Hindawi Publishing CorporationInternational Journal of GeophysicsVolume 2013 Article ID 612375 13 pageshttpdxdoiorg1011552013612375

Research ArticleEvaluation of Vapor Pressure Estimation Methods for Use inSimulating the Dynamic of Atmospheric Organic Aerosols

A J Komkoua Mbienda1 C Tchawoua2 D A Vondou1 and F Mkankam Kamga1

1 Laboratory of Environmental Modeling and Atmospheric Physics Department of Physics Faculty of Science University of Yaounde 1PO Box 812 Yaounde Cameroon

2 Laboratory of Mechanics Department of Physics Faculty of Science University of Yaounde 1 PO Box 812 Yaounde Cameroon

Correspondence should be addressed to A J Komkoua Mbienda kombiendgmailcom

Received 24 March 2013 Accepted 5 June 2013

Academic Editor Robert Tenzer

Copyright copy 2013 A J Komkoua Mbienda et alThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

The modified Mackay (mM) the Grain-Watson (GW) Myrdal and Yalkovsky (MY) Lee and Kesler (LK) and Ambrose-Walton(AW) methods for estimating vapor pressures (119875vap) are tested against experimental data for a set of volatile organic compounds(VOC) 119875vap required to determine gas-particle partitioning of such organic compounds is used as a parameter for simulating thedynamic of atmospheric aerosols Here we use the structure-property relationships of VOC to estimate 119875vap The accuracy of eachof the aforementionedmethods is also assessed for each class of compounds (hydrocarbons monofunctionalized difunctionalizedand tri- andmore functionalized volatile organic species) It is found that the bestmethod for eachVOCdepends on its functionality

1 Introduction

Atmospheric aerosols (AA) have a strong influence on theearthrsquos energy balance [1] and a great importance in theunderstanding of climate change and human health (respira-tory and cardiac diseases cancer)They are complexmixturesof inorganic and organic compounds with compositionvarying over the size range from a few nanometers to severalmicrometers Given this complexity and the desire to con-trol AA concentration models that accurately describe theimportant processes that affect size distribution are crucialTherefore the representation of particle size distributionis of interest in aerosol dynamics modeling However inspite of the impressive advances in the recent years ourknowledge of AA and physical and chemical processes inwhich they participate is still very limited compared tothe gas phase [2] Several models have been developed thatinclude a very thorough treatment of AA processes such asin Adams and Seinfeld [3] Gons et al [4] and Whitby andMcMurry [5] Indeed the evolution of size distribution of AAis made by a mathematical formulation of processes calledthe general dynamic equation (GDE) It is well known thatthe first step in developing a numerical aerosol model is toassemble expressions for the relevant physical processes The

second step is to approximate the particle size distributionwith a mathematical size distribution function Thus thetime evolution of the particle size distribution of aerosolsundergoing coagulation deposition nucleation and conden-sationevaporation phenomena is finally governed by GDE[1] This latter phenomenon is characterized by the mass flux119868119894for volatile species 119894 between gas phase and particle which

is computed using the following expression [6]

119868119894=

119889119898119894

119889119905= 2120587119863

119892

119894119889119901119891FS (119870119899119894 120572119894) (119888

119892

119894minus 119888119904

119894) (1)

119891FS describes the noncontinuous effects [7] When 119868119894ge

0 (119868119894

le 0) there is condensation (evaporation) 119888119904

119894is

assumed to be at local thermodynamic equilibrium with theparticle composition [8] and can be obtained from the vapourpressure (119875vap

119894) of each volatile compound 119894 with average

molar mass of the atmospheric aerosol mole fraction andactivity coefficient through the following equation

119888119904

119894= 119909

120574119875vap119894

119898106

119877119879 (2)

where 119875vap119894

is given by the Clausius-Clapeyron law

119875vap119894

(119879) = 119875vap119894

(298) exp[minus(119867vap119877)((1119879)minus(1298))] (3)

2 International Journal of Geophysics

Parameters in (1)ndash(3) are named in Table 1In (3) 119867vap is equal to 156 kJmol as stated by Derby

et al [8] Consequently the vapour pressures of all aerosolcompounds are needed to calculate the mass flux of con-densing and evaporating compounds The knowledge of 119875vap

119894

for organic compound 119894 at the atmospheric temperature 119879

is required whenever phase equilibrium between gas phaseand particle is of interest Often most of the compounds ableto condense have experimental vapor pressures unavailableand because of that their estimation becomes necessary Tosolve this problem of estimation many methods have beendeveloped For example in Tong et al [9] a method basedon atomic simulation is applied only for compounds bearingacid moieties Quantum-mechanical calculations are makingsteady effort in vapor pressure prediction (Banerjee et al[10] Diedenhofen et al [11]) Furthermore current mod-els describing gas-particle partitioning use semiempiricalmethods for vapor pressure estimation based on molecularstructure often in the form of a group contribution approachTherefore these methods require in most cases molecularstructures (eg boiling point 119879

119887 critical temperature 119879

119888

and critical pressure 119875119888) which usually have themselves to

be estimated For example The MY method [12] was usedby Griffin et al [13] and Pun et al [14] for modeling theformation of secondary organic aerosol Jenkin [15] in a gasparticle partitioning model used the modified form of theMackay method [16] Some methods (Pankow and Asher[17] Capouet and Muller [18]) assume a linear logarithmicdependence (ln119875vap

119894) on several functional groups but this

consideration fails when multiple hydrogen bonding groupsare present Furthermore more investigations are needed toclarify which method can give values closer to the exper-imental data Camredon and Aumont [19] Compernolleet al [20] and Barley and McFiggans [21] have made anassessment of different vapor pressure estimation methodswith experimental data for compounds of relatively highervolatility For this latter reason large differences in theestimated vapor pressure have been reported

In this paper our focus will be on the (i) evaluationof a number of vapor pressure estimation methods againstexperimental data using all volatile organic compoundspresent in our database and (ii) assessment of the accuracy ofeach of thesemethods on the base of each class of compounds

The rest of the paper is organized as follows In Section 2we describe experimental data and methods The results arepresented in Section 3 Finally we summarize our finding inSection 4

2 Data and Vapor PressureEstimation Methods

21 Experimental Data The molecules selected in thisstudy have been identified during in situ campaigns [22]and during chamber experiments [23] In fact they arehydrocarbons monofunctionalized and multifunctionalizedspecies and bearing alcohol aldehyde ketone carboxylicacid ester ether and alkyl nitrate functions The exper-imental vapor pressures are taken from NIST chemistry

Table 1 Nomenclature

Parameters Names119868119894

Mass flux for volatile species 119894119889119901

The particle wet diameter119898119894

Mass of species 119894119863119892

119894Molar diffusivity in the air of species 119894

119888119892

119894Gas-phase concentration of species 119894

119891FS Fuchs-Sutugin function119888119904

119894Concentration at the surface of species 119894

119877 Gas constant119879 Temperature in Kelvin119867vap Vaporisation enthalpy119909 Mole fraction120574 Activity coefficient119875vap119894

Vapour pressure of each volatile compound 119894

website (httpwwwnistgovchemestry) and from Myrdaland Yalkowsky [12] Asher et al [24] Lide [25] Yams [26]and Boulik et al [27] and they have a range from 10

minus8 atmto 1 atm Molecular properties (boiling point critical tem-perature and critical pressure) are also taken from the NISTchemistry website All vapor pressure estimation methodsused in this study take into account these properties In mostcases these properties have also to be estimated

22 Estimation of Molecular Properties

221 Boiling Temperature 119879119887 Using the boiling temperature

of Joback [28] and its extension the group contributiontechnique denoted by 119879Job

119887is written as

119879Job119887

= 198 +sum

119894

119873119894119905119887119894 (4)

where 119905119887119894

is the contribution of group 119894 and 119873119894is the

occurrence of this group in the molecule As in CamredonandAumont [19] the extension ismade by adding some othergroup contribution to take into account molecules bearinghydroperoxidemoiety (ndashOOH) alkyl nitratemoiety (ONO

2)

and peroxyacyl nitrate moiety (ndashC(=O)OONO2) Thus the

first group is divided into the existing Joback groups ndashOndashand ndashOH The second group value is provided by the NISTchemistry website and the last group value is provided byCamredon and Aumont [19] using boiling point value fromBruckmann and Willner [29]

222 Critical Temperature 119879119888 We have used Joback [28]

and Lydersenrsquos [30] techniques to estimate 119879119888 Denoting by

119879Job119862

and 119879Lyd119888

the Joback and Lydersen critical temperaturesrespectively we have

119879Job119888

=119879119887

0 584 + 0 965sum119894119873119894119905119894minus (sum119894119873119894119905119894)2

