Fundamentals of Polymer Engineering Part 13 doc

... Inc.12.12.ThePMMAsampleofExample12.5andProblem12.11isstretchedinuniaxialtension.Willshearyieldingorcrazingoccurfirst?Atwhatvalueofs1?12 .13. Apolystyrenesampleofunitvolumeissubjectedtoafatiguetestatatemperatureof50Candfrequencyof10Hz.UsethedataofFigures12.7and12.15toestimatetheinitialrateoftemperatureriseinthesample.Assume ... Inc.FIGURE 12.8 Effect of temperature on the stress–strain cur ves of polystyrene melts.(From Ref. 13. )FIGURE 12.9 Qualitative effect of temperature on the elastic modulus of polymers.496 Chapter ... Inc.mentionedinChapter2.Torecapitulate,thepolymerfreevolumeisthedifferenceinthesamplevolumeandtheactualvolumeoccupiedbytheatomsandmolecules.Thefreevolumeiszeroatabsolutezerotemperatureanditincreasesasthetemperatureincreases.Slowcoolingallowsforacloserapproachtoequilibriumandalowerfreevolumerelativetomaterialsubjectedtorapidcooling.Thus,theslowlycooledsamplehastobeheatedtoahighertemperatureinorderthattherebeenoughfreevolumeforthemoleculestomovearound,andthisimpliesahigherTg.InadditiontochangesinTgwithcoolingrate,wealsoobservevolumerelaxationwhenapolymersamplethatwasrapidlycooledissubsequentlyheatedtoatemperatureclosetoTgandheldthereforsometime.Materialshrinkagealsooccurs,accompaniedbychangesinthemechanicalpropertiesofthesolidpolymer.Thephenomenonisknownasphysicalaging[15]andisthesubjectofconsiderableresearchbecauseofitsinfluenceonpropertiessuchascreep[16].Theglasstransitiontemperatureofapolymerdependsonanumberoffactors,includingthepolymermolecularweight.Themolecular-weightdepen-dencecanbeseeninFigure12.11,wheretheTgofpolystyreneisplottedasafunctionofthenumber-averagemolecularweight[3,17].Thesedatacanberepresentedmathematicallybythefollowingequation[18]:Tg¼Tg1KMMnð12:3:1ÞThisvariationofTgwithmolecularweightcanagainberelatedtothefreevolume[19].Asthemolecularweightdecreases,thenumberdensityofchainendsincreases.BecauseeachchainendisassumedtocontributeafixedamountoffreeFIGURE12.10Variationofvolumeorenthalpyofpolymerswithtemperature.498Chapter...

... A., and D. H. Sebastian, Principles of Polymerization Engineering, Wiley, New York, 1983.4. Kumar, A., and S. K. Gupta, Fundamentals of Polymer Science and Engineering, TataMcGraw-Hill, New ... Experimental Validation of ReversiblePolymerization, Ph.D. thesis, Department of Chemical Engineering, Indian Institute of Technology, Kanpur, India, 1988.Step-Growth Polymerization 143Copyright ... 3.1. As a matter of fact, one of the practical methods of achieving a PDI of more than 2 is to partiallyrecycle a portion of the product stream, as shown in Figure 3.4 [19–22].Polymerization...

