Conformational analysis of polymers: methods and techniques for structure-property relationships and

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Conformational Analysis of Polymers: Methods and Techniques for Structure-Property Relationships and Molecular Design Sasanuma Y.

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ConformationalAnalysisofPolymers

ConformationalAnalysisofPolymers

MethodsandTechniquesforStructure-Property

RelationshipsandMolecularDesign

YujiSasanuma

ChibaUniversity(retired)

Chiba,Japan

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LibraryofCongressCataloging-in-PublicationData

Names:Sasanuma,Yuji,author.

Title:Conformationalanalysisofpolymers:methodsandtechniquesfor structure-propertyrelationshipsandmoleculardesign/YujiSasanuma.

Description:Hoboken,NJ:Wiley,[2023]|Includesbibliographical referencesandindex.

Identifiers:LCCN2022049542(print)|LCCN2022049543(ebook)|ISBN 9781119716358(hardback)|ISBN9781119716594(adobepdf)|ISBN 9781119716662(epub)

Subjects:LCSH:Polymers–Conformation.

Classification:LCCQD381.S2872023(print)|LCCQD381(ebook)|DDC 547/.7–dc23/eng20230113

LCrecordavailableathttps://lccn.loc.gov/2022049542

LCebookrecordavailableathttps://lccn.loc.gov/2022049543

Coverdesign:Wiley

Coverimage:©FlavioCoelho/GettyImages

Setin9.5/12.5ptSTIXTwoTextbyStraive,Chennai,India

Asmythanksto thosewholedmetoscience, thosewhohaveworkedwithme, and myfather,mother,wife,andson