119879Lyd119888

=119879119887

0 567 + sum119894119873119894119905119894minus (sum119894119873119894119905119894)2

(5)

International Journal of Geophysics 3

New group contributions have been added by Camredonand Aumont [19] for hydroperoxide alkyl nitrate and perox-yacyl nitrate moieties

119905ndashOOH119888

= 119905ndashOndash119888

+ 119905ndashOH119888

119905ndashONO2119888

= 119905ndashOndash119888

+ 119905ndashNO2119888

119905ndashC(=O)OONO2119888

= 119905ndashC(=O)O119888

+ 119905ndashOndash119888

+ 119905ndashNO2119888

(6)

223 Critical Pressure 119875119888 The two techniques listed in the

previous section have been used to estimate critical pressure119875119888 Here it is also assumed that 119875

119888is the sum of group

contributions Therefore denoting by 119875Job119888

and 119875Lyd119888

theJoback and Lydersen critical pressures respectively we canwrite

119875Job119888

=1

(0 113 + 0 0032119899 minus sum119894119873119894119901119894)2

119875Lyd119888

=119872

(0 34 minus sum119894119873119894119901119894)2

(7)

where 119872 is the molar mass 119899 is the number of atoms in themolecule and 119901

119894is the critical pressure contribution of group

119894 The new group contributions described in the previoussubsection are taken into account here

23 Vapor Pressure EstimationMethods As said earlier manymethods for vapor pressure estimation have been developedand are based on the Antoine or on the extended form of theClausius-Clapeyron equation Let us present in what followseach of the five methods used

231 The Myrdal and Yalkowsky (MY) Method The MYmethod [12] starts from the extended form of the Clausius-Clapeyron equation obtained by using Eulerrsquos cyclic relationHere the expression of 119875vap is given by

ln119875vap=

Δ119878119887(119879119887minus 119879)

119877119879+

Δ119862119901119887

119877(119879119887minus 119879

119879minus ln

119879119887

119879) (8)

where Δ119878119887is the vaporization entropy at the boiling temper-

ature 119862119901119887

is the gas-liquid heat capacity and 119877 is the gasconstant Δ119878

119887used in this method is an empirical expression

given by Myrdal et al [31]

Δ119878119887= 86 + 04120591 + 1421HBN (9)

In (9) the parameters 120591 and HBN which characterize themolecular structure represent the torsional bond (see Vidal[32]) and the hydrogen bonding number (see [19 Section312]) respectively Δ119862

119901119887is a linear dependence of 120591 [32]

Δ119862119901119887

= minus (90 + 25120591) (10)

Thus in the MY method vapor pressure is estimated bythe relatively simplified formula

ln119875vap= minus (21 2 + 0 3120591 + 177HBN) (

119879119887minus 119879

119879)

+ (10 8 + 0 25120591) ln119879119887

119879

(11)

232 The Modified Mackay (mM) Method Often calledsimplified expression of Baum [33] this method is also basedon the extended form of the Clausius-Clapeyron equationThe simplifying assumption here is to consider the ratioΔ119862119901119887Δ119878119887to be constant [34]

Δ119862119901119887

Δ119878119887

= minus08 (12)

In (12) the vaporization entropy Δ119878119887 takes into account

the van der Waals interactions and is based upon theTroutonrsquos rule For its calculation Lyman [35] has suggestedthe following expression

Δ119878119887(119879119887) = 119870119891(36 6 + 8 31 ln119879

119887) (13)

where119870119891is a structural factor of Fishtine [36] which corrects

many polar interactions It has different values as follows

(i) 119870119891= 1 for nonpolar and monopolar compounds

(ii) 119870119891= 104 for compounds with a weak bipolar char-

acter(iii) 119870

119891= 11 for primary amines

(iv) 119870119891= 13 for aliphatic alcohols

Finally themMmethod is reduced to the following equation

ln119875vap= 119870119891(4 4 + ln119879

119887) (1 8

119879119887minus 119879

119879minus 0 8 ln

119879119887

119879) (14)

233 The Grain-Watson (GW) Method The GW method isbased on the following equation [37]

ln119875vap=

Δ119878

119877

[

[

1 minus

(3 minus 2119879119901)119898

119879119901

minus 2119898(3 minus 2119879119901)119898minus1

sdot ln119879119901]

]

(15)

where119898 = 04133minus02575119879119901and119879119901is inversely proportional

to 119879119887(119879119901= 119879119879

119887) Δ119878 has the same form like that used in the

mMmethod

234 The Lee and Kesler (LK) Method Like the methodsdescribed previously the LK method required critical tem-perature critical pressure and boiling temperature Here thevapor pressure is estimated on the base of Pitzer expansion[38]

ln119875vap119903

= 1198910(119879119903) + 119908119891

1(119879119903) (16)

4 International Journal of Geophysics

where 119875vap119903

is reduced vapor pressure 119879119903is reduced temper-

ature and 119908 is the Pitzerrsquos acentric factor which accounts forthe nonsphericity of molecules

119908 =minus ln119875119888minus 1198910(120579)

1198911 (120579)(17)

with 120579 = 119879119887119879119888 In (16) and (17) 1198910 and 119891

1 are the Pitzerrsquosfunctions which are polynomials in 119879

119903 Lee and Kesler have

suggested the following equations [39]

1198910(119879119903) = 5 92714 minus

609648

119879119903

minus 128862 ln119879119903+ 0169347 ln1198796

119903

1198911(119879119903) = 152518 minus

156875

119879119903

minus 134721 ln119879119903+ 043577 ln1198796

119903

(18)

235TheAmbrose-Walton (AW)Method AWmethod [40] isalso based on the Pitzer expansion They have reported theiranalytical expressions of Pitzerrsquos functions in the form of aWagner type of vapor pressure equation

1198910(119879119903)

=minus59761120591 + 129874120591

15minus 060394120591

25minus 106841120591

5

119879119903

1198911(119879119903)

=minus503365120591 + 111505120591

15minus 541217120591

25minus 746628120591

5

119879119903

(19)

In (19) 120591 = 1 minus 119879119903

3 Results

31 Molecular Properties We present in this section theresults obtained for the Joback and Lydersen techniquesdescribed previously The accuracy of each of the five vaporpressure estimation methods used in this study is assessedtaking into account the reliability of pure substance propertyestimates The reliability of the two techniques presented inSection 22 is therefore crucial

In Figure 1 where the results of Joback technique aredisplayed 119879Job

119887is plotted against experimental values for a

set of 253 volatile organic compounds The scatter tends tobe larger for boiling temperature higher than 500K Thecorrelation coefficient (1198772 = 097) shows that estimatedvalues match very well experimental 119879

119887 The root mean

square error (RMSE) and the mean absolute error (MAE)are respectively 1760K and 1265 K This MAE agrees with129 K and 121 K calculated in Reid et al [39] and Camredonand Aumont [19] for a set of 252 and 438 volatile organiccompounds respectively Hence these results show that 119879Job

119887

300

350

400

450

500

550

600

650

300 350 400 450 500 550 600 650

TJob

b(K

)

Texpb

(K)

N = 253

R2= 097

Figure 1 Estimated boiling point for a set of 253 species versusexperimental values for the Joback technique The black line is the1 1 diagonal

can be used in vapor pressure estimationmethodsMoreoverJoback reevaluated Lydersenrsquos group contribution schemeHe added several new functional groups and deducted newcontribution values

The two techniques for the estimation of 119879119888are compared

to experimental data of 138 compounds in Figure 2Figures 2(a) and 2(b) show that the Joback and Lydersen

techniques give similar results for119879119888values lower than 700K

Joback technique shows a negative bias for 119879119888higher than

700K This technique gives for the overall compounds anRMSE of 2498K This value is higher than the 1981 K pro-vided by the Lydersen techniqueThemean bias error (MBE)for 119879Job119888

and 119879Lyd119888

is minus49 and minus19 respectively These resultsand Figures 2(a) and 2(b) show clearly that Joback techniqueunderpredicts critical temperature mostly for compoundswhich can be condensed onto particle phase with highboiling temperature The experimental group contributionsprovided by Lydersen are therefore more accurate than thoseprovided by Joback Thus the Lydersen technique is morereliable than the Joback technique to estimate 119879

119888

Figure 3 shows 119875Job119888

and 119875Lyd119888

versus experimental valuesfor a set of 117 compounds The RMSE is 45 atm and 26 atmfor Joback and Lydersen respectively According to Figures3(a) and 3(b) 119875

119888estimated by Lydersen matches fairly better

(1198772 = 095) experimental data than 119875119888estimated by Joback

(1198772 = 085) Joback technique considerably overpredictscritical pressure with MBE of 195 K higher than 039Kobtained with the Lydersen technique In fact besides groupcontribution Lydersen technique takes into account molec-ular weight Therefore the Lydersen technique is retainedto the critical pressure estimation in this paper This is inagreement with Poling et al [38] who found that the Lydersentechnique is one of the best techniques for estimating criticalproperties For the five vapor pressure estimation methodsdescribed previously we will use estimated 119879

