结晶聚合物的小角X射线散射研究

结晶聚合物的小角X射线散射研究 第31卷 VolI31 第1期 No.1 西南师范大学(自然科学版) JournalofSouthwestChinaNormalUniversity(NaturalScience) 2006年2月 Feb.2006 文章编号:1000—5471c2006)O1—0075—06 StudyofSemicrystallinePolymers bySmall—AngleX—rayScattering? LEIxiao-wei DoptofPhysicsandElectronInformationEngineering.ChongqingUniversityofArtsandSci ences-Chongqing402760?Chna Abstract:Theevaluationofstructureparametersinasemicrystallinepolymerthree— phasesystembysmallang1eX- rayscatteringwasinvestigated.Theconclusionisthatthecrystallinityandthelamellarthickn essarenotconsstent withthoseintwo— phasesystem.TheanalysisofsomesemicrystallinepolymersamplesindicatesthattheBragg 1ong periodapproachestothecorrelationfunctionlongperiodplusthethicknessofthetransitionla yer?ThereasonISthe interpahselayers'existenceinrealsemicrystallinepolymers. Kevwords:small-angleX—rayscattering;crystalpolymer;three— phasestructure;correlationfunction CLCnilmher:0434.1Documentcode:A Semicrystallinepolymerssuchaspolyethylene,polypropylene,andnylonformthin(100500A) crvstal1inelame11aeseparatedbyanamorphouslayercontainingchainfolds,ends,andintercrystalline tiesL1].Sma11anglex— rayscattering(SAXS)onsemicrystallinepolymershasbecomeoneofthemajotOOl forstructureresearchesL一引. Tsvankin[.]comparedmodelscatteringcurvestoexperimentaldata'and KortleveandVonkdevelopedfittingproceduresforthecorrelationfunction.SAXShasbeenusedtoob— tainthedensitvcorrelationfunctionacrosslamellarstacksinsemicrystallingpolymers.UntilStrobland Schneider[7]foundamethodwhichdoesnotrelyonspecificmodelassumptionsandcanbeapplieddirectlY withouttherequirementofparametervariation,thecorrelationfunctioncandirectlyyieldbyusmgasimple geometrica1constructionthefollowingstructureparameters:thespecificinnersurface'thecrystallinity' theaveragelame11arthickness,thelongspacingand,ifscatteringintensitiesaremeasuredinabsoluteVal— ues,theelectrondensitydifferencebetweencrystallineandamorphousregions.Nowadaysthecorrelation functionisoneofthemostappliedmethodsforevaluationofstructureparametersofsemicrYstallmepolY— mer.Thoughthereareothermethods}. StroblandSchneiner'sworkaimedatthe"correspondingidealtwo— phasesystem"withsharpbounda— riesorigina11v,thoughtheirresultsareappliedtothree— phasestructuresamplesfrequentlY?AtPresent theorvandexDerimenthaveledtotheconclusionthatacrystal— amorphousinterphaseexistsinlamellar semicrvstallinepolyme.一'.Whenusingathree— phasemodelwithaninterphaseoflinearelectrondensi- tvvariationtoreinvestigatethework,itisfoundthatalthoughmostconceptsintwo-phasesystemcanbeenaP— Dliedwithoutanvchange,thecrystallinityandtheaveragelamellarthicknessneednewconsiderations? SomeDarameterscanbederivedeitherfromthescatteringcurveofasampledirectlyor,alter上1ourler ?收稿日期:2005—06—06 作者简介:雷晓蔚(1967一),女,重庆人,副教授,主要从事凝聚态物理的研究 76西南师范大学(自然科学版)第31卷 transformation,fromthecorrelationfunction.Suchasthelongspacing,itcanbeobtainedfromthescat— teringcurvebyusingBragglaw,orfromthecorrelationfunction.NeverthelesstheBragglongspacingand thelongspacingofthecorrelationfunctionaredifferentremarkably.WeemploySAXStheoryandoptical theorytointerpretthephenomenonsuccessfullyandthiscanberegardedastheevidenceoftheinterphase existenceagain. 