ARTICLE IN PRESS

1352-2310/$ - se

doi:10.1016/j.at

�CorrespondE-mail addr

(M. Camredon

Atmospheric Environment 40 (2006) 2105–2116

www.elsevier.com/locate/atmosenv

Assessment of vapor pressure estimation methods for secondaryorganic aerosol modeling

Marie Camredon�, Bernard Aumont

Laboratoire Interuniversitaire des Systemes Atmospheriques, UMR-CNRS-7583, Universites Paris 12 et Paris 7,

Avenue du General de Gaulle, 94000 Creteil, France

Received 30 April 2005; received in revised form 1 September 2005; accepted 14 November 2005

Abstract

Vapor pressure (Pvap) is a fundamental property controlling the gas–particle partitioning of organic species. Therefore

this pure substance property is a critical parameter for modeling the formation of secondary organic aerosols (SOA).

Structure–property relationships are needed to estimate Pvap because (i) very few experimental data for Pvap are available

for semi-volatile organics and (ii) the number of contributors to SOA is extremely large. The Lee and Kesler method, a

modified form of the Mackay equation, the Myrdal and Yalkowsky method and the UNIFAC-poL method are commonly

used to estimate Pvap in gas–particle partitioning models. The objectives of this study are (i) to assess the accuracy of these

four methods on a large experimental database selected to be representative of SOA contributors and (ii) to compare the

estimates provided by the various methods for compounds detected in the aerosol phase.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Vapor pressure; Secondary organic aerosols; Gas–particle partitioning modeling; Structure–property relationship

1. Introduction

Volatile organic compounds (VOC) emitted intothe atmosphere are progressively oxidized, leadingto the formation of a myriad of intermediates, morefunctionalized and thus more polar and less volatilethan their parent compounds (e.g., Aumont et al.,2005). These semi-volatile species form secondaryorganic aerosol (SOA) by nucleation and/or con-densation on pre-existing aerosols (i.e., absorptionand/or adsorption). The dominant process control-ling this gas–particle partitioning is expected to be

e front matter r 2005 Elsevier Ltd. All rights reserved

mosenv.2005.11.051

ing author. Fax: +331 45 17 15 64.

ess: camredon@lisa.univ-paris12.fr

).

an absorption mechanism (Pankow, 1994a,b; Odumet al., 1996; Hoffmann et al., 1997; Griffin et al.,1999; Kalberer et al., 2000). The equilibrium oforganic species can then be described on the basis ofRaoult’s law

Pi ¼ gixiPvapi , (1)

where Pi is the partial pressure of a species i in thegas phase, gi and xi are its activity coefficient and itsmole fraction in the aerosol phase, respectively, andPvapi is its vapor pressure as a pure liquid, subcooled

if necessary (Seinfeld and Pankow, 2003), at thetemperature of interest. Note that whether absorp-tion or adsorption is controlling the partitioning,both need vapor pressure data (Pankow, 1994a,b).Vapor pressure is, therefore, a fundamental

.

ARTICLE IN PRESSM. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–21162106

property controlling the gas–particle partitioning oforganics and is thus a key parameter for SOAformation models.

Organic gas–particle partitioning models basedon fully explicit (e.g., Stroud et al., 2004; Jenkin,2004) or lumped (e.g., Pun et al., 2002; Griffin et al.,2003; Dechapanya et al., 2003) oxidation schemesrequire vapor pressure values for every semi-volatileorganic compound generated in the gas-phasemechanism. Indeed vapor pressures of compoundsable to condense significantly are low, expected toreach values below 10�10 atm (e.g., Seinfeld andPankow, 2003). Measuring vapor pressure in suchranges is problematic and very few experimentaldata for such species are available. Furthermore, thenumber of contributors to SOA formation isextremely large. Vapor pressure data required todevelop these models far exceed the number ofspecies for which experimental vapor pressures areavailable. Estimation methods are therefore re-quired to evaluate this parameter in SOA formationmodels. These methods need to be applicable to thewide range of compounds involved in SOA produc-tion. Current models describing SOA formation usesemi-empirical methods for vapor pressure esti-mates based on (or coupled with) group contribu-tion approaches. For example, the Lee and Kesler(L&K) method (e.g., Reid et al., 1986) was used byStroud et al. (2004) to estimate the vapor pressure ofspecies in the University of Leeds’ Master ChemicalMechanism (MCM) (Jenkin et al., 2003; Saunderset al., 2003). Kamens et al. (1999), in a gas–particlemodel for a-pinene, and Jenkin (2004), in theMCM, used a modified form of the Mackay (mM)method (Mackay et al., 1982). The Caltech Atmo-spheric Chemistry Mechanism (CACM), developedby Pun et al. (2002) and Griffin et al. (2003), is basedon vapor pressure estimates provided by the Myrdaland Yalkowsky (M&Y) method (Myrdal andYalkowsky, 1997). Pankow et al. (2001) andSeinfeld et al. (2001), modeling the formation ofSOA from four monoterpenes and from cyclohex-ene, used the UNIFAC method to predict vaporpressure (Fredenslund and Rasmussen, 1979; Jensenet al., 1981). Asher et al. (2002) have optimized theUNIFAC-poL method for vapor pressure estimationon the basis of multifunctional oxygen-containingorganic compounds.