119887 119879119888 and 119875

119888

because there is in general a lack of experimental data

International Journal of Geophysics 5

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TJob

c(K

)

N = 138

R2= 093

(a)

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TLyd

c(K

)

N = 138

R2= 095

(b)

Figure 2 Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersentechnique The black line is the 1 1 diagonal

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PJob

c(atm

)

N = 117

R2= 085

(a)

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PLyd

c(atm

)

N = 117

R2= 095

(b)

Figure 3 Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen techniqueThe black line is the 1 1 diagonal

Some of the five methods described in Section 23 need119875119888 119879119888 and 119879

119887 while others need only 119879

119888and 119879

119887 This last

pure substance property is estimated by the Joback techniqueand the two critical properties are estimated by the Lydersentechnique

32 Evaluation of Vapor Pressure Estimation Methods Theaccuracy of each method is assessed in terms of the meanabsolute error (MAE) the main bias error (MBE) andthe root mean square error (RMSE) (Table 3) The MBEmeasures the average difference between the estimated andexperimental values while the MAE measures the averagemagnitude of the error The RMSE also measures the error

magnitude but gives some greater weight to the larger errorsTheir expressions are given by

MBE =1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)

MAE =1

119873

119873

sum

119894=1

10038161003816100381610038161003816log119875vap

est119894 minus log119875vapexp119894

10038161003816100381610038161003816

RMSE = radic1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)2

(20)

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

2 International Journal of Geophysics

Parameters in (1)ndash(3) are named in Table 1In (3) 119867vap is equal to 156 kJmol as stated by Derby

et al [8] Consequently the vapour pressures of all aerosolcompounds are needed to calculate the mass flux of con-densing and evaporating compounds The knowledge of 119875vap

119894

for organic compound 119894 at the atmospheric temperature 119879

is required whenever phase equilibrium between gas phaseand particle is of interest Often most of the compounds ableto condense have experimental vapor pressures unavailableand because of that their estimation becomes necessary Tosolve this problem of estimation many methods have beendeveloped For example in Tong et al [9] a method basedon atomic simulation is applied only for compounds bearingacid moieties Quantum-mechanical calculations are makingsteady effort in vapor pressure prediction (Banerjee et al[10] Diedenhofen et al [11]) Furthermore current mod-els describing gas-particle partitioning use semiempiricalmethods for vapor pressure estimation based on molecularstructure often in the form of a group contribution approachTherefore these methods require in most cases molecularstructures (eg boiling point 119879

119887 critical temperature 119879

119888

and critical pressure 119875119888) which usually have themselves to

be estimated For example The MY method [12] was usedby Griffin et al [13] and Pun et al [14] for modeling theformation of secondary organic aerosol Jenkin [15] in a gasparticle partitioning model used the modified form of theMackay method [16] Some methods (Pankow and Asher[17] Capouet and Muller [18]) assume a linear logarithmicdependence (ln119875vap

119894) on several functional groups but this

consideration fails when multiple hydrogen bonding groupsare present Furthermore more investigations are needed toclarify which method can give values closer to the exper-imental data Camredon and Aumont [19] Compernolleet al [20] and Barley and McFiggans [21] have made anassessment of different vapor pressure estimation methodswith experimental data for compounds of relatively highervolatility For this latter reason large differences in theestimated vapor pressure have been reported

In this paper our focus will be on the (i) evaluationof a number of vapor pressure estimation methods againstexperimental data using all volatile organic compoundspresent in our database and (ii) assessment of the accuracy ofeach of thesemethods on the base of each class of compounds

The rest of the paper is organized as follows In Section 2we describe experimental data and methods The results arepresented in Section 3 Finally we summarize our finding inSection 4

2 Data and Vapor PressureEstimation Methods

21 Experimental Data The molecules selected in thisstudy have been identified during in situ campaigns [22]and during chamber experiments [23] In fact they arehydrocarbons monofunctionalized and multifunctionalizedspecies and bearing alcohol aldehyde ketone carboxylicacid ester ether and alkyl nitrate functions The exper-imental vapor pressures are taken from NIST chemistry

Table 1 Nomenclature

Parameters Names119868119894

Mass flux for volatile species 119894119889119901

The particle wet diameter119898119894

Mass of species 119894119863119892

119894Molar diffusivity in the air of species 119894

119888119892

119894Gas-phase concentration of species 119894

119891FS Fuchs-Sutugin function119888119904

119894Concentration at the surface of species 119894

119877 Gas constant119879 Temperature in Kelvin119867vap Vaporisation enthalpy119909 Mole fraction120574 Activity coefficient119875vap119894

Vapour pressure of each volatile compound 119894

website (httpwwwnistgovchemestry) and from Myrdaland Yalkowsky [12] Asher et al [24] Lide [25] Yams [26]and Boulik et al [27] and they have a range from 10

minus8 atmto 1 atm Molecular properties (boiling point critical tem-perature and critical pressure) are also taken from the NISTchemistry website All vapor pressure estimation methodsused in this study take into account these properties In mostcases these properties have also to be estimated

22 Estimation of Molecular Properties

221 Boiling Temperature 119879119887 Using the boiling temperature

of Joback [28] and its extension the group contributiontechnique denoted by 119879Job

119887is written as

119879Job119887

= 198 +sum

119894

119873119894119905119887119894 (4)

where 119905119887119894

is the contribution of group 119894 and 119873119894is the

occurrence of this group in the molecule As in CamredonandAumont [19] the extension ismade by adding some othergroup contribution to take into account molecules bearinghydroperoxidemoiety (ndashOOH) alkyl nitratemoiety (ONO

2)

and peroxyacyl nitrate moiety (ndashC(=O)OONO2) Thus the

first group is divided into the existing Joback groups ndashOndashand ndashOH The second group value is provided by the NISTchemistry website and the last group value is provided byCamredon and Aumont [19] using boiling point value fromBruckmann and Willner [29]

222 Critical Temperature 119879119888 We have used Joback [28]

and Lydersenrsquos [30] techniques to estimate 119879119888 Denoting by

119879Job119862

and 119879Lyd119888

the Joback and Lydersen critical temperaturesrespectively we have

119879Job119888

=119879119887

0 584 + 0 965sum119894119873119894119905119894minus (sum119894119873119894119905119894)2

119879Lyd119888

=119879119887

0 567 + sum119894119873119894119905119894minus (sum119894119873119894119905119894)2

(5)

International Journal of Geophysics 3

New group contributions have been added by Camredonand Aumont [19] for hydroperoxide alkyl nitrate and perox-yacyl nitrate moieties

119905ndashOOH119888

= 119905ndashOndash119888

+ 119905ndashOH119888

119905ndashONO2119888

= 119905ndashOndash119888

+ 119905ndashNO2119888

119905ndashC(=O)OONO2119888

= 119905ndashC(=O)O119888

+ 119905ndashOndash119888

+ 119905ndashNO2119888

(6)

223 Critical Pressure 119875119888 The two techniques listed in the

previous section have been used to estimate critical pressure119875119888 Here it is also assumed that 119875

119888is the sum of group

contributions Therefore denoting by 119875Job119888

and 119875Lyd119888

theJoback and Lydersen critical pressures respectively we canwrite

119875Job119888

=1

(0 113 + 0 0032119899 minus sum119894119873119894119901119894)2

119875Lyd119888

=119872

(0 34 minus sum119894119873119894119901119894)2

(7)

where 119872 is the molar mass 119899 is the number of atoms in themolecule and 119901

119894is the critical pressure contribution of group

119894 The new group contributions described in the previoussubsection are taken into account here

23 Vapor Pressure EstimationMethods As said earlier manymethods for vapor pressure estimation have been developedand are based on the Antoine or on the extended form of theClausius-Clapeyron equation Let us present in what followseach of the five methods used

231 The Myrdal and Yalkowsky (MY) Method The MYmethod [12] starts from the extended form of the Clausius-Clapeyron equation obtained by using Eulerrsquos cyclic relationHere the expression of 119875vap is given by

ln119875vap=

Δ119878119887(119879119887minus 119879)

119877119879+

Δ119862119901119887

119877(119879119887minus 119879

119879minus ln

119879119887

119879) (8)

where Δ119878119887is the vaporization entropy at the boiling temper-

ature 119862119901119887

is the gas-liquid heat capacity and 119877 is the gasconstant Δ119878

119887used in this method is an empirical expression

given by Myrdal et al [31]

Δ119878119887= 86 + 04120591 + 1421HBN (9)