Contents

Preface xii

Acknowledgments xvi

AbouttheAuthor xvii

Acronyms xviii

PartIFundamentalsofPolymerPhysicalChemistry 1

1StereochemistryofPolymers 3

1.1Configuration 3

1.2ConnectionTypeofMonomericUnits 5

1.3NitrogenInversion 5

1.4Conformation 8

1.5SecondaryStructure 9

1.6DoubleHelix 11

2ModelsforPolymericChains 13

2.1SpatialConfigurationofPolymericChain 13

2.2FreelyJointedChain 13

2.3FreelyRotatingChain 15

2.4SimpleChainwithRotationalBarrier 16

2.5GaussianChain 17

3LatticeModel 21

3.1LatticeModelofSmallMolecules 21

3.2Flory–HugginsTheory 22

3.2.1EntropyofPolymericChain 22

3.2.2EnthalpyofMixing 25

3.2.3ChemicalPotential 26

3.2.4Excluded-VolumeEffectI 28

3.2.5Excluded-VolumeEffectII 32

3.2.6PhaseEquilibrium 35

3.3IntrinsicViscosity 36

3.3.1Stockmayer–FixmanPlot 37 Exercise 38

4RubberElasticity 41

4.1ThermodynamicsofRubberElasticity 41

4.2AdiabaticStretching:Gough–JouleEffect 45

4.3PhenomenologicalTheory:AffineModel 46

4.4TemperatureDependenceofChainDimensioninRubber 48

PartIIQuantumChemistry 51

5AbInitioMolecularOrbitalTheory 55

5.1SchrödingerEquation 55

5.2WaveFunction 56

5.3BasisSet 57

5.4Hartree–FockMethod 58

5.5Roothaan–HallEquation 59

5.6ElectronCorrelation 60

6DensityFunctionalTheory 63

6.1ExchangeandCorrelationFunctionals 65

6.2Dispersion-forceCorrection 67

7SolventEffect 69

8StatisticalThermodynamicsforQuantumChemistry 75

8.1TranslationalMotion 76

8.2RotationalMotion 77

8.3VibrationalMotion 78

8.4ElectronicExcitation 80

8.5Thermochemistry 81

9NMRParameters 85

9.1ChemicalShift 86

9.1.1Example:DeterminationofReactionProcessfromNMRChemical Shifts 88

9.2IndirectSpin–SpinCouplingConstant 92

9.2.1Example1:CalculationofVicinalCouplingConstantsofCyclic Compound 93

9.2.2Example2:DerivationofKarplusEquationandIts Application 95

10PeriodicQuantumChemistry 99

10.1DirectLatticeandReciprocalLattice 99

10.2BlochFunction 100

10.3One-electronCrystalOrbital 101

10.4StructuralOptimization 102

10.5CrystalElasticity 104

10.6VibrationalCalculation 108

10.7ThermalChemistry 110

10.8Cohesive(InterchainInteraction)Energy 112

PartIIIStatisticalMechanicsofChainMolecules:Rotational IsomericStateScheme 115

11ConventionalRISScheme 117

11.1ChainDimension 121

12RefinedRISScheme 125

12.1RISSchemeIncludingMiddle-rangeIntramolecular Interactions 129

13Inversional–RotationalIsomericState(IRIS)Scheme 137

13.1PseudoasymmetryforPolyamines 137

13.2Inversional–RotationalIsomerization 137

13.3StatisticalWeightMatricesof Meso and Racemo di-MEDA 138

13.4StatisticalWeightMatricesofPEI 139

13.5DiadProbabilityandBondConformation 142

13.6CharacteristicRatio 144

13.7OrientationalCorrelationBetweenBonds 145

13.8SolubilityofPolyamines 148

14RISSchemeCombinedwithStochasticProcess 151

14.1PolymericChainswithInternallyRotatableSideChains 153

PartIVExperimentalMethods 161

15NuclearMagneticResonance(NMR) 163

15.1ConformationalAnalysisofIsotacticPoly(propyleneoxide) 163

15.1.1 1 HNMRVicinalCouplingConstant 164

15.1.2AbinitioMOCalculation 168

15.1.3RISAnalysisofBondConformations 171

15.1.4Configuration-dependentProperties 172

15.2Carbon-13NMRChemicalShiftsofDimericPropyleneOxides 173

15.2.1TheoreticalBasis 175

15.2.2 13 CNMRSpectraandAssignment 176

15.2.3CalculationofChemicalShiftbyRISScheme 179

15.3ModelCompoundofPoly(ethyleneterephthalate) 181

16ScatteringMethods 187

16.1StaticLightScattering(SLS) 187

16.1.1InstrumentationandSamplePreparationforSLS 189

16.1.2ApplicationofSLS:ChainDimensionsofPolysilanesinthe Θ State 191

16.2DynamicLightScattering(DLS) 195

16.2.1ApplicationofDLS:SizeDistributionofPolystyreneLatex Particles 197

16.2.2ApplicationofSLSandDLStoPoly(N -methylethyleneimine) Solutions 198

16.3Small-angleNeutronScattering(SANS) 201

16.3.1ApplicationofSANStoAmorphousPET 204

PartVApplications:ConformationalAnalysisandElucidationof Structure–PropertyRelationshipsofPolymers 207

17Polyethers 215

17.1Poly(methyleneoxide)(PMO) 215

17.2Poly(ethyleneoxide)(PEO) 217

17.3Poly(propyleneoxide)(PPO) 226

17.4Poly(trimethyleneoxide)(PTrMO) 228

17.5Poly(tetramethyleneoxide)(PTetMO) 229

18Polyamines 235

18.1Poly(ethyleneimine)(PEI) 236

18.2Poly(N -methylethyleneimine)(PMEI) 237

18.3Poly(trimethyleneimine)(PTMI)andPoly(N -methyltrimethyleneimine) (PMTMI) 238

19Polyphosphines 241

19.1PossibilityofPhosphorusInversion 241

19.2IntramolecularInteractionsRelatedtoPhosphorus 243

19.3RISCalculation 244

19.4FunctionsandStability 248

20Polysulfides 249

20.1Poly(methylenesulfide)(PMS) 249

20.1.1CrystalStructureofPMS 253

x Contents

20.2Poly(ethylenesulfide)(PES) 253

20.3Poly(propylenesulfide)(PPS) 260

20.4Poly(trimethylenesulfide)(PTrMS) 265

21Polyselenides 269

21.1Poly(methyleneselenide)(PMSe) 269

21.1.1CrystalStructureofPMSe 270

21.2Poly(ethyleneselenide)(PESe) 274

21.3Poly(trimethyleneselenide)(PTrMSe) 276

21.4Summary 277

22AlternatingCopolymersIncludingEthylene-imine,Ethylene-oxide, andEthylene-sulfideUnits 279

22.1SynthesisofP(EI-ES) 286

23AromaticPolyester(PET,PTT,andPBT) 289

23.1CorrectionforMP2Energyof �� –�� Interaction 290

23.2DipoleMomentandMolarKerrConstant 293

23.3ConfigurationalProperties 296

23.4CrystalStructure 297

24AliphaticPolyesters 301

24.1Poly(glycolicacid)(PGA)andPoly(2-hydroxybutyrate)(P2HB) 301

24.1.1MOCalculationandNMRExperiment 302

24.1.2RISCalculation 305

24.1.3PeriodicDFTCalculationonPGACrystal 309

24.2Poly(lacticacid)(Poly(lactide),PLA) 312

24.2.1MOCalculationandNMRExperiment 313

24.2.2RISCalculation 317

24.3Poly((R)-3-hydroxybutyrate)(P3HB) 321

24.3.1NMRExperiment 321

24.3.2MOCalculation 323

24.3.3RISCalculationandComparisonwithExperiment 325

24.3.4CrystalStructure 326

24.4Poly(�� -caprolactone)(PCL) 327

24.4.1MOCalculation 328

24.4.2NMRExperiment 330

24.4.3RISCalculation 330

24.4.4CrystalStructure 332

24.4.5CrystalElasticity 333

24.5Poly(ethylenesuccinate)(PES)andPoly(butylenesuccinate)(PBS) 336

24.5.1NMRExperiment 337

24.5.2MOCalculation 338

24.5.3RISCalculation 339

24.5.4CrystalStructure 340

24.6BiodegradabilityofPolyesters 342

25Polycarbonates 347

25.1Poly(ethylenecarbonate)(PEC)andPoly(propylenecarbonate) (PPC) 348

25.1.1NMRExperiment 351

25.1.2MOCalculation 351

25.1.3RISCalculation 353

25.2Poly(cyclohexenecarbonate)(PCHC) 357

25.2.1MOCalculation 358

25.2.2NMRExperiment 360

25.2.3RISCalculation 361

25.2.4CoherenceNumber 364

26Nylon4 367

26.1MOCalculation 368

26.2NMRExperiment 370

27AromaticPolyester,Polythionoester,Polythioester,Polydithioester, Polyamide,andPolythioamide 373

27.1MOCalculation 375

27.2BondConformation 377

27.3RISCalculation,ThermalProperties,andSolubility 380

28Polysilanes 383

28.1MolecularDynamics 384

28.1.1GeneralProcedures 384

28.1.2PDBSandPDHS 384

28.1.3PMPrS 387

28.2RISCalculation 387

28.3PhysicalProperties 388

29Polyethylene(PE) 391

AFORTRANComputerProgramforRefinedRISCalculationson Polyethylene 399

BAnswersofProblems 423

Bibliography 431 Index 465

Preface

Inthelate1920sandearly1930s,Carothers’steamofDuPontreportedthesynthesisofsomealiphaticpolyesters[63–65].Unfortunately,thepolyestersmelted attoolowtemperaturestobecommercialized.Meanwhile,Lemoigneextracted analiphaticpolyester,poly((R)-3-hydroxybutyrate)(P3HB),fromabacterium, Bacillusmegaterium [277,278].TheequilibriummeltingpointofP3HBisas highas203 ∘ C.Theasymmetricstructureandsterichindranceofthemethyl sidechainrestrictthedegreeofconformationalfreedomoftheP3HBchainand, consequently,leadtothehighmeltingpoint.Nowadays,P3HBattractsattention frompolymerchemistsandengineersbecauseofitscarbonneutrality,namely biosynthesisandbiodegradability.Therelationshipsbetweenconformational characteristicsandthermalpropertiesofpolymersareoftendiscussedinthisbook.

