Polymers, Liquid Crystals, and Low-Dimensional Solids

I. Polymers.- 1. Introduction to Polymeric Structure and Polymers.- 1.1. Classification.- 1.1.1. Linear Chains and Networks.- 1.1.2. Periodic and Aperiodic Polymers.- 1.1.3. Homopolymers and Copolymers.- 1.1.4. Single-Component Polymers.- 1.2. Main Types of Polymerization Reaction.- 1.2.1. Condensation Polymerization.- 1.2.2. Addition Polymerization.- 1.3. Imperfection Types in a Linear Homopolymer Chain.- 1.3.1. End Groups.- 1.3.2. Molecular Length (Weight) Distribution.- 1.3.3. Isomerism.- 1.4. Formulas of Some Important Polymers.- 1.4.1. Condensation Polymers.- 1.4.2. Addition Polymers.- 1.5. Melting Range of Polymers; Specialty Materials.- 1.5.1. Conventional Polymers.- 1.5.2. Specialty Materials.- 1.6. The Physical State.- 1.6.1. Resumé of the Amorphous State.- 1.6.2. The Usefulness of Polymers in Terms of Their Physical State.- 2. Crystallinity and Kinetics of Crystallization.- 2.1. Basic Classifications.- 2.1.1. Generalities.- 2.1.2. Sources of Lattice Imperfections in Polymers.- 2.1.3. Modes of Crystallization.- 2.2. Crystal Structure.- 2.2.1. The Unit Cell.- 2.2.2. Chain Conformations.- 2.2.3. Chain Packing.- 2.2.4. Crystal Structure Determination.- 2.3. Degree of Crystallinity.- 2.3.1. The Principle of the Determination.- 2.3.2. Methods of Determination.- 2.3.3. An Appreciation of the Different Methods.- 2.4. Kinetics of Crystallization.- 2.4.1. Rates of Crystallization.- 2.4.2. The Xc vs t Curves.- 2.4.3. Morphological vs True Crystallinity.- 2.4.4. Primary and Secondary Crystallization.- 2.4.5. Textures.- 2.4.6. Analytical Treatment of Crystallization Kinetics.- 2.5. Spherulites.- 2.5.1. Optical Properties of Spherulites.- 2.5.2. Morphology of Spherulites.- 2.5.3. The Fine Structure of Spherulites.- 3. The Basic Crystal Unit.- 3.1. Single-Crystal Lamella.- 3.1.1. Discovery and Description.- 3.1.2. The Chain-Folding Model.- 3.1.3. Fold Length l.- 3.2. Theories of Chain Folding.- 3.2.1. Framework of the Kinetic Theories.- 3.2.2. Further Developments and Problems.- 3.2.3. Growth Rates.- 3.2.4. Melting Behavior as a Function of l.- 3.2.5. Comparison of Crystallization from Solution and Melt.- 3.2.6. Some New Perspectives in Crystallization Theories.- 3.3. Morphology of Chain-Folded Crystals.- 3.3.1. Monolayer Crystals.- 3.3.2. Multilayer Crystals.- 3.4. Fold Structure — Nature of Amorphous Material.- 3.4.1. The Issues.- 3.4.2. Experimentation in Aid of the Fold-Surface Problem.- 3.4.3. Outcome of the Enquiries.- 3.5. Neutron Scattering Experiments: The Chain Trajectory.- 3.5.1. Technique and Potential.- 3.5.2. Angular Ranges.- 3.5.3. Some Results.- 3.6. Alternative Morphologies.- 3.6.1. Extended-Chain-Type Crystals.- 3.6.2. Micellar Crystals (Crystal Gels).- 4. Other Classes of Crystallization.- 4.1.Crystallization Concurrent with Polymerization (Nascent Polymers).- 4.2. Orientation-Induced Crystallization.- 4.2.1. General.- 4.2.2. Morphological Background.- 4.2.3. Mode of Chain Extension.- 4.2.4. Structure of Shish-Kebabs.- 4.2.5. Properties of Shish-Kebabs.- 4.2.6. Some Practical Consequences.