... !1:39¼14;876Inclosingthissection,wenotethat,fromEq.(8.6.8),½ZM=NAisthevolumeofapolymermoleculemultipliedby2.5,whereascNA=Misobviouslythenumberofpolymermoleculesperunitvolume.Asaconsequence,½Zc,whichistheproductofthesetwoquantities,representsthevolumefractionofpolymermultipliedby2.5.Ifthisnumberissmallcomparedtounity,thepolymersolutionisconsideredtobedilute;ifitisoftheorderofunity,thesolutionisconsideredmoderatelyconcentratedwithanearcertaintyofintermolecularinteractions.8.7GELPERMEATIONCHROMATOGRAPHYThesimplestconceptualmethodofdeterminingthemolecularweightdistributionofapolymersampleistoseparatethepolydispersesampleintoitsconstituentfractionsandthenmeasurethemolecularweightofeachfractionusinganyofthetechniquesdiscussedsofar.Thisisexactlywhatusedtobedoneuntilthecommercializationinthemid-1960softheprocedureknownasgelpermeationchromatography(GPC)orsize-exclusionchromatography.Intheoldmethod,apolymerinsolutionwasfractionatedeitherbythesequentialadditionofnonsolventsorbytheprogressiveloweringoftemperature(seeChapter9forthetheoryofpolymer–polymerphaseequilibrium).However,thiswasaverytediousandtime-consumingprocessthatwasobviouslyill-suitedtoroutinelaboratoryprocedures.ThenewmethodofGPCusesthefactthatlargepolymermoleculesareexcludedfromthesmallchannelsinaporousgel,withtheresultthatdifferentmolecularweightfractionstraveldownacolumnpackedwiththeporousmediumatdifferentrates,leadingtoseparationbasedonsize.AschematicdiagramofaGPCsetupisshowninFigure8.11.Solventismade ... Inc.alkali.Ifablanksolutionofthebenzylalcoholpluschloroformrequired5mLofthebase,howmanycarboxylendgroupswerecontainedinthepolymersample?Solution:Because30mLof0.105gramequivalentperliterofthebasereactedwiththepolymer,theconcentrationofgramequivalentsofendgroupswasð30Þð10À6Þð0:105Þ0:15¼21Â10À6equivalentspergram8.3COLLIGATIVEPROPERTIESItiseasilyobservedthatdissolvinganonvolatilesoluteinaliquidresultsinadepressionofthefreezingpoint;thatis,thetemperatureatwhichasolidphaseisformedfromsolutionislowerthanthetemperatureatwhichthepuresolventfreezes.Thisistheprincipleatworkinanicecreammakerandinsnowremovalwhensaltisusedtomeltandtherebyremovesnowandicefromroads.Besidesloweringthefreezingpoint,theadditionofanonvolatilesolutealsoreducesthevaporpressureatagiventemperature,withtheconsequencethatthesolutionboilsatahighertemperaturethanthepuresolventdoes.Furthermore,asolutioncandevelopalargeosmoticpressure(explainedlater),whichcanbemeasuredwithrelativeease.Thesefoureffects—depressionoffreezingpoint,elevationofboilingpoint,loweringofsolventvaporpressure,anddevelopmentofanosmoticpressure—arecalledcolligativepropertiesandtheydependonlyonthenumberconcentrationofthesoluteinsolutioninthelimitofinfinitedilution.Thus,beginningwithaknownmassofsolute,aknowledgeofanyofthesecolligativepropertiesrevealsthetotalnumberofmoleculesinsolution,which,inturn,allowscomputationofthenumber-averagemolecularweight.However,therelativemagnitudeoftheseeffectsissuchthatasthemolecularweightofthesoluteincreasesandthenumberofmoleculesinagivensamplemassdecreases,notallfourcolligativepropertiescanbemeasuredwithequalaccuracyorease;indeed,membraneosmometryisthemethodofchoiceformeasuringthenumber-averagemolecularweightofhighpolymers.Phaseequilibriumisthebasicprincipleusedtoobtainexpressionsforthemagnitudeofthedifferentcolligativeproperties.Itisknownfromthermo-dynamicsthatwhentwophasesareinequilibrium,thefugacity,^ff,ofagivencomponentisthesameineachphase.Thus,if,asshowninFigure8.1,purevaporA ... distribution as a function of the logarithm of thedegree of polymerization.Measurement of Molecular Weight 373Copyright © 2003 Marcel Dekker, Inc.eredlater)andifthesizeofthescatteringparticlesissmallcomparedtothewavelengthoftheincidentlight,thenwehavethefollowing[15]:IyI0¼2p2ð1þcos2yÞðdn=dcÞ2McNAl4r2ð8:4:1Þinwhichnistherefractiveindexofthegas,cisthemassconcentration,NAisAvogadro’snumber,andMisthemolecularweightoftheparticles.Accordingtothisequation,whichisknownastheRayleighequation,ifNisfixed,thescatteringintensityisproportionaltothesquareofthemolecularweightbecausecequalsNM=NA.Thus,iftherewereamixtureoftwokindsofparticles,withonekindbeingmuchlargerthantheother,thecontributionofthelargerparticlestothescatteredlightintensitywouldbethedominantone.Thisfactisusedtogreatadvantageindeterminingthemolecularweightofpolymericsolutesinsolution.Inthissituation,forlightscatteringfromanidealpolymersolution,Eq.(8.4.1)ismodifiedtoreadasfollows[15]:IyI0¼2p2ð1þcos2yÞn20ðdn=dcÞ2cNAl4r2=Mð8:4:2Þinwhichn0istherefractiveindexofthesolventandnnowbecomestherefractiveindexofthesolution,whereasMisthemolecularweightofthepolymerandcitsmassconcentration.Equation(8.4.2)isvalidonlyatinfinitedilution.Forfiniteconcentrations,theuseofavirialexpansionofthetypeintroducedinEq.(8.3.22)leadstoIyI0¼2p2ð1þcos2yÞn20ðdn=dcÞ2cNAl4r2ð1=Mþ2A2cþ3A3c2þÁÁÁÞð8:4:3ÞandEq.(8.4.3)properlyreducestoEq.(8.4.2)whenctendstozero.Formostpolymermolecules,thelimitationthattheparticlesizebemuchsmallerthanthewavelengthoflight,which,inpractice,meansthatallmoleculardimensionsshouldbelessthanl=20,istoorestrictive.Whentheparticlesizebecomescomparabletothewavelengthoftheincidentbeam,scatteringoccursfromdifferentpartsofthesamemolecule,resultingininterferenceduetophasedifferences.ThistendstoprogressivelyreduceIyasyincreases.TheresultcanbeseeninTable8.2,whichlistsdataforpolystyrene-in-toluenesolutions.However,because...

... value of De or,equivalently, of the interaction parameter is needed to assure polymer polymer miscibility.Example 9.4: If the 1 g of polymer of Example 9.1 is diss olved in 9 g of adifferent polymer ... and composed of a series of segments the size of a solvent molecule.The number of segments in each polymer molecule is m, which equals V2=V1,theratio of the molar volume of the polymer to ... 1n0mÀ1ð9:3:2ÞThe total number of ways of arranging all of the n2 polymer molecules, Op,istheproduct of the number of ways of arranging each of the n2molecules in sequence.This...

