第三章高分子溶液3.1高分子的溶解性判據(jù)3.5高分子凝膠的熱力學3.3稀溶液的熱力學性質和高分子構象3.4亞濃溶液的熱力學性質和高分構象3.2高分子溶液的熱力學-Flory-Huggins理論3.6聚電解質溶液3.9高分子溶液的流體力學性質3.7高分子共混物的熱力學3.8嵌段共聚物的熱力學初步Chapt.3PolymerSolutionsThesolutionprocesssolventpolymersampleswelledsamplepolymertruesolutionThisprocessisusuallyslowercomparedwithsmallmolecules,andstronglydependentonthechemicalstructuresandcondensedstatesofthesamples.

Crosslinkedpolymer:onlycanbeswelled. CrystallinePE:dissolveatthetemperatureapproachedtoits meltingtemperature. CrystallineNylon6,6:dissolvedatroomtemperaturebyusingthe solventwithstronghydrogenbonds.3.1Criteria(判據(jù))ofPolymerSolubilitySolubilityoccursonlywhentheDGmixisnegative.Gibbsfreeenergyofmixing(DE/v)cohesiveenergydensity(內聚能密度)d=(DE/v)1/2

:solubilityparameter(溶度參數(shù))

1-1+

2-2

1-2+1-21.Hildebrandenthalpyofmixing(混合焓)1:solvent;2:polymerP123.2ThermodynamicsofPolymerSolutions

(1)Entropyofmixingforidealsolution(2)EntropyofmixingforpolymersolutionsThelatticemodelassumesthatthevolumeisunchangedduringmixing.Eachrepeatingunitofthepolymer(segment)occupiesonepositioninthelatticeandsodoeseachsolventmolecule.Themixingentropyisstronglyinfluencedbythechainconnectivityofthepolymercomponent.Flory-Hugginstheory(LatticeModel(格子模型))體系中有N1個溶劑分子+N2個鏈段數(shù)為x的高分子總格子數(shù):N=N1+xN2已有j個高分子放入,剩下N-xj個空格,求第j+1個高分子的放置方式Wj+1???1.放置第j+1個高分子的第1個鏈段的概率N-xj2.放置第j+1個高分子的第2個鏈段的概率Z(N-xj-1)/N3.放置第j+1個高分子的第3個鏈段的概率(Z-1)(N-xj-2)/N….(Z-1)(N-xj-x+1)/Nx.放置第x個鏈段的概率1st2stN2stchainEntropyofmixingfromFHtheoryxthsegment1st4th3rd2ndZ

Z–1Entropyofsolution:總方式FreeEnergyofFHTheoryHugginsEnthalpy:GibbsFreeEnergy:摩爾數(shù)分子數(shù)一般通式ForPolymerSolutionsx1=1Chemicalpotentials(化學位):(forsolvent)(forpolymer)Inthecaseoff2<<1,c<1/2,goodsolventc=1/2,thetaQsolventc>1/2,poorsolventc=1/2,有熱效應的“理想溶液”???Osmoticpressure(滲透壓):PPolymersolutionpuresolventPP當f2>>1/x,即f22>>f2/x當f2<<1/x(0.5-c)或c=1/2secondVirialcoefficentPolymerShapesinDiluteSolutionsconcentrationP/RTcA2<0,>1/2;poorsolventA2>0,<1/2;goodsolventA2=0,=1/2;QconditionCoil-globuletransitionExpanded,unperturbed,andcollapsedchainsThecoil-globuletransitioninasolutionofpolystyreneincyclohexane.TheradiusofgyrationRgandthehydrodynamicradiusRhofthepolymershowadramaticchangeastemperaturepassesthroughtheQtemperature.(Sun,S.T.;etc.J.Chem.Phys.

