Structure and Rheology of Molten Polymers

Name: Structure and Rheology of Molten Polymers | From Structure to Flow Behavior and Back Again
Brand: Hanser Publications
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From Structure to Flow Behavior and Back Again

John M. Dealy Daniel J. Read Ronald G. Larson(Author)

Hanser Publications (Publisher)

1st Edition

Published on 12. February 2018

610 pages

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Recent advances in polymer science have made it possible to relate quantitatively molecular structure to rheological behavior. At the same time, new methods of synthesis and characterization allow the preparation and structural verification of samples having a range of branched polymeric structures. This book unites this knowledge to enable production of polymers with prescribed processability and end-product properties. Methods of polymer synthesis and characterization are described, starting from fundamentals. The foundations of linear viscoelasticity are introduced, and then the linear behavior of entangled polymers is described in detail. This is followed by a discussion of the molecular modeling of linear behavior. Tube models for both linear and branched polymers are presented. The final two chapters deal with nonlinear rheological behavior and tube models to describe nonlinearity. In this second edition, each chapter has been significantly rewritten to account for recent advances in experimental methods and theoretical modeling. It includes new and updated material on developments in polymer synthesis and characterization, computational algorithms for linear and nonlinear rheology prediction, measurement of nonlinear viscoelasticity, entanglement detection algorithms in molecular dynamics, nonlinear constitutive equations, and instabilities. Contents: - Structure of Polymers - Polymerization Reactions and Processes - Linear Viscoelasticity - Fundamentals - Linear Viscoelasticity - Behavior of Molten Polymers - Tube Models for Linear Polymers - Fundamentals - Tube Models for Linear Polymers - Advanced Topics - Determination of Molecular Weight Distribution Using Rheology - Tube Models for Branched Polymers - Nonlinear Viscoelasticity - Tube Models for Nonlinear Viscoelasticity of Linear and Branched Polymers

