Crystals and Crystallinity in Polymers

CLAUDIO DE ROSA, PhD, is Full Professor of Industrial and Macromolecular Chemistry at the University of Napoli. His research examines the relationships between molecular structure and the physical properties of polymers. He also studies polymers that form into nanostructures by self-assembly. FINIZIA AURIEMMA, PhD, is Associate Professor of Industrial and Macromolecular Chemistry at the University of Napoli. She conducts theoretical and experimental studies of partially ordered macromolecular systems and polymer gels.

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 - and -Forms of iPP, 206 4.2.4.3 Stacking Faults in the -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( -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 -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 -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