Polymer Melt Rheology and Flow Birefringence

Assumption of a Temporary Network Structure?.- 2.3 The Most Simple Rubberlike Liquid Model.- 2.3.1 Introduction.- 2.3.2 Formulation of the Theory.- 2.3.2.1 Application to Several Types of Shear Flow.- 2.3.2.2 Application to Elongational Flow.- 2.3.2.3 Problems with Inversion.- 2.3.3 Preliminary Discussion.- 2.3.4 Equivalent Formulations of the Discussed Theory.- 2.3.5 Incorporation of Temperature Changes into the Integral Equation.- 2.3.6 Optical Means to Prove the Validity of the Simple Rubberlike Liquid Theory.- 2.4 More General Discussion of Quasi-Linear Models.- 2.4.1 The Corotational Model.- 2.4.2 Codeformational Models.- 2.4.2.1 Introduction.- 2.4.2.2 Covariant and Contravariant Time Derivatives.- 2.4.2.3 Equations Equivalent to Lodge's Original Formulation.- 2.4.3 The Independent Alignment Model.- 2.4.3.1 Formal Presentation.- 2.4.3.2 Some Physical Considerations.- 2.4.3.3 Evaluation.- 2.4.3.4 Shear Flow.- 2.4.3.5 Elongational Flow.- 2.4.3.6 Damping Functions.- 2.4.3.7 Postscript.- 2.5 Quasi-Linear Models Containing Adjustable Elements.- 2.5.1 Introduction.- 2.5.2 The n-Measure of Strain.- 2.5.3 The Experimental Damping Function.- 2.5.3.1 Introduction.- 2.5.3.2 Experimental Evidence in Shear.- 2.5.3.3 Non-Linear Shear Creep.- 2.5.3.4 How to Find the Damping Function for an Extension Experiment.- 2.5.3.5 Non-Linear Extensional Creep.- 2.5.4 The Irreversibility of the Disentanglement Process.- 2.5.4.1 Introduction.- 2.5.4.2 The Triple Step-Strain Experiment in Shear.- 2.5.4.3 Description of Recovery Experiments.- 2.5.5 A Differential Type Constitutive Equation Containing Time Dependent Structural Parameters.- 2.5.5.1 Introduction.- 2.5.5.2 Formulation of the Theory.- 2.5.5.3 Evaluation for Steady Homogeneous Shear Flow.- 2.5.5.4 Description of Other Deformations with Given Strain History.- 2.5.5.5 Creep and Recovery.- 2.5.5.6 Free Volume as a Structural Parameter.- 2.5.6 The Non-Affine Displacement of Temporary Network Junctions.- 2.5.6.1 Description of the Network Model.- 2.5.6.2 General Discussion.- 2.5.6.3 Some Comments with Respect to the Usefulness of the Theory.- 2.6 A Theory Derived from a Different Basic Principle.- 2.6.1 Model Considerations.- 2.6.2 Discussion of Results.- 2.6.2.1 Steady State and Relaxation.- 2.6.2.2 Recovery.- 2.6.2.3 Evaluation of Model Parameters.- 2.6.3 Comparison with Experiment.- References of Chapter 2.- 3 Prospects for Predictions on a Moleculat Basis.- 3.1 General Introduction.- 3.2 Relaxion Processes in a Polmer Melt.- 3.2.1 Description of the Model.- 3.2.2 Various Phases of Relaxation.- 3.2.2.1 The Ultra-Fast Phase A of Stress Relaxation.- 3.2.2.2 Equations for the Stress Tensor.- 3.2.2.3 The Second or "Equilibration" Phase (Phase B) of the Stress Relaxation.- 3.2.2.4 The Third or "Disengagement" Phase (Phase C) of the Stress Relaxation.- 3.2.3 Experimental Evidence.- 3.2.3.1 Relaxation after Application of a Step Shear Strain.- 3.2.3.2 Relaxation after Stretching.- 3.3 General Flow Behavior of Polymer Melts.- 3.3.1 The Constitutive Equation.- 3.3.2 The Linear Viscoelastic Properties of the Model.- 3.3.2.1 Monodisperse Samples.- 3.3.2.2 Polydisperse Samples.- 3.3.3 The Non-Linear Properties of the Model.- 3.3.4 A More Elaborate Model.- 3.3.5 Conclusions.- References of Chapter 3.- 4 Industrial Applications.- 4.1 Molecular Orientation.- 4.1.1 The Linear Theory of Strain Recovery after Partial Relaxation.- 4.1.2 Experimental Observations Related to Product Quality.- 4.2 Injection Moulding.- 4.2.1 Two types of Birefringence.- 4.2.2 Heat Transfer During Mould Filling.- 4.2.2.1 A Verbal Description.- 4.2.2.2 Boundary Layer Approach to Mould Filling.- 4.2.2.3 Comparison with Experiment and Discussion.- References of Chapter 4.- Appendix A: Linear Visco-Elasticity.- A.1 Hooke's Law in Complex Notation.- A.2 Stress Relaxation and Creep.- A.3 Elastico-Viscous Flow and Recovery.- A.4 Some Comments with Respect to the Interconversion of Material Functions.- A.5 Mechanical Spectra.- A.6 Interconversion Formulae Based on the Relaxation Time Spectrum.- A.7 Calculation of the Relaxation Time Spectrum from Experimental Material Functions.- References of Appendix A.- Appendix B: The Time-Temperature Superposition Principle.- B.1 Introduction.- B.2 The WLF-Equation.- B.3 The Free Volume Concept.- B.4 Unified Description of the Temperature Denpendence of the Zero-Shear Viscosity.- References of Appendix B.- Appendix C: The Measurement of Birefringence Effects.- C.1 Matrix Representation of Optical Components.- C.2 Calculations of Intensities of Beams Emerging from the Analyser.- C.3 How to Cope with Imperfections of Windows and Polarizing Prisms.- C.4 Description of the Modulator.- C.5 Problems with Quickly Changing Birefringence Effects.- References of Appendix C.