Melt Rheology and Its Role in Plastics Processing

This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten poly­ mers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed deriva­ tions of equations. The processing operations are described qualita­ tively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery. The audience for which the book is intended is also dual in It includes scientists and engineers whose work in the nature. plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degra­ dation. The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose.

1. Introduction to Rheology.- 1.1 What is Rheology?.- 1.2 Why Rheological Properties are Important.- 1.3 Stress as a Measure of Force.- 1.4 Strain as a Measure of Deformation.- 1.4.1 Strain Measures for Simple Extension.- 1.4.2 Shear Strain.- 1.5 Rheological Phenomena.- 1.5.1 Elasticity; Hooke’s Law.- 1.5.2 Viscosity.- 1.5.3 Viscoelasticity.- 1.5.4 Structural Time Dependency.- 1.5.5 Plasticity and Yield Stress.- 1.6 Why Polymeric Liquids are Non-Newtonian.- 1.6.1 Polymer Solutions.- 1.6.2 Molten Plastics.- 1.7 A Word About Tensors.- 1.7.1 Vectors.- 1.7.2 What is a Tensor?.- 1.8 The Stress Tensor.- 1.9 A Strain Tensor for Infinitesimal Deformations.- 1.10 The Newtonian Fluid.- 1.11 The Basic Equations of Fluid Mechanics.- 1.11.1 The Continuity Equation.- 1.11.2 Cauchy’s Equation.- 1.11.3 The Navier-Stokes Equation 40 References.- 2. Linear Viscoelasticity.- 2.1 Introduction.- 2.2 The Relaxation Modulus.- 2.3 The Boltzmann Superposition Principle.- 2.4 Relaxation Modulus of Molten Polymers.- 2.5 Empirical Equations for the Relaxation Modulus.- 2.5.1 The Generalized Maxwell Model.- 2.5.2 Power Laws and an Exponential Function.- 2.6 The Relaxation Spectrum.- 2.7 Creep and Creep Recovery; The Compliance.- 2.8 Small Amplitude Oscillatory Shear.- 2.8.1 The Complex Modulus and the Complex Viscosity.- 2.8.2 Complex Modulus of Typical Molten Polymers.- 2.8.3 Quantitative Relationships between G*(?) and MWD.- 2.8.4 The Storage and Loss Compliances.- 2.9 Determination of Maxwell Model Parameters.- 2.10 Start-Up and Cessation of Steady Simple Shear and Extension.- 2.11 Molecular Theories: Prediction of Linear Behavior.- 2.11.1 The Modified Rouse Model for Unentangled Melts.- 2.11.1.1 The Rouse Model for Dilute Solutions.- 2.11.1.2 The Bueche Modification of the Rouse Theory.- 2.11.1.3 The Bueche-Ferry Law.- 2.11.2 Molecular Theories for Entangled Melts.- 2.11.2.1 Evidence for the Existence of Entanglements.- 2.11.2.2 The Nature of Entanglement Coupling.- 2.11.2.3 Reptation.- 2.11.2.4 The Doi-Edwards Theory.- 2.11.2.5 The Curtiss-Bird Model.- 2.11.2.6 Limitations of Reptation Models.- 2.12 Time-Temperature Superposition.- 2.13 Linear Behavior of Several Polymers 94 References.- 3. Introduction to Nonlinear Viscoelasticity.- 3.1 Introduction.- 3.2 Nonlinear Phenomena.- 3.3 Theories of Nonlinear Behavior.- 3.4 Finite Measures of Strain.- 3.4.1 The Cauchy Tensor and the Finger Tensor.- 3.4.2 Strain Tensors.- 3.4.3 Reference Configurations.- 3.4.4 Scalar Invariants of the Finger Tensor.- 3.5 The Rubberlike Liquid.- 3.5.1 A Theory of Finite Linear Viscoelasticity.- 3.5.2 Lodge’s Network Theory and the Convected Maxwell Model.- 3.5.3 Behavior of the Rubberlike Liquid in Simple Shear Flows.- 3.5.3.1 Rubberlike Liquid in Step Shear Strain.- 3.5.3.2 Rubberlike Liquid in Steady Simple Shear.- 3.5.3.3 Rubberlike Liquid in Oscillatory Shear.- 3.5.3.4 Constrained Recoil of Rubberlike Liquid.- 3.5.3.5 The Stress Ratio (N1/?) and the Recoverable Shear.- 3.5.4 The Rubberlike Liquid in Simple Extension.