Nonlinear polymer rheology : macroscopic phenomenology and molecular foundation

468 Pages·2018·22.288 MB·English

by  Wang, Shi-Qing

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NonlinearPolymerRheology
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Nonlinear Polymer Rheology
MacroscopicPhenomenologyandMolecularFoundation
Shi-QingWang
UniversityofAkron,Ohio,US
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Thiseditionfirstpublished2018
©2018JohnWiley&Sons,Inc
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LibraryofCongressCataloging-in-PublicationData
Names:Wang,Shi-Qing,author.
Title:Nonlinearpolymerrheology:macroscopicphenomenologyandmolecular
foundation/byShi-QingWang.
Description:Hoboken,NJ:JohnWiley&Sons,2017.|Includesindex.|
Identifiers:LCCN2017019098(print)|LCCN2017036798(ebook)|ISBN
9781119029052(pdf)|ISBN9781119029045(epub)|ISBN9780470946985
(cloth)
Subjects:LCSH:Polymers–Rheology.
Classification:LCCTA455.P58(ebook)|LCCTA455.P58W3552017(print)|DDC
541/.2254–dc23
LCrecordavailableathttps://lccn.loc.gov/2017019098
CoverdesignbyWiley
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
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v
Contents
Preface xv
Acknowledgments xix
Introduction xxi
AbouttheCompanionWebsite xxxi
PartI LinearViscoelasticityandExperimentalMethods 1
1 PhenomenologicalDescriptionofLinearViscoelasticity 3
1.1 BasicModesofDeformation 3
1.1.1 Startupshear 4
(cid:2) 1.1.2 StepStrainandShearCessationfromSteadyState 5 (cid:2)
1.1.3 DynamicorOscillatoryShear 5
1.2 LinearResponses 5
1.2.1 ElasticHookeanSolids 6
1.2.2 ViscousNewtonianLiquids 6
1.2.3 ViscoelasticResponses 7
1.2.3.1 BoltzmannSuperpositionPrincipleforLinearResponse 7
1.2.3.2 GeneralMaterialFunctionsinOscillatoryShear 8
1.2.3.3 StressRelaxationfromStepStrainorSteady-StateShear 8
1.2.4 MaxwellModelforViscoelasticLiquids 8
1.2.4.1 StressRelaxationfromStepStrain 9
1.2.4.2 StartupDeformation 10
1.2.4.3 Oscillatory(Dynamic)Shear 11
1.2.5 GeneralFeaturesofViscoelasticLiquids 12
1.2.5.1 GeneralizedMaxwellModel 12
1.2.5.2 LackofLinearResponseinSmallStepStrain:ADilemma 13
1.2.6 Kelvin–VoigtModelforViscoelasticSolids 14
1.2.6.1 CreepExperiment 15
1.2.6.2 StrainRecoveryinStress-FreeState 15
1.2.7 WeissenbergNumberandYieldingduringLinearResponse 16
1.3 ClassicalRubberElasticityTheory 17
1.3.1 ChainConformationalEntropyandElasticForce 17
1.3.2 NetworkElasticityandStress–StrainRelation 18
1.3.3 AlternativeExpressionintermsofRetractionForceandAreal
StrandDensity 20
References 21
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vi Contents
2 MolecularCharacterizationinLinearViscoelasticRegime 23
2.1 DiluteLimit 23
2.1.1 ViscosityofEinsteinSuspensions 23
2.1.2 Kirkwood–RisemanModel 24
2.1.3 ZimmModel 24
2.1.4 RouseBead-SpringModel 25
2.1.4.1 StokesLawofFrictionalForceofaSolidSphere(Bead) 26
2.1.4.2 BrownianMotionandStokes–EinsteinFormulaforSolidParticles 26
2.1.4.3 EquationsofMotionandRouseRelaxationTimeτ 27
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2.1.4.4 RouseDynamicsforUnentangledMelts 28
2.1.5 RelationshipbetweenDiffusionandRelaxationTime 29
2.2 EntangledState 30
2.2.1 PhenomenologicalEvidenceofchainEntanglement 30
2.2.1.1 ElasticRecoveryPhenomenon 30
2.2.1.2 RubberyPlateauinCreepCompliance 31
2.2.1.3 StressRelaxation 32
2.2.1.4 ElasticPlateauinStorageModulusG′ 32
2.2.2 TransientNetworkModels 34
2.2.3 ModelsDepictingOnsetofChainEntanglement 35
2.2.3.1 PackingModel 35
2.2.3.2 PercolationModel 38
2.3 Molecular-LevelDescriptionsofEntanglementDynamics 39
2.3.1 ReptationIdeaofdeGennes 39
2.3.2 TubeModelofDoiandEdwards 41
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2.3.3 Polymer-Mode-CouplingTheoryofSchweizer 43
2.3.4 Self-diffusionConstantversusZero-shearViscosity 44
2.3.5 EntangledSolutions 46
2.4 TemperatureDependence 47
2.4.1 Time–TemperatureEquivalence 47
2.4.2 Thermo-rheologicalComplexity 48
2.4.3 SegmentalFrictionandTerminalRelaxationDynamics 49
References 50
3 ExperimentalMethods 55
3.1 ShearRheometry 55
3.1.1 ShearbyLinearDisplacement 55
3.1.2 ShearinRotationalDevice 56
3.1.2.1 Cone-PlateAssembly 56
3.1.2.2 ParallelDisks 57
3.1.2.3 CircularCouetteApparatus 58
3.1.3 Pressure-DrivenApparatus 59
3.1.3.1 CapillaryDie 60
3.1.3.2 ChannelSlit 61
3.2 ExtensionalRheometry 63
3.2.1 BasicDefinitionsofStrainandStress 63
3.2.2 ThreeTypesofDevices 64
3.2.2.1 InstronStretcher 64
