量子力学预测PCBs的亨利定律常数

Environ.Sci.Technol.XXXX,xxx,000–000

QuantumMechanicalPredictionsoftheHenry’sLawConstantsandTheirTemperatureDependenceforthe209PolychlorinatedBiphenylCongeners

KATHYL.PHILLIPS,?STANLEYI.SANDLER,?

RICHARDW.GREENE,?,§ANDDOMINICM.DITORO*,§

CenterforMolecularandEngineeringThermodynamics,

DepartmentofChemicalEngineering,UniversityofDelaware,150AcademyStreet,Newark,Delaware19716,Delaware

DepartmentofNaturalResourcesandEnvironmentalControl,WatershedAssessmentBranch,820SilverLakeBoulevard,Suite220,Dover,Delaware19904,andDepartmentofCivilandEnvironmentalEngineering,UniversityofDelaware,DuPontHall,Newark,Delaware19716,

ReceivedApril1,2008.RevisedmanuscriptreceivedAugust6,2008.AcceptedAugust13,2008.

TheHenry’slawconstants(HLCs)forall209polychlorinatedbiphenyl(PCB)congenerswerepredictedat25°Cusingthequantummechanical(QM)continuumsolvationmodelsCOSMO-SACandSM6,andtrendswereexamined.COSMO-SACHLCswerealsopredictedforallcongenersat4,11,18,and31°C.ThetemperaturedependencesoftheHLCswereusedtocalculateenthalpyofsolvation(?HS)values.At25°C,COSMO-SACandSM6predictedsimilarvaluesoftheHLC,whichareconsistentwithallbutoneoftheavailablesetsof

measurements,andhavesmallerroot-mean-squarepredictionerrorsthanothermodelstested.ThissupportsthevalidityoftheQMvalues,andtherecommendationoftheirusein

environmentaltransportandfatemodels.IntercongenertrendsintheHLCsappeartobedominatedbythestrengthofPCB-waterpolarinteractions.TheCOSMO-SACpredictionsbetween4and31°CindicatethatthetemperaturedependenceoftheHLCissimilarforallcongeners.Atlowtemperatures,theHLCpredictionsforseveralheavycongenersaresubstantially

higherthanrecentlyreportedmeasurements,supportingclaimsintheliteraturethattheselow-temperaturedataareinaccurate.

Introduction

Atmospherictransportisakeyprocessintheglobalredistributionofpolychlorinatedbiphenyls(PCBs)(1).TheHenry’slawconstant(HLC)isafundamentalpropertydescribingtheexchangebetweentheatmosphereandsurfacewaters.ThelackofaccurateHLCvaluesposesamajorprobleminmodelingthetransportandfateofPCBsinthe

*Correspondingauthorphone:(302)831-4092;fax:(302)831-3640;e-mail:dditoro@UDel.edu.?

DepartmentofChemicalEngineering,UniversityofDelaware.?

DelawareDepartmentofNaturalResourcesandEnvironmentalControl.§

DepartmentofCivilandEnvironmentalEngineering,UniversityofDelaware.

Published on Web 10/15/2008

10.1021/es800876wCCC:$40.75

?XXXXAmericanChemicalSociety

environment,anecessarystepforperformingriskassess-mentsanddevelopingenvironmentalremediationstrategies.HLCshavebeenmeasuredforselectedcongeners(2–17),commonlyat25°C.ThelargestexperimentaldatasetsatthistemperaturearethoseofBrunneretal.(11),whomeasuredHLCsfor58congenersusingaconcurrent?owtechnique,andBamfordetal.(13),whousedamodi?edgas-strippingmethodtomeasureHLCsfor26congeners.Thetotalityofdataat25°C(Figure1A)arehighlyscattered,andreportedvaluesforsomeindividualcongenersdifferbyuptoalmost2ordersofmagnitude.Differenttrendswithchangesinthenumberofchlorinesubstituents(NCl)areapparentintheHLCdata.Furthermore,measurementsformanycongenersareunavailable.Consequently,consensusislackingonthevaluesoftheHLCs,particularlyfortheheaviercongeners.

