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Crystals and Crystallinity in Polymers: Diffraction Analysis of Ordered and Disordered Crystals

Crystals and Crystallinity in Polymers: Diffraction Analysis of Ordered and Disordered Crystals

Claudio De Rosa, Finizia Auriemma

ISBN: 978-1-118-69079-6

Aug 2013

480 pages

$128.99

Description

Provides the tools needed to master and apply the fundamentals of polymer crystallography

Using core concepts in physics, chemistry, polymer science and engineering, this book sheds new light on the complex field of polymer crystallography, enabling readers to evaluate polymer crystallization data and determine the best methods to use for their investigations. The authors set forth a variety of tested and proven methods for analyzing ordered and disordered structures in polymer crystals, including X-ray diffraction, electron diffraction, and microscopy. In addition to the basics, the book explores several advanced and emerging topics in the field such as symmetry breaking, frustration, and the principle of density-driven phase formation.

Crystals and Crystallinity in Polymers introduces two new concepts in crystallinity and crystals in synthetic polymers. First, crystallinity in polymeric materials is compatible with the absence of true three-dimensional long-range order. Second, the disorder may be described as a structural feature, using the methods of X-ray scattering and electron diffraction analysis.

The book begins by introducing the basic principles and methods for building structural models for the conformation of polymer crystal chains. Next, it covers:

  • Packing of macromolecules in polymer crystals
  • Methods for extracting structural parameters from diffraction data
  • Defects and disorder in polymer crystals
  • Analytical methods for diffuse scattering from disordered polymer structures
  • Crystal habit
  • Influence of crystal defects and structural disorder on the physical and mechanical properties of polymeric materials

Crystals and Crystallinity in Polymers examines all the possible types of structural disorder generally present in polymer crystals and describes the influence of each kind of disorder on X-ray and electron diffraction patterns. Its comprehensive, expert coverage makes it possible for readers to learn and apply the fundamentals of polymer crystallography to solve a broad range of problems.