The four methods listed above are commonlyused to estimate the vapor pressure of organics inaerosols. The ability of these structure–propertyrelationships to accurately estimate the vapor

pressure of polar and/or low volatility organicsmust be assessed for the purpose of SOA modeling.Asher et al. (2002) have compared the accuracy ofthe L&K, M&Y and UNIFAC-poL methods on thebasis of experimental vapor pressures for 33 polarcompounds. The objectives of this study are (i) toassess the accuracy of the four methods listed aboveusing a larger database of semi-volatile organics and(ii) to compare the estimates provided by thesemethods for compounds detected in particulatematter. Section 2 describes the experimental data-base selected for this study. The four vapor pressureestimation methods are presented in Section 3. InSection 4 we give the results of their accuracy.Section 5 shows a comparison between thesemethods for species detected in the aerosol phase.

2. The database

Experimental vapor pressures are taken fromBoublık et al. (1984), Lide (2005), Yaws (1994),Myrdal and Yalkowsky (1997), Asher et al. (2002)and from the NIST chemistry website (http://webbook.nist.gov/chemistry). The database used inthis study is given in Appendix A (http://www.lisa.univ-paris12.fr/mod/pub/AE25203/AppendixA). Weuse experimental vapor pressures (Pvap) measured inthe temperature range of 270–320K. Temperaturedependencies of Pvap are based on parameteriza-tions (e.g., the Antoine equation) and are detailed inAppendix A. Pure substance properties, i.e., boilingpoint ðTbÞ, critical temperature ðT cÞ and criticalpressure (Pc), are also taken from the NISTchemistry website if available.

As mentioned above, candidate compounds forSOA formation are polar and/or low vapor pressurespecies. Progressive gas-phase oxidation of atmo-spheric VOC leads to the formation of highlyoxygenated species (e.g., Finlayson-Pitts and Pitts,2000) that include alcohol, ketone, aldehyde,carboxylic acid, alkyl nitrate, hydroperoxide and/or peroxyacyl nitrate functions (e.g., Atkinson,2000). Additional functionalities, such as ester andether groups, are also found in trace amounts inthe troposphere owing to significant emissions(e.g., Emission Database for Global AtmosphericResearch—Version 2, http://www.rivm.nl/geia/docu-mentation). Most of those moieties have alreadybeen detected in particulate matter. For example,molecules bearing ester, ether, alcohol, ketone,aldehyde and carboxylic acid moieties have beenidentified in the condensed phase during in situ

ARTICLE IN PRESSM. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–2116 2107

campaigns (e.g., Claeys et al., 2004; Yue and Fraser,2004; Limbeck et al., 2005; Yu et al., 2005) as well asduring chamber experiments (e.g., Forstner et al.,1997; Kalberer et al., 2000; Jang and Kamens, 2001;Larsen et al., 2001; Jaoui and Kamens, 2003a–c;Jaoui et al., 2003, 2004; Kleindienst et al., 2004).Alkyl nitrate and peroxyacyl nitrate fragments havealso been detected in the aerosol phase (e.g., Jangand Kamens, 2001). Additionally, hydroperoxidemoieties have been simulated as making up asignificant fraction of particulate organic matter(Bonn et al., 2004). Molecules selected for this studyand included in the database are therefore hydro-carbons and mono- or multifunctional speciesbearing the moieties listed above. The experimentaldata set drawn upon for this study includes vaporpressures of about 270 organics, of which around200 are oxygenated. In this database, experimentalvapor pressures range from 10�8 to 1 atm fortemperatures between 270 and 320K.