HLCsofPCBshavealsobeenmodeledbymanygroups(11,14,15,18–30).However,mostmodelsare?ttedtomeasuredHLCsandthereforesufferfromtheuncertaintyinthedata.PredictivemodelsfortheHLCsofallcongenershavebeenpublished.Burkhardetal.(20)predictedtheHLCsfromtheratiosofvaporpressuresandsolubilitiescalculatedbymodelingdataforselectedcongeners(Figure1B).AbrahamandAl-Hussaini(29)usedchromatographicdatatodevelopalinearfreeenergyrelationshipforthepropertiesofPCBs(Figure1C).TheSPARC(31)methodcanbeusedtopredictpropertiesfororganiccompoundsusingmolecularinterac-tionmodelsbasedonchemicalstructuretheory,andcalibratedusingexperimentaldata(32–36)(Figure1D).Thesepredictionsarenotincloseagreementwitheachother,nordotheyconsistentlysupportanysetofmeasuredHLCs.(Astatisticalanalysisofthepredictionerrorsispresentedsubsequently.)Therefore,alackofconsensusremains.MostworkonHLCsforPCBshasbeenperformedatambienttemperatures.However,HLCisahighlytemper-ature-dependentproperty,andtransportandfatemodelingrequiresknowledgeofHLCsoverarangeofenvironmentallyrelevanttemperatures.AsmallbodyofworkexistsonthetemperaturedependenceofHLCsforPCBs,includingmeasurements(12,13)andcalculations(14,20,37).However,theresultsareinconsistent,anduncertaintyaboutthetemperaturedependenceremains.

Inthisstudy,twoquantummechanics(QM)basedcontinuumsolvationmodels,COSMO-SAC(38–40)andSM6(41),wereemployedtopredictHLCsforallPCBcongenersat25°C.COSMO-SAC,theonlyoneofthemodelsthatcanbeappliedatdifferenttemperatures,wasalsousedtopredictHLCsforallcongenersovertheenvironmentallyrelevanttemperaturerangeof4-31°C.TheQM-basedmethodspredicttheHLCfromacombinationofindividualsolvationterms,eachofwhichofferinsightintotheeffectsthatgiverisetotheHLCvaluesandtheintercongenertrends.AdditionalinsightisgainedbyexaminingtheQM-determinedthree-dimensionalstructureforeachcongener.

OverviewofModels

TheQMmodelsusedinthisstudyarebothwellestablishedandhavebeendescribedindetailelsewhere(COSMO-SAC(38–40);SM6(41)).Abriefoverviewisincludedhere.

COSMO-SAC.TheConductor-likeScreeningModel(COS-MO)developedbyKlamtandSchu¨u¨rmann(42)isaQM-basedmodelinwhichthesolventisrepresentedbyahomogeneousmediumcharacterizedsolelybyitsdielectricconstant.Conceptually,suchcontinuumsolvationmodelstakeasolutemoleculefromanidealgasandplaceitina

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9

A

FIGURE1.HLCsforPCBcongenersat25°C.(A)Experimentaldata:O,HassettandMilicic(5);3,Dunnivantetal.(8,9);4,FendingerandGlotfelty(10);+,Brunneretal.(11);9,Bamfordetal.(13);],Fangetal.(http://wendang.chazidian.comuetal.(16):x,gas-strippingmethod(GSM),!,modi?edGSM,4,(crossedtriangle),integratedGSM.Errorbarsindicatestandarddeviation,wherereported.(B-D)Predictedvaluesfromtheliterature:(B)],Burkhardetal.(20);(C)4,AbrahamandAl-Hussaini(29),eq10intheirpaper;(D)3,SPARC(31).(E,F)Predictedvaluesfromthiswork:(E)O,COSMO-SAC;(F)O,SM6.cavityformedwithinthedielectricmedium.Theinterfacebetweenthecavityandthemediumisreferredtoasthesolventaccessiblesurface.Anychargedistributionofthesolutewillpolarizethemedium,leadingtoachargedistributiononthesolventaccessiblesurface,fromwhichtheinteractionenergiesofthesurfacescanbeevaluated(42,43).Thefreeenergyoftransferfromthegasphasetothecondensedphaseisreferredtohereasthefreeenergyofsolvation,?GS,andisdirectlyrelatedtotheHLCby

HLC)lim

j?GSfL

)RTexp

xf0x(55.4×103)RT

vaporpressure(Pvap)andthein?nitedilutionactivity

coef?cientinwater(γW).ThemolefractionsolubilityofanyveryslightlysolublecompoundisthereciprocalofγW.TheproductofPvap(Pa)andγWgivesanestimateoftheHLC,assumingidealgasbehavior.