1TheCorrelationFunctionofThreel-PhaseSystem Themodelusedinthisworktodescribethescatteringfromalamellarstructuresampleisthelamellar three— phasestructure,whichisdefinedasconsistingofalternatingparallelcrystallineandamorphousla— mellaeconnectedbytransitionlayerswhichareplacedinstgckslargeenoughnottoperturbthe smallangle x— rayscattering[….Inthefollowingwewillassumethattheelectrondensityvariationoccurpredominantly alongthedirectionperpendiculartothelamellae,aslongaswestaywithinalamellarstack.Am orphous regionswithdensityandcrystalliteswithadensityinthecorealternatealongthelamellardirec tion withinterlayers,densityofwhichchangeslinearlyfromto,betweenthem.Theprofileofelectr on densityforthemodelisshowninFig.1.Inthiscase,thedensitydistributionalongthedirection normalto lamellaezcanberepresentedby r/(z)=== . ,dI<一 2 一 卫吾且-(1z1一手),导<1z1<d+E(1) , d+E<II<导 r/(z+L)一r/(z) HereEistheinterphasewidth,disthelamellarthickness, andListhelongperiod.Theaveragedensitywithinastack (andthatofthewholesystem)willbecalled(r/>.There— fore,weareabletorestrictourdiscussiontoonedimen— sionalelectrondensitycorrelationfunctionK(z) K(z)一([r/(z)一(r/>]Er/(z+z)一()])(2) wheretheangularbracketsindicateaveragingoverallcoor— dinateszwithinalamellarstack.Thisfunctionwasevalua— tedfromthesmall—anglescatteringcurvef(s) rx K(z)一l@rsJ(s)cos2~szds(3) |『7J ?—————一三——————『7 /.'E . K-- I d+E; 2 andaretheElectronDensitiesoftheCrystalline andAmorphousPhasesRespectively Fig,1ElectronDensityProfileofthe LamellarThree.PhaseStructure sdenotesthescatteringvector 4nsinO S, whereand0arethewavelengthandtheBragganglerespectively.In tion,weevaluatetheintegral (4) ordertoobtainthecorrelationrune— K(z)一1 J [一 A/2 / [7(z)一(7)][7(z+z)一'7)]dz, Here?denotestheaveragingrangeforz.Itgives (5) 第1期IElXiao—wei:StudyofSemicrystallinePolymersbySmall—AngleX—rayScattering77 K(z)一 (一)1z3— zz 十十 2E一 ],Izl<E (一)[一z++E一],E<lzI<d 壶一[丢(一z一],d<lzl<+E 一 [一++2E一d-k-E~lzl<(+2E) 一 l(r/,一rb)2(d+E) , d+2E<lzl<导'onlywhend+2E<导 K(L+z)一K(z) TheresultisshowninFig.2.InthiscasethereisastraightlinesegmentinthecentralsectionofK( z). Itsslopeisrelatedtothespecificinnersurfaceby 警一c一? Afterextrapolationthelinereachesz一0attheinvariant Q—w(1一)(一)(8) withw--whdoesn.trepresentthecrysIal?n卜 Q tyw一d ofthesampleoftwophasestructureyet[. L Thisshouldbeadvertent.Anotherpointweshouldno— ticeisthatextrapolationoftheothersideofthelinedoes notintersectthebaselineABattheabscissaz—d.Ac— cordingtoformula(8),itisthesecondendpointofthe straight—linesegmentinthecorrelationfunctioncurve whoseabscissadenotesthelamellarthicknessd.From thedrawing,wecanalsoobtainthetransitionthickness E,whichistheabscissaofthefirstendpointofthe straight—linesegment,andthelongperiodL,whichis thepositionofthefirstpeak. D /\一 U一 Q,E,dandLaretheInvariant,theTransitionThickness, theLamellarl'hicknessandtheLongPeriodRespectively Fig.2SchematicPlotoftheCorrelation FunctionoftheThree—PhaseStructureSystem 2ExperimentsandResults Thepolymersamplesforexperimentswereneatisotacticpolypropylenes(i-PP),whichfrom Beijing ResearchInstituteofChemicalIndustry.Thesampleswereextrudedintosliceswithathickne ssof2mm at220?.Allsliceswerefoundtobemacroscopicallyhomogeneousandtoexhibitexcellentopticalclari— tyE引. Thelongperiodcanbeobtaineddirectlyfromthescatteringcurve.Wecanseenolessthanonei nter— ferencemaximumonthescatteringcurveofasemicrystallinepolymer.Afterdeterminingthe angleposition ofthemaximum,Bragglawcanbeusedtosolvethelongspacing,whichiscalledtheBragglongperiod here.Asanexample,wepresenttheSAXScurveofsampleNo6inFig.3.Inthefigure,theinterference peakcorrespondstoscattervectors一0.36nm,.UsingBragglaw,LsinO —,wecanyieldtheBragglong periodofthesampleisL^一17.43nm. AstothescatteringcurveinFig.3,aFortranprogramhasbeenwrittentoevaluatethedataofitscor— relationfunction.Thelongperiodofthecorrelationfunctionofthesamplecanbemeasuredthroughthe correlationfunctionplot.Whenusingthismethodtodeterminestructureparametersofasample,allow— ancemustbemadeforthefactthatthecorrelationfunctionintheoriginisverysensitivetoexperimental 78西南师范大学(自然科学版)第31卷 