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Intro
Preface to the Second Edition
Preface to the First?Edition
Contents
1 Introduction
1.1 Melt Structure and Its Effect on?Rheology
1.2 Overview of This Book
1.3 Applications of the Information Presented
1.4 Supplementary Sources of Information
References
2 Structure of?Polymers
2.1 Molecular Size
2.1.1 The Freely-Jointed Chain
2.1.2 The Gaussian Size Distribution
2.1.2.1 Linear Molecules
2.1.2.2 Branched Molecules
2.1.3 The Dilute Solution and the Theta State
2.1.4 Polymer Molecules in the Melt
2.2 Molecular Weight Distribution
2.2.1 Monodisperse Polymers
2.2.2 Average Molecular Weights and Moments of the Distribution
2.2.3 Continuous Molecular Weight Distribution
2.2.4 Distribution Functions
2.2.5 Narrow Distribution Samples
2.2.6 Bimodality
2.3 Tacticity
2.4 Branching
2.5 Intrinsic Viscosity
2.5.1 Introduction
2.5.2 Rigid Sphere Models
2.5.3 The Free-Draining Molecule
2.5.4 Non-Theta Conditions and the Mark-Houwink-Sakurada Equation
2.5.5 Effect of Polydispersity
2.5.6 Effect of Long-Chain Branching
2.5.7 Effects of Short-Chain Branching
2.5.8 Determination of Intrinsic Viscosity-Extrapolation Methods
2.5.9 Effect of Shear Rate
2.6 Other Structure Characterization Methods
2.6.1 Membrane Osmometry
2.6.2 Light Scattering
2.6.3 Gel Permeation Chromatography
2.6.3.1 MWD of Linear Polymers
2.6.3.2 GPC with Branched Polymers
2.6.3.3 GPC with LDPE
2.6.3.4 Interactive Chromatography
2.6.3.5 Field Flow Fractionation
2.6.4 Mass Spectrometry (MALDI-TOF)
2.6.5 Nuclear Magnetic Resonance
2.6.6 Separations Based on Crystallizability: TREF, CRYSTAF, and CEF
2.6.7 Bivariate (Two-Dimensional) Characterizations
2.6.8 Molecular Structure from Rheology
2.7 Summary
References
3 Polymerization Reactions and?Processes
3.1 Introduction
3.2 Classifications of Polymers and?Polymerization Reactions
3.3 Structural Characteristics of Polymers
3.3.1 Introduction
3.3.2 Chemical Composition-Role of Backbone Bonds in Chain Flexibility
3.3.3 Chemical Composition-Copolymers
3.3.4 Tacticity
3.3.5 Branching
3.4 Living Polymers Having Prescribed Structures
3.4.1 Anionic Polymerization
3.4.2 Living Free-Radical Polymerization (Reversible?Deactivation?Radical Polymerization-RDRP)
3.4.3 Model Polyethylenes for Research
3.5 Industrial Polymerization Processes
3.6 Free-Radical Polymerization of?Low-Density Polyethylene (LDPE)
3.6.1 Shear Modification
3.7 Linear Polyethylene via?Complex?Coordination?Catalysts
3.7.1 Catalyst Systems
3.7.2 Branching in High-Density Polyethylene
3.7.3 Ultrahigh Molecular Weight Polyethylene
3.8 Linear Low-Density Polyethylene via?Ziegler-Natta?Catalysts
3.9 Single-Site Catalysts
3.9.1 Metallocene Catalysts
3.9.2 Long-Chain Branching in Metallocene Polyethylenes
3.9.3 Post-Metallocene Catalysts
3.10 Polypropylene
3.11 Reactors for Polyolefins
3.12 Polystyrene
3.13 Summary
References
4 Linear Viscoelasticity-Fundamentals
4.1 Stress Relaxation and?the?Relaxation?Modulus
4.1.1 The Boltzmann Superposition Principle
4.1.2 The Maxwell Model for the Relaxation Modulus
4.1.3 The Generalized Maxwell Model and?the?Discrete?Relaxation?Spectrum
4.1.4 The Continuous Relaxation Spectrum
4.2 The Creep Compliance and?the?Retardation Spectrum
4.3 Experimental Characterization of?Linear?Viscoelastic Behavior
4.3.1 Oscillatory Shear
4.3.2 Experimental Determination of the Storage and Loss Moduli
4.3.3 Creep Measurements
4.3.4 Other Methods for Monitoring Relaxation Processes
4.4 Calculation of Relaxation Spectra from?Experimental Data
4.4.1 Discrete Spectra
4.4.2 Continuous Spectra
4.5 Time-Temperature Superposition
4.5.1 Time/Frequency (Horizontal) Shifting
4.5.2 The Modulus (Vertical) Shift Factor
4.5.3 Validity of Time-Temperature Superposition
4.6 Time-Pressure Superposition
4.7 Alternative Plots of?Linear?Viscoelastic?Data
4.7.1 Van Gurp-Palmen Plot of Loss Angle Versus Complex Modulus
4.7.2 Cole-Cole Plots
4.8 Summary
References
5 Linear Viscoelasticity-Behavior of Molten Polymers
5.1 Introduction
5.2 Zero-Shear Viscosity of Linear Polymers
