Thermal Expansion of Polymers

Preface vii

1 Fundamentals of Polymer 1
1.1 What Is Polymer? 1
1.1.1 What Molecular Weight Should a Substance Be Defined as "Polymer"? 1
1.1.2 Primary, Secondary, and Higher-ordered Structures 4
1.1.3 Secondary Structure 5
1.1.4 Higher-order Structure 7
1.2 Polymer ABC, Alloy, Blend, and Composite 13
1.2.1 Interfaces in Polymer Alloy and Blend 14
1.2.2 Phase Diagram and Flory-Huggins Theory 18
1.2.3 Polymer Composite 23

2 Fundamentals of Thermal Expansion 31
2.1 Definition of Thermal Expansion 31
2.2 Mechanism of Thermal Expansion of Material in a Solid, Liquid, and Gas State 38
2.2.1 Solid, Especially Crystal Lattice 38
2.2.2 Liquid 41
2.2.3 Gas 47
2.3 Mechanism of Thermal Expansion of Polymers 48
2.3.1 Free Volume of Polymer 49
2.3.2 Thermal Expansion of Crystal Lattice in Crystalline Polymers 59
2.4 Phenomenon That Occurs When Two Materials with Different Thermal Expansions Are Combined 77
2.4.1 Phase Diagram of Polymer Blend with Which Two Polymers Have Different Thermal Expansions 77
2.4.2 Thermal Stress Generated in a Structure Made of Two Different Materials with Different Thermal Expansion Coefficients 80

3 Thermal Expansion Theory of Crystal Axis in Crystal Lattice of Crystalline Polymers 89
3.1 Linear Chain Model 89
3.1.1 Modeling 89
3.2 Self-consistent Harmonic Model 98
3.2.1 Modeling 99
3.2.2 Comparison of the Model with Experimental Data 102
3.3 Spring-in-medium Model 103
3.3.1 Preparation for Construction of Thermal Expansion Model 104
3.3.2 Comparison of the Model with Experimental Data 107
3.4 Comparison with Experimental Data 110

4 Measurement of Thermal Expansion 115
4.1 Measurement of Bulk CVTE 115
4.1.1 Volume Dilatometry 115
4.1.2 PVT Behavior Measurement 118
4.2 Measurement of Bulk Coefficient of Linear Thermal Expansion (CLTE) by TMA 128
4.2.1 Expansion/Compression Mode 129
4.2.2 Tension Mode 130
4.2.3 Penetration Mode 131
4.3 Emerging Technologies of Evaluation of Thermal Expansion 136
4.3.1 PALS for Evaluation of Temperature Dependence of Free Volume 136
4.3.2 Temperature-variable X-ray Scattering Using Synchrotron Radiation for Linear Thermal Expansion in Amorphous and Crystalline Phase 144
4.3.3 Laser Interferometry 153
4.3.4 Digital Image Correlation Method 155
4.3.5 Temperature-variable AFM 160

5 Composite Theory of Thermal Expansion 169
5.1 General Review of Theories of Thermal Expansion of Polymer Composites 169
5.1.1 Rule-of-Mixtures 170
5.1.2 Thermal Expansion of Spherical Particle Reinforced Composites 171
5.1.3 Thermal Expansion of Cylindrical-shaped Inclusion or Fiber-reinforced Composites 175
5.2 Thermal Expansion Theory by Schapery 180
5.2.1 Thermoelastic Energy Principles 182
5.2.2 Volume Thermal Expansion Coefficient 185
5.2.3 Linear Thermal Expansion Coefficient 190
5.3 Wang-Kwei Model for Polymer Composites Containing Spherical Inclusions 195
5.4 Spherical Shell Model for Polymer Blends with Layered Shells by Manabe and Takayanagi 200
5.5 Chow Model for the Linear and Volume Thermal Expansion Coefficients of the Polymer Composite with Ellipsoidal Inclusions 205
5.6 Mori-Tanaka Theory to Accommodate Polymer Composites with Versatile Shapes of Fillers 208
5.6.1 Introduction of Eshelby Equivalent Inclusion Method and Eshelby's Tensor as a Basic Theory 209
5.6.2 Mori-Tanaka Mean Field Theory 215
5.6.3 Self-consistent Model 223

6 Reduction Technologies of Thermal Expansion 227
6.1 Reduction of Thermal Expansion by Fillers 227
6.1.1 General Consideration of Reduction of Thermal Expansion by Fillers 228
6.1.2 Reduction of Thermal Expansion Using Nano-fillers 230
6.1.3 Reduction of Thermal Expansion of Composite by the Fillers with Negative Thermal Expansion (NTE) 251
6.2 Reduction of Thermal Expansion by Introducing Structural Constraints into Polymer Backbone 258
6.2.1 Chemical Cross-linking 258
6.2.2 Rigid Functional Group 260
6.3 Reduction of Thermal Expansion by Oriented Molecules 266
6.4 Reduction of Thermal Expansion by Polymer Blends, in Particular, Elastomers 273

References 287
Index 292