errorsinthetailofthescatteringcurve[.Inordertodecreasetheaffectoferrorsatlargevaluesofs. Porod'slawisusedtocorrectthedata.Porod'slawforsmeareddatainthecaseofslitcollimationis,(s) 一 KPs一.exp(一 4,r),hereKPisPorod'sconstant,andisaparameterpertainingtothethicknessof transitionlayers.Thislawisemployedtopredictthescatteringdataofasampleathighangles.Onthe otherhand,sincewehaveblockedthecentralraysupintheexperimentalprocedure,thescatteringdataa— round0degreesislost.ThispartofdataisextrapolatedtomakeupbyusingGuinierlaw[.Intheendwe obtainthecorrelationfunctiondataofsampleNo6andplotitinFig.4.Fromtheplot.somestructurepa— rameterscanberead:thecorrelationfunctionlongperiodL===14.61nm,thetransitionlayerthicknessE 一 2.56nm.CompareLwithL,itisfoundthattheyarenotequa1.Allexperimentalsamples'resultsare listinTable1.FromtheResults,itisfoundthattheBragglongperiodofasampleisneartoitscorrela— tionfunctionlongperiodplusthethicknessofthetransitionlayers.Inthefollowing,weapplySAXStheo— ryandopticaltheorytoanalyzetherelationshipbetweentheBragglongperiodandthecorrelationfunction longperiod. scatteringvectors/rim Fig,3TheScatteringCurveofSampleNo6 ' { : oE/101520 z Fig.4TheCorrelationFunctionCurveofSampleNo6 Table1EvaluationandAnalysisofStructureParametersofPolymerSamples(nm) 3Discussion Forthetwo— phasestructure.showninFig.5(a),whenanincominglightisincidentonthesurfaceof asample,thesampleproducesscatteredraysgoingthroughtheinnerofit.Becauseelectrondensitiesare notthesameonthetwosidesofinterfacesbetweenamorphousandcrystallinelayers,thatis,theelectron densitydistributionisnotevenaroundinterfaces,sotheincidentraysdonotscatteraxiallysymmetrically throughinterfaces.Somescatteredraysarereflectedregularlyontheinterfacesbetweenamorphousand crystallinelayers.Otherraystransversetheinterface.Reflectedraysatasuitableanglewillshapeinter— ferencepeaksonthescatteringcurve.ThisanglecorrespondstothelongperiodL.Bragglaw,LsinO一 n2,cantellit.Accordingtotheabovetheory,thecorrelationfunctionmethodcansupplythislongperiod either.Fromthefigure,itwillbeeasytolearnthatthesetwolongperiodsshouldbeequa1. However,whenencounteringasampleofthree— phasestructure,thisconclusionisnotrightagain. Fig.5(b)illustratesthesituation.Inthiscase.theinterphaselayerscanbeconsideredasbeingcomposed ofcountlessfolia.Twofacesofeveryfoliumhavedifferentareaelectrondensities,buttheareaelectron 一-善rI?IDJB},占一?II售一^I瓷一 第1EIXiao-wei:StudyofSemicrystallinePolymersbySmall—AngleX—rayScattering79 densitvoneitherfaceisconstant.ThereforewhenscatteredrayscomeIntosomefoliumIninterpnaselaY— ers.thevwillproducereflectionandtransmission.Becauseeveryreflected(ortransmitted)lacehasacon— stantelectrondensity,soreflectedraysortransmittedraysexhibitsomeregularity.Similartothetwo— Dhasesvstem'scase,thereflectedraysandtransmittedrayscorrespondingtoasuitableanglewillforman interferencemaximumonthescatteringcurve.Unlikethetwo— phasesystem'scase,ItISnotonlyan1nter— facethatDr0ducesreflectionandtransmission,butitisthewholetransitionlayersthatproducereflection andtransmission.Hence,theinterferencemaximumshouldcorrespondtoananglerange.SeenfromFlg?5 (b),thisang1erangecorrespondstotheperiodrangefromL— EtoL+E.AccordingtoBragglawLsin0一 , Ls一4不,heres一 4nsin0/Aisthescatteringvector.Therefore,thescatteringvectorsoftheanglescorre— sDondingtoperiodsL— EandL+Ecanbesolved,supposingtobes1ands2respectively.Ihisanglerange corresDondstothescatteringvectorrangefrom1tos2,sonormally,singlepeakswillnotoccuronthe scatteringcurve.Itwillbeaninterferencepeakbandthatoccursonthescatteringcurve.Ihebandscope.s fromsto,.However,infact,onlyawidepeakisseenonthescatteringcurve,notapeakband?Iherea— sontoarisethephenomenonisinterpretedinthefollowing. :::: ?) la 2 , ,,, nb !!! d! 