Deformation and Flow of Polymeric Materials (eBook)

Preface 5
Contents 8
1 Introduction 15
1.1…General Aspects of Polymeric Materials 15
1.2…Nomenclature 17
1.3…General Classification of Polymeric Materials 18
References 19
2 Physical Structure of Macromolecules 20
2.1…Structure and Brownian Motion of Macromolecules 20
2.2…Molar Mass and Molar Mass Distribution 23
2.3…The Random Walk Problem in Three Dimensions 32
2.4…Macromolecules in Solution 38
2.5…Statistical Shape of Linear Macromolecules in Theta -Solution 44
2.6…Statistical Shape of Macromolecules in Good Solvents 48
2.7…Analysis of Branched Macromolecules 50
2.8…Size of Macromolecules in the Glassy and Molten State 53
References 54
3 Experimental Methods to Determine Molecular Quantities 55
3.1…Osmometry 55
3.2…Viscometry 61
3.3…Light Scattering 74
3.4…Gel Permeation Chromatography 80
References 87
4 Structure and States of Polymers 89
4.1…Classification of Polymeric Materials 89
4.2…Molecular Structure of Amorphous Polymers 99
4.3…States of Order of Uncross-Linked Amorphous Polymers 101
4.4…Influence of Molar Mass and Cross-Linking Density 106
4.5…Semicrystalline Polymers 111
4.5.1 Features of Crystallinity 111
4.5.2 States of Order 116
4.5.3 Crystallization 122
4.6…The Specific Volume of Polymers 123
4.6.1 The Specific Volume of Amorphous Polymers 123
4.6.2 The Free Volume Theory 127
4.6.3 Volume Relaxation and Physical Aging 129
References 131
5 Linear Viscoelastic Deformation Behavior in Simple Shear 133
5.1…Theoretical Description of the Deformation Behavior of Polymers 133
5.2…Creep, Creep Recovery, and Stress Relaxation 134
5.3…The Principle of Superposition 139
5.4…Relaxation and Retardation Spectra 142
5.5…The Creep Recovery Experiment 149
5.6…The Creep Compliance of Amorphous Polymers 152
5.7…Relations Between Creep and Stress Relaxation 161
5.8…Oscillatory Experiments 167
5.9…Approximate Relations Between Measurable Viscoelastic Functions 179
5.10…The Viscoelastic Behavior of Amorphous Polymers in Shear 189
References 198
6 Time-Temperature Shift of Mechanical Properties 200
6.1…The Significance of the Time-Temperature Shift for the Description of the Deformation Behavior of Polymers 200
6.2…The Time-Temperature Shift Principle 201
6.3…The Time-Temperature Shift of the Glass-Rubber Transition 204
6.4…The Time-Temperature Shift in the Flow Region of Amorphous Polymers 214
6.5…The Time-Temperature Shift in the Flow Region of Semicrystalline Polymers 221
6.6…The Time-Temperature Shift of Secondary Transitions in the Glassy State 227
References 233
7 Linear Viscoelastic Deformation Under Three-Dimensional Stresses 234
7.1…The Stress Tensor and the Equations for the Balance of Forces 234
7.2…The Strain Tensor for Small Deformations 238
7.3…The Rheological Equation of State for Isotropic Linear Elastic Materials (Hookean Theory of Elasticity) 241
7.4…The Rheological Equation of State for Isotropic Linear Viscoelastic Materials at Small Deformations 242
7.5…Simple Shear 244
7.6…Isotropic Compression 245
7.7…Uniaxial Tensile Stress 246
7.8…The Viscoelastic Functions for Amorphous Uncross-Linked Polymers 250
References 252
8 Fundamentals of the Rheology of Large Deformations 253
8.1…Kinematics of Large Deformations 253
8.2…Deformation Gradient and Finite Strain Tensors 257
8.3…Relative Deformation Gradient and Relative Strain Tensors 260
8.4…The Rate of Strain Tensor 264
8.5…Dynamics of Deformable Bodies 266
8.6…Eigenvalues and Invariants of the Stress Tensor 269