- 5. Hierarchical Nature of Macromolecular Structure.- 5.1. Introduction.- 5.1.1. Crystalline Constituents.- 5.1.2. Amorphous Constituents.- 5.2. Crystal Defects.- 5.2.1. Defects Within the Crystal Lattice.- 5.2.2. Defects Beyond the Level of the Lattice.- 5.3. Thermal Behavior.- 5.3.1. Amorphous Material.- 5.3.2. Crystal Lattice.- 5.3.3. Melting Range.- 5.4. Deformation.- 5.4.1. Polymers as Self-Structured Composites.- 6. Influence of Processing on Polymeric Materials.- 6.1. Polymeric Processing.- 6.2. General Comments on Influence of Flow.- 6.3. Dumbbell Model.- 6.3.1. Shear Flow.- 6.3.2. Elongational Flow.- 6.3.3. Other Flows.- 6.4. Multiplicity of Friction Points: Rouse-Zimm Model.- 6.5. Concentrated Systems.- 6.6. Effects of Flow on Crystallization.- 6.7. Recent Developments.- References and Bibliography for Part I.- II. Liquid Crystals.- 7. Structural Classification of Thermotropic Liquid Crystals.- 7.1. Introduction.- 7.2. Rod-Like Molecules.- 7.2.1. Effect of Pressure on Polymorphism.- 7.2.2. The Reentrant Phenomenon.- 7.3. Disk-Like Molecules.- 8. Nematic Liquid Crystals.- 8.1. Elastic Properties.- 8.1.1. Basic Equations.- 8.1.2. Determination of the Elastic Constants: The Freedericksz Effect.- 8.1.3. Orientational Fluctuations and Light Scattering.- 8.1.4. Disclinations.- 8.2. Viscous Properties.- 8.2.1. Experimental Determination of the Viscosity Coefficients.- 8.2.2. Viscous Torques.- 8.2.3. Orientational Relaxation.- 8.3. Nematic-Isotropic Transition.- 8.3.1. Molecular Theories of the Nematic Phase.- 8.3.2. Short-Range Order Effects in the Isotropic Phase: The Landau-de Gennes Model.- 8.3.3. Near-Neighbor Correlations.- 9. Cholesteric Liquid Crystals.- 9.1. Optical Properties.- 9.2. Flow Properties.- 10. Smectic Liquid Crystals.- 10.1. Smectic A.- 10.1.1. Continuum Theory of Smectic A.- 10.1.2. The Smectic A — Nematic Transition.- 10.1.3. Bilayer Smectic A and the Reentrant Phenomenon.- 10.2. Smectic.- 10.3. Flexoelectricity in Liquid Crystals.- 10.4. Ferroelectric Liquid Crystals.- 11. Optical Applications of Liquid Crystals.- 11.1. Why Use Liquid Crystals for Optical Applications?.- 11.1.1. Mechanical Properties of Liquid Crystal Phases.- 11.1.2. Coupling to External Fields.- 11.1.3. Coupling to Light.- 11.1.4. Conclusion.- 11.2. Optical Properties of Textures.- 11.2.1. Orientation of Uniform Textures.- 11.2.2. Optical Properties of Twisted Textures.- 11.2.3. Use of Dichroic Dyes in Solution.- 11.3. Texture Distortions Under the Action of an Electric Field.- 11.3.1. Electrically Controlled Birefringence.- 11.3.2. Twisted Nematic Valve.- 11.3.3. Dynamic-Scattering Mode.- 11.3.4. Texture Changes in Cholesterics.- 11.4. Multiplexing of Liquid-Crystal Displays.- 11.4.1. Response Time of Liquid-Crystal Texture Instabilities.- 11.4.2. Multiplexing Liquid Crystals.- 11.4.3. Parallel Addressing.- 11.5. Applications of Smectics.- 11.5.1. Mechanical Properties of Smectic Textures.- 11.5.2. Electric Field Effects on Smectic A.- 11.5.3. The Thermally Excited Optical Smectic Valve.- 11.5.4. The Thermal Electric X-Y Addressed Smectic.