1980,73,5971.)c~1/kT!!!3.3ChainConformationsinDiluteSolutionsidealchainrealchaininsolutions鏈包含的體積h3鏈段的體積vc(1)P(h)mnh一個鏈段占有的體積分數(shù)vc/h3其他鏈段不與之發(fā)生重疊的概率(1-vc/h3)整條鏈兩兩鏈段都不發(fā)生重疊的總概率體積排除修正能量權重修正溶液中真實單鏈的末端距概率分布函數(shù)W(h,x)(2)E(h)當c=1/2,理想高斯鏈2.Polymerchainingoodsolvents-

methodIITwobodyinteractionisveryimportantc<1/2h~x3/5twobodyinteraction:excludedvolumerepulsionsolvent-segmentinteractionsecondVirialcoefficentconformationentropy+Howtogetidealchain?c=1/2h2~N1QTemperatureQSolutionWhendoesthefreelyjointedchainworks－等效自由連接鏈“Coarse-grained”(粗?；?picture:R(2)降低高分子鏈的分辨率-消除局部剛性和旋轉不自由將鏈重新劃分成有效鏈節(jié)數(shù)Ne和有效鏈節(jié)長度lechain

headchainend(1)調節(jié)溶劑-鏈節(jié)的作用屏蔽掉體積排除效應和鏈節(jié)-鏈節(jié)相互作用達到Q溫度的溶液,測得無擾尺寸<h2>0~N溶劑排斥作用3.Polymerchaininpoorsolvents-MethodIITf2f’f”InPolymerrichPhase:ConcentrationinCoil:PolymerShapesinDiluteSolutions(1)Polymerinagoodsolvent

<h2>~<S2>~N6/5(2)PolymerinaQsolvent

<h2>~<S2>~N1(3)Polymerinapoorsolvent<h2>~<S2>~N2/3c~1/kT!!!Coil-globule

transitioncT3.4

Semi-diluteSolutionsofPolymersindependentonMp~c9/4Osmoticpressuremeasuredforsamplesofpoly(-methylstyrene)dissolvedintoluene(25C).MolecularweightvarybetweenM=7104(uppermostcurve)andM=7.47106(lowestcurve).(Noda,I.;etal.Macromolecules

1981,14,668.)P/c~c1P/c~c5/4f2<<1f22>>f2/xP/c~c0ScalingLawofsemi-dilutesolutionInsemi-diluteregime,PisindependentonN:Forgoodsolvent,v=3/5,thereforem=5/4.Osmoticpressure:5/41

Apparentcorrelationlengthxapp:

xappisindependentonN:Forgoodsolvent,v=3/5,thereforem=-3/4.app3.5ConcentratedSolutionsofPolymers1.高分子-增塑劑2.紡絲液3.凝膠和凍膠Flory-HugginsfreeenergyofagelV0<h2>1/2swellingl3V0l<h2>1/2BasicEquationofGelSwellingm1m10m1=m10Dm1=m1-m10=0Q=V/V0=1/f2(1)求c(2)求MVolumePhaseTransitionofGelsTheory,t=1-2c~1-2/TExperiment3.6SolutionsofPolyelectrolytes

－+－C++++++－－－－－－－－－－+++++++++－－－－++++－－－－－－－++++－－－－++++－－－－++++++++++++C+3.7ThermodynamicsofPolymerMixturesWhyaretwokindsofpolymersnotcompatible?EntropyofMixingPolymer/PolymerSolvent/SolventSolvent/SolventThePhaseBehaviorofPolymerMixturesHowtojudgeit‘shomogeneousstateorinhomogeneousstate?Whatisthemechanismofphaseseparation?DGf2V1DG1+(1-V1)DG2-DG<0?PhaseDiagramandPhaseEquilibriumPhase1Phase2THowtocalculatethephasediagramfromfreeenergy?

Phase1Phase2f2V1f21V2f22+T對DG作切線Y=A+Bf2,切點f2*DGf2f2*切點*斜率BDG*=A+Bf2*AFindingthephaseequilibriumconditionsDGf2f2*f2**對DG作的切線方程為要使相平衡條件滿足必須作一根這樣的切線滿足唯有同時通過兩個切點的共切線(1)Phaseequilibriumcurve–binodal作T(c)

~[f2*(T),f2**(T)]binodalcurve(2)Metastable/unstablelimits-spinodalDGf2SpinodalcurvePhase1Phase2f2V1f21V2f22+unstablemetastable拐點(3)CriticalpointCriticalpointSpinodal和binodal的交點:Forsymmetricdi-blocksf=0.5Forsymmetricblendsx1=x2x=NForpolymersolutionsx=NCriticalpointsdependenceofNForblendsForsolutionsx1=1Tf2TQx2Poorsolventc>0.5qsolventc=0.5UCST/LCSTEndothermicsymmetricalpolymermixturewithlowermiscibilitygap.Exothermalsymmetricalpolymermixturewithuppermiscibilitygap.Lowercriticalsolutiontemperature(LCST)Uppercriticalsolutiontemperature(UCST)

WhyUCSTorLCSTcisthekeyissue.0cTcdisp0cTcf.v0cTc.s.iDispersionforce:~1/Tmonotonicdecreasing,cdisp

0asT

.Freevolumeeffect:MonotonicincreasingwithT,small,butpositiveatlowT.

