Introduction A useful characteristic in assessing the vitrification behavior of glassforming - PDF document

Ausefulcharacteristicinassessingthevitrificationbehaviorofglass-formingliquidsandpolymersisthe,whichreferstothesteepnessofsemi-log-arithmicplotsoftheviscosityorstructuralrelaxationtime(orforpolymers,thelocalsegmentalrelaxationtime)vs.T[1–4].Insuchananalysis,theglasstransitiontemperature,,iscommonlytakentobethetemperatureatwhichtherelaxationtimeassumessomearbitrarylongvalue,e.g.,100s.Inadditiontobeingausefulmetricoftemperaturesensitivity,thefragilityisofinterestbecauseofitscorrelationtootherpropertiesofthematerial,suchasthebreadthoftherelaxationfunction[5],thechemicalstructure[6–9],diffusionpropertiesinthesuper-cooledregime[10,11],Poisson’sratiooftheglass[12],vibrationalmotions[13],Brillouinscatteringintensities[14,15]andeventononlinearbehaviorintheglassystate[16,17].Althoughfragilitiesareusuallydeterminedfromrelaxationmeasurements(e.g.,as dTT(/)isthedielectricormechanicalrelaxationtime),thekineticsoftheglasstransition,asinfluencedbythedeparturefromequilibriumduringcooling,canberelatedtothelocalrelaxationdynamicsandhencetofragility[18].Uponcoolingthroughtheenthalpydepartsfromitsequilibriumvalue,withthenonequilibriumstateidentifiedbyitsfictivetem.Thefictivetemperatureisdefinedasthetemperatureatwhichthenonequilibriumglasswouldbeinequilibrium[19–21].Thedegreeofdeparturefromequilibrium,andhence,dependontherateof.Thus,thevariationofthefictivetempera-ture,determinedfromtheheatcapacitymeasureddur-ingheatingfollowingcoolingatvariousrates,canbeusedtodefineanenthalpicfragility.Pastwork,usingconventionalDSC,hasshowngoodcorrespondencebetweenenthalpicandrelaxationmeasuresoffragili-ties[22–24].Morerecently,TMDSChasbeenusedtostudytheglasstransition[25–27],andinparticularetal.usedMDSCtomeasureenthalpicfragilities[28,29].Intheirmethod,thefrequencyofthetemperatureoscillationwasvariedwiththeconsequentchangeinusedtocalculatefragility.Thus,thisapplicationofMDSCissimilartoalternatingcurrentcalorimetry,asdevelopedbyBirgeandNagel[30,31].AdrawbacktotheMDSCmethodofetal.isthatthefrequencyrangeislimitedtoaboutonedecade,duetotherequirementforsufficientdatasamplingoveraperiodofthetemperatureoscillation[29].InthepresentworkweutilizeMDSCtodetermineenthalpicfragilitiesfromthedependenceofthefictivetemperatureoncoolingrate.Thus,afixedoscillationfrequencyisused,andthedynamicrangeofthemethodisgovernedbytherangeofaccessiblecoolingrates.Thiscanroutinelyextendto2decades.Theexperimentswerecarriedoutonaseriesofpolychlorinatedbiphenyls(PCB),varyinginchlorineAkadémiaiKiadó,Budapest,Hungary©2006AkadémiaiKiadó,BudapestSpringer,Dordrecht,TheNetherlandsJournalofThermalAnalysisandCalorimetry,Vol.83(2006)1,87–90ENTHALPYRELAXATIONANDFRAGILITYINPOLYCHLORINATEDC.M.RolandandR.CasaliniChemistryDivision,Code6120,NavalResearchLaboratory,Washington,DC20375-5342,USAGeorgeMasonUniversity,ChemistryDepartment,Fairfax,VA22030,USAWeemploytemperaturemodulatedDSC(TMDSC)todeterminethedependenceofthefictivetemperatureoncoolingrateforaseriesofpolychlorinatedbiphenyls(PCB).Fromtheslopesofsemi-logarithmicplotsofcoolingrate.fictivetemperature,thelatternormalizedbythefictivetemperatureforanarbitrarycoolingrate,wedeterminetheenthalpicfragilities.Despitesignificantdifferencesinglasstransitiontemperatureandchemicalstructure(specificallychlorinecontent),thePCBhavethesamefragility.ThevalueofthefragilitydeterminedusingTMDSCisconsistentwiththefragilitypreviouslydeterminedusingdielectricrelaxationchlorinatedbiphenyl,fragility,glasstransition,PCB,TMDSC *Authorforcorrespondence:roland@nrl.navy.mil Downloaded from http://polymerphysics.net Downloaded from http://polymerphysics.net content.PCBarecongenerandisomermixtures,withdeterminedbytheaveragechlorinecontent.Especiallyintriguingisthatthefragility,asdeterminedbydielectricspectroscopyatatmosphericpressure,isthesameforPCBhavingchlorinecontentsrangingfrom42to62mass%[32].Thepresenceofpolar,bulkychlorineatomswouldbeexpectedtoincreaseintermolecularcooperativity,andhenceincreasethefragility[9].Thus,weuseTMDSCtodetermineenthalpicfragilitiesonthreePCB,andcomparethesevaluestotheresultsfromrelaxationmeasurements.Samplesemployedhereinwerepolychlorinatedbiphenyls(MonsantoAroclors),obtainedfromJ.SchragoftheUniversityofWisconsin.Thesamplesaredesignatedbytheirmass-averagechlorinecontent,PCB42,PCB54andPCB62.TMDSCwascarriedoutusingaTAInstrumentsQ100,usingliquidnitrogencooling.Sampleswerecooledfromtheliquidstateto50°Cbelow,at,from0.1to10Cmin.After5min,thiswasfollowedbyheatingat2Cmin.Thetemperaturemodulationwas0.5°C,witha40speriod.Theabsolutevalueoftheheatcapacitywasobtainedaftercalibrationusingasyntheticsapphire[33].InFig.1aredisplayedrepresentativeTMDSCdataforPCB42.Thecurveforthetotalheatcapacity(Fig.1a)showstheusualovershootduetoenthalpyrecovery.Thiskineticcomponentisisolatedinthenonreversingheatcapacitycurve(Fig.1c),whosepeakreflectsthedegreeofdeparturefromequilibriumduringthecooling.Integrationofthispeakyieldsanareausedtocalculatethefictivetemperature.Withdecreasingcoolingrate,thereisalargerovershootinthetotalheatflowcurve,andacorrespondingincreaseinthepeakofthenonreversingheatflow.Thereversingheatca-pacityisessentiallyinvarianttoFromthereversingheatflowcurveinFig.1b,wecalculatetheheatcapacityfortheglassandtheequilibriumliquid.Overtherangeoftemperaturemeasuredherein(ca.50°Coneithersideof),boththeglassyandliquidheatcapacitycanberepresentedbyalinearfunctionoftemperatureCabTwiththebest-fitparametersforthethreePCBgiveninTable1.Todeterminethe(cooling-ratedependent)fictivetemperatures,weconstructaparallelogram,havingverticalsidesdefinedbytherespectiveglassyandliquid.Theboundaryonthehightemperaturesideisdefinedbytheinflectionofthereversingheatflowcurve.Thisquantityisthecommon,determinedbyconventionalDSC;itsvalueisgiveninTable1foracoolingrateequalto2CminFigure2illustratesthemethodforobtainingasthelocationofthelowtemperaturesideoftheparallelogram,suchthattheareaisequalofthepeakinthecorrespondingnon-reversingheatflowcurve.Obviously,,exceptfortheliquidinequilibrium,J.Therm.Anal.Cal.,83,2006ROLAND,CASALINI Fig.1a–TotalheatcapacityforPCB42,measuredduringheatingat2Cmin,followingcoolingattherates=5,2,0.5,0.2and0.1Cmin;b–reversingcomponentoftheheatcapacity,alongwiththefitstoEq.