優(yōu)選結(jié)晶動(dòng)力學(xué)和結(jié)晶熱力學(xué)補(bǔ)充材料當(dāng)前第1頁\共有15頁\編于星期三\10點(diǎn)ProcessofPolymerCrystallization

Twosteps:1.Nucleation(成核)processSizeDG0embryosupercritic.sizestablecriticalnucleusDG=Gcrystal–Gmelt,DG=DH–TDSGcrystal=Gbulk+SAsDG=Gbulk-Gmelt

+SAs

=DGf+SAsA

isthesufaceareaand

DGfisthe

bulkfreeenergychange.abcSchematicrepresentationofthechangeinfreeenergyasafunctionofsizeillustratingthenucleationprocessTypesofcrystalnuclei.(a)primary(初次),(b)secondary(二次),(c)tertiary(三次)nucleus.

Homogeneous(均相)andheterogeneous(異相)nucleation當(dāng)前第2頁\共有15頁\編于星期三\10點(diǎn)Estimatethecriticalnucleussize

Forprimarynucleus

Forsecondarynucleus當(dāng)前第3頁\共有15頁\編于星期三\10點(diǎn)平衡熔點(diǎn)Tm0的測定方法Gibbs-Thomson方程：Hoffman-Weeks方程：HoffmanJD,WeeksJJ.J.Res.Natl.Bur.Std.(U.S.)1962,66A,13-28.熔融線當(dāng)前第4頁\共有15頁\編于星期三\10點(diǎn)熔融線結(jié)晶線Hoffman-Weeks和Gibbs-Thomson方程的聯(lián)系Hoffman-Weeks曲線的斜率,等于熔融線和結(jié)晶線的斜率之比。當(dāng)前第5頁\共有15頁\編于星期三\10點(diǎn)ThermodynamicsofCrystallization:

2.MeltingpointofPolymermixtureChemicalPotentialofPolymerinamorphousphaseConsiderasystemofPolymer/Impuritymixture:ChemicalPotentialofonemonomerunitofpolymerinamorphousphasePolymeriscompatiblewithimpuritybutcan’tco-crystallizewithimpurity當(dāng)前第6頁\共有15頁\編于星期三\10點(diǎn)Effectsof“Impurities”onTmConditionofPhaseEquilibriumSuperscriptofC:CrystallinePhaseSuperscriptofI:AmorphousPhase當(dāng)前第7頁\共有15頁\編于星期三\10點(diǎn)Effectsof“Impurities”onTmForx2,x1=1Forend-groupeffects:1=2/N,=0Forcopolymeralternatingcopolymer:P<<XARandomcopolmer:P=XABlockCopolymer:P>>XA1P:ProbabilityofcrystallineunitwithsequentialconnectionNote:Forpolymerblendspolymer/smallmoleculepolymer/polymer當(dāng)前第8頁\共有15頁\編于星期三\10點(diǎn)2.LinearGrowthofPolymerCrystallizationTemperaturedependenceoflineargrowthrate(線生長速度)Temperaturedependenceoftheradialgrowthrateuofspherulitesinisotacticpolystyrene(left),polyamid6(center)andpoly(tetramethl-p-silpheylenesiloxane)(right).Tf:equilibriummeltingtemperature.SurfacenucleationonsubstratewithlengthLwitharateiLineargrowthrateG:thegrowthrateofcrystalperpendiculartothesubstratel:foldlength;a:widthofstem;b:thicknessofthestem;g:substratecompletionrate當(dāng)前第9頁\共有15頁\編于星期三\10點(diǎn)Avrami指數(shù)n生長類型均相成核n=生長維數(shù)+1異相成核n=生長維數(shù)三維生長(球狀晶體)n=3+1=4n=3+0=3二維生長(片狀晶體)n=2+1=3n=2+0=2一維生長(針狀晶體)n=1+1=2n=1+0=1=空間維數(shù)+時(shí)間維數(shù)當(dāng)前第10頁\共有15頁\編于星期三\10點(diǎn)Kineticsmodelsofoverallcrystallization1.FreegrowthmodelR~vtb.newnucleusproduced-

homogeneousa.constantnumbersofnucleus-

heterogeneoust+DttDttI*nucleationratet當(dāng)前第11頁\共有15頁\編于星期三\10點(diǎn)Poisson’sraindropproblemIfraindropsfallrandomlyonapondcreatingexpandingcircularwaves,whatisthechancethatthenumberofwavescreatedbydifferentraindropswhichpassoverarepresentativepointPuptotimetisexactlyn?Kineticsmodelsofoverallcrystallization-Avrami2.ImpingementmodelPPoissondistributionWhatisthechancethatnowavereachesagivenpointPinspace?heterogeneoushomogeneousTheAvramiequationfor3DE(t):wavespreadingareaduringtWhiletorvisverysmallor當(dāng)前第12頁\共有15頁\編于星期三\10點(diǎn)1.Johnson-Mehl方程（I、u不隨時(shí)間而變）設(shè)新相β在母相α中成核，并經(jīng)過一段孕育期τ以后長大成球狀新相半徑一個(gè)新相體積dτ時(shí)間間隔內(nèi)成核的β相數(shù)