8.7…Transformation of the Strain Tensors and the Rate of Strain Tensor to Principal Axis 275
8.7.1 Time-Dependent Simple Shear 278
8.7.2 Multidimensional Time-Dependent Incompressible (Isochoric) Extension 281
References 283
9 Large Deformations of Polymers 284
9.1…Stress-Strain Behavior of Polymeric Materials 284
9.2…Rheological Equation of State for Isotropic Elastic Materials 289
9.3…Rheological Equation of State for the Ideal Rubber 293
9.4…Statistical Theory of Rubber Elasticity 298
References 304
10 Equations of State for Polymer Melts 305
10.1…Introduction 305
10.2…Rheological Equation of State for the Elastic Liquid After Lodge 306
10.2.1 The Constitutive Equation 306
10.2.2 The Lodge Liquid in Time-Dependent Simple Shear 309
10.2.3 The Lodge Liquid in a Stressing Experiment in Simple Shear 310
10.2.4 The Lodge Liquid in Shear Creep and Creep Recovery 313
10.2.5 The Lodge Liquid in Harmonic Oscillation in Simple Shear 315
10.2.6 The Calculation of the Relaxation Spectrum from Dynamic Data 318
10.2.7 Calculation of the Retardation Spectrum from the Relaxation Spectrum 322
10.2.8 The Lodge Liquid in Isochorous Multidimensional Extension 327
10.3…Rheological Equations of State After Wagner 332
10.3.1 The Constitutive Equation 332
10.3.2 The Wagner Theories in Time-Dependent Simple Shear 334
10.3.3 The Wagner Theories for Uniaxial Extension 340
10.4…The Theory of the Temporary Entanglement Network 344
10.4.1 The Strain Tensor and the Molecular Orientation 344
10.4.2 The Temporary Entanglement Network with and Without Slip 346
10.5…The Doi-Edwards Theory 351
10.5.1 The Constitutive Equations of the Doi-Edwards Theory 351
10.5.2 The Doi--Edwards Theory 2 for Simple Shear and Multiaxial Extension 355
10.6…Theory of the Molecular Stress Function (MSF) 360
10.6.1 The Constitutive Equation of the MSF-Theory 360
10.6.2 The MSF Theory for Simple Shear and Multiaxial Extension 362
A.1. Appendix A: The Averages lang(uvprime)rangle and lang(ln uvprime)rangle and the Components of the Strain Tensor 366
References 370
11 Shear Rheology 371
11.1…Experiments at Constant Shear Rate (Stressing Experiments) 372
11.2…Relation Between the Time and Shear-Rate Dependence of the Viscosity 375
11.3…Dynamic-Mechanical Experiments 376
11.3.1 Relations Between Dynamic-Mechanical and Stressing Experiments (Cox-Merz Rule) 378
11.3.2 Van Gurp-Palmen Plot 380
11.3.3 Large Amplitude Oscillations (LAOS) 381
11.4…Creep Recovery Experiments 381
11.4.1 Comparison of Creep Recovery with Dynamic-Mechanical Experiments 385
11.5…Capillary Rheometry 386
11.5.1 Viscosity Functions 387
11.5.2 Numerical Descriptions of Viscosity Functions 388
11.5.3 Entrance Pressure Loss 390
11.5.4 Extrudate Swell 391
References 394
12 Extensional Rheology 395
12.1…Basics of Uniaxial Extension 395
12.2…Multiaxial Extensions 397
12.3…Experimental Devices for Uniaxial Extension 400
12.3.1 Elongational Rheometer After Meissner 401
12.3.2 Rheometrics Extensional Rheometer 403
12.3.3 Sentmanat Extensional Rheometer 404
12.3.4 Filament Stretching Rheometer 405
12.3.5 Tensile Rheometer After M•nstedt 406
12.4…Experimental Devices for Multiaxial Extension 408
12.4.1 Hachmann-Meissner Rheometer 409
12.4.2 Lubricated Squeeze-Flow Rheometer 409
12.5…Fundamental Features of Uniaxial Flow 410
12.5.1 Comparison of Basic Experiments at Constant Elongational Rate or Tensile Stress 410
12.5.2 Dependence of the Elongational Viscosity on Elongational Rate 415
12.5.3 Dependence of the Recoverable Tensile Compliance on Stress 417