In1941,WhinfieldandDicksonacquiredaBritishpatentonaromaticpolyesters includingpoly(ethyleneterephthalate)(PET),poly(trimethyleneterephthalate) (PTT),andpoly(butyleneterephthalate)(PBT)[520].Thedifferenceinstructure amongthesepolyestersisonlythenumberofmethyleneunitsbetweenthe benzenerings.Thehighequilibriummeltingpoint(262 ∘ C)ofPETisduepartly totheintermolecular �� –�� interactionbetweenthebenzenerings.Thearomatic polyestersareindustriallymanufacturedallovertheworld.PETismoldedto fibers,films,andbottles;PTTissoflexibleastobeusedforsportswearsand carpets;andPBTissosuperiorinimpactresistanceastobeusedintoothand paintbrushes,gears,andmachineparts.Theusagesofthearomaticpolyesters aremainlyduetothemechanicalproperties.ThecrystallineYoung’smodulus inthechain-axisdirectionofPETis182GPa,thatofPTTisassmallas7.1GPa, andthatofPBT(�� form)is20.8GPa[266].Inthecrystal,PETliesinasomewhat distortedall-transstructure,whereasPTTandPBTformbendedtggtanddistortedg+ g+ tg g conformations,respectively.Here,t,g+ ,andg representtrans, gauche+ ,andgauche states,respectively.Inthisbook,themechanicalproperties ofpolymersarefrequentlyinterpretedintermsofchainconformations.

Asdescribedaboveandwillbeshownlater,higherorderstructuresandthermal andmechanicalpropertiesofpolymersdependonconformationalcharacteristics,

morefundamentally,theprimarystructure–whatthecomponentatomsand chemicalbondsareandhowtheyarearranged.Furthermore,scientistshave facedwiththefactthatproteinscomposedofonly20aminoacidsformunique secondary,tertiary,andquaternarystructuresandexhibitspecificfunctions. Consequently,polymerscientistshavereachedtheconceptofmoleculardesign: wemaypredicttheprimarystructure(s)fromwhichthedesiredhigherorder structures,physicalproperties,andfunctionsarerealized.

InJapan,theideaofmoleculardesignwasadvocatedearlyon.In1972,abook consistingofthreevolumes,titled“MolecularDesignofPolymers,”waspublished byTheSocietyofPolymerScience,Japan[239].Inthebook,Kawaidefinedthe moleculardesignasfollows:First,onemustrevealthecorrelationsbetween thechemicalstructuresandphysicalproperties.Next,oneactuallysynthesizes thepolymerwiththestructurethatisexpectedtoshowthedesiredproperties.

Ontheotherhand,Kambara’smoleculardesignisdifferent:whenanewpolymer issuggested,namelyitsconstituentatomsandchemicalbondsarespecified,to predictthestructuresandmorphologytobeformedtherefromisthemolecular design.Kambara’sconceptistopredictthehigherorderstructuresfromthe primarystructure,whereasKawai’sideaismoreidealistic;themoleculardesign shouldbetoproposetheprimarystructurethatactualizessuchhigherorder structures,physicalproperties,andfunctionsasdesired.Inordertorealize eithermoleculardesign,asbothKawaiandKambarasuggested,itisrequisiteto establishrelationshipsbetweentheprimarystructure,higherorderstructures, and,furthermore,ifpossible,propertiesandfunctions.

Forthatpurpose,itisessentialtoelucidatethestructuresandpropertiesof asinglepolymericchain.Fromanexperimentalviewpoint,itissignificantto determinebondconformationsoftheskeletalbondsvia,forexample,NMR andrevealtheconformationalcharacteristicsand,furthermore,toinvestigate theconfigurationalpropertiesofthepolymericchaininthe Θ statefreefrom theexcluded-volumeeffectvia,forexample,scatteringmethods.Fromatheoreticalviewpoint,thefreeenergiesandgeometricalparametersofindividual conformationsofapolymericchainareevaluatedbyquantumchemistry,and theBoltzmannfactorsaresummedoverallconformationstoyieldthepartition functionfromwhichvariousthermodynamicfunctionscanbederivedaccording tostatisticalmechanicaltheorems.

However,apolymerchainformsanenormous(astronomical)numberofconformations.Forexample,undertherotationalisomericstate(RIS)approximation basedonthethreestates(t,g+ ,andg ),asinglepolyethylenechainof100mer shows3200 (approximately2.7 × 1095 )conformations.Theaverage ⟨M ⟩ ofamolecularparameter Mi ,dependingontheconformations,maybecalculatedfrom

where Ei istheenergyofconformation i, N isthetotalnumberofconformations, R isthegasconstant, T istheabsolutetemperature,and Z isthepartitionfunction definedas

Toevaluate ⟨M ⟩,onemustsolvetheSchrödingerequationforeachconformation,obtainitsground-stateenergy,andrepeatthisprocedure N times;however, suchcolossalcomputationsareimpossibleforthetimebeingatleast,apartfrom theremotefuture.Fortunately,statisticalmechanicsofchainmolecules,designatedastheRISscheme,hasbeendevelopedandformulatedasmatrixoperations. AccordingtotheRISscheme,onecanexactlycalculatethebondconformations, variousconfigurationalproperties,andthermodynamicfunctionsofunperturbed polymericchains(lyinginthe Θ state).TheearlystudiesoftheRISschemewere summarizedinFlory’sbook[141],theensuingstudiescanbefoundinMatticeand Suter’sbook[307],andRehahn,Mattice,andSuter’sbookcollectedalmostallRIS modelsreporteduntiltheendof1994[383].