HLC≈PvapγW

(

155.4×103

)

(2)

()

(1)

whereHLCisin(Pam3)/mol,xandjfL(Pa)are,respectively,themolefractionandfugacityofthesoluteinthesolution,themolarvolumeofwater(55.4×103mol/m3)isaunitconversionfactor,Risthegasconstant(8.314J/(molK)),T(K)istheabsolutetemperature,and?GSisinJ/mol.

IntheCOSMOmethod,whichisimplementedinseveralQMpackagesincludingDMol3(44),thesurface-chargedensitycalculationissimpli?edbytreatingthedielectricmediumasaperfectconductor(in?nitedielectricconstant)(42,43).AnextensiontoCOSMO,theCOSMO-SegmentActivityCoef?cient(COSMO-SAC)modelthenappliessta-tisticalthermodynamicstothesurface-chargedistributionintheconductortoaccountfortheinteractionsbetweenthemoleculeandthesolvent.COSMO-SAC,developedbyLinandSandler(38,39)andre?nedbyWangetal.(40),isavariationontheKlamtCOSMO-RS(realsolvents)model(45,46).

UsingtheQM-calculatedenergies,COSMO-SACcanthenbeusedtopredictthermodynamicproperties,includingthe

B

9

SM6.TheSolvationModel6(SM6)isaQM-basedcontinuumsolvationmodeldevelopedbyCramer,Truhlarandco-workers,andisimplementedintheSMXGAUSSsoftware(47).However,SM6employsadistinctlydifferentapproachtopredicttheHLC.SM6partitions?GSintothreecontributions(41)

?GS)?Eelec+GP+?GCDS

(3)

The?Eelectermisthechangeintheinternalelectronicenergyofthesoluteinmovingfromthegasphasetotheliquidphaseata?xedgeometry(41).Inthiswork,gas-phasegeometrieswereusedratherthanreoptimizingthesolutegeometryintheliquidphase,becausethedifferencein?GSresultingfromreoptimizationisgenerallylessthantheaverageerrorinthemodel,andthemodelhasbeenparametrizedusinggas-phasestructures(41).Thepolariza-tioncontribution,GP,accountsforthechangeinthesolutefreeenergybecauseofelectrostaticinteractionsbetweenthechargedistributionofthesoluteandthebulkelectric?eldofthesolvent(41,48).ThesetermsarecomputedusingQM.Theterm?GCDSaccountsforallremainingcontributionsto?GS,whichincludethefreeenergychangesduetoelectrostaticinteractionsbetweenthesoluteand

solvent

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moleculesinthe?rstsolvationshell(41).Theseshort-rangeinteractionscanbeattributedtocavityformation(C),dispersion(D),andchangesinthesolventstructure(S)duetothepresenceofthesolute(48).?GCDSisanempiricaltermthatiscalculatedusingatomicsurfacetensions(41).

Methods

Throughoutthiswork,PCBcongenersarereferredtobytheirIUPACnamesandnumbers(TableS1oftheSupportingInformation)(49).Predictionsweremadeforall209con-genersusingbothCOSMO-SACandSM6.

COSMO-SAC.Toprepareastartinggeometryforeachcongener,wesketechedthestructureusingGaussView3.09(50),andthegas-phasegeometrywasoptimizedwithGaussian03(51)usingdensityfunctionaltheory(DFT)withtheB3LYPfunctionalandthe6-31G(d,p)basisset.Afrequencycalculationwasincludedtoverifythatthestructurerepresentedaminimuminthepotentialenergysurface.Toimprovetheinitialguessofthestructure(52),thiswasfollowedbyamolecularmechanicsenergyminimizationcalculationusingtheAmber(53)force?eld.The?nalgeometry,togetherwiththegas-phasemolecularenergy,wasobtainedfromafurtherDFTgas-phaseoptimizationusingDMol3(44)withtheVWN-BPdensityfunctional,DNPv4.0.0basisset,arealspacecutoffof5.50Å,anda“?ne”numericalintegrationgrid.ThesearetherecommendedDMol3settingsforCOSMOcalculations(54)andhavebeenusedinparametrizationofCOSMO-SAC(40,http://wendang.chazidian.comingtheoptimized(gas-phase)geometry,asingle-pointenergycalculationinthecondensedphasewasthenperformedusingDMol3withthe“COSMOsolvation”environmentand“conductor”asthesolvent(othersettingswereunchangedfromthepreviousstep).Themolecularweightandanestimateoftheliquiddensityforeachcongener(requiredforthevaporpressurecalculation)wereobtainedfromref56.Forallcompounds,theCOSMO-SACprogram,incorporatingthecalculationmethodandparametersdescribedin(40,52),wasusedtocalculatePvap(Pa)andγWateachtemperatureofinterest.HLCwaspredictedusingeq2.

