Foreword ....................................................... xv
Preface ...................................................... xvii
Authors ....................................................... xxi
Chapter 1 Polymer Melt Fracture Pictures ....................... 1
1.1 Optical Microscopy ......................................... 2
1.2 Scanning Electron Microscopy .............................. 10
Reference ...................................................... 20
Chapter 2 Polymer Characteristics ............................. 21
2.1 Polymers .................................................. 22
2.1.1 Polymer Architecture ............................... 24
2.1.2 Molar Mass Distribution ............................ 28
2.1.3 Polymerization Processes ........................... 32
2.2 Polymer Characterization .................................. 35
2.2.1 Polymer Architecture ............................... 35
2.2.1.1 Spectrometry: Ultraviolet, Visible,
Infrared, and Raman ....................... 36
2.2.1.2 Nuclear Magnetic Resonance Spectrometry ... 36
2.2.1.3 Density ................................... 39
2.2.1.4 Thermal Analysis .......................... 39
2.2.2 Molar Mass, Molar Mass Distribution ................ 40
2.2.2.1 Dilute Solution Viscosity ................. 41
2.2.2.2 Light Scattering .......................... 43
2.2.2.3 Colligative Property Measurement
Techniques ................................ 44
2.2.2.4 Gel Permeation Chromatography ............. 45
2.2.2.5 Fractionation ............................. 46
2.2.2.6 Rheology .................................. 47
2.3 General Observation .................................. 49
References ................................................ 50
Chapter 3 Polymer Rheology .................................... 53
3.1 Continuum Mechanics ....................................... 53
3.2 Scalars, Vectors, and Tensors ............................. 54
3.3 Stress Tensor ............................................. 58
3.4 Strain Tensors ............................................ 59
3.4.1 Finger Tensor ...................................... 59
3.4.2 Rate of Deformation and Vorticity Tensor ........... 63
3.4.3 Relation between Finger Tensor В and Rate of
Deformation Tensor D ............................... 65
3.5 Equations of Motion ....................................... 65
3.5.1 Transport Theorem .................................. 66
3.5.2 Mass Balance ....................................... 67
3.5.3 Momentum Balance ................................... 68
3.6 Constitutive Equations .................................... 71
3.6.1 Elastic Behavior ................................... 71
3.6.2 Viscous Behavior ................................... 72
3.6.3 Viscoelastic Behavior .............................. 75
3.6.4 Linear Viscoelasticity ............................. 78
3.6.5 Compliance Function ................................ 80
3.7 General Observation ....................................... 84
References ................................................ 84
Chapter 4 Polymer Processing .................................. 87
4.1 Extrusion ................................................. 87
4.1.1 Granulation ........................................ 88
4.1.2 Film Blowing ....................................... 88
4.1.3 Film and Sheet Casting ............................. 93
4.1.4 Extrusion Blow Molding ............................. 95
4.1.5 Wire Coating ....................................... 97
4.1.6 Pipe and Profile ................................... 98
4.1.7 Fiber Spinning ..................................... 98
4.1.8 Co-Extrusion ...................................... 101
4.2 Injection Molding ........................................ 102
4.3 Rotational Molding ....................................... 103
4.4 Calendering .............................................. 103
4.5 General Observation ...................................... 104
References ............................................... 105
Chapter 5 Melt Fracture Experiments .......................... 109
5.1 Constant-Pressure and Constant-Rate Experiments .......... 110
5.1.1 Discontinuous Flow Curves ......................... 114
5.1.2 Continuous Flow Curves ............................ 120
5.2 Flow Visualization ....................................... 122
5.2.1 Particle Tracking ................................. 124
5.2.2 Flow Birefringence ................................ 126
5.2.3 Stacked Colors A .................................. 130
5.3 Critical Numbers ......................................... 131
5.3.1 Reynolds Number ................................... 132
5.3.2 Weissenberg and Deborah Number .................... 132
5.3.3 Recoverable Strain ................................ 134
5.3.4 Critical Stress ................................... 135
5.4 Melt Fracture Observation ................................ 139
5.4.1 Microscopy ........................................ 139
5.4.2 Profilometry ...................................... 140
5.4.3 Indirect Methods .................................. 141