(1)intheglassyandliquidstates;c–nonreversingheatflowcurves,whichexhibitapeakwhoseintensityisameasureofthestructuralrecoveryTable1Glasstransitiontemperature,fictivetemperature,fitsofthereversingheatcapacitydata,andfragilitydeterminedforthethreePCB/Jg/Jg/Jg/JgPCB42225.1217.50.6646.1·100.4091.19·10PCB54252.7245.00.6105.4·100.4091.41·10274.3265.00.2736.3·10 =2°Cminequation1 forwhichthefictivetemperaturebecomestheglasstransitiontemperature.Thedependenceofthefictivetemperatureoncoolingrateyieldsanapparentactivationenthalpyforstructuralrecovery[18].Theslopeofsemi-logarith-micplotsofasafunctionoftheinversefictivetem-peraturenormalizedbyareferencetemperaturede-finesanenthalpicfragility, d(Tf,refForthereferencetemperature,f,ref,weusethefictivetemperaturemeasuredforCmin.Thisisarelativelyslowcoolingrate,correspondingtoalargervalueofthestructuralrecoverytime.ResultsforthethreePCBaredisplayedinFig.3.Overtherangeofthemeasurements(twodecadesofcoolingrate),thedataareroughlylinear;thatis,isnotafunctionoftemperature(althoughitisafunctionoff,ref).ThearegiveninTable1.Wefindthatwithintheexperimentalerror,thefragilityisindependentofthechlorinecontentofthePCB,6.DielectricspectroscopyresultsonthesesamePCBhavebeenreported,andsimilarlyisthesameforthedifferentPCB[32,34].Inthesamefashionthattheenthalpicfragilityvarieswith,therelaxationmeasuresofdependonthevalueoftherelaxationtimeusedtodefinethereferencetemperature.Usingf,ref=100s),dielectricspectroscopyyields=63[32],whilef,ref=10s)=58[34].ThelargervalueofasmeasuredbyMDSCreflectsthefactthatthestructuralrecoverytimeCminislongerthan100s.(Notethatvarious‘rulesofthumb’havebeenproposed;e.g.,Cmin=38s[16]and10Cmin=100s[3]).Ifweusedataforahighercoolingratetodefinef,refCmindecreasesfrom78to69.Highercoolingrates,necessarytomorecloselymatchthedi-electricdata,lacksufficientprecisionforareliabledeterminationofMDSCprovidesafacilemeanstodeterminethefragil-ity,oneoftheimportantcharacteristicsofthesuper-cooleddynamicsofglass-formingliquids.Inconven-tionalDSCexperiments,theequilibriumheatflowisconvolutedwiththeenthalpyrecovery.MDSCavoidsthisproblem,allowingthefictivetemperaturetobedeterminedinamorestraightforwardmanner.Inthisstudy,wefoundthatforpolychlorinatedbiphenyls,thefragilityextractedfromtheenthalpykineticsisconsistentwithdeterminationsfromdielectricrelaxationspectroscopy.TheunusualfeatureofthePCBisthattheirfragilityisindependentofchlorinecontent.ThisinvarianceofthefragilityisconsistentwiththeequivalenceoftherelaxationfunctionsforthePCB[32],butsurprisinggiventheexpectedconnectionbetweenchemicalstructureandrelaxationproperties[9].Thislackofcorrelationbetweenmolecularstructureandfragilityarisesfromthefactthatthelattermetricreflectsbothvolume(density)andtemperaturecontributions.Aswehaverecentlyshowed,especiallyfornon-polymericglass-formers,suchasPCB,volumeexertsastronginfluenceonthedynamics[35,36].Moreover,arecentinvestigationfoundthatthecontributionofvolumetotheglasstransitiondynamicsincreaseswithincreasingchlorinecontentofPCB[34,37].ItisonlywhentheisochoricfragilityisJ.Therm.Anal.Cal.,83,2006ENTHALPYRELAXATIONANDFRAGILITYINPOLYCHLORINATEDBIPHENYLS Fig.2Reversingheatcapacitycurve(lowerpanel)forPCB42duringheatingat2Cmin,followingcoolingatCmin,todepictthemethodusedtocalculatethefictivetemperature,istakenastheinflectionpoint,isdefinedfromtheparallelogramhavinganareaequaltotheintegralintensityofthepeakinthenonreversingheatcapacitycurve(upperpanel) Fig.3InversecoolingrateasafunctionofinversefictivetemperaturenormalizedbyCmin–PCB54and––PCB62.TheslopesyieldthefragilitieslistedinTable1 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DOI:10.1007/s10973-005-7221-7J.Therm.Anal.Cal.,83,2006ROLAND,CASALINI