SM6.Foreachcongener,theGaussianB3LYP/6-31G-(d,p)gas-phaseoptimizedstructure(asabove)wasused.Asingle-pointliquid-phaseenergycalculationwasperformedwiththeSMXGAUSSprogram(47)runninginmode2,usingtheSM6solvationmodelandtheB3LYP/6-31G(d)theoryandbasisset,withwaterasthesolvent.TheHLCwascalculatedfromthe?GSvalueat25°Cusingeq1.

FIGURE2.RMSEinlog(HLC)foreachsetofpredictionsfromeachmajordatasetforthePCBsat25°C.Experimentaldata(numbersinbrackets{}indicatenumberofdatapoints):whitebars,Dunnivantetal.(8,9){17};diagonalstripespointinguptoright,Brunneretal.(11){58};diagonalstripespointingdowntoright,Bamfordetal.(13){26};crosshatch,Fangetal.(15){12};horizontalstripes,Lauetal.(16)(GSM{8},modi?edGSM{9},integratedGSM{9});blackbars,overall,excludingBrunneretal.(11)dataset{81}.Predictionsfromtheliterature:Burkhardetal.(20);AbrahamandAl-Hussaini(29);SPARC(31).Predictionsfromthiswork:COSMO-SAC;SM6.

Dunnivantetal.(8,9)data,whiletheCOSMO-SACandSM6predictionsbestagreewiththeBamfordetal.(13)data.TheSPARCpredictionsarenotincloseagreementwithanyofthedatasets.

Thedatasetscomprisedifferentcongeners;therefore,cautioniswarrantedindirectlycomparingtheRMSEsfordifferentdatasets.Forinstance,theDunnivantetal.(8,9)datadonotincludeanycongenerswithmorethansixchlorines,whereastheBamfordetal.(13)dataincludeseveralheavycongenersforwhichtheexperimentaluncertaintyintheHLCisgreatest.

Gossetal.(57)claimedthattheBamfordetal.(13)HLCsaretoohighfortheheavycongeners,possiblyduetocongenersorptiononthegasbubblesurfacefollowedbytransfertothegasphase.However,theBurkhardetal.(20)HLCsareincloseagreementwiththeBamfordetal.(13)measurementsforallcongenerswithsevenormorechlorines(panelsAandBinFigure1);theCOSMO-SACandSM6predictionsareslightlyhigherthanthesedataforseveralheavycongeners(panelsA,E,andFinFigure1).Therefore,theBamfordetal.(13)HLCvaluesdonotappeartobetoohighfortheheavycongeners,ashasbeenclaimed(57).

ThereareconsistentlylargedeviationsbetweenallmodelsandthedataofBrunneretal.(11).Ifthosedataareexcluded,theoverallRMSEforeachmodelusingtheremainingdata(theblackbarsinFigure2)indicatesthattheQMmodelsbestagreewiththeremainingdata.TheoverallRMSEislowerforSM6thanforCOSMO-SAC,whichisnotsurprisingsinceSM6usesanempiricalcorrection(?GCDS),andSM6isparametrizedusingHLCdata,whereasCOSMO-SACdoesnotrelyonanyHLCdata.TheQMvaluesoftheHLCs,andinparticular,theSM6values,arethereforerecommended.RelationshipbetweenHLCandDegreeofChlorination(at25°C).TheCOSMO-SACandSM6modelsbothpredictanaverageincreaseintheHLCastheNCl(orequivalently,themolecularweight)increases(seetheSupportingInfor-mation,AandBinFigureS1;FigureS1Cshowsdata,forcomparison).Inbothcases,signi?cantvariabilitywithineachhomologueindicatesthattheHLCalsodependsstronglyonotherfactors,aresultconsistentwithmostexperimentaldata(8,9,13,15,16),aswellasliteraturepredictions(20,29).AsNClincreases,theincreaseintheCOSMO-SACvalueofγWoutweighstheaccompanyingdropinPvap(seetheSupportingInformation,FigureS1D;eq2),resultinginthepredictedNCl-dependenceoftheHLCs.Similarly,for