Itisknownthattheconfigurationalpropertiesofunperturbedpolymericchains dependonlyonshort-rangeintramolecularinteractions[141];therefore,theconformationalenergiesmayalsobeevaluatedfromasmallmodelcompoundwith thesamebondsequenceasthatofthepolymer.Inordertoderivetheconformationalenergiesfromquantumchemicalcalculations,therefore,oneneednottreat thepolymeritselfbutthesmallmodelcompoundinstead.TheMOcomputations onthemodelaresufficientlypracticalevenifahigh-levelMOtheoryincluding electroniccorrelationsisemployed,togetherwithlargebasissets.

TheRISschemecanexactlycharacterizeunperturbedpolymericchainsin dilutesolutions,amorphousphases,andmelts.However,polymerscientistshave alsobeendesiringtoacquireprecisetheoreticalinformationonthestructures andpropertiesofsolid-statepolymers.Fortunately,thedensityfunctionaltheory (DFT)underperiodicboundaryconditionshasenabledustocalculatethe electronicstructuresofcrystals[120].Themethodologycanalsobeappliedto polymercrystalsandyieldthefollowinginformation:optimizedcrystalstructure (latticeconstantsandatomicpositions);intermolecularinteractionenergy correctedforthebasissetsuperpositionerror(BSSE);thermodynamicfunctions; andvibrationalspectroscopicfrequencyandintensity.TheDFTcalculationshave shownthatthechainconformationisalsotheprincipalfactorinthestructures andpropertiesofpolymercrystals.

PartIofthisbookdescribesthefundamentalphysicalchemistrythatis necessarytounderstandthecharacteristicsofpolymersandstudytheirconformations.Thecontentsarestereochemistry,polymermodels,andthelatticemodel (theFlory–Hugginstheory);molecularcharacteristics;solutionproperties;and

rubberelasticity.Thispartiswrittensoastobeunderstoodwithoutdifficulty bygraduateandundergraduatestudentswhohavelearnedgeneralchemistry. Derivationsofsomeimportantequations,whicharemostlyomittedfromtextbooksandoriginalpapers,aregivenasproblems,andtheanswersarepresented inAppendixB.

PartIIexplainsthequantumchemistryusedinconformationalanalysis, togetherwithawealthofpracticalapplications.ThecontentsaretheSchrödinger equation,theHartree–Fockmethod,electroncorrelations,DFT,dispersion-force correction,solventeffect,generalstatisticalmechanics,NMRparameters,and periodicDFTforcrystals.

PartIIIexplainstheRISschemeincludingmathematicalexpressionsand theirderivations.ThecontentsaretheconventionalRISscheme,therefined RISscheme,theRISschemeincludingmiddle-rangeinteractions,inversional–rotationalisomericstate(IRIS)scheme,theRISschemewithstochasticprocesses, andtheRISschemewithinternallyrotatablesidechains.

PartIVintroducestypicalexperimentalmethodsforconformationalanalysisof polymers.Thecontentsarebroadlydividedintotwoportions:NMRspectroscopy andscatteringtechniques.TheformerdealswithNMRvicinalcouplingconstants toevaluatebondconformationsandchemicalshiftstodeterminestereo-and regiosequences.Thelatterhalfexplainshowtodeterminemolecularcharacteristics,chaindimensionsinsolutionsandmeltsviastaticlightscattering(SLS), dynamiclightscattering(DLS),andsmall-angleneutronscattering(SANS).

PartVexemplifiesanumberofstudiesonthefollowingpolymers:polyethers, polyamines,polyphosphines,polysulfides,polyselenides,alternatingcopolymers ofamine,ether,andthioetherunits,polyesters,polycarbonates,nylon4,substitutedanalogsofaromaticpolyesters,polysilanes,andpolyethylene.

AppendixApresentsaFORTRANsourcecodeforrefinedRIScalculationson polyethylene.

AppendixBpresentsanswersoftheproblemsgiveninthetext.

Inthisbook,alargenumberofmathematicalsymbolsandphysicalquantities areused;therefore,thesamealphabeticandGreeklettersareoftenassignedto differentparameters,andthesamephysicalquantityisoccasionallyrepresented bydifferentsymbols.Thedihedralangleisdefinedintwoways:theconvention ofpolymerscience,trans ∼ 0∘ andgauche± ∼±120∘ ,andtheIUPACrecommendation,trans ∼ 180∘ andgauche± ∼∓60∘ .Theformerandlatterareemployed mainlyintheRISandMOcalculations,respectively.

