5. Time Temperature Superposition Principle 2013-14

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1、5.Time-TemperatureSuperpositionPrinciple·Itisthoughtthatthereisageneralequivalencebetweentimeandtemperaturedependenceoftheviscoelasticpropertiesofpolymers·Forinstanceapolymerthatdisplayrubberycharacteristicsunderagivensetoftestingconditionscanbeinducedtoshowglassybeh

2、aviourbyeither:⇒reducingthetemperature⇒increasingthetestingrateorfrequency5.Time-TemperatureSuperpositionPrinciple·Thistypeofbehaviourisseenbyexaminingthevariationoftheshearcompliance,J,ofapolymerwithtestingfrequencymeasuredatdifferenttemperaturesShearcompliance,J,da

3、taforpolyisobutyleneoverarangeoftemperatures(-35to80°C).5.Time-TemperatureSuperpositionPrinciple·Itwasfoundempiricallythatallthecurvescouldbesuperposedbykeepingonefixedandshiftingalltheotherbydifferentamounts(ashiftfactora)horizontallyparallelTtothelogwaxisExampleoft

4、hetime–temperaturesuperpositionprincipleusingshearcompliance,J,dataforpolyisobutylene.5.Time-TemperatureSuperpositionPrinciple·Theshiftfactoramaybedefinedasfollows:T⇒choosearbitraryreferencetemperatureTtofixonecurves⇒wisthefrequencyofapointonthecurveatTwithassparticu

5、larcompliance⇒ifwisthefrequencyofapointwiththesamecomplianceonacurveatadifferenttemperature,then:loga=logw-logw=log(w/w)Tss·Theshiftfactorisafunctionoftemperatureonly5.Time-TemperatureSuperpositionPrinciple·Muchoftheearlyworkontime-temperaturesuperpositionwasdonebyWi

6、lliams,LandelandFerryandtheyproposedthatacouldbegivenbyanequationoftheform:T-C(T-T)1sloga=TC+(T-T)2swhereCandCareconstantsandTisthereference12stemperature·ThisisnormallycalledtheWLFequationandholdsextremelywellinthevicinityoftheglasstransitionTg5.Time-TemperatureSupe

7、rpositionPrinciple·IfTistakenhasTmeasuredbyastaticmethodthen:sgg-C(T-T)1gloga=TgC+(T-T)2gandthenewconstantsCgandCgbecome‘universal’with12valuesof17.4and51.6Krespectively·TheWLFmastercurveisaveryusefulwayofpresentingthemechanicalbehaviourofapolymer·TheWLFequationisals

8、ousefulinpredictingthemechanicalbehaviourofapolymeroutsidetheexperimentalrangeoftemperatureandfrequency(ortime)available