SM6,

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ResultsandDiscussion

HLCsat25°C.TheCOSMO-SACandSM6HLCpredictionsat25°C(seetheSupportingInformation,TableS1)areplottedinpanelsEandFinFigure1,respectively.Thesepredictionsareincloseagreement,andbothagreewellwithsomeofthemeasurements(Figure1A)acrossthewholerangeofcongeners.

Theagreementbetweeneachsetofpredictionsandeachdatasetisquanti?edbytherootmean-square-errorofprediction(RMSE)inlog(HLC)

RMSE)

??

∑(y

i)1

n

i,obs-yi,pred)

2

n

(4)

wherey)log(HLC/((Pam3)/mol)),“obs”and“pred”refertotheobservedandpredictedvalues,respectively,andnisthenumberofpointsinthedataset.Figure2comparestheRMSEsforthevariouspredictionsandthemajordatasets(seetheSupportingInformation,TableS2).TheAbrahamandAl-Hussaini(29)andBurkhardetal.(20)predictionsbothagreemostclosely(i.e.,RMSEissmallest)withthe

C

theGPvalueincreases(becomeslessnegative)withincreasingNClbyanamountgreaterthanthecombineddecreasein?Eelecand?GCDS(seetheSupportingInformation,FigureS1E;eqs1and3).

ThedecreaseinPvapand?GCDSvalueswithincreasingNClisatleastpartiallyattributabletotheincreasingmolecularsize,whichisassociatedwithbothincreasingstrengthofthedispersioninteractionsandincreasedenergycostsforcavityformation.

TheincreaseinγWandthereductioninthemagnitudeofGP(|GP|)indicatethat,asNClincreases,solute-solventinteractionsbecomelessfavorable,onaverage,becauseofadecreaseinstabilizingpolarizationeffects.Asaresult,thereisagreatertendencyforthecongenertopartitionintothegasphase.Polarsolute-solventinteractionsappeartoplayaprincipalroleindeterminingthevaluesoftheHLCs.Inparticular,theveryhighSM6HLCvaluefordecachlorobi-phenyl(PCB209)resultsprimarilyfromthesmall|GP|relativetothevaluesforothercongeners.

Toinvestigatethesepolarizationeffects,theSM6|GP|valueshavebeenexaminedrelativetothedipolemomentsfortheoptimized(B3LYP/6-31G(d,p))structures.Onaverage,|GP|increases(congener-waterpolarinteractionsbecomemorefavorableandHLCdecreases)asthemagnitudeofthemoleculardipolemoment(“moleculardipole”)increases(seetheSupportingInformation,FigureS2),asexpected.How-ever,thereissubstantialvariationintheGPvaluesamongthecongenersthatcannotbeaccountedforbydifferencesinthemoleculardipoles.Forinstance,3,3′,4,4′,5,5′-hexachlo-robiphenyl(PCB169)anddecachlorobiphenyl(PCB209)bothhavezeromoleculardipolemomentsduetotheirsymmetricsubstitutionpatterns;however,theirGPvaluesare-12.0and-1.3kJ/mol,respectively.

Someofthisvariationcanbeexplainedbythedifferencesinlocaleffects,whichSchwarzenbach(28)believesareimportantindeterminingmolecularinteractions.Here,wede?nea“localdipole”foreachringasthemagnitudeofthedipolemomentforamoleculewiththesamesubstitutionpatternononeringbutconnectedtoaphenylringwithnochlorines.Forexample,thetwolocaldipolesfor2,3′,4-trichlorobiphenylaretakentobethemoleculardipolesof2,4-dichlorobiphenyland3-chlorobiphenyl.Thesumofthelocaldipolesforacongeneristermedthe“totallocaldipole”.InthecaseofPCB169,thelocaldipolesarerelativelystrong,leadingtoenhancedPCB-waterinteractions.Incontrast,PCB209lacksstronglocaldipolesbecauseofthecompletechlorinationofbothrings,whichmayexplaintheobserveddifferenceinGP.