In (9) the parameters 120591 and HBN which characterize themolecular structure represent the torsional bond (see Vidal[32]) and the hydrogen bonding number (see [19 Section312]) respectively Δ119862

119901119887is a linear dependence of 120591 [32]

Δ119862119901119887

= minus (90 + 25120591) (10)

Thus in the MY method vapor pressure is estimated bythe relatively simplified formula

ln119875vap= minus (21 2 + 0 3120591 + 177HBN) (

119879119887minus 119879

119879)

+ (10 8 + 0 25120591) ln119879119887

119879

(11)

232 The Modified Mackay (mM) Method Often calledsimplified expression of Baum [33] this method is also basedon the extended form of the Clausius-Clapeyron equationThe simplifying assumption here is to consider the ratioΔ119862119901119887Δ119878119887to be constant [34]

Δ119862119901119887

Δ119878119887

= minus08 (12)

In (12) the vaporization entropy Δ119878119887 takes into account

the van der Waals interactions and is based upon theTroutonrsquos rule For its calculation Lyman [35] has suggestedthe following expression

Δ119878119887(119879119887) = 119870119891(36 6 + 8 31 ln119879

119887) (13)

where119870119891is a structural factor of Fishtine [36] which corrects

many polar interactions It has different values as follows

(i) 119870119891= 1 for nonpolar and monopolar compounds

(ii) 119870119891= 104 for compounds with a weak bipolar char-

acter(iii) 119870

119891= 11 for primary amines

(iv) 119870119891= 13 for aliphatic alcohols

Finally themMmethod is reduced to the following equation

ln119875vap= 119870119891(4 4 + ln119879

119887) (1 8

119879119887minus 119879

119879minus 0 8 ln

119879119887

119879) (14)

233 The Grain-Watson (GW) Method The GW method isbased on the following equation [37]

ln119875vap=

Δ119878

119877

[

[

1 minus

(3 minus 2119879119901)119898

119879119901

minus 2119898(3 minus 2119879119901)119898minus1

sdot ln119879119901]

]

(15)

where119898 = 04133minus02575119879119901and119879119901is inversely proportional

to 119879119887(119879119901= 119879119879

119887) Δ119878 has the same form like that used in the

mMmethod

234 The Lee and Kesler (LK) Method Like the methodsdescribed previously the LK method required critical tem-perature critical pressure and boiling temperature Here thevapor pressure is estimated on the base of Pitzer expansion[38]

ln119875vap119903

= 1198910(119879119903) + 119908119891

1(119879119903) (16)

4 International Journal of Geophysics

where 119875vap119903

is reduced vapor pressure 119879119903is reduced temper-

ature and 119908 is the Pitzerrsquos acentric factor which accounts forthe nonsphericity of molecules

119908 =minus ln119875119888minus 1198910(120579)

1198911 (120579)(17)

with 120579 = 119879119887119879119888 In (16) and (17) 1198910 and 119891

1 are the Pitzerrsquosfunctions which are polynomials in 119879

119903 Lee and Kesler have

suggested the following equations [39]

1198910(119879119903) = 5 92714 minus

609648

119879119903

minus 128862 ln119879119903+ 0169347 ln1198796

119903

1198911(119879119903) = 152518 minus

156875

119879119903

minus 134721 ln119879119903+ 043577 ln1198796

119903

(18)

235TheAmbrose-Walton (AW)Method AWmethod [40] isalso based on the Pitzer expansion They have reported theiranalytical expressions of Pitzerrsquos functions in the form of aWagner type of vapor pressure equation

1198910(119879119903)

=minus59761120591 + 129874120591

15minus 060394120591

25minus 106841120591

5

119879119903

1198911(119879119903)

=minus503365120591 + 111505120591

15minus 541217120591

25minus 746628120591

5

119879119903

(19)

In (19) 120591 = 1 minus 119879119903

3 Results

31 Molecular Properties We present in this section theresults obtained for the Joback and Lydersen techniquesdescribed previously The accuracy of each of the five vaporpressure estimation methods used in this study is assessedtaking into account the reliability of pure substance propertyestimates The reliability of the two techniques presented inSection 22 is therefore crucial

In Figure 1 where the results of Joback technique aredisplayed 119879Job

119887is plotted against experimental values for a

set of 253 volatile organic compounds The scatter tends tobe larger for boiling temperature higher than 500K Thecorrelation coefficient (1198772 = 097) shows that estimatedvalues match very well experimental 119879

119887 The root mean

square error (RMSE) and the mean absolute error (MAE)are respectively 1760K and 1265 K This MAE agrees with129 K and 121 K calculated in Reid et al [39] and Camredonand Aumont [19] for a set of 252 and 438 volatile organiccompounds respectively Hence these results show that 119879Job

119887

300

350

400

450

500

550

600

650

300 350 400 450 500 550 600 650

TJob

b(K

)

Texpb

(K)

N = 253

R2= 097

Figure 1 Estimated boiling point for a set of 253 species versusexperimental values for the Joback technique The black line is the1 1 diagonal

can be used in vapor pressure estimationmethodsMoreoverJoback reevaluated Lydersenrsquos group contribution schemeHe added several new functional groups and deducted newcontribution values

The two techniques for the estimation of 119879119888are compared

to experimental data of 138 compounds in Figure 2Figures 2(a) and 2(b) show that the Joback and Lydersen

techniques give similar results for119879119888values lower than 700K

Joback technique shows a negative bias for 119879119888higher than

700K This technique gives for the overall compounds anRMSE of 2498K This value is higher than the 1981 K pro-vided by the Lydersen techniqueThemean bias error (MBE)for 119879Job119888

and 119879Lyd119888

is minus49 and minus19 respectively These resultsand Figures 2(a) and 2(b) show clearly that Joback techniqueunderpredicts critical temperature mostly for compoundswhich can be condensed onto particle phase with highboiling temperature The experimental group contributionsprovided by Lydersen are therefore more accurate than thoseprovided by Joback Thus the Lydersen technique is morereliable than the Joback technique to estimate 119879

119888

Figure 3 shows 119875Job119888

and 119875Lyd119888

versus experimental valuesfor a set of 117 compounds The RMSE is 45 atm and 26 atmfor Joback and Lydersen respectively According to Figures3(a) and 3(b) 119875

119888estimated by Lydersen matches fairly better

(1198772 = 095) experimental data than 119875119888estimated by Joback

(1198772 = 085) Joback technique considerably overpredictscritical pressure with MBE of 195 K higher than 039Kobtained with the Lydersen technique In fact besides groupcontribution Lydersen technique takes into account molec-ular weight Therefore the Lydersen technique is retainedto the critical pressure estimation in this paper This is inagreement with Poling et al [38] who found that the Lydersentechnique is one of the best techniques for estimating criticalproperties For the five vapor pressure estimation methodsdescribed previously we will use estimated 119879

119887 119879119888 and 119875

119888

because there is in general a lack of experimental data

International Journal of Geophysics 5

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TJob

c(K

)

N = 138

R2= 093

(a)

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TLyd

c(K

)

N = 138

R2= 095

(b)

Figure 2 Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersentechnique The black line is the 1 1 diagonal

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PJob

c(atm

)

N = 117

R2= 085

(a)

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PLyd

c(atm

)

N = 117

R2= 095

(b)

Figure 3 Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen techniqueThe black line is the 1 1 diagonal

Some of the five methods described in Section 23 need119875119888 119879119888 and 119879

119887 while others need only 119879

119888and 119879

119887 This last

pure substance property is estimated by the Joback techniqueand the two critical properties are estimated by the Lydersentechnique

32 Evaluation of Vapor Pressure Estimation Methods Theaccuracy of each method is assessed in terms of the meanabsolute error (MAE) the main bias error (MBE) andthe root mean square error (RMSE) (Table 3) The MBEmeasures the average difference between the estimated andexperimental values while the MAE measures the averagemagnitude of the error The RMSE also measures the error

magnitude but gives some greater weight to the larger errorsTheir expressions are given by

MBE =1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)

MAE =1

119873

119873

sum

119894=1

10038161003816100381610038161003816log119875vap

est119894 minus log119875vapexp119894

10038161003816100381610038161003816

RMSE = radic1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)2

(20)

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Applied ampEnvironmentalSoil Science

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Mining

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Journal of

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OceanographyInternational Journal of

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Atmospheric SciencesInternational Journal of

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OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MineralogyInternational Journal of

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ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 3

New group contributions have been added by Camredonand Aumont [19] for hydroperoxide alkyl nitrate and perox-yacyl nitrate moieties

119905ndashOOH119888

= 119905ndashOndash119888

+ 119905ndashOH119888

119905ndashONO2119888

= 119905ndashOndash119888

+ 119905ndashNO2119888

119905ndashC(=O)OONO2119888

= 119905ndashC(=O)O119888

+ 119905ndashOndash119888

+ 119905ndashNO2119888

(6)

