini-ties of the species. When mixed with ambient extracts, adipicacid exhibited activity coefficients significantly less than unity,which suggests that the volatility of this compound could bestrongly suppressed in ambient aerosol, favoring its partitioningto the aerosol phase. The tested water extract of ambient aerosolexhibited behavior consistent with average molecular weight ofabout 180 g/mol and average volatility of C8–C10 dicarboxylicacids.

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