- 11.5.5. Ferroelectric C*. The Bistable Optical Switch.- References for Part II.- III. Low-Dimentional Solids.- 12. Chemical Bonding.- 12.1. Outline.- 12.2. Linear Polyenes.- 12.2.1. Free-Electron Model: Absorption Spectra as Function of Chain Length.- 12.2.2. Linear Combination of Atomic Orbitals (LCAO) Hückel Approximation.- 12.2.3. Alternating Bond Lengths.- 12.2.4. Effect of Electron-Electron Interactions.- 12.3. Platinum Chain Compounds.- 12.3.1. Tight-Binding (LCAO) Results.- 12.3.2. Role of Ligands.- 12.4. Two-Dimensional Layer Compounds I.- 12.4.1. Structure of Transition Metal-Dichalcognide Layer Compounds.- 12.4.2. Trigonal-Prismatic Coordination.- 12.4.3. Crystal-Field Splitting of d-Levels.- 12.4.4. Molecular-Orbital Calculations.- 12.4.5. Effect of ?-Bonding.- 12.4.6.Role of d-Covalency in Stabilizing Trigonal- Prismatic Coordination.- 12.5. Two-Dimensional Layer Compounds II.- 12.5.1. Electronic Structure of Borazole.- 12.5.2. Broadening of ?-Levels into Bands.- 12.6. Molecular Scattered Wave Calculations I: Treatment of TTF-TCNQ.- 12.6.1. Molecular Structure of Cation and Anion.- 12.6.2. Energy Levels of TCNQ- and TTF+.- 12.6.3. Approximation to Energy Levels of a Crystal.- 12.6.4. Photoemission Spectrum.- 12.7. Molecular Scattered Wave Calculations II: Treatment of Polymer (SN)X.- 12.7.1. Square and Open S2N2.- 12.7.2. S4N4 Chain.- 12.7.3. X-Ray Photoelectron Spectrum.- 12.7.4. Interaction of Two S4N4 Chains.- 12.7.5. Band-Structure of (SN)X.- 12.8. Electron Density Description of the Ground State of Molecules.- 12.8.1. Simplest Theory of Inhomogeneous Electron Gas.- 12.8.2. Value of the Chemical Potential in a Neutral Atom or Molecule.- 12.8.3. Relation Between Total Energy and Sum of Orbital Energies.- 12.8.4. Inclusion of Density Gradients and Electron Correlation.- Appendix A12.1. Alternation of Bond Lengths in Long Conjugated Chain Molecules.- Appendix A12.2. Partitioning of the Space of a Molecule (and One-Body Potential).- 13. Phase Transitions and Dimensionality.- 13.1. Cooperative Behavior and Phase Transitions.- 13.1.1. Basic Aspects of Cooperative Behavior and Phase Transitions.- 13.1.2. Criticality.- 13.1.3. Correlation Functions.- 13.2. Systems and Models Exhibiting Transitions.- 13.2.1. Magnetic Systems.- 13.2.2. Alloys.- 13.2.3. Liquid-Gas Systems.- 13.2.4. Melting.- 13.2.5. ?-Transition in He4.- 13.2.6. Superconductivity.- 13.2.7. Peierls’ Transition.- 13.2.8. Mott and Anderson Transitions.- 13.2.9. Structural Transitions; Jahn-Teller Transition.- 13.2.10. Ferroelectric Transitions.- 13.2.11. Percolation.- 13.2.12. Summary.- 13.2.13. Bose Condensation.- 13.3. Mean-Field Theory.- 13.3.1. Mean-Field Theory for Magnetic Systems.- 13.3.2. Ornstein-Zernicke Theory.- 13.3.3. Crntical Exponents of Mean-Field and Ornstein-Zernicke Theories.- 13.3.4. Mean-Field Theory for Superconductivity.- 13.3.5. Mean-Field Theory for Jahn-Teller Transitions.- 13.3.6. Critique of Mean Field Approaches.- 13.4. Excitations.- 13.4.1. Ground States.- 13.4.2. Low-Lying Excitations.- 13.4.3. Random-Phase Approximation.- 13.4.4. Broken Symmetry.