Asameasureofthecombinedmolecularandlocaleffects,theaverageofthemoleculardipoleandthetotallocaldipole(the“averagedipole”)wascalculatedforeachcongener(seetheSupportingInformation,FigureS3andTableS1).Withinmosthomologues,SM6predictsanaverageincreasein|GP|astheaveragedipoleincreases,whichisexpected.However,inhomologue1,theaveragedipoleforthethreemonosub-stitutedPCBsincreasesbut|GP|decreasesasthechlorinepositionchangesfromorthotometatopara.ThischangeinGPcannotbeexplainedbytheaveragedipoles.Withinotherhomologues,theaveragedipolesaccountformuchofthevariationinGP,butotherfactorsalsoappeartobeimportant.Inparticular,asforhomologue1,substitutionintheorthopositionappearstoleadtohigher|GP|values.Itisnotclearwhyortho-substitutionmaycauseenhancedcongener-waterpolarinteractions,butthismayrelatetochangesintheplanarityofthebiphenylringstructure(seefurtherdiscussionbelow).

RelationshipbetweenHLCandSubstitutionPattern(at25°C).SM6predictsanaverageincreaseinHLCwithineachhomologueasthenumberofortho-chlorinesincreases(seetheSupportingInformation,FigureS4B).Thistrend(the

D

9

“orthoeffect”)hasalsobeenwidelyreportedintheliterature(8,9,11,13,20).Ithasbeenpostulated(8,9,13)thatortho-substitutionleadstostericallyhinderedstructureswithreducedrotationalfreedomatthephenyl-phenylbond,resultinginahighlynoncoplanararrangementofthephenylringsthataffectsthePCB-watermolecularinteractions.Toinvestigatethishypothesis,weexaminedthedihedralanglebetweenthephenylringsintheoptimized(B3LYP/6-31G(d,p)structureforeachcongenerinrelationtothesubstitutionpatternandtheSM6HLCprediction.Thedihedralangles(seetheSupportingInformation,TableS1)arefoundtobebetween37and90°,indicatingthatallcongenersaremoststableinanonplanarconformation.Thisisconsistentwithexperimental?ndings(58),andappearstoberelatedtothesmallestangleatwhichthereisnooverlapbetweenadjacentortho-atoms,reportedelsewhere(20)as39°forcongenerswithnoortho-substituents.

Theaverageangleincreasessystematicallywithincreasingdegreeofortho-chlorination(seetheSupportingInformation,FigureS5).Variabilityinangleofupto12°forcongenerswitha?xednumberofortho-chlorinesistheresultofthespeci?csubstitutionpattern.Inparticular,substitutioninanytwoadjacentpositionsontherings,and/oranunevendistributionofsubstituentsbetweentheringsleadstohigherangles.

Astheangleincreases,thereisanaverageincreaseintheSM6HLCpredictionswithineachhomologue(seetheSupportingInformation,FigureS6).ThisisrelatedtothestrongpositivecorrelationbetweentheSM6?GCDSvalueandtheangle(ornumberofortho-chlorines)forcongenerswithinahomologue(seetheSupportingInformation,FigureS7C).Thisresultsuggeststhattheorthoeffectmayberelatedtothereducedabilityofstericallyhinderedcongenerstoundergoshort-rangeinteractions.However,thereissub-stantialvariabilityintheSM6HLCswithinahomologuethatisnotaccountedforbychangesinangle.Thiscanbeassociatedwithdifferencesinthe?EelecandGPterms(seetheSupportingInformation,FigureS7C),thesumofwhichisdominatedbylong-rangesolute-solventinteractions.UnliketheSM6predictions,theorthoeffectintheCOSMO-SACpredictedHLCsoccursonlywithinsomehomologues(seetheSupportingInformation,FigureS4A).TheCOSMO-SACPvapvaluesincrease(onaverage)withincreasingortho-substitutionwithineveryhomologue(seetheSupportingInformation,FigureS7A),whichisconsistentwithPvapmeasurements(59,60)andalsotheconclusionsofBurkhardetal.(20).However,theorthoeffectisnotthedominanttrendintheCOSMO-SACHLCswithinallhomo-loguessincethecontributionmadebyγW(seetheSupportingInformation,FigureS7B)isalsoimportant.