Preface xi

1 Configuration and Conformation of Macromolecules in Polymer Crystals 1

1.1 Crystals of Polymers, 1

1.2 Constitution and Configuration of Crystalline Polymers, 3

1.2.1 Constitution, 3

1.2.2 Configuration, 5

1.2.3 Relative Configurations, 14

1.3 Conformation, 18

1.4 Relationships among Internal Parameters of Macromolecules, 19

1.5 Conformation of Polymer Chains in the Crystalline State, 21

1.5.1 Basic Principles, 21

1.5.2 The Equivalence Principle, 21

1.5.2.1 Symmetry Relations for Cylindrical Coordinates, 29

1.5.2.2 Application of the Equivalence Principle: Stereoregular Vinyl Polymers, 31

1.5.3 Principle of Minimum Conformational Internal Energy, 33

1.5.4 Relationships between Internal Coordinates and Conformational Parameters, 36

1.6 Helical Conformations in Isotactic and Syndiotactic Polymers, 46

1.7 Conformational Energy Calculations, 51

1.7.1 Setting Up Molecular Models: Coordinate Transformations, 52

1.7.2 Calculation of the Conformational Energy for Isotactic and Syndiotactic Polymers, 54

1.8 Helical Conformation and Optical Activity, 66

1.9 Alternating Copolymers, 68

1.10 Polydienes, 73

1.11 Nonhelical Chain Conformations of Isotactic Polymers, 78

References, 81

2 Packing of Macromolecules in Polymer Crystals 88

2.1 General Principles, 88

2.2 The Principle of Density (Entropy)-Driven Phase Formation in Polymers, 92

2.3 Symmetry Breaking, 96

2.4 Impact of Chain Folding on Crystal Structure Symmetry, 103

2.5 Frustrated Polymer Crystal Structures, 107

2.6 Chiral Crystallization of Polymers with Helical Chain Conformations, 110

2.7 Packing Effects on the Conformation of Polymer Chains in Crystals: The Case of Aliphatic Polyamides, 113

References, 118

3 Methods in Crystal Structure Determination from X-Ray Diffraction 123

3.1 X-Ray Diffraction of Semicrystalline Polymers, 123

3.1.1 Basic Principles, 123

3.1.2 Experimental Techniques for Polymer Crystals, 128

3.2 Fourier Synthesis and the Phase Problem in Crystallography, 134

3.3 X-Ray Fiber Diffraction Analysis, 140

3.3.1 Determination of the Fiber Period and the Bragg Distances of Diffraction Peaks, 140

3.3.2 Analysis of Nonhelical and Helical Structures, 142

3.3.3 The Structure Factor of a Single Molecule: The Continuous Helix, 144

3.3.4 CCV Formula for Helical Structures, 147

3.3.5 The Case of Incommensurable Helices, 153

3.3.6 Calculation of Structure Factors of a Single Helical Chain, 162

3.3.7 Calculation of Structure Factors of Crystals of Helical Molecules Including More Than One Chain per Unit Cell, 163

3.4 Determination of Parameters of the Unit Cell and Indexing of the Diffraction Pattern, 165

3.4.1 X-Ray Diffraction Data from Oriented Fibers, 165

3.4.2 X-Ray Diffraction Data from Powder Samples, 170

3.5 Measure of the Integrated Intensities of the Reflections and Corrections for Geometric (Lorentz), Polarization, and Absorption Factors, 171

3.6 Calculation of Structure Factors, 174

3.7 Structural Refinement, 180

3.8 Form of Diffraction Pattern and Broadening due to the Laue Function, 181

References, 183

4 Defects and Disorder in Polymer Crystals 185

4.1 Classification of Different Types of Structural Disorder, 185

4.2 Crystals with Partial Three-Dimensional Order (Class A): Disorder with Three-Dimensional Periodicity Maintained for Only Some Characterizing Points of the Structure, 191