223 Critical Pressure 119875119888 The two techniques listed in the

previous section have been used to estimate critical pressure119875119888 Here it is also assumed that 119875

119888is the sum of group

contributions Therefore denoting by 119875Job119888

and 119875Lyd119888

theJoback and Lydersen critical pressures respectively we canwrite

119875Job119888

=1

(0 113 + 0 0032119899 minus sum119894119873119894119901119894)2

119875Lyd119888

=119872

(0 34 minus sum119894119873119894119901119894)2

(7)

where 119872 is the molar mass 119899 is the number of atoms in themolecule and 119901

119894is the critical pressure contribution of group

119894 The new group contributions described in the previoussubsection are taken into account here

23 Vapor Pressure EstimationMethods As said earlier manymethods for vapor pressure estimation have been developedand are based on the Antoine or on the extended form of theClausius-Clapeyron equation Let us present in what followseach of the five methods used

231 The Myrdal and Yalkowsky (MY) Method The MYmethod [12] starts from the extended form of the Clausius-Clapeyron equation obtained by using Eulerrsquos cyclic relationHere the expression of 119875vap is given by

ln119875vap=

Δ119878119887(119879119887minus 119879)

119877119879+

Δ119862119901119887

119877(119879119887minus 119879

119879minus ln

119879119887

119879) (8)

where Δ119878119887is the vaporization entropy at the boiling temper-

ature 119862119901119887

is the gas-liquid heat capacity and 119877 is the gasconstant Δ119878

119887used in this method is an empirical expression

given by Myrdal et al [31]

Δ119878119887= 86 + 04120591 + 1421HBN (9)

In (9) the parameters 120591 and HBN which characterize themolecular structure represent the torsional bond (see Vidal[32]) and the hydrogen bonding number (see [19 Section312]) respectively Δ119862

119901119887is a linear dependence of 120591 [32]

Δ119862119901119887

= minus (90 + 25120591) (10)

Thus in the MY method vapor pressure is estimated bythe relatively simplified formula

ln119875vap= minus (21 2 + 0 3120591 + 177HBN) (

119879119887minus 119879

119879)

+ (10 8 + 0 25120591) ln119879119887

119879

(11)

232 The Modified Mackay (mM) Method Often calledsimplified expression of Baum [33] this method is also basedon the extended form of the Clausius-Clapeyron equationThe simplifying assumption here is to consider the ratioΔ119862119901119887Δ119878119887to be constant [34]

Δ119862119901119887

Δ119878119887

= minus08 (12)

In (12) the vaporization entropy Δ119878119887 takes into account

the van der Waals interactions and is based upon theTroutonrsquos rule For its calculation Lyman [35] has suggestedthe following expression

Δ119878119887(119879119887) = 119870119891(36 6 + 8 31 ln119879

119887) (13)

where119870119891is a structural factor of Fishtine [36] which corrects

many polar interactions It has different values as follows

(i) 119870119891= 1 for nonpolar and monopolar compounds

(ii) 119870119891= 104 for compounds with a weak bipolar char-

acter(iii) 119870

119891= 11 for primary amines

(iv) 119870119891= 13 for aliphatic alcohols

Finally themMmethod is reduced to the following equation

ln119875vap= 119870119891(4 4 + ln119879

119887) (1 8

119879119887minus 119879

119879minus 0 8 ln

119879119887

119879) (14)

233 The Grain-Watson (GW) Method The GW method isbased on the following equation [37]

ln119875vap=

Δ119878

119877

[

[

1 minus

(3 minus 2119879119901)119898

119879119901

minus 2119898(3 minus 2119879119901)119898minus1

sdot ln119879119901]

]

(15)

where119898 = 04133minus02575119879119901and119879119901is inversely proportional

to 119879119887(119879119901= 119879119879

119887) Δ119878 has the same form like that used in the

mMmethod

234 The Lee and Kesler (LK) Method Like the methodsdescribed previously the LK method required critical tem-perature critical pressure and boiling temperature Here thevapor pressure is estimated on the base of Pitzer expansion[38]

ln119875vap119903

= 1198910(119879119903) + 119908119891

1(119879119903) (16)

4 International Journal of Geophysics

where 119875vap119903

is reduced vapor pressure 119879119903is reduced temper-

ature and 119908 is the Pitzerrsquos acentric factor which accounts forthe nonsphericity of molecules

119908 =minus ln119875119888minus 1198910(120579)

1198911 (120579)(17)

with 120579 = 119879119887119879119888 In (16) and (17) 1198910 and 119891

1 are the Pitzerrsquosfunctions which are polynomials in 119879

119903 Lee and Kesler have

suggested the following equations [39]

1198910(119879119903) = 5 92714 minus

609648

119879119903

minus 128862 ln119879119903+ 0169347 ln1198796

119903

1198911(119879119903) = 152518 minus

156875

119879119903

minus 134721 ln119879119903+ 043577 ln1198796

119903

(18)

235TheAmbrose-Walton (AW)Method AWmethod [40] isalso based on the Pitzer expansion They have reported theiranalytical expressions of Pitzerrsquos functions in the form of aWagner type of vapor pressure equation

1198910(119879119903)

=minus59761120591 + 129874120591

15minus 060394120591

25minus 106841120591

5

119879119903

1198911(119879119903)

=minus503365120591 + 111505120591

15minus 541217120591

25minus 746628120591

5

119879119903

(19)

In (19) 120591 = 1 minus 119879119903

3 Results

31 Molecular Properties We present in this section theresults obtained for the Joback and Lydersen techniquesdescribed previously The accuracy of each of the five vaporpressure estimation methods used in this study is assessedtaking into account the reliability of pure substance propertyestimates The reliability of the two techniques presented inSection 22 is therefore crucial

In Figure 1 where the results of Joback technique aredisplayed 119879Job

119887is plotted against experimental values for a

set of 253 volatile organic compounds The scatter tends tobe larger for boiling temperature higher than 500K Thecorrelation coefficient (1198772 = 097) shows that estimatedvalues match very well experimental 119879

119887 The root mean

square error (RMSE) and the mean absolute error (MAE)are respectively 1760K and 1265 K This MAE agrees with129 K and 121 K calculated in Reid et al [39] and Camredonand Aumont [19] for a set of 252 and 438 volatile organiccompounds respectively Hence these results show that 119879Job

119887

300

350

400

450

500

550

600

650

300 350 400 450 500 550 600 650

TJob

b(K

)

Texpb

(K)

N = 253

R2= 097

Figure 1 Estimated boiling point for a set of 253 species versusexperimental values for the Joback technique The black line is the1 1 diagonal

can be used in vapor pressure estimationmethodsMoreoverJoback reevaluated Lydersenrsquos group contribution schemeHe added several new functional groups and deducted newcontribution values

The two techniques for the estimation of 119879119888are compared

to experimental data of 138 compounds in Figure 2Figures 2(a) and 2(b) show that the Joback and Lydersen

techniques give similar results for119879119888values lower than 700K

Joback technique shows a negative bias for 119879119888higher than

700K This technique gives for the overall compounds anRMSE of 2498K This value is higher than the 1981 K pro-vided by the Lydersen techniqueThemean bias error (MBE)for 119879Job119888

and 119879Lyd119888

is minus49 and minus19 respectively These resultsand Figures 2(a) and 2(b) show clearly that Joback techniqueunderpredicts critical temperature mostly for compoundswhich can be condensed onto particle phase with highboiling temperature The experimental group contributionsprovided by Lydersen are therefore more accurate than thoseprovided by Joback Thus the Lydersen technique is morereliable than the Joback technique to estimate 119879

119888

Figure 3 shows 119875Job119888

and 119875Lyd119888

versus experimental valuesfor a set of 117 compounds The RMSE is 45 atm and 26 atmfor Joback and Lydersen respectively According to Figures3(a) and 3(b) 119875

119888estimated by Lydersen matches fairly better

(1198772 = 095) experimental data than 119875119888estimated by Joback

(1198772 = 085) Joback technique considerably overpredictscritical pressure with MBE of 195 K higher than 039Kobtained with the Lydersen technique In fact besides groupcontribution Lydersen technique takes into account molec-ular weight Therefore the Lydersen technique is retainedto the critical pressure estimation in this paper This is inagreement with Poling et al [38] who found that the Lydersentechnique is one of the best techniques for estimating criticalproperties For the five vapor pressure estimation methodsdescribed previously we will use estimated 119879

119887 119879119888 and 119875

119888

because there is in general a lack of experimental data

International Journal of Geophysics 5

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TJob

c(K

)

N = 138

R2= 093

(a)