Availability of experimental measurements limitsthe development of this database. To our knowl-edge, Pvap for species bearing the hydroperoxide orperoxyacylnitrate functions are only available forcyclohexyl hydroperoxide (Yaws, 1994) and forPAN (Bruckmann and Willner, 1983). Therefore,the contribution of these two groups cannot beassessed correctly. Very little data are available forvapor pressures lower than 10�6 atm, i.e., in therange of interest for SOA formation. The accuracyof the estimation methods can therefore not beevaluated for very low Pvap and an extrapolation isnecessary.

3. Description of vapor pressure estimation methods

3.1. The Lee and Kesler (L&K) method

In this approach the reduced pressure Prð¼ P=PcÞ

is expressed as a function of the reduced tempera-ture T rð¼ T=T cÞ. The variation of the reducedvapor pressure (Pvap

r ) is given by (e.g., Reid et al.,1986)

lnPvapr ¼ f ð0ÞðT rÞ þ wf ð1ÞðT rÞ, (2)

where f ð0Þ and f ð1Þ are the Pitzer’s functions and w isthe acentric factor. w is calculated as a function ofT c;Pc and Tb (see Eq. (2-3.4) in Reid et al., 1986).Lee and Kesler proposed an analytical formula forf ð0Þ and f ð1Þ leading to satisfactory Pvap estimations(see Eqs. (7-2.7) and (7-2.8) in Reid et al., 1986).

Pure substance properties (Tb;Tc and Pc) arerequired in the L&K method. Since these para-meters are not available for every species of interest,they must be estimated using additional structure–properties relationships. The reliability of the L&Kmethod must thus be assessed taking into accountthe accuracy of pure substance property estimates.Therefore, results presented in Sections 4 and 5always use estimates for pure substance propertieseven if experimental data are available. Somemethods used to estimate Tb;Tc and Pc are brieflydescribed below. Their reliability is discussedcomparing estimates with experimental propertiesfor the organics selected in this study.

3.1.1. Boiling point estimation

The Joback group contribution method can beused to estimate Tb (e.g., Reid et al., 1986).Additional group contributions are added hereto take into account molecules bearing the alkylnitrate moiety (ONO2), the peroxyacyl nitratemoiety (CðOÞOONO2) and the hydroperoxide moiety(OOH). The group contribution for the nitrate moietyis fitted from eight experimental Tb values providedby the NIST chemistry website; we obtain a value ofDTONO2

b ¼ 112:10K with a standard deviation of4.8K. Data provided by Bruckmann and Willner(1983) for the PAN lead to DT

CðOÞOONO2

b ¼ 157:42K.To our knowledge, no additional data are availablefor species bearing the peroxyacyl nitrate moiety, orfor species bearing the hydroperoxide moiety. Theincrement value for OOH is calculated from acombination of existing Joback’s contributions andset to DTOOH

b ¼ DT2O2b þ DTOH

b .Fig. 1 shows estimated Tb versus experimental

values for compounds presented in Appendix A.The mean absolute error (MAE) of Tb estimation is12.1K. This result is in agreement with the MAE of12.9K calculated by Reid et al. (1986) for a set of438 organic compounds. Stein and Brown (1994)found a larger absolute error of 28.9K for a set of4280 compounds. As shown in Fig. 1, Tb estimatesmatch fairly well with experimental data for theselected set of species ðR2 ¼ 0:97Þ, and show nosystematic bias. Stein and Brown (1994) showed anoverprediction of Tb values above 500K. Theyexpanded and corrected the Joback method using aset of 4426 experimental boiling points. For ourdatabase, corrections provided by Stein and Brownimprove Tb estimates slightly with: (i) a MAE of9.5K, (ii) a correlation coefficient of R2 ¼ 0:98 and(iii) a regression line equation of y ¼ 10:7þ 0:97x

ARTICLE IN PRESS

300 350 400 450 500 550 600 650300

350

400

450

500

550

600

650

y = -10.2 + 1.04xR2 = 0.97N = 252

TbJO

B(K

)

TbEXP(K)

Fig. 1. Boiling points estimated with the Joback method versus

experimental values. The continuous and dashed lines are,

respectively, the y ¼ x and regression lines.

400

500

600

700

800

400 500 600 700 800 900400

500

600

700

800

TcJO

B(K

)T

cAM

B(K

)

TcEXP(K)

y = -25.4 + 1.05xR2 = 0.96N = 139

y = 81.8 + 0.85xR2 = 0.93N = 139

(a)

(b)

Fig. 2. Estimated T c versus experimental values for (a) the

Joback and (b) the Ambrose methods. The continuous and

dashed lines are, respectively, the y ¼ x and regression lines.

M. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–21162108

(see Appendix B: http://www.lisa.univ-paris12.fr/mod/pub/AE25203/AppendixB). In the followingsections Stein and Brown’s modifications are how-ever not used, in order to avoid circularity in theassessment. The circularity arises because aroundone-third of the boiling points used to develop thecorrections were extrapolated to 1 atm using theL&K method (e.g., Reid et al., 1986), which is oneof the vapor pressure estimation methods assessedin this study. Instead, we predict Tb in this studyusing the Joback method. In addition, we note thatintroducing Stein and Brown’s corrections does notimprove the accuracy of Pvap estimated with theL&K method, nor with the M&Y and mM methodspresented below (see Appendix B).

3.1.2. Critical temperature estimation

Two group contribution methods for T c estima-tion are tested in this study: the Joback and theAmbrose methods (Reid et al., 1986). To be usefulfor the purpose of SOA modeling, group contribu-tions for ONO2, CðOÞOONO2 and OOH must beadded to those methods. However, to our knowl-edge, no T c value is available for compoundsbearing these functionalities. These group incre-ments are evaluated using existing group contribu-tions: DTONO2

c ¼ DT2O2c þ DTNO2

c , DTCðOÞOONO2c ¼

DTCðOÞOc þ DTONO2

c , and DTOOHc ¼ DT2O2

c þ DTOHc .

Fig. 2 compares estimated versus experimental Tc

for compounds presented in Appendix A. TheJoback method estimates Tc values with a MAEof 17.6K, larger than the MAE of 4.8K found byReid et al. (1986) on a set of 400 compounds. Asshown in Fig. 2a the Joback method considerably

underpredicts Tc for high values and shows a largenegative bias. The Ambrose method estimates Tc

with a MAE of 17.3K. Reid et al. (1986) found thismethod to be more accurate, estimating Tc with aMAE of 4.3K for a set of 400 compounds. TheAmbrose method of Tc estimation matches experi-mental values fairly well for this set of compoundsðR2 ¼ 0:96Þ and is more reliable than the Jobackmethod for compounds of interest for SOA forma-tion, i.e., compounds with a high boiling point(see Fig. 2). The Ambrose method of T c estimationis retained in this study.

3.1.3. Critical pressure estimation

The Joback and the Ambrose structure–propertymethods (Reid et al., 1986) are tested for estimationof Pc. We evaluate Pc group increments for organicsbearing ONO2, CðOÞOONO2 or OOH moietiesusing existing group contributions, as describedabove for T c. Fig. 3 plots estimated versus experi-mental Pc values for compounds presented inAppendix A. Both estimation methods give aMAE of 1.66 atm, in agreement with the MAE of2.1 and 1.8 atm for the Joback and for the Ambrose

ARTICLE IN PRESS

20

30

40

50

60

70

80

90

20 30 40 50 60 70 80 90 10020

30

40

50

60

70

80

90

PcA

MB(a

tm)

PcEXP(atm)

y = 3.57 + 0.90xR2 = 0.95N = 119

y = -1.67 + 1.07xR2 = 0.96N =119

(a)

(b)

PcJO

B(a

tm)

Fig. 3. Estimated Pc versus experimental values for (a) the

Joback and (b) the Ambrose methods, continuous and dashed

lines are, respectively, the y ¼ x and regression lines.

M. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–2116 2109

methods respectively found by Reid et al. (1986) onthe basis of 390 compounds. In this study, theAmbrose method is used to evaluate Pvap for theL&K calculation.

3.2. The expanded forms of the Clausius– Clapeyron

equation

Several vapor pressure estimation methods arebased on the Clausius–Clapeyron equation. Whenintegrating from the temperature of interest to theboiling point and assuming that the organic aerosolphase is a liquid phase (subcooled if necessary), Pvap

is expressed as

lnPvap ¼DSbðTb � TÞ

RTþ

DCpb

R

Tb � T

T� ln

Tb

T

� �,

(3)

where R is the gas constant, DSb the vaporizationentropy at the boiling point and DCpb the gas–liquidheat capacity. Various empirical parameterizationsor group contribution methods can be used forevaluating DSb and DCpb (e.g., Reid et al., 1986;Baum, 1998; Schwarzenbach et al., 2003).