5.2.1 Effect of Molecular Weight
5.2.2 Effect of Polydispersity
5.3 The Relaxation Modulus
5.3.1 General Features
5.3.2 How Can a Melt Act like a Rubber?
5.4 The Storage and Loss Moduli
5.5 The Creep and Recoverable Compliances
5.6 The Steady-State Compliance
5.7 The Plateau Modulus
5.7.1 Determination of GN0
5.7.2 Effects of Short Branches and Tacticity
5.8 The Molecular Weight between?Entanglements, Me
5.8.1 Definitions of Me
5.8.2 Molecular Weight between Entanglements (Me) Based?on?Molecular?Theory
5.9 Rheological Behavior of Copolymers
5.10 Effect of Long-Chain Branching on?Linear Viscoelastic Behavior
5.10.1 Introduction
5.10.2 Ideal Branched Polymers
5.10.2.1 Zero-Shear Viscosity of Ideal Stars and Combs
5.10.2.2 Steady-State Compliance of Model Star Polymers
5.10.3 Storage and Loss Moduli of Model Branched Systems
5.10.4 Randomly Branched Polymers
5.10.5 Low-Density Polyethylene
5.11 Use of Linear Viscoelastic Data to?Determine Branching Level
5.11.1 Introduction
5.11.2 Correlations Based on the Zero-Shear Viscosity
5.12 Summary
References
6 Tube Models for Linear Polymers-Fundamentals
6.1 Introduction
6.2 The Rouse-Bueche Model for?Unentangled Polymers
6.2.1 Introduction
6.2.2 The Rouse Model for the Viscoelasticity of a Dilute Polymer Solution
6.2.3 Bueche's Modification for an Unentangled Melt
6.3 Entanglements and the Tube Model
6.3.1 The Critical Molecular Weight for Entanglement MC
6.3.2 The Plateau Modulus GN0
6.3.3 The Molecular Weight Between Entanglements Me
6.3.4 The Tube Diameter a
6.3.5 The Equilibration Time te
6.3.6 Identification of Entanglements and Tubes in Computer Simulation
6.4 Modes of Relaxation
6.4.1 Reptation
6.4.2 Primitive Path Fluctuations
6.4.3 Reptation Combined with Primitive Path Fluctuations
6.4.4 Constraint Release-Double Reptation
6.4.4.1 Monodisperse Melts
6.4.4.2 Bidisperse Melts
6.4.4.3 Polydisperse Melts
6.4.5 Rouse Relaxation within the Tube
6.5 An Alternative Picture for Entangled Polymers: Slip-Links
6.6 Summary
References
7 Tube Models for Linear Polymers-Advanced Topics
7.1 Introduction
7.2 Limitations of Double Reptation Theory
7.3 Constraint-Release Rouse Relaxation in?Bidisperse Melts
7.3.1 Non-Self-Entangled Long Chains in a Short-Chain Matrix
7.3.2 Self-Entangled Long Chains in a Short-Chain Matrix
7.3.3 Thin Tubes, Fat Tubes, and the Viovy Diagram
7.4 Polydisperse Melts and "Dynamic?Dilution"
7.4.1 Polydisperse Chains
7.4.2 Tube Dilation or "Dynamic Dilution"
7.5 Input Parameters for Tube Models
7.6 Summary
References
8 Determination of?Molecular Weight Distribution Using?Rheology
8.1 Introduction
8.2 Viscosity Methods
8.3 Empirical Correlations Based?on?the?Elastic Modulus
8.4 Methods Based on Double Reptation
8.5 Generalization of Double Reptation
8.6 Dealing with the Rouse Modes
8.7 Models that Account for Additional Relaxation Processes
8.8 Determination of Polydispersity Indexes
8.9 Summary
References
9 Tube Models for Branched Polymers
9.1 Introduction
9.2 General Effect of LCB on Rheology
9.2.1 Qualitative Description of Relaxation Mechanisms in?Long-Chain-Branched Polymers
9.3 Star Polymers
9.3.1 Deep Primitive Path Fluctuations
9.3.2 Dynamic Dilution
9.3.3 Comparison of Milner-McLeish Theory to Linear Viscoelastic Data
9.3.3.1 Monodisperse Stars
9.3.3.2 Bidisperse Stars
9.3.3.3 Star/Linear Blends
9.4 Multiply Branched Polymers
9.4.1 Dynamic Dilution for Polymers with Backbones
9.4.2 Branch Point Motion
9.4.3 Backbone Relaxation
9.5 Tube Model Algorithms for Polydisperse Branched Polymers
9.5.1 "Hierarchical" and "BoB" Dynamic Dilution Models
9.5.2 The "Time-Marching" Algorithm
9.5.3 Data and Predictions for Model Polymers and Randomly Branched?Polymers
9.6 Slip-Link Models for Branched Polymers
9.6.1 Symmetric Star Polymers and Blends with Linear Polymers
9.6.2 Branch Point Hopping in Slip-Link Simulations
9.7 Summary
References
10 Nonlinear Viscoelasticity
10.1 Introduction
10.2 Nonlinear Phenomena-A Tube Model Interpretation
10.2.1 Large Scale Orientation-The Need for a Finite Strain Tensor