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TLyd

c(K

)

N = 138

R2= 095

(b)

Figure 2 Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersentechnique The black line is the 1 1 diagonal

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PJob

c(atm

)

N = 117

R2= 085

(a)

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PLyd

c(atm

)

N = 117

R2= 095

(b)

Figure 3 Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen techniqueThe black line is the 1 1 diagonal

Some of the five methods described in Section 23 need119875119888 119879119888 and 119879

119887 while others need only 119879

119888and 119879

119887 This last

pure substance property is estimated by the Joback techniqueand the two critical properties are estimated by the Lydersentechnique

32 Evaluation of Vapor Pressure Estimation Methods Theaccuracy of each method is assessed in terms of the meanabsolute error (MAE) the main bias error (MBE) andthe root mean square error (RMSE) (Table 3) The MBEmeasures the average difference between the estimated andexperimental values while the MAE measures the averagemagnitude of the error The RMSE also measures the error

magnitude but gives some greater weight to the larger errorsTheir expressions are given by

MBE =1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)

MAE =1

119873

119873

sum

119894=1

10038161003816100381610038161003816log119875vap

est119894 minus log119875vapexp119894

10038161003816100381610038161003816

RMSE = radic1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)2

(20)

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geological ResearchJournal of

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Geology Advances in

4 International Journal of Geophysics

where 119875vap119903

is reduced vapor pressure 119879119903is reduced temper-

ature and 119908 is the Pitzerrsquos acentric factor which accounts forthe nonsphericity of molecules

119908 =minus ln119875119888minus 1198910(120579)

1198911 (120579)(17)

with 120579 = 119879119887119879119888 In (16) and (17) 1198910 and 119891

1 are the Pitzerrsquosfunctions which are polynomials in 119879

119903 Lee and Kesler have

suggested the following equations [39]

1198910(119879119903) = 5 92714 minus

609648

119879119903

minus 128862 ln119879119903+ 0169347 ln1198796

119903

1198911(119879119903) = 152518 minus

156875

119879119903

minus 134721 ln119879119903+ 043577 ln1198796

119903

(18)

235TheAmbrose-Walton (AW)Method AWmethod [40] isalso based on the Pitzer expansion They have reported theiranalytical expressions of Pitzerrsquos functions in the form of aWagner type of vapor pressure equation

1198910(119879119903)

=minus59761120591 + 129874120591

15minus 060394120591

25minus 106841120591

5

119879119903

1198911(119879119903)

=minus503365120591 + 111505120591

15minus 541217120591

25minus 746628120591

5

119879119903

(19)

In (19) 120591 = 1 minus 119879119903

3 Results

31 Molecular Properties We present in this section theresults obtained for the Joback and Lydersen techniquesdescribed previously The accuracy of each of the five vaporpressure estimation methods used in this study is assessedtaking into account the reliability of pure substance propertyestimates The reliability of the two techniques presented inSection 22 is therefore crucial

In Figure 1 where the results of Joback technique aredisplayed 119879Job

119887is plotted against experimental values for a

set of 253 volatile organic compounds The scatter tends tobe larger for boiling temperature higher than 500K Thecorrelation coefficient (1198772 = 097) shows that estimatedvalues match very well experimental 119879

119887 The root mean

square error (RMSE) and the mean absolute error (MAE)are respectively 1760K and 1265 K This MAE agrees with129 K and 121 K calculated in Reid et al [39] and Camredonand Aumont [19] for a set of 252 and 438 volatile organiccompounds respectively Hence these results show that 119879Job

119887

300

350

400

450

500

550

600

650

300 350 400 450 500 550 600 650

TJob

b(K

)

Texpb

(K)

N = 253

R2= 097

Figure 1 Estimated boiling point for a set of 253 species versusexperimental values for the Joback technique The black line is the1 1 diagonal

can be used in vapor pressure estimationmethodsMoreoverJoback reevaluated Lydersenrsquos group contribution schemeHe added several new functional groups and deducted newcontribution values

The two techniques for the estimation of 119879119888are compared

to experimental data of 138 compounds in Figure 2Figures 2(a) and 2(b) show that the Joback and Lydersen

techniques give similar results for119879119888values lower than 700K

Joback technique shows a negative bias for 119879119888higher than

700K This technique gives for the overall compounds anRMSE of 2498K This value is higher than the 1981 K pro-vided by the Lydersen techniqueThemean bias error (MBE)for 119879Job119888

and 119879Lyd119888

is minus49 and minus19 respectively These resultsand Figures 2(a) and 2(b) show clearly that Joback techniqueunderpredicts critical temperature mostly for compoundswhich can be condensed onto particle phase with highboiling temperature The experimental group contributionsprovided by Lydersen are therefore more accurate than thoseprovided by Joback Thus the Lydersen technique is morereliable than the Joback technique to estimate 119879

119888

Figure 3 shows 119875Job119888

and 119875Lyd119888

versus experimental valuesfor a set of 117 compounds The RMSE is 45 atm and 26 atmfor Joback and Lydersen respectively According to Figures3(a) and 3(b) 119875

119888estimated by Lydersen matches fairly better

(1198772 = 095) experimental data than 119875119888estimated by Joback

(1198772 = 085) Joback technique considerably overpredictscritical pressure with MBE of 195 K higher than 039Kobtained with the Lydersen technique In fact besides groupcontribution Lydersen technique takes into account molec-ular weight Therefore the Lydersen technique is retainedto the critical pressure estimation in this paper This is inagreement with Poling et al [38] who found that the Lydersentechnique is one of the best techniques for estimating criticalproperties For the five vapor pressure estimation methodsdescribed previously we will use estimated 119879

119887 119879119888 and 119875

119888

because there is in general a lack of experimental data

International Journal of Geophysics 5

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TJob

c(K

)

N = 138

R2= 093

(a)

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TLyd

c(K

)

N = 138

R2= 095

(b)

Figure 2 Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersentechnique The black line is the 1 1 diagonal

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PJob

c(atm

)

N = 117

R2= 085

(a)

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PLyd

c(atm

)

N = 117

R2= 095

(b)

Figure 3 Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen techniqueThe black line is the 1 1 diagonal

Some of the five methods described in Section 23 need119875119888 119879119888 and 119879

119887 while others need only 119879

119888and 119879

119887 This last

pure substance property is estimated by the Joback techniqueand the two critical properties are estimated by the Lydersentechnique

32 Evaluation of Vapor Pressure Estimation Methods Theaccuracy of each method is assessed in terms of the meanabsolute error (MAE) the main bias error (MBE) andthe root mean square error (RMSE) (Table 3) The MBEmeasures the average difference between the estimated andexperimental values while the MAE measures the averagemagnitude of the error The RMSE also measures the error

magnitude but gives some greater weight to the larger errorsTheir expressions are given by

MBE =1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)

MAE =1

119873

119873

sum

119894=1

10038161003816100381610038161003816log119875vap

est119894 minus log119875vapexp119894

10038161003816100381610038161003816

RMSE = radic1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)2

(20)

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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International Journal of

Geophysics

OceanographyInternational Journal of

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Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

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MeteorologyAdvances in

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Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 5

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TJob

c(K

)

N = 138

R2= 093

(a)

400 500 600 700 800 900400

500

600

700

800

900

Texpc (K)

TLyd

c(K

)

N = 138

R2= 095

(b)

Figure 2 Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersentechnique The black line is the 1 1 diagonal

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PJob

c(atm

)

N = 117

R2= 085

(a)

0 20 40 60 80 1000

20

40

60

80

100

Pexpc (atm)

PLyd

c(atm

)

N = 117

R2= 095

(b)

Figure 3 Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen techniqueThe black line is the 1 1 diagonal

Some of the five methods described in Section 23 need119875119888 119879119888 and 119879

119887 while others need only 119879

119888and 119879

119887 This last

pure substance property is estimated by the Joback techniqueand the two critical properties are estimated by the Lydersentechnique

32 Evaluation of Vapor Pressure Estimation Methods Theaccuracy of each method is assessed in terms of the meanabsolute error (MAE) the main bias error (MBE) andthe root mean square error (RMSE) (Table 3) The MBEmeasures the average difference between the estimated andexperimental values while the MAE measures the averagemagnitude of the error The RMSE also measures the error

magnitude but gives some greater weight to the larger errorsTheir expressions are given by

MBE =1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)

MAE =1

119873

119873

sum

119894=1

10038161003816100381610038161003816log119875vap

est119894 minus log119875vapexp119894

10038161003816100381610038161003816

RMSE = radic1

119873

119873

sum

119894=1

(log119875vapest119894 minus log119875vap

exp119894)2

(20)