TemperatureDependenceofHLCs.ThetemperaturedependenceoftheHLCisquanti?edbytheenthalpyofsolvation,?HS,thatcanbeobtainedfrom

dln(HLC/(RT))-?HS

)

dTRT2

(5)

where?HSisinJ/mol.Integratingthisequation,assuming

?HSisconstantoverthetemperaturerangeofinterest,yields

ln

)+constant(HLCRT)RT

?HS

(6)

sothat?HSisobtainedfromtheslopeofthelinearregression

ofln(HLC/RT)against1/T.

HLCswerepredictedat4,11,18,25,and31°CusingCOSMO-SAC(seetheSupportingInformation,TableS1andFigureS8).SimilarcalculationscouldnotbeperformedwithSM6sincethismodelisonlyforpredictionsat25°C,anditstemperature-dependentextension,SM6T(61),cannotbeappliedtochlorine-containingcompounds.Forallcongeners,

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FIGURE3.EnthalpiesofsolvationforPCBsdeterminedfromHLCvaluesatvarioustemperatures.Experimentaldata:3,tenHulscheretal.(12);9,Bamfordetal.(13).Predictionsfromtheliterature:],Burkhardetal.(20);+,Paasivirtaetal.(37).Predictionsfromthiswork:?,COSMO-SAC.

theCOSMO-SACHLCsincreasewithincreasingtemperature,indicatingnegative?HSvalues,asreportedelsewhere(12,13,20,37).COSMO-SACpredictsanincreaseinPvapandadecreaseinγWwithincreasingtemperature(seetheSupportingInformation,TableS1).Asexpected,thetem-peraturedependenceofPvap(averagechangeof878%per25°C)ismuchgreaterthanthatofγW(averagechangeof40.5%per25°C).

Figure3comparestheCOSMO-SACpredictionsfor?HS(seetheSupportingInformation,TableS1)withvaluesfromtheliterature.InaseparateevaluationforcompoundsthatarestructurallysimilartoPCBs,aRMSEof7.2kJ/molwasdeterminedfortheCOSMO-SAC?HSvalues(seetheSupportingInformation,pageS8,FigureS9,TableS3).TheCOSMO-SAC?HSvaluesforallcongenersdifferfromeachotherbylessthan10kJ/mol,indicatingthattheHLCsofallcongenershavesimilartemperaturedependences.Consequently,intercongenertrendsintheCOSMO-SACHLCsareessentiallythesameateachtemperature.TheBurkhardetal.(20)?HSvalues(basedonHLCat0,15,25,and40°C)likewisespanasmallrange(lessthan25kJ/mol).However,theCOSMO-SAC?HSvaluesaresmallerinmagnitudeandhavenosystematicNCl-dependence,whereasthe?HSvaluesofBurkhardetal.(20)becomemoreexothermiconaveragewithincreasingNCl.ThesediscrepanciesmayinpartbeattributedtodifferenttreatmentofthetemperaturedependenceofγWinthetwomodels.Burkhardetal.(20)usedsolubilitymeasurementsforPCB4andbiphenylatdifferenttemperaturestoestimateanaveragetemperaturedependenceofγW,takentobethesameforallcongeners.Theirestimateofa28.8%decreaseinγWbetween0and25°CisingoodagreementwiththeCOSMO-SACpredictionsforPCB4(30.6%decreaseinγWper25°Crise)andothermonosubstitutedcongeners.However,COSMO-SACpredictsstronginter-congenervariationinthetemperaturedependenceofγW,rangingfromachangeof28.9-56.6%per25°C.Thetemperaturedependencegenerallyincreaseswithin-creasingNCl.Underestimatingthetemperaturedepen-denceofγWwouldresultin?HSvaluesthataretoohighlyexothermic.

tenHulscheretal.(12)experimentallydeterminedvaluesof?HSforthreecongenersthataresimilartotheCOSMO-SACandBurkhardetal.(20)values.Paasivirtaetal.(37)estimatedthetemperaturedependenceoftheHLCfor11congenersusinganapproachsimilartothatofBurkhardetal.(20),producingcomparableresults.