Effectiveinteractionparameterceff:DispersionforcesFreevolumeeffectsSpecificinteractionsSpecificinteraction:Always<0,decreasingmagnitudewithincreasingT.A>0UCSTA<0LCSTPhaseEquilibrium在某一溫度下,達到熱力學平衡的兩相平衡點(1)自由能曲線作共切線取兩切點法(2)數(shù)值解1.相平衡線2.spinodal線與相分離機理和動力學有關PhaseSeparationDynamics達到兩相最終平衡的動力學過程與初始狀態(tài)的濃度有關在臨界組成附近,不穩(wěn)區(qū),spinodaldecomposition在相平衡線和spinodal線之間,亞穩(wěn)區(qū),nucleationandgrowthTquenching(淬火)TfPhasediagramandphaseseparationmechanisms在臨界組成附近,不穩(wěn)區(qū),spinodaldecompositionSpinodaldecompositionNucleationandgrowth(2)在相平衡線和spinodal線之間,亞穩(wěn)區(qū),nucleationandgrowthPhaseSeparationMechanisms1.Nucleationandgrowth(成核生長)mechanismf*f**Inmetastableregion,separationcanproceedonlybyovercomingthebarrierwithalargefluctuationincomposition.NucleationGrowthNucleationbarrier:withr:radiusofthenuclear;

s:excessfreeenergyperunitsurfacearea.droplet-dispersedphasePhaseSeparationMechanisms2.Spinodaldecomposition(亞穩(wěn)極限分解)mechanismInunstableregion,separationcanoccurspontaneouslyandcontinuouslywithoutanythermodynamicbarrier.f’f**EarlystageNosharpinterfaceLatestageWell-establishedinterfacesCoarseningprocessf*Co/bi-continuousphaseExamplesofPhaseSeparationDynamics3.8TheromodynamicsofBlockCopolymersdiblocktriblockrandommultiblockfourarmstarblockgraftcopolymerSelf-assemblyofDiblockCopolymersMeltsSolidsSolutionsMicrophase(mesophase,nanophase)separation(微相分離)isdrivenbychemicalincompatibilitiesbetweenthedifferentblocksthatmakeupblockcopolymermolecules.Micellization(膠束化)occurswhenblockcopolymerchainsassociateinto,oftenspherical,micelles(膠束)indilutesolutioninaselectivesolvent(選擇性溶劑).Inconcentratedsolution,micellescanorderintogels(凝膠).Crystallizationofthecrystallineblockfrommeltoftenleadstoadistinct(usuallylamellar(片晶))structure,withadifferentperiodicityfromthemelt.MicrophaseSeparationofDiblockCopolymers(BCPs)Phasediagramfisthevolumefractionofonecomponent.fcontrolswhichorderedstructuresareaccessedbeneaththeorder-disordertransition.cNexpressestheenthalpic-entropicbalance.Itisusedtoparameterizeblockcopolymerphasebehavior,alongwiththecompositionofthecopolymer.HomogeneousStateorderdisorderorderorderStructurallyOrderStateStructurallyOrderStateMicrophaseSeparationofTriblockCopolymersThermodynamicsofMicrophaseSeparationMinimizeinterfacialareaandMaximizechainconformationalentropy(MIN-MAXPrinciple)F:freeenergyperchainN:numberofsegments(=NA+NB)a:Kuhnlengthva

a3,aA

aBL:domainperiodicityS:interfacialareaperchaingAB:interfacialenergyperareacAB:segment-segmentinteractionparameterS,gABL/2Lamellarstructureand(Helfand,E.;Tagami,Y.PolymerLetters,1971,9,741)entropicspringtermThermodynamicsofMicrophaseSeparationFreeenergyoflamellae:enthalpictermUsingwehaveThus,theoptimumperiodofthelamellaeandthelamellarfreeenergyare:andAssume