3.2.2.2 Meissner-LikeSentmanatExtensionalRheometer 65
3.2.2.3 FilamentStretchingRheometer 65
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3.3 InSituRheostructuralMethods 66
3.3.1 FlowBirefringence 66
3.3.1.1 StressOpticalRule 67
3.3.1.2 BreakdownofStress-OpticalRule 68
3.3.2 Scattering(X-Ray,Light,Neutron) 69
3.3.3 Spectroscopy(NMR,Fluorescence,IR,Raman,Dielectric) 69
3.3.4 MicrorheologyandMicroscopicForceProbes 69
3.4 AdvancedRheometricMethods 69
3.4.1 SuperpositionofSmall-AmplitudeOscillatoryShearandSmallStep
StrainduringSteadyContinuousShear 69
3.4.2 RateorStressSwitchingMultistepPlatform 70
3.5 Conclusion 70
References 71
4 CharacterizationofDeformationFieldUsingDifferentMethods 75
4.1 BasicFeaturesinSimpleShear 75
4.1.1 WorkingPrincipleforStrain-ControlledRheometry:HomogeneousShear 75
4.1.2 Stress-ControlledShear 76
4.2 YieldStressinBingham-Type(Yield-Stress)Fluids 77
4.3 CasesofHomogeneousShear 79
4.4 Particle-TrackingVelocimetry(PTV) 79
4.4.1 SimpleShear 80
4.4.1.1 VelocitiesinXZ-Plane 80
(cid:2) 4.4.1.2 DeformationFieldinXYPlane 80 (cid:2)
4.4.2 ChannelFlow 82
4.4.3 OtherGeometries 83
4.5 Single-MoleculeImagingVelocimetry 83
4.6 OtherVisualizationMethods 83
References 84
5 ImprovedandOtherRheometricApparatuses 87
5.1 LinearlyDisplacedCocylinderSlidingforSimpleShear 88
5.2 Cone-PartitionedPlate(CPP)forRotationalShear 88
5.3 OtherFormsofLargeDeformation 91
5.3.1 DeformationatConvergingDieEntry 91
5.3.2 One-DimensionalSqueezing 92
5.3.3 PlanarExtension 95
5.4 Conclusion 96
References 97
PartII Yielding–PrimaryNonlinearResponsestoOngoingDeformation 99
6 WallSlip–InterfacialChainDisentanglement 103
6.1 BasicNotionsofWallSlipinSteadyShear 104
6.1.1 SlipVelocityV andNavier–deGennesExtrapolationLengthb 104
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6.1.2 CorrectionofShearFieldduetoWallSlip 105
6.1.3 CompleteSlipandMaximumValueforb 106
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6.2 Stick–SlipTransitioninControlled-StressMode 108
6.2.1 Stick–SlipTransitioninCapillaryExtrusion 108
6.2.1.1 AnalyticalDescription 108
6.2.1.2 ExperimentalData 109
6.2.2 Stick–SlipTransitioninSimpleShear 111
6.2.3 LimitingSlipVelocityV∗forDifferentPolymerMelts 113
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6.2.4 CharacteristicsofInterfacialSlipLayer 116
6.3 WallSlipduringStartupShear–InterfacialYielding 116
6.3.1 TheoreticalDiscussions 117
6.3.2 ExperimentalData 118
6.4 RelationshipbetweenSlipandBulkShearDeformation 120
6.4.1 TransitionfromWallSliptoBulkNonlinearResponse:Theoretical
Analysis 120
6.4.2 ExperimentalEvidenceofStressPlateauAssociatedwithWallSlip 122
6.4.2.1 ACaseBasedonEntangledDNASolutions 122
6.4.2.2 EntangledPolybutadieneSolutionsinSmallGapDistance
H∼50μm 123
6.4.2.3 VerificationofTheoreticalRelationbyExperiment 126
6.4.3 InfluenceofShearThinningonSlip 127
6.4.4 GapDependenceandIndependence 128
6.5 MolecularEvidenceofDisentanglementduringWallSlip 131
6.6 UncertaintiesinBoundaryCondition 134
6.6.1 OscillationsbetweenEntanglementandDisentanglementUnderConstant
Speed 134
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6.6.2 OscillationsbetweenStickandSlipunderConstantPressure 134
6.7 Conclusion 134
References 135
7 YieldingduringStartupDeformation:FromElasticDeformationtoFlow 139
7.1 YieldingatWi<1andSteadyShearThinningatWi>1 140
7.1.1 ElasticDeformationandYieldingforWi<1 140
7.1.2 SteadyShearRheology:ShearThinning 141
7.2 StressOvershootinFastStartupShear 143
7.2.1 ScalingCharacteristicsofShearStressOvershoot 144
7.2.1.1 ViscoelasticRegime(Wi <1) 145
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7.2.1.2 ElasticDeformation(Scaling)Regime(Wi >1) 145
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7.2.1.3 ContrastbetweenTwoDifferentRegimes 148
7.2.2 ElasticRecoilfromStartupShear:EvidenceofYielding 149
7.2.2.1 ElasticRecoilforWi >1 149
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7.2.2.2 IrrecoverableShearatWi <1 149
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7.2.3 MoreEvidenceofYieldingatOvershootBasedonRate-SwitchingTests 153
7.3 NatureofSteadyShear 154
7.3.1 SuperpositionofSmall-AmplitudeOscillatoryShearontoSteady-State
Shear 155
7.3.2 TwoOtherMethodstoProbeSteadyShear 157
7.4 FromTerminalFlowtoFastFlowunderCreep:Entanglement–Disentanglement
Transition 159
7.5 YieldinginStartupUniaxialExtension 163
7.5.1 MythwithConsidèreCriterion 163
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