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

6 International Journal of Geophysics

Table 2 MAE MBE and RMSE of vapor pressure computed based on various methods

GW LK mM MY AWMAE 03235 03240 03186 02652 03013MBE 00736 minus01513 00263 00270 minus00980RMSE 04496 04909 04426 03811 04525

Table 3 MAE MBE and RMSE of vapor pressure computed based on various methods for each class of compounds

GW LK mM MY AWHydrocarbonsMAE 01455 01303 01424 01251 01384MBE 00547 00427 00486 00054 00603RMSE 01983 01750 01930 01711 01848Monofunctionalized speciesMAE 03692 03168 01424 02699 02900MBE 00355 minus01712 minus00189 minus00402 minus01141RMSE 04992 04471 04955 03891 04130Difunctionalized speciesMAE 04494 05641 04109 04291 05063MBE 02875 minus03322 02084 02378 minus02456RMSE 05506 06978 05120 05398 06291Tri- and more functionalized speciesMAE 04407 05946 04596 04261 05489MBE 00536 minus03661 minus00339 01632 minus02739RMSE 05494 08386 05592 05065 07704

In (20)119875vapest119894 and119875

vapexp119894 are the estimated and experimental

values of VOC 119894 respectively and 119873 is the total numberof VOC We have also used linear correlation coefficientwhich measures the degree of correspondence between theestimated and experimental distributions

The logarithms of vapor pressures estimated at 119879 =

298K for different methods are compared in the scatter plotsshown in Figure 4 for a set of 262VOC CorrespondingMAEMBE and RMSE are given in Table 1 In this figure it isclear that all the five methods give similar scatter for vaporpressures higher than 10

minus5 atm The species concerned arehydrocarbons (Figure 5) For the set of 28 tri- and morefunctionalized species used in this study vapor pressures arelower than 10

minus2 atm (Figure 8)Figure 4(d) shows thatMYmethod is well correlated with

experimental values For this method we have one of the bestcorrelation coefficients 1198772 = 0968 This method shows nosystematic bias for vapor pressure lower than 10

minus5 atm whileit is not the case for other methods The MBE found here is0027This value is one of the lowest ones of the total VOC (seeTable 1) Thus the MYmethod does not show any systematicbias This method also provides the smallest values of MAEand RMSE (0265 and 0381 resp) These results are inagreement with those found by Camredon and Aumont [19]using Ambrose technique to estimate critical properties It isalso found that this method provides the smallest values ofthese errors for a set of 74 hydrocarbons (see Table 2) Thoseare compounds with vapor pressure higher than 10

minus2 atm

This result is not the same for mono- and difunctionalizedspecies whose errors are some of the largest ones The vaporpressures higher than 10

minus4 atm are fairly well estimatedUsing a set of 45 multifunctional compounds Barley andMcFiggans [21] found that MY method tends to overpredictvapor pressure of lower volatility compounds Furthermoreit is important to note that MY method provides one ofthe poor results for difunctionalized VOC (see Table 2)Thus for a set of 32 difunctionalized VOC estimation valuesfit the experimental ones with a coefficient 119877

2= 0957

(Figure 7) which is the smallest value obtained for this classof species Vapor pressures are overpredicted with a biasof 024 while the RMSE = 054 is of the same order ofmagnitude as those obtained by other methods In contrastFigure 8 shows that MY method has the best correlation fortri- and more functionalized species and is therefore the bestmethod to estimate vapor pressure for this class of speciesThe systematic errors reported in Table 2 allow us to concludethat assumption Indeed the peculiarity of theMYmethod isthat it takes into account the molecular structure

Figure 4(c) displays the results for the mM method Thismethod gives one of the lowest scatterings with a coefficient1198772= 0957 and agrees with other methods for the highest

vapor pressures It shows a positive bias (MBE = 0026)for the total set of 262VOC As the GW method the mMmethod tends to overpredict vapor pressures lower than10minus6 atm Furthermore these methods describe vaporisation

entropy by taking into account van der Waals interactions

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 7

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

GW

(atm

)

R2= 0957

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

LK(a

tm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0957

logP

vap

mM

(atm

)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

R2= 0968

logP

vap

MY

(atm

)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0logPvap

exp (atm)

logP

vap

AW

(atm

)

R2= 0968

(e)

Figure 4 Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW (b) LK (c) mM(d) MY and (e) AWmethods The black line is the 1 1 diagonal

The root mean square error (RMSE = 0442) is close to thoseprovided by GW and AW methods The mM method isthen less appropriate than the four others for all classes ofVOC

Figure 5(c) shows that the predicted values match theexperimental values with a coefficient 119877

2= 096 for 32

difunctionalized species For this class of species estimatesare provided with a positive bias (MBE = 0208) and anRMSE of 0512These are the best values obtained from all thefive methods (see Table 2) for difunctionalized species ThusmM method is more accurate than others to estimate vaporpressure for difunctionalized species but does not provide

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

8 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0959

log Pvapexp (atm)

log P

vap

GW

(atm

)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0967

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0962

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0966

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 5 Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW (b) LK (c) mM (d)MY and (e) AWmethods The black line is the 1 1 diagonal

good results for monofunctionalized (Figure 3) and tri- andmore functionalized species (Figure 5)

It can be seen in Figure 7 that estimated values providedby GW method are strongly correlated with experimentalvalues (1198772 = 0960) for difunctionalized speciesThismethodtends to overpredict vapor pressure for this class of species

(MBE = 0288) but does not show any bias for other classes ofspecies (Table 2) Figure 8 shows that we have very acceptableresults for tri- and more functionalized species with RMSEand MAE equal to 0549 and 0440 respectively

Except for tri- and more functionalized species (seeFigure 8) it is clear from Figures 4 to 7 that the LK method

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 9

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0930

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0932

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0964

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 6 Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW (b)LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

gives accurate values based upon best correlation coefficientvalues This method is the second best one of the fivemethods but it has the greatest systematic bias (RMSE =0490 MAE = 032) for the total set of VOC and fordifunctionalized species (RMSE = 070 MAE = 056) TheMAE of hydrocarbons and monofunctionalized species are

0142 and 036 respectively For these species Figures 5 and6 give the best correlations

The AW and LK methods are both based on Antoinersquosequation According to all figures plotted it is clear thatthese two methods give very similar results The peculiarityof AW is that for the monofunctionalized compounds

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

10 International Journal of Geophysics

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0960

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0957

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0961

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 7 Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW (b) LK(c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

the predicted and experimental values are strongly correlatedwith a coefficient 1198772 = 09638

Vapor pressures for a set of 74 hydrocarbons are higherthan 10

minus3 atm It is found for the five methods that estimatedvalues for this class of species are well correlated (Figure 5)

Furthermore vapor pressures of tri- andmore functionalizedspecies are below 10

2 atm (Figure 8) For this class of speciesLK method yields a weak correlation and has the largest pos-itive bias Therefore this method is the least reliable to esti-mate vapor pressure for tri- and more functionalized species

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 11

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0900

log P

vap

GW

(atm

)

log Pvapexp (atm)

(a)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0898

log P

vap

LK(a

tm)

log Pvapexp (atm)

(b)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0901

log P

vap

mM

(atm

)

log Pvapexp (atm)

(c)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0923

log P

vap

MY

(atm

)

log Pvapexp (atm)

(d)

minus8

minus6

minus4

minus2

0

minus8 minus6 minus4 minus2 0

R2= 0899

log P

vap

AW

(atm

)

log Pvapexp (atm)

(e)

Figure 8 Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a)GW (b) LK (c) mM (d) MY and (e) AWmethods The black line is the 1 1 diagonal

4 Conclusion

Wehave evaluated in this study five vapor pressure estimationmethods useful for simulating the dynamics of atmosphericorganic aerosols These are the Myrdal and Yalkovsky (MY)

the Lee and Kesler (LK) the Grain-Watson (GW) themodified Mackay (mM) and the Ambrose-Walton (AW)methods Some of them are based on the Antoine equationwhile others are based on the extended form of the Clausius-Clapeyron equation But all of them take into account boiling

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

12 International Journal of Geophysics

temperature 119879119887and (or) critical temperature 119879

119888 Therefore

Joback technique has been used to estimate 119879119887 while the

Lydersen technique was found to be better for 119879119888estimation

When using Joback to provide the 119879119887values LK AW

and MY are the best three methods for all classes of speciesMoreover for a set of 262 volatile organic compounds andas illustrated in the scatter plots and errors computed theMY method which appears to be the best one fails fordifunctionalized species For these latter species the mMmethod provides good results according to the correlationcoefficient1198772 = 0960 and the least errors reported in Table 2GW method is the least reliable which provides the lowestresults for all VOC and also for each class of species Pre-dictions made with the AWmethod for monofunctionalizedspecies are more reliable than those made with the other fourmethods employing the Joback technique to provide the 119879