... Chapter 13 Copyright © 2003 Marcel Dekker, Inc. 13 PolymerDi¡usion 13. 1INTRODUCTIONInengineeringpractice,weroutinelyencounterthediffusionofsmallmoleculesthroughsolidpolymers,thediffusionofpolymermoleculesindiluteorconcen-tratedsolution,andthetransportofmacromoleculesthroughpolymermelts.WecameacrossdiffusionindilutesolutionwhenwedevelopedthetheoryoftheultracentrifugeinChapter8asamethodofdeterminingpolymermolecularweight. ... Inc.whichsaysthatMðtÞ=M1isauniquefunctionofDt=L2.Here,ierfcðxÞisgivenbyð1=ffiffiffippÞeÀx2Àxð1ÀerfxÞ.OnplottingEq. (13. 3.18),wefindthat[18,34]MðtÞM1¼2DtpL21=2 13: 3:19ÞuntilthepointthatMðtÞ=M1equals0.5.ThislinearrelationshiponlogarithmiccoordinatesfacilitatestheevaluationofDfromexperimentaldata.Detailsofhowwemightconductsuchexperimentsabovethepolymerglasstransitiontempera-turehavebeenprovidedbyDudaetal.[35].DudaandVrentashavealsoshownhowwemightdeterminetheconcentrationdependenceofdiffusioncoefficientsfromaminimumamountofdatafromsorptionexperiments[36].Equations (13. 3.18)and (13. 3.19)havebeenemployedbyShahetal.todeterminethediffusivityofwaterinvinylesternanocomposites[37].AsdiscussedinChapter11,nanocompositesaremadebydispersingplateletsofmontmorrilonite(clay)inpolymer,andFigure13.6,takenfromtheworkofShahetal.,showsindividualplateletsintheformofdarklines.Rectangularsamplesofthenanocompositewereimmersedin25Cwater,andtheincreaseinweightwasnotedwithincreasingtimeofimmersion.Representativesorptionresultsfornanocompositescontaining0.5wt%clayareshowninFigure13.7,and,asexpected,dataonsamplesofdifferentthicknessessuperposewhenplottedasMðtÞ=M1versust1=2=L.ThevalueofthediffusioncoefficientcomputedusingEq. (13. 3.19)canbeinsertedintoEq. (13. 3.18)togivethecompletetheoreticalcurve,andthisisalsoshowninFigure13.7;thefitbetweenFickiantheoryandexperimentisexcellent.Itisalsoremarkablethattheadditionofsuchaminuteamountofclayisfoundtoreducethemoisturediffusioncoefficientby50%.Inthecaseofadesorptionexperiment(duringthefinalstages),theequivalentformofEq. (13. 3.18)isgivenbythefollowing[18]:ddtfln½MðtÞÀM1g¼Àp2D4L2 13: 3:20Þandaplotofln½MðtÞÀM1versustimeshouldapproachastraightline,whoseslopeisgivenbytheright-handsideofEq. (13. 3.20).Theuseofthistechniquefordiffusivitymeasurementisillustratedinthenextexample.ExtensivedataonthediffusioncoefficientofgasesandvaporsinpolymerscanbefoundinthebookeditedbyCrankandPark[18,34].Example13.5:Figure13.8showsthegravimetricdataofSaleemetal.forthedesorption of chloroform from a 0.15-mm-thick film of ... þd2¼d22tdcAdx 13: 9:2ÞFIGURE 13. 17 Reptation in a polymer melt.FIGURE 13. 18 Model of the diffusion process.562 Chapter 13 Copyright © 2003 Marcel Dekker, Inc.Solution:TheslopeofthestraightlineinFigure13.8isln10À2Àln10À1ð120À70Þ60¼À7:68Â10À4andthismustequalÀp2D=ð0:015Þ2.Asaresult,D¼1:75Â10À8cm2=sec. 13. 4DIFFUSIVITYOFSPHERESATINFINITEDILUTIONTheoreticalpredictionofthediffusioncoefficientofspheresmovingthroughalow-molecular-weightliquidisaproblemthatwasexaminedbyEinsteinattheturnofthiscentury[39].Thissituationisofinteresttothepolymerscientistbecauseisolatedpolymermoleculesinsolutionactasrandomcoils.Theanalysisbeginsbyshowingthattheosmoticpressureisthedrivingforcefordiffusion.ThisisdonebycarryingouttheexperimentillustratedinFIGURE13.7Watersorptioncurveat25CforthenanocompositeshowninFig .13. 6.(From...