5.4.4 Melt Fracture Quantification ...................... 144
5.5 Change of Slope .......................................... 147
5.6 Wall Slip ................................................ 148
5.6.1 The Mooney Method ................................. 148
5.6.2 The Laun Method ................................... 151
5.6.3 Other Methods ..................................... 153
5.7 Compressibility .......................................... 154
5.8 General Observation ...................................... 155
References ............................................... 156
Chapter 6 Melt Fracture Variables ............................ 167
6.1 Polymer Architecture ..................................... 167
6.2 Polymer-Processing Variables ............................. 174
6.2.1 Length-Radius Ratio ............................... 174
6.2.2 Die Entry and Exit Angle .......................... 179
6.2.3 Die Construction Material ......................... 182
6.2.4 Die Surface Roughness ............................. 184
6.2.5 Die Surface Modifier .............................. 186
6.2.6 Temperature ....................................... 187
6.3 General Observation ...................................... 192
References ............................................... 193
Chapter 7 Understanding Melt Fracture ........................ 201
7.1 Melt Fracture Mechanisms ................................. 202
7.1.1 Reynolds Turbulence ............................... 202
7.1.2 Thermal Catastrophe ............................... 202
7.1.3 Stress-Induced Fractionation ...................... 202
7.1.4 Fracture .......................................... 202
7.1.5 Cavitation ........................................ 205
7.1.6 Interfacial Slip .................................. 205
7.1.6.1 Microscopic Mechanisms—Cohesive
Failure .................................. 207
7.1.6.2 Microscopic Mechanisms—Adhesive
Failure .................................. 209
7.2 The Constitutive Approach ................................ 211
7.2.1 Phenomenology ..................................... 211
7.2.2 Relaxation Oscillations ........................... 212
7.2.3 Numerical Simulations ............................. 214
7.2.4 Molecular Considerations .......................... 215
7.3 General Understanding .................................... 218
7.4 General Observation ...................................... 225
References ............................................... 226
Chapter 8 Advanced Polymer Rheology .......................... 233
8.1 Molar Mass, Zero-Shear Viscosity, and Recoverable
Compliance ............................................... 234
8.2 Continuous Models and Frame Invariance ................... 237
8.2.1 Upper-Convected Maxwell Model ..................... 239
8.2.2 Johnson-Segalman-(Oldroyd) Models ................. 241
8.2.2.1 Johnson-Segalman Model ................... 241
8.2.2.2 Johnson-Segalman-Oldroyd Model ........... 244
8.2.3 Kaye-Bernstein-Kearsley-Zapas Model ............... 245
8.3 Microscopic Models ....................................... 248
8.3.1 Rouse Model ....................................... 250
8.3.2 Reptation Model ................................... 253
8.3.3 Branching ......................................... 258
8.3.4 Pom-Pom Model ..................................... 259
8.4 Molar Mass Distribution and Linear Viscoelasticity ....... 261
8.5 General Observation ...................................... 263
References ............................................... 263
Chapter 9 Modeling Melt Fracture ............................. 267
9.1 The Relaxation-Oscillation Model ......................... 268
9.2 Coupling RO and Constitutive Equations ................... 271
9.3 Slip-Boundary Conditions ................................. 275
9.4 A Rheological Model Including Wall Slip .................. 280
9.5 Bulk and Interfacial Viscosity Balance for Different
Polymers ................................................. 284
9.6 Flow Curve and Melt Fracture Relation .................... 287
9.6.1 "Spurt" Distortions ............................... 288
9.6.2 Surface Distortions ............................... 288
9.6.3 Volume Distortions ................................ 290
9.7 General Observation ...................................... 290
References ............................................... 291
Chapter 10 Preventing Melt Fracture ........................... 295
10.1 Additives ................................................ 295
10.1.1 Slip Agents ....................................... 297
10.1.2 Polymer Blends .................................... 298
10.1.3 Wax ............................................... 299
10.1.4 Fillers ........................................... 299
10.2 Extruder and Processing Conditions .................. 300
10.3 Dealing with Melt Fracture ............................... 303
10.3.1 Melt Fracture Checklist ........................... 305
10.4 General Observation ...................................... 305
References ............................................... 306
Index ......................................................... 313
|