一 ' — II (a)Two.phasestructuremodelWhenraysareincidentatanangle correspondingtoLr,reflectedrayswillproduceinterference E}?_—一,c———?II (b)Three.phasestructuremodelThespacingLbetweenarytwoadjacent foliamarkedbyAorBintransitionlarersrangesfromLc-EtoLc+E Fig.5SketchPlottoExplainHowInterferencePeaksareFormedontheScatteringCurve ofaPolymerSample(Note:TransmittedRaysare0mitted) Ifthedistributionofopticalintensityisevenalongthescatteringanglerangeonthescattermgcurve, aninterferencebandwilloccuronthescatteringcurve.Butinfact,intheprocedureofsmall— anglex—ray scatteringthedistributionofopticalintensityisnotevenalongthescatteringangle.IthasthestrongestIn— tensitvat0degrees,anddecayssharplywhenthediffractionanglebecomeslarger.Atthelargeangle range,theintensitydistributionobeysPorod'slaw,whichisthatinthetailoftheSAXScurvetheintensi— tvdecreasesinproportionto 一.fortheslitcollimationsystem.ThisisthereasonthatwedonotseeanIn— terferencebandonthescatteringcurve.Asanexample,chooseL一12nm,E一 2nm.Accordingto Porod'law,theintensitycorrespondingtoLI—L+Ebytheintensitycorrespondingto1-2一L 一Eis J】/J2一(2/1)..ApplyingBragg'slaw,Lsin0一,一4n,soJ1/J2一(Ll/I2).一(14/10).一 2?74? Fhismeansthatonthescatteringcurvetheintensityinthetailoftheinterferencebanddecreasessharply, soweonlvseeaninterferencepeak,notaband.Furthermore,thispeakdoesnotcorrespondtoth e sample'slongperiodLanditapproachestocorrespondtoL+Eevenmore? 4Conclusion Whenusingthecorrelationfunctiontoevaluatestructureparametersofsemicrystallinepoly mer,al— thoughmostresultswiththethree—phasemodelarethesameasthosewiththetwo— phasemodel,thecrys— tal1inityinthethree-phasesystemsh.uldbereplacedby叫一—d+一 E . Atthesametime,thelamel1arthick— nessdisequa1totheabscissaoftheseeondendpointofthestraight— linesegmentinthecorrelationfunc— 8O西南师范大学(自然科学版)第31卷 tioncurve.TheBragglongperiodofasemicrystallinepolymerisnot periodbecauseoftheexistenceoftheinterphaselayer.Itapproaches References: [1]ZengXB.UngarG,SpellsSJ.eta1.Crystal— AmorphousPolymerInterfaceStrdiedbyNeutronandX—RayScatteringon IabeledBinaryUltralongAlkanes[J].PhysRevIett,2003(90):155508(1—4). [2]YinJing—Hua,MoZhi— Shen.Modernmacromolecularphysics(Volume2)[M].Beijing:SciencePress(inChinese), 2001.473—474. [3]MartinC,EeckhautG,MahendrasingamA,eta1.Micro— SAXSandForce/StrainMeasurementsDuringtheTensileDe— formationofSingleStrutsofanElastomericPolyurethaneFoam[J].JSynchrotronRad,2000( 7):245—250. [4]CreaghDC,()'NeilPaPM,MartinDJ.SynchrotronRadiationStudyoftheRelationBetwe enStructureandStrainin PolyurethaneElastomers[J].JSynchrotronRad,1997(4):163—168. [5]TsvankinDYa,ZubovYUA,KitaigorodskiiAI.CalculationofLongPeriodsinPolymersandDeterminationoftheSizes ofCrystallitesandAmorphousRegions[J].JPolymSci,1968,C6:4081—409l- [6]VonkCG.InvestigationofNon—IdealTwo—PhasePolymerStructuresbySmall— AngleX,RayScattering[J].JAppl Cryst,1973(6):81—86. [7]StroblGR,SchneiderM.DirectEvaluationoftheElectronDensityCorrelationFunctionofPartiallyCrystallilaePoly— mers[J].JPolymSciPolymPhysEd,1980(18):1343—1359. [8]DidierVillers.AOne-DimensionalModelforSmall—AngleX— RayScatteringfromCrystallineBlockCopolymers[J].Acta Cryst,2003(A59):132—137. [9]BenjaminS.Hsiao,RaviKVerma.ANovelApproachtoExtractMorphologicalVariablesinCrystallinePolymersfrom Time-ResolvedSynchrotronSAXSData[j].jSynchrotronRad,1998(5):23—29. [10]FloryPJ,YoonDY,DillKA.I'heInterphaseinLamellarSericrystallinePolymers[J].Macromolecules,1984(17): 862——868. [11]YoonDY,FloryPJ.Macromolecules,1984(17):868—871. [12]HahnBR,WendorffJH,YoonDY.DielectricRelaxationoftheCrystal— AmorphousInterphaseinPoly(Vinylidene Fluoride)anditsBlendswithPoly(MethylMethaerylate)[J].Macromolecules,1985,18(4):718—7