3.2.1. The modified Mackay (mM) equation

Mackay et al. (1982) tested Eq. (3) for vaporpressure estimation using DSb evaluated from theKistiakowsky expression and assuming constantDCpb=DSb (see Eq. (4-33) in Schwarzenbach et al.,2003). In this study, we use the Mackay methodwith modifications provided by Vetere (e.g., Reidet al., 1986; Baum, 1998) to improve the accuracy ofDSb. This method will be called hereafter as themodified Mackay (mM) method. Pvap is then afunction of the molecular mass and Tb, which weestimate using the Joback structure–property rela-tionship method. Note that our tests of the mMmethod in Sections 4 and 5 use the Joback methodto estimate Tb even if experimental values areavailable.

3.2.2. The Myrdal and Yalkowsky (M&Y) method

Myrdal and Yalkowsky (1997) tested anotherapproach to estimate DSb and DCpb for Eq. (3).They inserted the empirical expression of DSb

developed by Myrdal et al. (1996) and evaluated aparameterization fitting well experimental vaporpressure data for DCpb. Pvap is then a function of Tb

and of parameters linked to the molecular structure:the torsional bond (taking into account the effectivetorsion number of a molecule) and the hydrogenbond number (HBN). As in the case of the L&Kmethod, Tb is estimated using the Joback struc-ture–property relationship method. Our tests of theM&Y method in Sections 4 and 5 use Tb estimatesprovided by the Joback method, even if experi-mental values are available.

A group contribution for the hydroperoxidemoiety is unavailable by the M&Y method. Thecontribution for this group must be taken intoaccount in the HBN formula. In this study HBN iscalculated as

HBN ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiOHþ COðOHÞ þOOH

pþ 0:33

ffiffiffiffiffiffiffiffiffiffiNH2

p

MW,

(4)

where OH, CO(OH), OOH and NH2 are, respec-tively, the number of alcohol, carboxylic acid,hydroperoxide and primary amine moieties in thespecies and MW is molecular weight.

3.3. The UNIFAC-poL method

UNIFAC is a group contribution method devel-oped to obtain the Gibbs energy of a substance in a

ARTICLE IN PRESSM. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–21162110

given mixture (Fredenslund et al., 1977). Thismethod has been used to estimate vapor pressuredata (Fredenslund and Rasmussen, 1979; Jensenet al., 1981). The difference between the free energyof a compound i in the pure liquid state at TðGiÞ

and the reference state, i.e., the perfect gas at T andP ¼ 1 atm ðG0

i Þ, can be written as (Fredenslund andRasmussen, 1979)

Gi � G0i ¼ RT lnP

vapi ¼

Xk

nðiÞk Dgk

þ RTX

k

nðiÞk lnGðiÞk , ð5Þ

where nðiÞk is the number of groups of type k in thespecies i; Dgk the difference at T between the Gibbsenergy of group k in the pure liquid state and in thereference state, and GðiÞk the residual UNIFAC termof the group k (Reid et al., 1986). Jensen et al.(1981) linked the Dgk expression to the structure ofthe molecule and to the temperature. Asher et al.(2002) applied this method to the estimation ofvapor pressure of mono- and multi-functionalizedorganic compounds and provided empirical groupcontributions optimized on the basis of 76 polarcompounds. Contributions have been optimized forthe following moieties: –CH3, –CH2, 4CH�,4Co (cyclic and non-cyclic), and for –OH,CH3CðOÞ–, –CHO and –C(O)OH.

This method does not provide vapor pressureestimates for all compounds present in the database:some group contributions are lacking (e.g., forfragments bearing double bonds, ether, ester,nitrate, peroxyacylnitrate, hydroperoxide moieties).Evaluation of Dgk and/or GðiÞk for these groups isbeyond the scope of this study.

4. Assessment of the vapor pressure estimation

methods

Vapor pressures for compounds listed in Appen-dix A are estimated using the four methods withT ¼ 270; 280; 290; 300; 310 and 320K. Fig. 4 shows(i) estimated versus experimental logðPvap

i Þ and (ii)the differences D logðPvap

i Þ ¼ logPvapEST;i � logP

vapEXP;i

as multiple box plots for various ranges of Pvap.Reliability of the methods is discussed on the basisof the MAE and of the mean bias error (MBE)calculated for the logarithm of vapor pressure, i.e.