Bamfordetal.(13)reported?HSvaluesfor26congenersdeterminedfromthetemperaturedependenceofthemea-suredHLCsthatvaryfrom-14.5to-167kJ/mol.Thislargerangeandthehighlynegative?HSvaluesforseveralofthe

heaviercongenersareinconsistentwithallothervaluesintheliterature.Bamfordetal.(13)notedthatthemagnitudeof?HSshouldapproximatethedifferencebetweentheenthalpyofvaporization(?HVAP)andtheenthalpyofsolu-bilization(?HSOL).Howevertheirsevenmosthighlyexo-thermic?HSvaluesaregreaterinmagnitudethanthecorresponding?HVAPvaluesfromtheliterature,suggesting?HSOLvaluesthataremorehighlyexothermicthanthosereportedforanyotherorganiccompound(57).Gossetal.(57)pointedoutthattheBamfordetal.(13)datadisplayagreaterrangeofenthalpyvalueswithinahomologuethanpreviouslyreportedforanyothersetofcloselyrelatedisomers.Gossetal.(57)proposedthatthelowtemperatureHLCsofBamfordetal.(13)maybeerroneouslyhighforsomecongenersastheresultofenhancedPCBadsorptiontothebubblesurfaceatlowtemperatures.Astemperatureisreduced,agreementbetweentheCOSMO-SACandBam-fordetal.(13)HLCsateachtemperature(seetheSupportingInformation,FigureS10)systematicallyworsens,supportingclaimsthatthelowtemperaturemeasurementsareinac-curate.Thegreatestdiscrepanciesappearinthelowtem-peraturemeasurementsfortheheavycongeners,forwhichthepredictedCOSMO-SACHLCvaluesaregreaterthantheBamfordetal.(13)values.However,themechanismproposedbyGossetal.(57)cannotexplainthehighlynegativeenthalpiesdeterminedbyBamfordetal.(13)fortheheavycongeners.AlthoughBamfordetal.(62)havedefendedtheaccuracyoftheirdata,theCOSMO-SACresultstogetherwithotherworkintheliteraturestronglysuggeststhattheBamfordetal.(13)HLCmeasurementsareinaccurateatlowtemperatures.

Acknowledgments

ThisresearchwasfundedbytheNationalInstituteofEnvironmentalHealthSciencesthroughaSuperfundBasicResearchProgramGrant(5R01ES015444).KPisgratefultoShuWang,JeffreyFrey,RussellBurnett,PeiChiu,andPatrickMcMahonforassistance.

SupportingInformationAvailable

TableS1liststhePCBs,allHLCvaluesandotherpropertiespredictedbyCOSMO-SACandSM6,aswellasthedipolesandangles;TableS2liststheRMSEvaluesforlog(HLC);TableS3andFigureS9containtheresultsfromtheevaluationofCOSMO-SAC?HSvalues,discussedonpageS8(abovethe?gure);FigureS1showstheCOSMO-SACandSM6propertypredictionsasafunctionofNCl;FigureS2showstheSM6|GP|valuesversusthemoleculardipoles;FigureS3isaplotof|GP|asafunctionoftheaveragedipolewithinahomologue;FigureS4showstheCOSMO-SACandSM6HLCsasafunctionofthenumberofortho-chlorinesforcongenerswithinahomologue;FigureS5showstheangleversusthenumberofortho-chlorines;FigureS6showstheSM6HLCpredictionsasafunctionoftheangle,withinahomologue;FigureS7comprisesplotsofPvap,γW,?Eelec,GP,and?GCDSagainstthenumberofortho-chlorinesforcongenerswithinahomologue;FigureS8showstheCOSMO-SACpredictionsofselectedHLCsateachtemperature;andFigureS10comprisescrossplotsoftheCOSMO-SACpredictionswiththeBamfordetal.(13)measurementsofHLCateachtemperature.FiguresanddiscussionasPDF;tablesinExcelformat.ThismaterialisavailablefreeofchargeviatheInternetathttp://wendang.chazidian.com.

LiteratureCited

(1)MacDonald,R.W.;Barrie,L.A.;Bidleman,T.F.;Diamond,M.L.;

Gregor,D.J.;Semkin,R.G.;Strachan,W.M.;Li,Y.F.;Wania,F.;Alaee,M.;etal.ContaminantsintheCanadianArctic:5yearsofprogressinunderstandingsources,occurrenceandpathways.Sci.TotalEnviron.2000,254(2-3),

93–234.

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