12.5.4 Temperature Dependence 418
12.6…Comparison of Uniaxial and Multiaxial Extensions 421
12.7…Role of the Uniformity of Sample Deformation for the Accuracy of Extensional Experiments 423
References 425
13 Rheological Properties and Molecular Structure 427
13.1…Viscous Properties of Polymer Melts 428
13.1.1 Viscosity Functions in Dependence on Molecular Structure 428
13.1.2 Zero-Shear Viscosities 433
13.1.3 Analysis of Long-Chain Branched Polypropylenes Using eta o(Mw) 437
13.2…Elastic Properties 440
13.2.1 Quantities Reflecting Elasticity 440
13.2.2 Extrudate Swell in Dependence on Molecular Structure 440
13.2.3 Steady-State Linear Recoverable Compliance 443
13.2.3.1 Dependence on Molecular Structure 444
13.2.4 Recoverable Compliances at Higher Stresses 448
13.2.5 Conclusions on the Relationships Between Elasticity in Shear and Molecular Structure 449
13.3…Elongational Properties of Polymer Melts 450
13.3.1 Influence of Molar Mass and Molar Mass Distribution 450
13.3.2 Influence of Long-Chain Branches 453
13.3.3 Conclusions on the Relationships Between Elongational Viscosity and Molecular Structure 459
References 460
14 Thermorheological Behavior of Various Polymer Melts 461
14.1…Amorphous Polymers 461
14.2…Semicrystalline Polymers 464
14.2.1 Thermorheological Simplicity and Its Application to the Analysis of Short-Chain Branching 465
14.2.2 Thermorheological Complexity and Its Potential for the Analysis of Branching 469
14.2.3 Interpretation and Determination of the Vertical Shift Factor 472
References 475
15 Rheometry 476
15.1…Capillary Rheometry 476
15.1.1 Calculation of Shear Stress and Shear Rate 477
15.1.2 Velocity Profiles 482
15.1.3 Viscosity Functions and Bagley-Correction 483
15.2…Slit Rheometry 486
15.3…Rotational Rheometry 489
15.3.1 Plate-Plate Rheometer 489
15.3.2 Cone-and-Plate Rheometer 495
15.3.2.1 Alternative Derivation of the Equations for Shear Rate and Shear Stress 500
References 501
16 Measurements of Flow Fields of Polymer Melts by Laser-Doppler Velocimetry 502
16.1…Motivation 502
16.2…Measuring Principle and Setup of a Slit Die 503
16.2.1 Measuring Principle of Laser-Doppler Velocimetry 503
16.2.2 Experimental Setup of a Slit Die 505
16.3…Flow Fields in Different Sections of the Slit Die 506
16.3.1 Entrance Flow 507
16.3.1.1 Flow Profiles in the Reservoir 508
16.3.1.2 Flow Along the Channel Axis 509
16.3.1.3 Flow Beyond the Channel Axis 512
16.3.1.4 Secondary Flow of Linear and Long-Chain Branched Polyolefins 514
16.3.2 Flow Inside the Slit Capillary 516
16.3.3 Stick-Slip Phenomena Investigated by Laser-Doppler Velocimetry 519
16.3.3.1 Velocity Profiles in Region I 520
16.3.3.2 Velocity and Pressure Profiles in Region II 524
16.3.3.3 Velocity and Pressure Profiles in Region III 526
16.3.4 Flow at the Die Exit 528
16.3.4.1 Relation Between Exit Flow and ‘‘Shark Skin’’ 531
References 533
17 Rheological Properties and Processing 534
17.1…Melt Flow Rate 534
17.2…Role of Viscosity Functions 535
17.3…Influence of Additives on the Surface Defect ‘‘Shark Skin’’ 536
17.4…Flow Profiles Inside a Flat Die for Film Casting 540
17.4.1 Motivation 540
17.4.2 Experimental Device 541
17.4.3 Flow Profiles 542
17.5…Role of Elongational Viscosity for Processing 545
17.5.1 General Considerations 545
17.5.2 Uniformity of the Elongation of Samples with Different Strain Hardening 545
17.5.3 Uniformity of Films Blown from Two Polyethylenes with Different Strain Hardening 549
17.5.4 Elongational Viscosity and Foaming 551
References 554
SubjectIndex 555