4.2.1 Substitutional Isomorphism of Different Chains, 192

4.2.1.1 Disorder in the Positioning of Right- and Left-Handed Helical Chains, 192

4.2.1.2 Disorder in the Positioning of Up and Down Chains, 195

4.2.1.3 Disorder in the Orientation of Chains around the Chain Axis, 197

4.2.2 Substitutional Isomorphism of Different Monomeric Units, 200

4.2.3 Conformational Isomorphism, 202

4.2.4 Disorder in the Stacking of Ordered Layers of Chains (Stacking Fault Disorder), 204

4.2.4.1 Stacking Faults in Form I and Form II of sPP, 204

4.2.4.2 Stacking Faults in α- and γ-Forms of iPP, 206

4.2.4.3 Stacking Faults in the β-Form of sPS, 209

4.2.5 Conformational Kink-Band Disorder, 211

4.2.5.1 Conformational Kink-Band Disorder in PVDF, 212

4.2.5.2 Conformational Kink-Band Disorder in PE, 215

4.2.5.3 Conformational Kink-Band Disorder in sPP, 216

4.2.5.4 The Role of Kink-Band Disorder in the Cooperative Crystal–Crystal Polymorphic Transitions, 218

4.3 Solid Mesophases, 219

4.3.1 LCs in Small Molecules and Polymers, 222

4.3.2 Solid Mesophases in Polymers, 227

4.3.3 Solid Mesophases of Class B: Crystals with Three-Dimensional Long-Range Order of Not-Point-Centered Features, 229

4.3.3.1 Solid Mesophase in 1,4-trans-Poly(1,3-butadiene) (trans-PBD), 230

4.3.3.2 Poly(ε-caprolactame) (Nylon 6), 232

4.3.3.3 Poly(acrylonitrile) (PAN), 235

4.3.3.4 Ethylene–Propylene Random Copolymers, 239

4.3.3.5 Pseudohexagonal Form of PE at High Pressure and Temperature, 243

4.3.3.6 Poly(tetrafl uoroethylene) (PTFE), 245

4.3.3.7 Random Copolymers of Tetrafl uoroethylene with Fluorinated Comonomers, 251

4.3.3.8 Alternating Ethylene–Tetrafl uoroethylene (ETFE) Copolymers, 255

4.3.3.9 Alternating Ethylene-Norbornene Copolymers (ENCs), 264

4.3.3.10 Comblike Polymers, 271

4.3.4 Solid Mesophases of Class C: Crystals with Long-Range Positional Order in Only One or Two Dimensions, 271

4.3.4.1 Poly(ethylene terephthalate) (PET), 272

4.3.4.2 Isotactic Polypropylene (iPP), 275

4.3.4.3 Copolymers of iPP with Branched Comonomers, 276

4.3.4.4 Syndiotactic Polypropylene (sPP), 279

4.3.4.5 Copolymers of sPP, 284

4.3.4.6 Syndiotactic Polystyrene (sPS) and Methyl-Substituted Polystyrenes, 286

References, 287

5 Methods of Analysis of Diffuse Scattering from Disordered Structures of Polymers 296

5.1 Structural Disorder and Diffuse Scattering, 296

5.2 Methods of Diffraction Analysis from Disordered Crystals, 298

5.3 Long-Range Order in Disordered Lattices of Class A, 300

5.4 SRO in Disordered Crystals of Class A, 302

5.5 Short-Range Order in Disordered Crystals with Substitution-Type Disorder, 305

5.6 Short-Range versus Long-Range Order in Disordered Crystals of Classes B and C (Solid Mesophases), 309

5.7 Disordered Models with Perturbations Occurring over Continuous Ranges, 311

5.8 Basic Formulas for the Calculation of X-Ray Diffraction Intensity from Disordered Model Structures of Polymers, 316

5.8.1 Brief Overview of Basic Formalism in X-Ray Modeling, 316

5.8.2 Effect of Longitudinal Translational Disorder and Rotational Displacements of Chains about Their Axes: Explicit Formulas, 319

5.8.3 Substitutional and Translational Disorder in One Dimension, 321

5.9 Examples of Calculation of Average Diffracted Intensity of Structures Disordered in One Dimension, 328

5.9.1 Substitution-Type Disorder, 328

5.9.2 Translation-Type Disorder, 331

5.9.3 Stacking Fault Disorder in the β-Form of sPS, 333

5.10 Line and Surface Integration Method of Diffraction Intensity for Fibers and Powders of Polycrystalline Samples, 337

References, 338

6 Crystal Habits 341

6.1 Basic Remarks, 341

6.2 Rounded Lateral Habits, 347

6.3 Chain Folding, Molecular Orientation, and Sectorization, 349

6.3.1 Chain Tilting, 349

6.3.2 Sectorization, 350

6.3.3 Nonplanar Lamellae, 352

6.4 Twinning and Secondary Nucleation Theory, 355

6.5 Homoepitaxy, Morphology, Stem Orientation, and Polymorphism, 359

References, 367

7 Influence of Crystal Defects and Structural Disorder on the Physical and Mechanical Properties of Polymeric Materials 369

7.1 Introduction, 369

7.2 Stress-Induced Phase Transformations during Deformation, 371

7.3 Isotactic Polypropylene (iPP), 373

7.3.1 Influence of Stereo- and Regiodefects on the Crystallization Behavior of iPP, 374

7.3.2 Influence of Stereo- and Regiodefects on the Mechanical Properties of iPP, 378

7.3.3 Stress-Induced Phase Transformations of iPP during Tensile Deformation, 382

7.3.4 Elastic Properties and Phase Transformations in Stereodefective iPP, 388

7.3.5 Influence of Constitutional Defects on the Crystallization Behavior of iPP, 390

7.3.6 Influence of Constitutional Defects on the Physical Properties of iPP, 397

7.3.7 Influence of Conditions of Crystallization on the Physical Properties of iPP: The Mesomorphic Form, 406

7.3.7.1 Morphology of the Solid Mesophase of iPP, 407

7.3.7.2 Mechanical Properties of the Solid Mesophase of iPP, 412

7.3.7.3 Mechanical Properties of the γ-Form and Solid Mesophase in Metallocene iPPs, 417

7.4 Syndiotactic Polypropylene (sPP), 422

7.4.1 Influence of Stereodefects on the Crystallization Behavior of sPP, 424

7.4.2 Influence of Stereodefects on the Crystallization of the Mesomorphic Form of sPP, 427

7.4.3 Influence of Stereodefects on the Crystallization of trans-Planar and Helical Forms of sPP in Oriented Fibers: Stress-Induced Phase Transformations during Deformation, 428

7.4.4 Influence of Constitutional Defects on the Crystallization Behavior of sPP, 431

7.4.5 Physical and Mechanical Properties of sPP, 434

7.4.5.1 Influence of Stereodefects on the Mechanical Properties of sPP, 434

7.4.5.2 Mechanical Properties of the Solid Mesophase of sPP, 440

References, 442

Index 449