Chiba,Japan

August2022

Acknowledgments

Thestudiespresentedhereinaremostlycollaborationswiththeauthor’sstudents andfriends.Theauthorisdeeplyindebtedtothefollowingpeoplefortheir dedicationandenthusiasm(honorifictitlesomitted):TaisukeIwata,Akihiro Suzuki,HaruhisaKato,YasukazuKato,NobuyukiMiura,HajimeOhta,Yuichi Ohta,YugoHayashi,FutoshiNishimura,MisaSawanobori,MakikoYokoi,Hideto Ogura,TetsushiOno,ShinobuTakahashi,IkukoTouma,HiroakiWakabayashi, JunFujii,TakayukiIijima,TomoyoshiKaizuka,YoshihikoKuroda,Hiroki Matoba,EmiMiyazaki,SatoshiHattori,KenHikino,ShinichiImazu,JunArou, KohjiNakata,FumikoTeramae,HirokiYamashita,IppeiHamano,SatoshiIkeda, KentaroSugita,RyotaKumagai,TomohiroMiyai,AkinoriWatanabe,Shunsuke Asai,PeiNa,GouSuzuki,KentaTamura,SyugoEndo,NobuakiSuzuki,Yoko Ogawa,JunichiUchida,DaisukeAbe,YoichiHori,MasanaoMatsumoto,Takumi Inada,TakayukiIshibashi,YutaNonaka,TakuroSuzuki,YutoTanaka,YukiYamaguchi,ShioriKatsumata,ShogoMori,KouMoriya,DaichiTouge,SatoshiUzawa, YusukeWagai,TatsuyaIshii,RyosukeNagao,MasayukiNagasawa,TakumiWada, YuichiroFukuda,KoheiMiyamae,TsubasaSugita,YutaTakahashi,Daiki Nagai,MasakiOtsuki,TaigaKurita,MorihiroTakahashi,SyutoTanaka,Hiromi Yamamoto,DaisukeAoki,SominChoi,AzumiKawai,KohyoOno,Yusuke Kondo,NaofumiYoshida,YotaWatabe,ShotaAbe,MitsutoshiHoshide,Hiromu Kawasaki,YukoUesugi,ShunsukeKouchi,TakayukiMorita,RyotaOhmori, TomoyukiTomita,NaokiHayashi,SayakaIwabuchi,IkumiSaito,Shunsuke Shimomura,NaokiHamamoto,RenaIshida,RikoKaidu,YumaYoshida, ShinnosukeKogure,RyosukeOhnishi,MarinoYamamoto,AkiraKaito,Nobutaka Tanigaki,YoshikazuTanabe,ShinichiKinugasa,TakashiYarita,MuhammadA. Azam,RobertV.Law,andJoachimH.G.Steinke.

TheauthorthankstheeditorialstaffsofWiley,Ms.SkylerVanValkenburgh, Dr.AndreasSendtko,Mr.JonathanT.Rose,Ms.DimplePhilip,Ms.Sabeen Aziz,andMs.DevipriyaSomasundaramforinvitationtowritethisbook,cordial support,andcarefulwork.

AbouttheAuthor

YujiSasanuma,PhD,FormerlyDepartmentofAppliedChemistryandBiotechnology,GraduateSchoolandFacultyofEngineering,ChibaUniversity,Japan YSwasborninYokohama,Japan,inDecember1956andspenthisboyhood inKawasaki.Hereceivedbachelor’s(1980,supervisors:ProfessorIchitano UematsuandProfessorJunjiWatanabe)andmaster’s(1982,supervisors: ProfessorAkihiroAbeandProfessorIsaoAndo)degreesfromTokyoInstitute ofTechnology(DepartmentofPolymerChemistry).Between1982and1988,he workedinTorayIndustries,Inc.(TorayResearchCenter,Inc.)andengagedin materialcharacterizationbyX-raydiffractionandscattering.In1988,hereturned toTokyoInstituteofTechnologytostudyorientationalandconformational characteristicsofliquidcrystalswithProfessorAkihiroAbe.Afterhereceived doctor’sdegree(1992,chiefexaminer:ProfessorShintaroSasaki)fromTokyo InstituteofTechnology,hemovedtoNationalInstituteofMaterialsandChemical Research(DepartmentofPolymerPhysics)inTsukuba,wherehedevelopeda measurementsystem(equipmentandsoftware)forsmall-angleX-rayscattering andstudiedconformationalcharacteristicsandconfigurationalpropertiesof polyethers(1993–1997).In1997,hemovedtoChibaUniversityandcontinuously grappledwithconformationalanalysisofpolymers.InMarch2022,heretired fromChibaUniversityatthemandatoryageof65.

Acronyms

3HB(R)-3-hydroxybutyrate

ABAMA N -acetyl-�� -aminobutyricacid N ′ -methylamide

AMamorphous

BDMePE1,2-bis(dimethylphosphino)ethane

BDT2-tert-butyl-1,3-dithiane

BGDAbutyleneglycoldiacetate

BMePE1,2-bis(methylphosphino)ethane

BMePhPE1,2-bis(methylphenylphosphino)ethane

BMSeE1,2-bis(methylseleno)ethane

BMSeM1,2-bis(methylseleno)methane

BMSeP1,3-bis(methylseleno)propane

BMTE1,2-bis(methylthio)ethane

BMTP1,2-bis(methylthio)propane

BSSEbasissetsuperpositionerror

CCcoupledcluster

cc-pVQZDunning’scorrelationconsistentbasissets(quadruple)

cc-pVXZDunning’scorrelationconsistentbasissets

CCSD(T)coupledclustersingle–doubleandperturbativetriple

CGSTcontinuoussetofgaugetransformations

CHcyclohexane

CHCcyclohexenecarbonate

CHOcyclohexeneoxide

CIconfigurationinteraction

CIDconfigurationinteractionwithalldoublesubstitutions

CISDconfigurationinteractionwithallsingleanddoublesubstitutions

cis-DMDO cis-2,6,-dimethyl-1,4-dioxane

CONTINconstrainedregularizationmethodforinvertingdata

COSMOconductor-likescreeningmodel

COSYcorrelationspectroscopy

CPcounterpoise

CP/MAScross-polarization/magic-anglespinning

D2Grimme’sD2dispersion-forcecorrection

D3Grimme’sD3dispersion-forcecorrection

DCAdichloroaceticacid

DCB o-dichlorobenzene

DCMdichloromethane

DEPTdistortionlessenhancementbypolarizationtransfer

DFTdensityfunctionaltheory

DFT-Ddensityfunctionaltheorywithdispersion-forcecorrection

di-MEDA N , N ′ -dimethylethylenediamine

DLSdynamiclightscattering

DMB1,4-dimethoxybutane

DMCCdi(methoxycarbonyloxy)cyclohexane

DME1,2-dimethoxyethane

DMEDT2-(1,1-dimethylethyl)-1,4-dithiane

DMF N , N ′ -dimethylformamide

DMP1,2-dimethoxypropane

DMPA2,2-dimethoxy-2-phenylacetophenone

DMSdimethylsuccinate

DMSOdimethylsulfoxide

DMTdimethylterephthalate

DPCMdielectricpolarizablecontinuummodel

DSCdifferentialscanningcalorimeter

DSOdiamagneticspin–orbit

EDCethylenedichloride

EGDAethyleneglycoldiacetate

EGDBethyleneglycoldibenzoate

EGDMSethyleneglycoldi(methylsuccinate)