10.2.2 Chain Retraction and the Damping Function
10.2.3 Convective Constraint Release and Shear Thinning
10.3 Constitutive Equations
10.3.1 Boltzmann Revisited
10.3.2 Integral Constitutive Equations
10.3.3 Differential Constitutive Equations
10.4 Nonlinear Stress Relaxation
10.4.1 Doi and Edwards Predictions of the Damping Function
10.4.2 Estimating the Rouse Time of an Entangled Chain
10.4.3 Damping Functions of Typical Polymers
10.4.4 Normal Stress Relaxation
10.4.5 Double-Step Strain
10.5 Dimensionless Groups Used?to?Plot?Rheological?Data
10.5.1 The Deborah Number
10.5.2 The Weissenberg Number
10.6 Transient Shear Tests at Finite Rates
10.6.1 Stress Growth and Relaxation in Steady Shear
10.6.2 Large- and Medium-Amplitude Oscillatory Shear
10.7 The Viscometric Functions
10.7.1 Dependence of Viscosity on Shear Rate
10.7.1.1 Empirical Viscosity Models
10.7.1.2 Viscosity Function in Terms of Tube Models
10.7.1.3 Effect of Molecular Weight Distribution on Viscosity
10.7.1.4 Effect of Long-Chain Branching on Viscosity
10.7.2 Normal Stress Differences in Steady Simple Shear
10.8 Experimental Methods for?Shear?Measurements
10.8.1 Rotational Rheometers
10.8.1.1 Generating Step Strain
10.8.1.2 Flow Irregularities in Cone-Plate Rheometers
10.8.1.3 Measurement of the Second Normal Stress Difference
10.8.2 Sliding Plate Rheometers
10.8.3 Optical Methods-Flow Birefringence
10.8.4 Capillary and Slit Rheometers
10.8.5 The Cox-Merz Rule
10.9 Extensional Flow Behavior of Melts and?Concentrated Solutions
10.9.1 Introduction
10.9.2 Solutions versus Melts
10.9.3 Linear, Monodisperse Polymers
10.9.4 Effect of Polydispersity
10.9.5 Linear Low-Density Polyethylene
10.9.6 Model Branched Systems
10.9.7 Long-Chain Branched Metallocene Polyethylenes
10.9.8 Randomly Branched Polymers and LDPE
10.9.9 Stress Overshoot in Extensional Flow
10.10 Experimental Methods for?Extensional?Flows
10.10.1 Introduction
10.10.2 Rheometers for Uniaxial Extension
10.10.3 Uniaxial Extension-Approximate Methods
10.10.4 Rheometers for Biaxial and Planar Extension
10.11 Summary
References
11 Tube Models for Nonlinear Viscoelasticity of Linear and Branched Polymers
11.1 Introduction
11.2 Relaxation Processes Unique?to?the?Nonlinear Regime
11.2.1 Retraction
11.2.2 Convective Constraint Release
11.3 Monodisperse Linear Polymers
11.3.1 No Chain Stretch: The Doi-Edwards Equation
11.3.2 Chain Stretch: The Doi-Edwards-Marrucci-Grizzuti (DEMG) Theory
11.3.3 Convective Constraint Release (CCR) and the GLaMM Model
11.3.4 Toy Models Containing CCR and Chain Stretch
11.3.4.1 "Rolie-Poly" Model for CCR
11.3.4.2 Differential Model of Ianniruberto and Marrucci
11.3.5 Comparison of Theory with Data for Monodisperse Linear Polymers: Shearing Flows
11.3.6 Extensional Flows of Melts and Solutions of Linear Polymers
11.3.7 Constitutive Instabilities and Slip
11.3.8 Entanglement Stripping and Chain Tumbling
11.3.9 Processing Flows
11.4 Polydisperse Linear Polymers
11.5 Polymers with Long-Chain Branching
11.5.1 The Pom-Pom Model
11.5.2 Revisions to the Pom-Pom Model
11.5.2.1 Drag-Strain Coupling
11.5.2.2 Correction for Reversing Flows
11.5.2.3 Second Normal Stress Difference and Other Corrections: The?Extended Pom-Pom Model
11.5.2.4 Stress Overshoots, Accelerated Relaxation, and Entanglement Stripping
11.5.3 Empirical Multi-Mode Pom-Pom Equations for Commercial Melts
11.6 Towards Prediction of Nonlinear Viscoelasticity from Molecular Parameters
11.6.1 Seniority and Priority
11.6.2 Computational Prediction of Nonlinear Rheology for?Polydisperse?Branched?Polymers
11.7 Summary
References
12 State of the Art and?Challenges for?the Future
12.1 State of the Art
12.2 Progress and Remaining Challenges
Appendix?A: Structural?and Rheological Parameters for Several Polymers
Appendix?B: Some?Tensors Useful?in Rheology
Nomenclature
Author Index
Subject Index
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Structure and Rheology of Molten Polymers

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