... Inc.inwhichmandUareasyetunspecifiedfunctions,wegetthefactorableformoftheKaye–BKZequation[52,53]:~t¼ðtÀ1mðtÀt0Þ2@U@I1~CÀ1À2@U@I2~Cdt0ð14:10:23ÞBecausemandUareunspecifiedfunctions,ititpossibletopredictmostobservedrheologicalphenomenabypickingspecificfunctionalformsforthesequantities[7].AparticularformofEq.(14.10.23)thatdeservesspecialmentionistheoneresultingfromthetheoryofDoiandEdwards[54]andbasedonthereptationideaofdeGennes[32].Theseauthorsassumedthatupondeformationofthepolymer,stressrelaxationtookplacebytwoseparatemechanisms.Inthefirstinstancetherewasarapidretractionofthechainwithinthedeformedtube(seeFigure 13. 15ofChap .13) ,andinthesecondinstance,therewasslowdiffusionofthechain out of the original tube by the process of reptation. Within the confines of the ... Inc.adiscrete-relaxationtimespectrum,andwetypicallychoosebetweenoneandtworelaxationmodesperdecadeoffrequency.Figure14.14showsamastercurveofG0andG00valuesinatemperaturerangeof130–250Conaninjection-moldinggradesampleofpolystyrene;allofthedatahavebeencombinedbymeansofahorizontalshiftusingtime–temperaturesuperpositionwitha150CreferencetemperatureaccordingtotheprocedureofSection12.5.Thestress–relaxationmodulus(calculatedinthemannerofBaumgaertelandWinter)isdisplayedinFigure14.15alongwithactualstress–relaxationdataat150C;theagreementcouldnotbebetter.Theutilityofdynamicdataappearstogobeyondthetheoreticalapplica-tionsconsideredinthissection.Wefind,forexample,thatthemodulusofthecomplexviscosityZ*,definedasjZ*j¼½ðZ0Þ2þðZ00Þ21=2ð14:7:11ÞwhereZ0¼G00=oandZ00¼G0=o,whenplottedversusfrequency,oftensuper-poseswiththesteadyshearviscosityasafunctionoftheshearrate[19].ThisisknownastheCox–Merzrule,anditprovidesinformationaboutanonlinearpropertyfromameasurementofalinearproperty.NotethatZ0isgenerallycalledthedynamicviscosity.FIGURE14.14Mastercurveofstorageandlossmoduliofpolystyrene.Flow ... Inc.Ashear-thinningviscosityisnottheonlynon-Newtonianfeatureofthebehaviorofpolymericfluids;severalotherunusualphenomenaareobserved.If,inthesituationdepictedinFigure14.2,theshearrateissuddenlyreducedtozeroaftertheattainmentofasteadystate,low-andhigh-molecular-weightliquidsagainbehavedifferently.ThestressintheNewtonianfluidgoestozeroinstantly,butittakessometimetodisappearinthepolymer.Thetimescaleoverwhichthisstressrelaxationoccursisknownastherelaxationtimeandisdenotedbythesymboly.Additionally,ifasmall-amplitudesinusoidalstrainisimposedonthe polymer, theresultingstressisneitherinphasewiththestrainnoroutofphasewiththestrain:Thereisanout -of- phasecomponentrepresentingenergydissipa-tionandanin-phasecomponentrepresentingenergystorage(seeSect.12.4).Bothstressrelaxationandthephasedifferenceindynamicexperimentsareelasticeffects;wesaythatthepolymersarebothviscousandelastic(i.e.,viscoelastic).Intime-dependentflow,therelativeextentofthesetwoeffectsdependsonthevalueofthedimensionlessgroupknownastheDeborahnumber(De)anddefinedasfollows:De¼yTð14:1:1ÞwhereTisthecharacteristictimeconstantfortheprocessofinterest.ForlowvaluesofDe,thepolymerresponseisessentiallyliquidlike(viscous),whereasforhighvalues,itissolidlike(elastic).Afurthermanifestationofviscoelasticityistheswellingofajetofpolymeronemergingfroma‘‘die’’orcapillary.ThisisshowninFigure14.3.Dieswell,orjetswell,canbesuchthatDj=Deasilyexceeds2;thecorrespondingNewtonianvalueis1 .13. Thisistrueatverylowflowrates.Athighflowrates,dieswellreducesbutunstablebehaviorcalledmeltfracturecanoccur.Thejetcanbecomewavyorthesurfacecanbecomegrosslydistorted,assketchedinFigure14.4;theextentofdistortionisalsoinfluencedbythegeometryofthecapillary,itssurfacecharacter,andthepropertiesofthe polymer. NotethatmeltfractureisneverobservedwithNewtonianliquids.Thephenomenajustdescribedareinterestingtoobserveandexplain.Aquantitativedescriptionofthemis,however,essentialfordevelopingmodelsofFIGURE14.3Thedie-swellphenomenon.Flow...