MAE ¼1

n

Xi

logPvapEST;i � logP

vapEXP;i

��� ���, (6)

MBE ¼1

n

Xi

logPvapEST;i � logP

vapEXP;i

� �. (7)

The MAE values are plotted in Fig. 5 for eachmethod and for the various ‘‘classes’’ of compounds(i.e., hydrocarbons, alcohols, aldehydes andketones, carboxylic acids, esters, ethers, nitrates,di- and tri- or more functionalized species). TheMBE values are reported in Table 1 for eachmethod and for the various classes of compounds.

The L&K method gives reliable vapor pressureestimates (see Fig. 4a) correlated with a coefficientof R2 ¼ 0:95. This method estimates Pvap for the setof compounds listed in Appendix A within a factorof 2.1 on average, significantly better than the factorof 3 accuracy found by Asher et al. (2002). Fig. 4eshows that D logðPvapÞ increases when vapor pres-sure decreases. For compounds having experimentalvapor pressure below 10�4 atm, the estimatesmatch experimental data within a factor of 3.6 onaverage (see Fig. 4e). Estimates for each class ofcompound correlate reliably with experimental data(see Fig. 5). The most significant errors are foundfor di-functionalized ðMAE ¼ 0:503Þ and tri- ormore functionalized ðMAE ¼ 0:471Þ species (seeFig. 5). No systematic bias is highlighted for thetotal set of compounds ðMBE ¼ �0:036Þ. Thepredicted vapor pressures for each class of com-pounds do not possess a large bias ðjMBEjo0:241Þ(see Table 1). Reid et al. (1986) show that the L&Kmethod may underpredict Pvap if vapor pressuresare calculated at a temperature below Tb. Boilingpoints of organics selected for this study are high(i.e., greater than ambient temperature), howeverresults given in this section do not show thesystematic bias found by Reid et al. (1986).

The mM method gives estimates correlated with acoefficient R2 ¼ 0:95 (see Fig. 4b). Estimates matchexperimental values within a factor of 2.5 onaverage. Fig. 4f shows that D logðPvapÞ rises notablywith decreasing vapor pressure. For experimentalvapor pressure lower than 10�4 atm, this methodestimates vapor pressure within a factor of 5.7(see Fig. 4f). The tri- or more functionalized classgives MAE of up to 0.593 (see Fig. 5). This methodshows a large positive bias for the total set ofcompounds (MBE ¼ 0:240, see Fig. 5). Overesti-mates are found for all classes of compounds (seeTable 1).

The M&Y estimates are well correlated withexperimental values (see Fig. 4c, R2 ¼ 0:96). Thismethod estimates vapor pressure of species listed in

ARTICLE IN PRESS

y = -0.174 + 0.949xR2 = 0.95N = 850

log

Pva

p L&K

(a)

log

Pva

p mM

y = -0.283 + 0.815xR2 = 0.95N = 779

-6

-4

-2

y = -0.121 + 0.966xR2 = 0.96N = 850

log

Pva

p M&

Y

(b)

(c)-8

-6

-4

-2

-8

-6

-4

-2

-8

-8 -6 -4 -2 0

log PvapEXP

(atm)

-6

-4

-2

y = -0.003 + 1.040xR2 = 0.96N = 424

log

Pva

p U

(d)

-8

0

2

1

-1

0

2

1

-1

0

2

1

-1

0

2

1

-1

log

Pva

p U-

log

Pva

p EX

P

log

Pva

p L&K

- lo

g P

vap E

XP

log

Pva

p M&

Y -

log

Pva

p EX

P

(e)

(g)

(h)

log

Pva

p mM

- lo

g P

vap E

XP

(f)

N = 18 N = 143 N = 378 N = 311

N = 18 N = 143 N = 373 N = 245

N = 18 N = 143 N = 378 N = 311

N = 8 N = 78 N = 199 N = 139

Pvap <10

-6 atm

10-2 <P

vap <1atm

10-6 <P

vap <10-4 atm

10-4 <P

vap <10-2 atm

Fig. 4. Left panels: estimated Pvap versus experimental values for the (a) L&K, (b) mM, (c) M&Y and (d) UNIFAC-poL methods. The

continuous and dashed lines are, respectively, the y ¼ x and regression lines. Right panels: box plots of the differences between estimated

and experimental values for the (e) L&K, (f) mM, (g) M&Y and (h) UNIFAC-poL methods.

M. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–2116 2111

Appendix A within a factor of 2.0 on average. Thisvalue is higher than the factor of 1.45 shown byMyrdal and Yalkowsky (1997) for 260 speciescomprising hydrocarbons and mono-functionalizedcompounds only. However the M&Y methodappears to be more reliable than predicted by Asheret al. (2002), who estimated Pvap to within a factor

of about 3 on average. Fig. 4g shows thatD logðPvapÞ increases slightly for low vapor pres-sures. For compounds with experimental vaporpressure lower than 10�4 atm, the estimates matchexperimental data within a factor of 2.8 on average(see Fig. 4g). The largest errors are found for di-and tri- or more functionalized compounds

ARTICLE IN PRESSM. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–21162112

(MAE ¼ 0:453 and 0.469 respectively, see Fig. 5).Fig. 5 shows that vapor pressures of the otherclasses of molecules are estimated within an averagefactor of 2.2 or less. This evaluation does not showany systematic bias for the total set of speciesðMBE ¼ �0:029Þ.

Some values in the database have already beenused by Asher et al. (2002) for the optimizationof the UNIFAC-poL method (around 50%). There-fore, the evaluation performed here includessome circularity and must be taken cautiously. Thismethod gives estimations correlated with R2 ¼ 0:96(see Fig. 4d). UNIFAC-poL gives vapor pressureestimates within a factor of 2.2 of measurements.

L&K M&Y UmM

0

0.2

0.4

0.6

0.8hydrocarbonsalcoholsaldehydes, ketonescarboxylic acidsestersethersnitratesdi-functionalizedtri- & more functionalized

MA

E

Fig. 5. MAE for the different classes of molecules of the

logarithm of Pvap estimated by L&K, mM, M&Y and UNI-

FAC-poL methods.

Table 1

MBE of the logarithm of Pvap for the different classes of molecules ca

UNIFAC-poL methods

MBEL&K

Hydrocarbons 0.064

Mono-functionalized species

Alcohols �0.106

Aldehydes and ketones 0.125

Carboxylic acids 0.054

Esters �0.202

Ethers �0.241

Nitrates �0.144

Di-functionalized species �0.036

Tri- or more functionalized species �0.073

This result agrees with the average factor of about 2found by Asher et al. (2002). The largest errors arefound for compounds bearing aldehydes andketones moieties (see Fig. 5). Fig. 4h shows thatD logðPvapÞ does not increase for estimates of lowvapor pressure. For compounds with experimentalvapor pressures lower than 10�4 atm, the estimatesmatch experimental data within a factor of 2.5 onaverage (see Fig. 4h). The mean bias error is low(MBE ¼ �0:114 and see Table 1).

The mM method is less accurate than the threeothers. This method shows a large positive bias,suggesting that it is not suitable for extrapolation tolow vapor pressures. The L&K, M&Y and UNI-FAC-poL methods provide similar results for Pvap

estimates for the total set of species. These threemethods show no systematic bias and thereforeappear suitable for extrapolation to low vaporpressure. Indeed the L&K methods show a sig-nificant increase of D logðPvapÞ when Pvap decreases.The UNIFAC-poL and the M&Y methods appear tobe the most reliable for low vapor pressureestimation. In agreement with Asher et al. (2002),the UNIFAC-poL was found to be slightly moreaccurate than the M&Y method.

5. Comparison of vapor pressure estimates for

organic species found in aerosol phase

The relevance of gas–particle partitioning modelsis directly linked to the accuracy of Pvap estimates.These methods must be compared in order tohighlight the variability of the predictions for SOAcontributors (see the list in Appendix C, http://www.lisa.univ-paris12.fr/mod/pub/AE25203/AppendixC).

lculated for the estimations provided by L&K, mM, M&Y and

MBEmM MBEM&Y MBEU

0.030 �0.267

0.155 �0.213 �0.278

0.249 0.167 0.105

0.493 0.055 �0.161

�0.001 �0.127

0.230 �0.183

0.064 0.027

0.253 �0.030 0.026

0.517 �0.010

ARTICLE IN PRESS

-15

-10

-5

0

-15

-10

-5

0

log

Pva

p mM

log

Pva

p L&K

y = 0.618 + 1.172xR2 = 0.99N = 112

y = -0.425 + 0.965xR2 = 0.98N = 65

-15 -10 -5 0

log PvapM&Y

(atm)

(a)

(b)

(c)

y = -0.288 + 0.844xR2 = 0.99N = 112

-15

-10

-5

0

log

Pva

p U

log

Pva

p U-

log

Pva

p M&

Y

log

Pva

p mM

- lo

g P

vap M

&Y

lo

g P

vap L&

K -

log

Pva

p M&

Y

0

2

1

-2

-1

0

2

1

-2

-1

0

2

1

-2

-1

(d)