- 13.5. Instabilities and Fluctuations.- 13.5.1. Instabilities in Heisenberg Magnets.- 13.5.2. Instabilities in Ising Magnets.- 13.5.3. Lower Critical Dimensionality for Bose-Einstein Condensation.- 13.5.4. Instability of Low-Dimensional Crystal Lattices.- 13.5.5. Melting.- 13.6. Peierls’ Transition, Charge-Density Waves, Solitons, and Phasons.- 13.7. Quasi-Low-Dimensional Systems.- 13.7.1. Introduction.- 13.7.2. Weakly-Coupled-Layer Heisenberg Ferromagnet.- 13.8. Transitions Without Usual Long-Range Order; Kosterlitz-Thouless Transition.- 13.8.1. Introduction.- 13.8.2. Two-Dimensional XY Model and Superfluid.- 13.9. Critical Behavior.- 13.9.1. Exponents and Universality.- 13.9.2. Upper Critical Dimensionality, Power Counting.- 13.9.3. Homogeneity and Scaling.- 13.9.4. Renormalization Group Method.- 13.10. Critical Behavior of Low-Dimensional Systems.- 13.10.1. One-Dimensional Magnetic Systems.- 13.10.2. Two-Dimensional Magnetic Systems.- 13.10.3. Percolation and Other Disorder Problems.- 13.11. Concluding Remarks.- 14. Many-Electron Effects.- 14.1. Response to Electric and Magnetic Fields.- 14.1.1. Some General Formulas for the Dielectric Function.- 14.1.2. The Dielectric Function of a Uniform System.- 14.1.3. The Magnetic Susceptibility.- 14.2. Self-Consistent Independent-Particle Models.- 14.3. The Electron Liquid.- 14.3.1. Approximate Dielectric Functions.- 14.3.2. Collective Modes and Screening Effects.- 14.3.3. Comparison Between Different Approximations to the Dielectric Function.- 14.3.4. The One-Electron Spectrum.- 14.3.5. Effect of Correlations on Spin Susceptibility.- 14.3.6. Different Types of Ground States: Ferromagnetic, Wigner Lattice, Spin Density Waves, Charge Density Waves.- 14.4. The Two-Dimensional Electron Liquid.- 14.5. Partially Localized Electrons.- 14.5.1. Electron-Electron Interactions in Van der Waals Crystals.- 14.5.2. The Hubbard Hamiltonian.- 14.5.3. Discussion of the Hubbard Model.- 15. Space Charge Layers.- 15.1. Screening in One- and Three-Dimensional Systems.- 15.1.1. Screened Point Charge in Three Dimensions.- 15.1.2. Screening with One Spatial Variable.- 15.2. Physical Examples.- 15.2.1. p-n Junctions.- 15.2.2. The Jellium-Vacuum Interface.- 15.2.3. Semiconductor Surfaces.- 15.2.4. Schottky Barriers.- 15.2.5. Metal-Insulator-Semiconductor Systems.- 15.2.6. Elections on Liquid Helium.- 15.3. Experimental Probes of Space-Charge Layers.- 15.3.1. Capacitance.- 15.3.2. Conductance.- 15.3.3. Photoeffects.- 15.3.4. Interface Characterization.- 15.4. Semiconductor Inversion Layers.- 15.4.1. Quantum Effects.- 15.4.2. Transport Properties.- 15.4.3. Optical Properties.- 15.4.4. Impurity Bands and Localization.- 15.5. Two-Dimensional Physics: Some Examples.- 15.5.1. Coulomb Scattering.- 15.5.2. Bound States.- 16. Superconductivity via Electron-Phonon and Electron-Exciton Interactions.- 16.1. Electron-Phonon Hamiltonian.- 16.2. Canonical Transformation and Cooper Pair.- 16.3. Superconductivity: The Ground State.- 16.4. The Bogoliubov Equation.- 16.5. The Transition Temperature.- 16.6. Landau-Ginzburg Theory.