- 3.5.5 Comments on the Rubberlike Liquid Model.- 3.6 The BKZ Equation.- 3.7 Wagner’s Equation and the Damping Function.- 3.7.1 Strain Dependent Memory Function.- 3.7.2 Determination of the Damping Function.- 3.7.3 Separable Stress Relaxation Behavior.- 3.7.4 Damping Function Equations for Polymeric Liquids.- 3.7.4.1 Damping Function for Shear Flows.- 3.7.4.2 Damping Function for Simple Extension.- 3.7.4.3 Universal Damping Functions.- 3.7.5 Interpretation of the Damping Function in Terms of Entanglements.- 3.7.5.1 The Irreversibility Assumption.- 3.7.6 Comments on the Use of the Damping Function.- 3.8 Molecular Models for Nonlinear Viscoelasticity.- 3.8.1 The Doi-Edwards Constitutive Equation.- 3.9 Strong Flows; The Tendency to Stretch and Align Molecules.- References.- 4. Steady Simple Shear Flow and the Viscometric Functions.- 4.1 Introduction.- 4.2 Steady Simple Shear Flow.- 4.3 Viscometric Flow.- 4.4 Wall Slip and Edge Effects.- 4.5 The Viscosity of Molten Polymers.- 4.5.1 Dependence of Viscosity on Shear Rate.- 4.5.2 Dependence of Viscosity on Temperature.- 4.6 The First Normal Stress Difference.- 4.7 Empirical Relationships Involving Viscometric Functions.- 4.7.1 The Cox-Merz Rules.- 4.7.2 The Gleissle Mirror Relations.- 4.7.3 Other Relationships 176 References.- 5. Transient Shear Flows Used to Study Nonlinear Viscoelasticity.- 5.1 Introduction.- 5.2 Step Shear Strain.- 5.2.1 Finite Rise Time.- 5.2.2 The Nonlinear Shear Stress Relaxation Modulus.- 5.2.3 Time-Temperature Superposition.- 5.2.4 Strain-Dependent Spectrum and Maxwell Parameters.- 5.2.5 Normal Stress Differences for Single-Step Shear Strain.- 5.2.6 Multistep Strain Tests.- 5.3 Flows Involving Steady Simple Shear.- 5.3.1 Start-Up Flow.- 5.3.2 Cessation of Steady Simple Shear.- 5.3.3 Interrupted Shear.- 5.3.4 Reduction in Shear Rate.- 5.4 Nonlinear Creep.- 5.4.1 Time-Temperature Superposition of Creep Data.- 5.5 Recoil and Recoverable Shear.- 5.5.1 Creep Recovery.- 5.5.1.1 Time-Temperature Superposition; Creep Recovery.- 5.5.2 Recoil During Start-Up Flow.- 5.5.3 Recoverable Shear Following Steady Simple Shear.- 5.6 Superposed Deformations.- 5.6.1 Superposed Steady and Oscillatory Shear.- 5.6.2 Step Strain with Superposed Deformations.- 5.7 Large Amplitude Oscillatory Shear.- 5.8 Exponential Shear; A Strong Flow.- 5.9 Usefulness of Transient Shear Tests.- References.- 6. Extensional Flow Properties and Their Measurement.- 6.1 Introduction.- 6.2 Extensional Flows.- 6.3 Simple Extension.- 6.3.1 Material Functions for Simple Extension.- 6.3.2 Experimental Methods.- 6.3.3 Experimental Observations for LDPE.- 6.3.4 Experimental Observations for Linear Polymers.- 6.4 Biaxial Extension.- 6.5 Planar Extension.- 6.6 Other Extensional Flows.- References.- 7. Rotational and Sliding Surface Rheometers.- 7.1 Introduction.- 7.2 Sources of Error for Drag Flow Rheometers.- 7.2.1 Instrument Compliance.- 7.2.2 Viscous Heating.- 7.2.3 End and Edge Effects.- 7.2.4 Shear Wave Propagation.- 7.3 Cone-Plate Flow Rheometers.- 7.3.1 Basic Equations for Cone-Plate Rheometers.- 7.3.2 Sources of Error for Cone-Plate Rheometers.- 7.3.3 Measurement of the First Normal Stress Difference.- 7.4 Parallel Disk Rheometers.- 7.5 Eccentric Rotating Disks.- 7.6 Concentric Cylinder Rheometers.- 7.7 Controlled Stress Rotational Rheometers.- 7.8 Torque Rheometers.- 7.9 Sliding Plate Rheometers.- 7.9.1 Basic Equations for Sliding Plate Rheometers.- 7.9.2 End and Edge Effects for Sliding Plate Rheometers.- 7.9.3 Sliding Plate Melt Rheometers.- 7.9.4 The Shear Stress Transducer.- 7.10 Sliding Cylinder Rheometers.