(e)

(f)

N = 38 N = 58 N = 16

N = 38 N = 58 N = 16

N = 24 N = 31 N = 10

Pvap <10

-8 atm

10-4 <P

vap <1atm

10-8 <P

vap <10-4 atm

Fig. 6. Left panels: estimated Pvap versus Pvap estimated with the M&Y method for the (a) L&K, (b) mM and (c) the UNIFAC-poLmethods. The continuous and dashed lines are, respectively, the y ¼ x and regression lines. Right panels: box plots of the differences

between the logarithm of estimated Pvap and the logarithm of Pvap estimated with the M&Y method for the (d) L&K, (e) mM and (f)

UNIFAC-poL methods.

Table 2

MAE of the logarithm of Pvap between estimations provided by

the various methods

MAEmM MAEU MAEM&Y

MAEL&K 1.376 0.827 0.678

MAEmM 1.149 0.799

MAEU 0.431

M. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–2116 2113

Compounds listed in Appendix C were detectedduring field campaigns (Claeys et al., 2004; Matsu-naga et al., 2004; Yue and Fraser, 2004; Limbecket al., 2005; Yu et al., 2005) and smog chamberexperiments (Forstner et al., 1997; Jang and

Kamens, 2001; Jaoui and Kamens, 2003a–c; Jaouiet al., 2003; Kleindienst et al., 2004). About 100species are considered for this comparison.

The M&Y method is used as the ‘‘reference’’method to evaluate the deviations between the fourestimates since it allows for description of all speciestypes. Vapor pressures at 298K are calculatedfor compounds listed in Appendix C. Fig. 6 shows(i) log P

vapL&K;i; logP

vapmM;i and logP

vapU;i as a function of

logPvapM&Y;i and (ii) the differences between the

estimates for various ranges of Pvap. Table 2presents the MAE found between the methods.Molecules detected in the aerosol phase giveestimated vapor pressures reaching 10�15 atm. Esti-mates between the four methods differ widely,

ARTICLE IN PRESSM. Camredon, B. Aumont / Atmospheric Environment 40 (2006) 2105–21162114

sometimes by more than a factor of 100 (seeFig. 6). For vapor pressure higher than 10�4 atm,the L&K and M&Y methods yield comparableresults (Figs. 6a and d). However, the L&K methodsignificantly underestimates Pvap values below10�4 atm in comparison to the mM, the M&Y andthe UNIFAC-poL methods. The mM method greatlyoverpredicts values in comparison with the threeother methods for the lower ranges of Pvap (Fig. 6,Table 2). This result is in agreement with theoverestimation of Pvap highlighted in the previoussection. Estimates calculated by the M&Y methodand the UNIFAC-poL method are well correlated(R2 ¼ 0:98; Figs. 6c and f), even for low vaporpressure (Fig. 6f). Both these methods providecomparable estimates for species found in theaerosol phase, within an average factor of 2.7.

6. Conclusion

Four vapor pressure estimation methods basedon (or coupled with) structure–property relation-ships and in current use for SOA modeling havebeen tested: L&K, mM, M&Y and UNIFAC-poLmethods. An evaluation of the accuracy of thesefour methods has been performed on a largedatabase, selected to be representative of SOAcontributors. The mM method is found to be theleast reliable owing to a large positive bias. Theother three estimation methods are found to havesimilar reliability: L&K, M&Y and UNIFAC-poLmethods provide estimates within respective averagefactors of 2.1, 2.0 and 2.5 of experimental data. Nosystematic bias is found for L&K, M&Y andUNIFAC-poL methods, which therefore appearsuitable for extrapolation to low vapor pressure.The L&K methods show increases of the residualvalues when vapor pressures decrease. The UNI-FAC-poL and the M&Y method are found to be themost reliable for low vapor pressure estimates.

Predictions provided by these methods have beencompared for organic compounds detected inparticulate matter. The mM method is again foundto overpredict vapor pressure while the L&Kmethod underpredicts vapor pressure with respectto the predictions provided by the UNIFAC-poL andM&Y methods. The UNIFAC-poL and M&Ymethods give comparable results for low vaporpressure compounds (with an average factor of 2.7).However, the M&Y method provides estimates formore possible SOA contributors and appears there-

fore the most suitable method to predict Pvap forSOA formation modeling.

Acknowledgments

Helpful comments on the manuscript by A. Dutotand J. Lee-Taylor are gratefully acknowledged.

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