ELATEonlineapplicationforanalysisandvisualizationofelastictensors

EVexcludedvolume

EVEexcluded-volumeeffect

FCFermicontact

FMB1-fluoro-4-methoxybutane

GIAOgauge-independentatomicorbitalmethod

HBShydrogenbondstrength

HFHartree–Fock

HFIP1,1,1,3,3,3-hexafluoro-2-propanol

H–Hhead-to-head

H–KHohenberg–Kohn

h-PMShexagonalpoly(methylenesulfide)crystal

HSABhardandsoftacidsandbases

HSQCheteronuclearsingle-quantumcorrelation

H–Thead-to-tail

IEF-PCMpolarizablecontinuummodelusingtheintegralequation formalismvariant

IGLOindividualgaugesforlocalizedorbitals

IRISinversional-rotationalisomericstate

IUPACInternationalUnionofPureandAppliedChemistry

LAlacticacid

LAOCOONleast-squaresadjustmentofcalculatedonobservedNMRspectra

LClowcrystallinity

LCAOlinearcombinationofatomicorbitals

LCSTlowercriticalsolutiontemperature

LDlow-powerdecoupling

LDAlocal-densityapproximation

LMlatticemodel

LSlightscattering

LSDAlocalspin-densityapproximation

M2ONH N , N ′ -(ethane-1,2-diyl)dibenzamide

M2OOethane-1,2-diyldibenzoate

M2OS S, S′ -(ethane-1,2-diyl)dibenzothioate

M2SNH N , N ′ -(ethane-1,2-diyl)dibenzothioamide

M2SO O, O′ -(ethane-1,2-diyl)dibenzothioate

M2SSethane-1,2-diyldibenzodithioate

M3ONH N , N ′ -(propane-1,3-diyl)dibenzamide

M3OOpropane-1,3-diyldibenzoate

M3OS S, S′ -(propane-1,3-diyl)dibenzothioate

M3SNH N , N ′ -(propane-1,3-diyl)dibenzothioamide

M3SO O, O′ -(propane-1,3-diyl)dibenzothioate

M3SSpropane-1,3-diyldibenzodithioate

MAAmethyl2-acetoxyacetate

MAHmethyl6-acetoxyhexanoate

MDmoleculardynamics

MEMA N -(2-methoxyethyl)methylamine

MEMS2-methoxyethylmethylsulfide

MOmolecularorbital

MOAA2-methoxy-2-oxoethyl2-acetoxyacetate

MPMøller–Plesset

MP2theMøller–Plessetexpansiontruncatedatsecond-order

MRmonomerratio(ofPStoPMEI)

MTEMA N -(2-methylthioethyl)methylamine

MTT2-methyl-1,3,5-trithiane

NBOnaturalbondorbital

NISneutroninelasticscattering

NOBnotobserved

P(N -tosylEI-ES)poly(N -tosylethyleneimine-alt-ethylenesulfide)

P(EI-EO)poly(ethyleneimine-alt-ethyleneoxide)

P(EI-ES)poly(ethyleneimine-alt-ethylenesulfide)

P(EO-ES)poly(ethyleneoxide-alt-ethylenesulfide)

P2HBpoly(2-hydroxybutyrate)

P2ONHpoly(ethyleneterephthalamide)

P2OOpoly(ethyleneterephthalate)

P2OSpoly(ethylenedithioterephthalate)

P2SNHpoly(ethyleneterephthalthioamide)

P2SOpoly(ethylenethionoterephthalate)

P2SSpoly(ethylenetetrathioterephthalate)

P3HBpoly((R)-3-hydroxybutyrate)

P3ONHpoly(trimethyleneterephthalamide)

P3OOpoly(trimethyleneterephthalate)

P3OSpoly(trimethylenedithioterephthalate)

P3SNHpoly(trimethyleneterephthalthioamide)

P3SOpoly(trimethylenethionoterephthalate)

P3SSpoly(trimethylenetetrathioterephthalate)

P5OSpoly(pentamethylenedithioterephthalate)

PASprincipal-axissystem

PBSpoly(butylenesuccinate)

PBTpoly(butyleneterephthalate)

PCHCpoly(cyclohexenecarbonate)

PCLpoly(�� -caprolactone)

PCMpolarizedcontinuummodel

PDBProteinDataBank

PDBSpoly(di-n-butylsilane)

PDHSpoly(di-n-hexylsilane)

PDMSpoly(dimethylsilane)

PDO1,3-propanediol

PEpolyethylene

PECpoly(ethylenecarbonate)

PEIpoly(ethyleneimine)

PENpoly(ethylene-2,6-naphthalate)

PEOpoly(ethyleneoxide)

PEOXpoly(2-ethyl-2-oxazoline)

PESpoly(ethylenesulfide)orpoly(ethylenesuccinate)

PESepoly(ethyleneselenide)

PETpoly(ethyleneterephthalate)

PGApoly(glycolicacid)

PHphenol

Pippiperidinium

PLApoly(lacticacid)

PMEIpoly(N -methylethyleneimine)

PMEI-PSPMEIandPSlatex

PMePPpoly(1-methylphosphirane)

PMOpoly(methyleneoxide)

PMPLpoly(DL-�� -methyl �� -propiolactone)

PMPrSpoly(methyl-n-propylsilane)

PMSpoly(methylenesulfide)

PMSepoly(methyleneselenide)

PMTMIpoly(N -methyltrimethyleneimine)

POpropyleneoxide

PPCpoly(propylenecarbonate)

PPhPPpoly(1-phnylphosphirane)

Acronyms

PPOpoly(propyleneoxide)