- References.- 8. Flow in Capillaries, Slits and Dies.- 8.1 Introduction.- 8.2 Flow in a Round Tube.- 8.2.1 Shear Stress Distribution.- 8.2.2 Shear Rate for a Newtonian Fluid.- 8.2.3 Shear Rate for a Power Law Fluid.- 8.2.4 The Rabinowitch Correction.- 8.2.5 The Schummer Approximation.- 8.2.6 Wall Slip in Capillary Flow.- 8.3 Flow in a Slit.- 8.3.1 Basic Equations for Shear Stress and Shear Rate.- 8.3.2 Use of a Slit Rheometer to Determine N1.- 8.3.2.1 Determination of N1 from the Hole Pressure.- 8.3.2.2 Determination of N1 from the Exit Pressure.- 8.4 Pressure Drop in Irregular Cross Sections.- 8.5 Entrance Effects.- 8.5.1 Experimental Observations.- 8.5.2 Entrance Pressure Drop—the Bagley End Correction.- 8.5.3 Rheological Significance of the Entrance Pressure Drop.- 8.6 Capillary Rheometers.- 8.7 Flow in Converging Channels.- 8.7.1 The Lubrication Approximation.- 8.7.2 Industrial Die Design.- 8.8 Extrudate Swell.- 8.9 Extrudate Distortion.- 8.9.1 Surface Melt Fracture—Sharkskin.- 8.9.2 Oscillatory Flow in Linear Polymers.- 8.9.3 Gross Melt Fracture.- 8.9.4 Role of Slip in Melt Fracture.- 8.9.5 Gross Melt Fracture Without Oscillations.- References.- 9. Rheo-Optics and Molecular Orientation.- 9.1 Basic Concepts—Interaction of Light and Matter.- 9.1.1 Refractive Index and Polarization.- 9.1.2 Absorption and Scattering.- 9.1.3 Anisotropic Media; Birefringence and Dichroism.- 9.2 Measurement of Birefringence.- 9.3 Birefringence and Stress.- 9.3.1 Stress-Optical Relation.- 9.3.2 Application of Birefringence Measurements.- References.- 10. Effects of Molecular Structure.- 10.1 Introduction and Qualitative Overview of Molecular Theory.- 10.2 Molecular Weight Dependence of Zero Shear Viscosity.- 10.3 Compliance and First Normal Stress Difference.- 10.4 Shear Rate Dependence of Viscosity.- 10.5 Temperature and Pressure Dependence.- 10.5.1 Temperature Dependence of Viscosity.- 10.5.2 Pressure Dependence of Viscosity.- 10.6 Effects of Long Chain Branching.- References.- 11. Rheology of Multiphase Systems.- 11.1 Introduction.- 11.2 Effect of Rigid Fillers.- 11.2.1 Viscosity.- 11.2.2 Elasticity.- 11.3 Deformable Multiphase Systems (Blends, Block Polymers).- 11.3.1 Deformation of Disperse Phases and Relation to Morphology.- 11.3.2 Rheology of Immiscible Polymer Blends.- 11.3.3 Phase-Separated Block and Graft Copolymers.- References.- 12. Chemorheology of Reacting Systems.- 12.1 Introduction.- 12.2 Nature of the Curing Reaction.- 12.3 Experimental Methods for Monitoring Curing Reactions.- 12.3.1 Dielectric Analysis.- 12.4 Viscosity of the Pre-gel Liquid.- 12.5 The Gel Point and Beyond.- References.- 13. Rheology of Thermotropic Liquid Crystal Polymers.- 13.1 Introduction.- 13.2 Rheology of Low Molecular Weight Liquid Crystals.- 13.3 Rheology of Aromatic Thermotropic Polyesters.- 13.4 Relation of Rheology to Processing of Liquid Crystal Polymers.- References.- 14. Role of Rheology In Extrusion.- 14.1 Introduction.- 14.1.1 Functions of Extruders.- 14.1.2 Types of Extruders.- 14.1.3 Screw Extruder Zones.- 14.2 Analysis of Single Screw Extruder Operation.- 14.2.1 Approximate Analysis of Melt Conveying Zone.- 14.2.2 Coupling Melt Conveying to Die Flow.- 14.2.3 Effects of Simplifying Approximations.- 14.2.3.1 Geometric Factors.- 14.2.3.2 Leakage Flow.- 14.2.3.3 Non-Newtonian Viscosity.- 14.2.3.4 Non-Isothermal Flow.- 14.2.4 Solids Conveying and Melting Zones.- 14.2.4.1 Feeding and Solids Conveying.- 14.2.4.2 Melting Zone.- 14.2.5 Scale-Up and Simulation.- 14.2.5.1 Scale-Up.- 14.2.5.2 Simulation.- 14.3 Mixing, Devolatilization and Twin Screw Extruders.- ...