119887

For vapor pressure higher than 10minus2 atm all the five methods

give similar resultsThis work highlights that the choice of a method to pre-

dict vapor pressure of volatile organic compounds dependson the number of functional groups existing in the species

References

[1] J Seinfeld and S Pandis Amospheric Chemestry and PhysicsFrom a Pollution to Climate Change John Wiley amp Sons NewYork NY USA 1998

[2] M Tombette Modelisation des aerosols et de leurs proprialtesoptiques sur lrsquoEurope et lrsquoıle de France validation sensibilite etassimilation des donnees [These] Ecole nationale des ponts etchaussees 2007

[3] P Adams and J Seinfeld ldquoPredicting global aerosol size distri-butions in general circulation modelsrdquo Journal of GeophysicalResearch vol 107 no 19 pp AAC 4-1ndashAAC 4-23 2002

[4] S Gons L A Barrie J P Blanchet et al ldquoCanadian aerosolsmodule a size-segregated simulation of atmospheric aerosolprocesses for climate to and air quality models I Moduledevelopmentrdquo Journal of Geophysical Research vol 108 no 1pp AAC 3-1ndashAAC 3-16 2003

[5] E R Whitby and P H McMurry ldquoModal aerosol dynamicsmodelingrdquo Aerosol Science and Technology vol 27 no 6 pp673ndash688 1997

[6] E Debry Modelisation et simulation de la dynamique desaerosols atmospheriques [These] Ecole nationale des ponts etchaussees 2004

[7] B Dahneke Theory of Dispersed Multiphase Flow Academicpress New York NY USA 1983

[8] E Debry K Fahey K Sartelet B Sportisse and M TombetteldquoTechnical note a new SIze REsolved Aerosol Model(SIREAM)rdquo Atmospheric Chemistry and Physics vol 7 no6 pp 1537ndash1547 2007

[9] C Tong M Blanco W A Goddard III and J H SeinfeldldquoThermodynamic properties of multifunctional oxygenates inatmospheric aerosols from quantum mechanics and moleculardynamics dicarboxylic acidsrdquo Environmental Science and Tech-nology vol 38 no 14 pp 3941ndash3949 2004

[10] T Banerjee M K Singh and A Khanna ldquoPrediction ofbinary VLE for imidazolium based ionic liquid systems usingCOSMO-RSrdquo Industrial and Engineering Chemistry Researchvol 45 no 9 pp 3207ndash3219 2006

[11] M Diedenhofen A Klamt K Marsh and A Schafer ldquoPredic-tion of the vapor pressure and vaporization enthalpy of 1-n-alkyl-3-methylimidazolium-bis-(trifluoromethanesulfonyl)amide ionic liquidsrdquo Physical Chemistry Chemical Physics vol9 no 33 pp 4653ndash4656 2007

[12] P B Myrdal and S H Yalkowsky ldquoEstimating pure componentvapor pressures of complex organic moleculesrdquo Industrial andEngineering Chemistry Research vol 36 no 6 pp 2494ndash24991997

[13] R J Griffin K Nguyen D Dabdub and J H Seinfeld ldquoA cou-pled hydrophobic-hydrophilic model for predicting secondaryorganic aerosol formationrdquo Journal of Atmospheric Chemistryvol 44 no 2 pp 171ndash190 2003

[14] B K Pun R J Griffin C Seigneur and J H Seinfeld ldquoSec-ondary organic aerosol 2 Thermodynamic model for gasparticle partitioning of molecular constituentsrdquo Journal ofGeophysical Research D vol 107 no 17 pp AAC 4-1ndashAAC 4-152002

[15] M E Jenkin ldquoModelling the formation and composition ofsecondary organic aerosol from 120572- and 120573-pinene ozonolysisusing MCM v3rdquo Atmospheric Chemistry and Physics vol 4 no7 pp 1741ndash1757 2004

[16] D Mackay A Bobra D W Chan and W Y Shiu ldquoVapor pres-sure correlations for low-volatility environmental chemicalsrdquoEnvironmental Science and Technology vol 16 no 10 pp 645ndash649 1982

[17] J F Pankow and W E Asher ldquoSIMPOL1 a simple group con-tribution method for predicting vapor pressures and enthalpiesof vaporization of multifunctional organic compoundsrdquo Atmo-spheric Chemistry and Physics vol 8 no 10 pp 2773ndash27962008

[18] M Capouet and J-F Muller ldquoA group contribution methodfor estimating the vapour pressures of 120572-pinene oxidationproductsrdquo Atmospheric Chemistry and Physics vol 6 no 6 pp1455ndash1467 2006

[19] M Camredon and B Aumont ldquoAssessment of vapor pressureestimation methods for secondary organic aerosol modelingrdquoAtmospheric Environment vol 40 no 12 pp 2105ndash2116 2006

[20] S Compernolle K Ceulemans and J-F Muller ldquoTechnicalNote vapor pressure estimation methods applied to secondaryorganic aerosol constituents from 120572-pinene oxidation an inter-comparison studyrdquo Atmospheric Chemistry and Physics vol 10no 13 pp 6271ndash6282 2010

[21] M H Barley and G McFiggans ldquoThe critical assessmentof vapour pressure estimation methods for use in modellingthe formation of atmospheric organic aerosolrdquo AtmosphericChemistry and Physics vol 10 no 2 pp 749ndash767 2010

[22] L E Yu M L Shulman R Kopperud and L M Hilde-mann ldquoCharacterization of organic compounds collected dur-ing Southeastern Aerosol and Visibility Study water-solubleorganic speciesrdquo Environmental Science and Technology vol 39no 3 pp 707ndash715 2005

[23] M Jang and R M Kamens ldquoCharacterization of secondaryaerosol from the photooxidation of toluene in the presence ofNOx and 1-propenerdquo Environmental Science and Technologyvol 35 no 18 pp 3626ndash3639 2001

[24] W E Asher J F Pankow G B Erdakos and J H SeinfeldldquoEstimating the vapor pressures of multi-functional oxygen-containing organic compounds using group contributionmeth-odsrdquo Atmospheric Environment vol 36 no 9 pp 1483ndash14982002

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

International Journal of Geophysics 13

[25] D R Lide Handbook of Chemistry and Physics 86th edition1997

[26] C L Yams Hanbook of Vapour Pressure Vols 2 and 3 GuefPublishing Compagny Houston Tex USA 1994

[27] T Boulik V Freid and E Hala The Vapour Pressure of PureSubstances Elsevier Amsterdam The Netherlands 1984

[28] K J Joback and R C Reid ldquoEstimation of pure componentproperties from group contributionrdquo Chemical EngineeringCommunications vol 57 pp 233ndash243 1987

[29] PW Bruckmann and HWillner ldquoInfrared spectroscopic studyof peroxyacetyl nitrate (PAN) and its decomposition productsrdquoEnvironmental Science andTechnology vol 17 no 6 pp 352ndash3571983

[30] Y Nannoolal Development and critical evaluation of groupcontribution methods for the estimation of critical propertiesliquid vapour pressure and liquid viscosity of organic compounds[PhD thesis] University of Kwazulu Natal 2006

[31] P B Myrdal J F Krzyzaniak and S H Yalkowsky ldquoModifiedTroutonrsquos rule for predicting the entropy of boilingrdquo Industrialand Engineering Chemistry Research vol 35 no 5 pp 1788ndash1792 1996

[32] J Vidal Thermodynamique Application au Genie Chimique etAa lrsquoindustrie du Petroliere Technip Paris Farnce 1997

[33] E J Baum Chemical Property Estimation-Theory and Applica-tion section 63 Lewis Boca Raton Fla USA 1998

[34] R P Schwarzenbasch P M Gschwend and D M ImbodenEnvironmental Organic Chemistry John Wiley amp Sons NewYork NY USA 2nd edition 2003

[35] W J Lyman Environmental Exposure from Chemicals vol 1chapter 2 CRC Press Boca Raton Fla USA 1985

[36] S H Fishtine ldquoReliable latent heats of vaporizationrdquo Environ-mental Science amp Technology vol 55 pp 47ndash56 1963

[37] C F Grain ldquoVapor pressurerdquo inHandbook of Chemical PropertyEstimation Methods chapter 14 McGraw-Hill New York NYUSA 1982

[38] B E Poling J M Prausnitz and J P OrsquoConnellThe Propertiesof Gases and Iquids McGraw-Hill New York NY USA 5thedition 2001

[39] R C Reid J M Prausnitz and B E Poling The Propertiesof Gases and Liquids McGraw-Hill New York NY USA 4thedition 1986

[40] D Ambrose and J Walton ldquoVapor pressures up to their criticaltemperatures of normal alkanes and 1-alkoholsrdquo Pure andApplied Chemistry vol 61 pp 1395ndash1403 1989

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in