PPPpolyphosphine

PPSpoly(propylenesulfide)

PSpolystyrene

PSOparamagneticspin–orbit

PSTpulsesaturationtransfer

PTetMOpoly(tetramethyleneoxide)

PTMIpoly(trimethyleneimine)

PTrMOpoly(trimethyleneoxide)

PTrMSpoly(trimethylenesulfide)

PTrMSepoly(trimethyleneselenide)

PTTpoly(trimethyleneterephthalate)

PyONHpoly(alkylterephthalamide)

PyOSpoly(alkyldithioterephthalate)

PySNHpoly(alkylterephthalthioamide)

PySOpoly(alkylthionoterephthalate)

PySSpoly(alkyltetrathioterephthalate)

PyTS4poly(alkyltetrathioterephthalate)

QST2synchronoustransit-guidedquasi-Newtonmethodwithtwo moleculespecifications

RISrotationalisomericstate

RMSEroot-mean-squareerror

S4TPAtetrathioterephthalateacid

S4TPA-Piptetrathioterephthalateacidcomplexedwithpiperidinium

SANSsmall-angleneutronscattering

SAXSsmall-angleX-rayscattering

SCsinglechainorsemicrystalline

SCFself-consistentfield

SDspin-dipoleorstandarddeviation

S–FStockmayer–Fixman

SLSstaticlightscattering

SS(V)PEsurfaceandsimulationofvolumepolarizationforelectrostatics

SVPEsurfaceandvolumepolarizationforelectrostatics

TetCEtetrachloroethane

TetMGDBtetramethyleneglycoldibenzoate

tetra-MEDA N , N , N ′ , N ′ -tetramethylethylenediamine

TFAtrifluoroaceticacid

TFEtrifluoroethanol

THFtetrahydrofuran

TMStetramethylsilane

TOCOSYtotalcorrelationspectroscopy

TriCPHtrichlorophenol

TriMGDBtrimethyleneglycoldibenzoate

T–Ttail-to-tail

UCSTuppercriticalsolutiontemperature

VESTAvisualizationforelectronicandstructuralanalysis

ConformationalAnalysisofPolymers:MethodsandTechniquesforStructure-PropertyRelationships andMolecularDesign,FirstEdition.YujiSasanuma. ©2023JohnWiley&Sons,Inc.Published2023byJohnWiley&Sons,Inc.

StereochemistryofPolymers

1.1Configuration

Itiswellknownthatthedirection,position,andlengthofasidechain,arrangementsofthesidechains,andconnectionwaysofmonomericunitssignificantly influencetheconformationalcharacteristicsandspatialshapeofthepolymer. Suchstructuralcharacteristicsofpolymersaregenerallytermed configurations. InOxfordAdvancedLearner’sDictionary,theword“configuration”isexplained asfollows:anarrangementofthepartsofsomethingoragroupofthings;the formorshapethatthisarrangementproduces.Ifthemonomericunithasachiral center,itisassignedtoeither R or S enantiomer.Whetherthemonomericunit is R or S willbeduetothechiralityofthemonomeritselfandthemechanism ofpolymerization.Besides,thechaindimensionisoftentermed spatialconfiguration,whichwillbedeterminedbytheconformationalsequencealongthe polymericchain.Itshouldbenotedthattheword“configuration”hasbeenused indifferentsensesinpolymerchemistry.

Figure1.1representsvinylpolymerssuchaspolypropylene(R = CH3 ), poly(vinylchloride)(R = Cl),andpolystyrene(R = C6 H5 ).Whenthepolymeric chainintheall-transformisputonthepapersothatthemethinecarbonislocated belowasinFigure1.1,andifthesidechainRappearsonthefrontorbacksideof thepaper,thearrangementisdefinedas d or l form,respectively.Asillustrated ontherightofFigure1.1,ifthepolymericchainofall-d configuration(above)is rotatedaroundthecentralarrowby180∘ ,itwillbetheall-l structure(below).Such d and l definitionsaretemporary,thusdesignatedasFlory’spseudoasymmetry [140].Theconfigurationalrelationbetweentwoadjacentunits,diad,istermed asfollows: meso, dd and ll; racemo, dl and ld.Thediadwillstayinvarianteven aftertherotation;accordingly,itmaybepreferabletouse meso and racemo rather than d and l.Ifapolymericchainincludesonly meso diads,theconfigurational regularity,tacticity,isreferredtoasisotactic.Ifonly racemo diadsareincluded,

ConformationalAnalysisofPolymers:MethodsandTechniquesforStructure-PropertyRelationships andMolecularDesign,FirstEdition.YujiSasanuma.

©2023JohnWiley&Sons,Inc.Published2023byJohnWiley&Sons,Inc.

Figure1.1 Vinylpolymer[—CH2 CHR—]x withthedefinitionof d and l formsbasedon Flory’spseudoasymmetryand meso and racemo diads.

thetacticityistermedsyndiotactic.Whennoconfigurationalregularityisformed, thepolymericchainisatactic.

AsillustratedinFigure1.1,isotacticall-transvinylpolymershavetwoskeletal C—Cbondsinthemonomericunitandstickthesidechainsoutonlyononesideof thepaper,whilethesyndiotacticchainsshowthesidechainsonthefrontandback sidesalternately.Incontrast,tacticitiesofpolymerswithoddnumbersofskeletal bondsinthemonomericunit,alsobeingdefinedaccordingtothe meso and racemo diads,appeartobeoppositetothoseofvinylpolymers:thesidegroupsoftheisotacticchainappearalternately,andthoseofthesyndiotacticchainarefoundon thesameside(seeFigure1.2).

Figure1.2 Iso-andsyndiotacticpolymericchainswiththreeskeletalbondsinthe monomericunit.

Figure1.3 Portionsofiso-andsyndiotacticpoly(propyleneoxide)swiththedefinition ofthe meso and racemo diads.