... Inc.6.4RecyclingandDegradationofPolymers2856.5Conclusion287Appendix6.1:SolutionofEquationsDescribingIsothermalRadicalPolymerization287References293Problems2947.EmulsionPolymerization2997.1Introduction2997.2AqueousEmulsifierSolutions3007.3SmithandEwartTheoryforStateIIofEmulsionPolymerization3047.4EstimationoftheTotalNumberofParticles,Nt 313 7.5MonomerConcentrationinPolymerParticles,[M]3157.6DeterminationofMolecularWeightinEmulsionPolymerization3197.7EmulsionPolymerizationinHomogeneousContinuous-FlowStirred-TankReactors3247.8Time-DependentEmulsionPolymerization3267.9Conclusions334References335Problems3368.MeasurementofMolecularWeightandItsDistribution3408.1Introduction3408.2End-GroupAnalysis3428.3ColligativeProperties3438.4LightScattering3508.5Ultracentrifugation3548.6IntrinsicViscosity3588.7GelPermeationChromatography3648.8Conclusion369References369Problems3719.ThermodynamicsofPolymerMixtures3749.1Introduction374xiv ... Inc.12.MechanicalProperties48712.1Introduction48712.2Stress-StrainBehavior48812.3TheGlassTransitionTemperature49712.4DynamicMechanicalExperiments50112.5Time-TemperatureSuperposition50412.6PolymerFracture50812.7CrazingandShearYielding51112.8FatigueFailure51612.9ImprovingMechanicalProperties518References520Problems523 13. PolymerDiffusion526 13. 1Introduction526 13. 2FundamentalsofMassTransfer527 13. 3DiffusionCoefficientMeasurement531 13. 4DiffusivityofSpheresatInfiniteDilution542 13. 5DiffusionCoefficientforNon-ThetaSolutions546 13. 6Free-VolumeTheoryofDiffusioninRubberyPolymers547 13. 7GasDiffusioninGlassyPolymers552 13. 8OrganicVaporDiffusioninGlassyPolymers:CaseIIDiffusion557 13. 9Polymer- PolymerDiffusion560 13. 10Conclusion564References565Problems56914.FlowBehaviorofPolymericFluids57314.1Introduction57314.2ViscometricFlows57614.3Cone-and-PlateViscometer57814.4TheCapillaryViscometer58414.5ExtensionalViscometers58914.6BoltzmannSuperpositionPrinciple59214.7DynamicMechanicalProperties59514.8TheoriesofShearViscosity598xvi ... Inc.12.MechanicalProperties48712.1Introduction48712.2Stress-StrainBehavior48812.3TheGlassTransitionTemperature49712.4DynamicMechanicalExperiments50112.5Time-TemperatureSuperposition50412.6PolymerFracture50812.7CrazingandShearYielding51112.8FatigueFailure51612.9ImprovingMechanicalProperties518References520Problems523 13. PolymerDiffusion526 13. 1Introduction526 13. 2FundamentalsofMassTransfer527 13. 3DiffusionCoefficientMeasurement531 13. 4DiffusivityofSpheresatInfiniteDilution542 13. 5DiffusionCoefficientforNon-ThetaSolutions546 13. 6Free-VolumeTheoryofDiffusioninRubberyPolymers547 13. 7GasDiffusioninGlassyPolymers552 13. 8OrganicVaporDiffusioninGlassyPolymers:CaseIIDiffusion557 13. 9Polymer- PolymerDiffusion560 13. 10Conclusion564References565Problems56914.FlowBehaviorofPolymericFluids57314.1Introduction57314.2ViscometricFlows57614.3Cone-and-PlateViscometer57814.4TheCapillaryViscometer58414.5ExtensionalViscometers58914.6BoltzmannSuperpositionPrinciple59214.7DynamicMechanicalProperties59514.8TheoriesofShearViscosity598xvi...