- 16.7. Excitonic Mechanisms.- 16.8. Effects of Limited Dimensionality.- References for Part III.- IV. Special Topics.- 17. Biopolymer Electronic Phenomena.- 17.1. Ab-initio SCF-LCAO Crystal-Orbital Formalism.- 17.1.1. Simple Translational Symmetry.- 17.1.2. The SCF-LCAO-CO Method in the Case of a Combined Symmetry Operation.- 17.2. Semiempirical SCF-LCAO Crystal-Orbital Methods.- 17.2.1. The Semiempirical SCF-Electron (Pariser-Parr-Pople) Crystal-Orbital Method.- 17.2.2. The Semiempirical SCF All-Valence Electron (CNDO/2) Crystal-Orbital Method.- 17.3. Correction of the Virtual Levels and for Long-Range Correlation.- 17.3.1. Application of the Excitation Hamiltonian (ÔÂÔ) Method to Polymers.- 17.3.2. Correlation Corrections to the Hartree Fock Bands on the Basis of the Electron-Polaron Model.- 17.4. Applications to Periodic DNA and Protein Models.- 17.4.1. Periodic DNA Models.- 17.4.2. Periodic Protein Models.- 17.5. Treatment of Correlation in Polymers.- 17.5.1. Intermediate Exciton Theory for Excited States of Polymers.- 17.5.2. Discussion of the Correlation in the Ground State of Polymers.- 17.6. Methods for Treatment of Aperiodic Polymers.- 17.6.1. The Virtual Crystal, Coherent Potential Approximation (CPA), and SCF Resolvent Method.- 17.6.2. Negative-Factor Counting Techniques.- 17.7. Transport Properties of Biopolymers.- 17.8. From Electronic Structures to Biological Functions.- 17.8.1. Hypotheses for Tumor Development on the Molecular Level.- 17.8.2. Possible Local Effects of Carcinogens.- 17.8.3. Possible Nonlocal Effects of Carcinogens Bound to DNA.- 17.8.4. DNA-Protein Interaction and Its Possible Change Due to the Binding of a Carcinogen.- 18. Topological Defects and Disordered Systems.- 18.1. Classical Theory of Dislocations.- 18.1.1. Two Everyday Examples.- 18.1.2. Translation Dislocation Lines.- 18.1.3. Burgers Circuit and Burgers Vector.- 18.1.4. Disclinations.- 18.2. Point Defects.- 18.2.1. Defects in “Magnetic” Systems.- 18.2.2. Nematic Liquid Crystals.- 18.3. Homotopy Theory of Defects.- 18.3.1. The Problems.- 18.3.2. Mathematical Tools.- 18.3.3. Connection with Defects.- 18.3.4. General Homotopy Groups.- 18.4. Applications of the Topological Theory.- 18.4.1. Vector Order Parameter.- 18.4.2. Nematics.- 18.4.3. New Problems.- 18.4.4. The Many-Defect Problem.- 18.4.5. Limitations of the Method.- 18.5. Disordered Systems: Dilution and Competition.- 18.5.1. Dilution-Type Disorder.- 18.5.2. Competition-Induced Disorder.- 18.6. Percolation and Related Problems.- 18.6.1. The “Classical Theory”.- 18.6.2. Limitations of the Classical Theory.- 18.6.3. Approaches that Work.- 18.6.4. Phenomenological Renormalization.- 18.6.5. Related Problems.- 18.7. Frustration.- 18.7.1. Local Gauge Invariance.- 18.7.2. Is There a Spin-Glass Transition?.- 18.7.3. Connection with Lattice Gauge-Field Theories.- 18.8. Mean-Field Theory of Spin Glasses.- 18.8.1. The Sherrington-Kirkpatrick Model.- 18.8.2. Replica-Symmetry Breaking.- 18.8.3. The Random-Energy Model.- 18.8.4. The Projection Hypothesis for the S-K Model.- 18.9. Conclusion.- References for Part IV.