Sofar,theconfigurationsofpolymershavebeendiscussedaccordingtoFlory’s pseudoasymmetry.Ontheotherhand,thediadsandtacticitiesofthepolymeric chainscontainingtheabsolutelyasymmetriccarbonaredefinedwithrespectto the R or S centers.InFigure1.3,the meso and racemo diadsofpoly(propylene oxide)(PPO)areillustrated: meso, RR and SS; racemo, RS and SR.All meso and all racemo chainsarealsodesignatedasisotacticandsyndiotactic,respectively. InasmuchastherepeatingunitofPPOhasthreeskeletalbonds,the meso and racemo diadsaredefinedsimilarlyasthoseinFigure1.2.

1.2ConnectionTypeofMonomericUnits

Poly(propylenecarbonate)(PPC)hasthreetypesofconnectionsbetweenthe monomericunits.IftheCH(CH3 )andCH2 groupsaretermed“head”and“tail,” respectively,thethreeconnectionsarerepresentedashead-to-head(H—H,—CH (CH3 )—OC(=O)O—CH(CH3 )—),head-to-tail(H—T,—CH(CH3 )—C(=O)O— CH2 —),andtail-to-tail(T—T,—CH2 —C(=O)O—CH2 —)(seeFigure1.4).In addition,sincethemonomericunitofPPChasanasymmetriccarbonand assignedtoeither(R)-or(S)-opticalisomer,the meso and racemo diadsmaybe formed(Figure1.5)[415].

1.3NitrogenInversion

Commerciallyavailablepoly(ethyleneimine)(PEI)ismostlypreparedby ring-openingpolymerizationofaziridine,andsuchPEIstendtobranchatthe

Figure1.4 Threeconnectiontypesbetweentherepeatingunitsofpoly(propylene carbonate)(PPC):(a)head-to-tail(H—T);(b)head-to-head(H—H);and(c)tail-to-tail (T—T).Alltherepeatingunitshereare(R)-form.Source:Adaptedwithpermissionfrom reference[415].Copyright2017AmericanChemicalSociety.

nitrogensite.Therefore,toobtainlinearPEI([—CH2 —CH2 —NH—]x ),hydrolysisof,forexamplepoly(2-ethyl-2-oxazoline)hasbeenemployed.Inasmuchasit formsaggregateswithDNAandactsasagene-deliverypolymer,PEIhasattracted attentioninthefieldofgenetherapy.

Sincenitrogenistrivalent,thenitrogenatomofPEImaypossiblybeacenterof thepseudoasymmetry.Therefore, meso and racemo diadsand,furthermore,tacticitiesmaybedefinedforthelinearPEIchain.Inthe1980s,however,itwasfound thatamineshaveauniquenaturetermednitrogeninversion[55],whichcounterchangesthepositionsofthesubstituteandlonepairofthenitrogenatom.Even ifthesubstituteisasbulkyasthe tert-butylgroup,thenitrogeninversionrapidly occursatroomtemperature.

Figure1.6showsthenitrogeninversionof N ,N ′ -dimethylethylenediamine,a modelcompoundofPEI[403].Thenitrogeninversionalwaysswitchestheconfigurationbetween meso and racemo,andthetransitionstatehasahigherGibbs freeenergy(activationenergy)byapproximately4kcalmol 1 thanthe meso and racemo states.Inthetransitionstate,thelonepairseemsasifitwereaporbital, andthetwocarbon,nitrogen,andhydrogenatomsareseentobecoplanar.

Figure1.5 DiadsofPPC:(a) RR (meso);(b) RS (racemo);(c) SR (racemo);and(d) SS (meso). Source:Adaptedwithpermissionfromreference[415].Copyright2017American ChemicalSociety.

Figure1.6 Nitrogeninversionof N ,N ′ -dimethylethylenediamine,amodelcompoundof PEI.Source:[403]/ReproducedwithpermissionofAmericanChemicalSociety.

racemo
meso

1.4Conformation

Polymericchainsinsolutionsandmeltsalwayschangethespatialconfiguration owingtointernalrotationsaroundsinglebonds.Figure1.7showsNewmanprojectionsofthreestablestaggeredstates,namely,trans,gauche+ ,andgauche conformationsof n-alkanesandpolyethylene(PE).Inthetransconformation,the twocarbonatomsarelocatedoppositetoeachother.Ifthedistantcarbonatom isrotatedclockwise(counterclockwise)byabout120∘ ,thenewconformationis gauche+ (gauche ).Thehypothesisthatsuchstaggeredconformationsmayrepresentallrotationalstates,designatedastherotationalisomericstate(RIS)approximation,hasoftenbeenadoptedinpolymerchemistry.

Thedihedralangleofthetransstateisdefinedaseither0∘ or180∘ .Theformerdefinition(��)hasbeentraditionallyusedinpolymerscience,andthelatter (��)isrecommendedbytheInternationalUnionofPureandAppliedChemistry (IUPAC)[308].Accordingtotheformer,thegauche+ (notation:g+ )andgauche (g )statesare,respectively,positionedat �� ≈ 120∘ and 120∘ ,andaccordingtothe latter,thegauche+ (notation:G)andgauche (G)statesare,respectively,locatedat �� ≈ 60∘ and 60∘ .Itshouldbenotedthattheg+ andg conformationscorrespond tothe GandGstates,respectively.

Figure1.8showsthreestaggeredconformationsaroundtheCH(CH3 )—CH2 bondofpoly((R)-propyleneoxide)(PPO).InsymmetricchainssuchasPE,the gauche+ andgauche conformationsareequivalent(mirrorimagesofeachother intheNewmanprojection),whereasthoseofPPOarenonequivalentowingtothe asymmetricmethinecarbonatom.

Figure1.7 Rotational isomericstatesof n-alkanes andpolyethylene.

Figure1.8 Rotational isomericstatesof poly((R)-propyleneoxide) (PPO).

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