... molecular structure of the graft copolymer and the number of grafts formed. In addition, the length of the graft may vary, and the graftcopolymer often carries a fair amount of homopolymer.The ‘‘graft-onto’’ ... classification of polymers is based on molecularstructure. According to this system, the polymer could be one of the following:1. Linear-chain polymer 2. Branched-chain polymer 3. Network or gel polymer It ... Inc.values.TheendchemicalgroupsXandYcouldbethesameordifferent,andwhattheyaredependsonthechemicalreactionsinitiatingthepolymerformation.Uptothispoint,ithasbeenassumedthatalloftherepeatunitsthatmakeupthebodyofthepolymer(linear,branched,orcompletelycross-linkednetworkmolecules)areallthesame.However,iftwoormoredifferentrepeatunitsmakeupthischainlikestructure,itisknownasacopolymer.Ifthevariousrepeatunitsoccurrandomlyalongthechainlikestructure,thepolymeriscalledarandomcopolymer.Whenrepeatunitsofeachkindappearinblocks,itiscalledablockcopolymer.Forexample,iflinearchainsaresynthesizedfromrepeatunitsAandB,apolymerinwhichAandBarearrangedasiscalledanABblockcopolymer,andoneofthetypeiscalledanABAblockcopolymer.Thistypeofnotationisusedregardlessofthemolecular-weightdistributionoftheAandBblocks[7].Thesynthesisofblockcopolymerscanbeeasilycarriedoutiffunctionalgroupssuchasacidchloride(COCl),amines(...

... Inc.higherthehardnessandmodulus.Anotherfactorthatplaysamajorroleindeterminingthefinalpropertyofthepolymeristhechemicalnatureofthesurface.Mineralfillerssuchascalciumcarbonateandtitaniumdioxidepowderoftenhavepolarfunctionalgroups(e.g.,hydroxylgroups)onthesurface.Toimprovethewettingproperties,theyaresometimestreatedwithachemicalcalledacouplingagent.Couplingagentsarechemicalsthatareusedtotreatthesurfaceoffillers.Thesechemicalsnormallyhavetwoparts:onethatcombineswiththesurfacechemicallyandanotherthatiscompatiblewiththepolymer.Oneexampleisthetreatmentofcalciumcarbonatefillerwithstearicacid.Theacidgroupofthelatterreactswiththesurface,whereasthealiphaticchainsticksoutofthesurfaceandiscompatiblewiththepolymermatrix.Inthesameway,ifcarbonblackistobeusedasafiller,itisfirstmixedwithbenzoylperoxideinalcoholat45Cforatleast50handsubsequentlydriedinvacuumat11C[5].ThisactivatedcarbonhasbeenidentifiedashavingCÀOHbonds,whichcanleadtopolymerizationofvinylmonomers.Thepolymerthusformedischemicallyboundtothefillerandwouldthuspromotethecompatibilizationofthefillerwiththepolymermatrix.Mostofthefillersareinorganicinnature,andthesurfaceareaperunitvolumeincreaseswithsizereduction.Thenumberofsiteswherepolymerchainscanbeboundincreases,and,consequently,compatibilityimprovesforsmallparticles.Forinorganicfillers,silanesalsoserveascommoncouplingagents.SomeofthesearegiveninTable2.1.Themechanismofthereactionconsistsoftwosteps; ... Rosen, S. L., Fundamental Principles of Polymeric Materials, Wiley–Interscience,New York, 1982.3. Kumar, A., and S. K. Gupta, Fundamentals of Polymer Science and Engineering, TataMcGraw-Hill, New ... isfound to reduce with the degree of acetylation, the latter imparting higher strengthto the polymer. The main usage of the polymer is in the preparation of films andsheets. Films are used...

... application of a vacuum in order to obtain a polymer Reaction Engineering of Step-Growth Polymerization 169Copyright © 2003 Marcel Dekker, Inc.The total pressure PTis then the sum of partial ... condensation polymerization of two monomers A and B thatdo not mix. In such cases, the monomers diffuse to the interface andpolymerize there. Find the molecular weight of the polymer in terms of thediffusivities ... consistent with the equilibrium of polymerization. Try the formgiven in Eq. (3.5.2) first.4 .13. The rate of evaporation, Nw, of condensation product at y ¼ 0 in the film of Figure4.7isgivenbyNNw¼ðtft¼0D@W@yjy¼0dtAlso...