
Partially Ordered Systems
An Introduction
By: J. Friedel (Foreword by), Maurice Kleman, Oleg D. Laverntovich
Hardcover | 1 October 2002
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672 Pages
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From the reviews:
"This book is an attempt to show the unity of soft matter systems. ... It is noteworthy that the authors have emphasized and discussed in detail that the order parameter has two characteristics: an amplitude and a phase (also called a degeneracy parameter). ... This book gives the conceptual means to classify the various types of singularities of an ordered medium. ... This book will be very useful for researchers and postgraduate students." (K. M. Salikhov, Applied Magnetic Resonance, Vol. 27 (3-4), 2004)
"This monography on soft condensed matter originates from a series of lectures given by the authors ... . The book is clearly written by two world leading experts of the field, it is an excellent basis for a third cycle course on the physics of liquid crystals. The bibliography is up-to-date and a list of valuable interesting references is added. ... this book presents in a condensed but clear way many facets of a very rich and fascinating field. We recommend it ... ." (Jean-Pierre Gaspard, Physicalia, Vol. 26 (1), 2004)
| Foreword | p. v |
| Series Preface | p. xi |
| Preface | p. xiii |
| Condensed Matter: General Characters, the Chemical Bond, and Particle Interactions | p. 1 |
| Entropy in Disordered Systems | p. 2 |
| Central Forces and Directional Forces Between Atoms | p. 3 |
| Metallic Bond | p. 4 |
| Bonds Formed by Fluctuating Dipoles | p. 4 |
| Covalent Bond | p. 5 |
| Ionic Bond | p. 5 |
| From Ionic Bond to Covalent Bond in Crystals | p. 7 |
| Forces Between Molecules | p. 7 |
| Electrostatic Bond in a Dielectric Medium | p. 7 |
| Electric Dipoles | p. 8 |
| Induced Dipoles, Polarizability | p. 11 |
| Repulsive Forces | p. 13 |
| Empirical Potentials of Interactions | p. 18 |
| Water, Hydrogen Bond, and Hydrophilic and Hydrophobic Effects | p. 19 |
| van der Waals Forces Between Macroscopic Particles | p. 21 |
| Pairwise Summation of Molecular Forces; Hamaker Constant | p. 21 |
| Retardation Effects | p. 22 |
| London Interactions in a Medium, Lifshitz Theory | p. 27 |
| Casimir Interactions | p. 28 |
| Polymers and Biological Molecules | p. 29 |
| Synthetic Polymers | p. 29 |
| Aminoacids, Proteins | p. 31 |
| DNA | p. 36 |
| Associations of Proteins: TMV, Microtubules | p. 36 |
| Atomic and Molecular Arrangements | p. 42 |
| Atomic Order | p. 42 |
| Packing Densities | p. 42 |
| Liquids and Amorphous Media | p. 45 |
| Geometrical Frustration | p. 47 |
| Incommensurate Phases and Quasicrystals | p. 49 |
| Molecular Order | p. 53 |
| Plastic Crystals | p. 53 |
| The Building Blocks of Liquid Crystals | p. 55 |
| Classification of the Mesomorphic Phases | p. 59 |
| Isotropic Phases | p. 69 |
| Perturbations of the Crystalline Order | p. 71 |
| Weak Perturbations | p. 71 |
| Strong Perturbations | p. 72 |
| The Order Parameter: Amplitude and Phase | p. 76 |
| The Order Parameter Space | p. 77 |
| Superfluid Helium | p. 77 |
| Heisenberg Ferromagnets | p. 78 |
| X-Y Ferromagnets | p. 79 |
| Uniaxial Nematics | p. 80 |
| Crystalline Solids | p. 82 |
| Order-Disorder Transitions in Alloys | p. 83 |
| The Specific Order Parameter of Liquid Crystals: The Director | p. 83 |
| Microscopic Definition | p. 83 |
| Macroscopic Properties | p. 86 |
| Light Propagation in Anisotropic Media; Application to Director Fields | p. 90 |
| Fresnel Equation | p. 90 |
| Ordinary and Extraordinary Waves | p. 92 |
| Observations in Polarized Light. Microscopy | p. 95 |
| Phase Transitions | p. 105 |
| Landau-de Gennes Model of the Uniaxial Nematic-Isotropic Phase Transition | p. 106 |
| Nematic Order and Statistical Theory of Rigid Rodlike Particles | p. 109 |
| Free Energy of a Solution of Spherical Particles | p. 109 |
| Free Energy of a Solution of Rigid Rods | p. 113 |
| Maier-Saupe Mean Field Theory of the Isotropic-Nematic Transition | p. 115 |
| The Smectic A-Nematic Transition | p. 117 |
| Order Parameter | p. 117 |
| Ginzburg-Landau Expansion | p. 118 |
| Analogy with Superconductors | p. 120 |
| Characteristic Lengths | p. 121 |
| Anomalies of K[subscript 2] and K[subscript 3] Coefficients | p. 123 |
| Abrikosov Phases with Dislocations | p. 124 |
| Kosterlitz-Thouless Model of Phase Transitions | p. 129 |
| Elasticity of Mesomorphic Phases | p. 135 |
| Uniaxial Nematics and Cholesterics | p. 135 |
| Elastic Free Energy Density | p. 135 |
| Geometrical Interpretations of Director Deformations | p. 137 |
| Material Elastic Constants | p. 140 |
| Lamellar Phases | p. 143 |
| Free Energy Density | p. 143 |
| Splay and Saddle-Splay Deformations | p. 145 |
| Free Energy Density for Small Deformations | p. 148 |
| Free Energy of a Nematic Liquid Crystal in an External Field | p. 149 |
| Standard Applications of the Elasticity of Nematics | p. 153 |
| Minimization of the Free Energy in the Generic Case | p. 153 |
| Hybrid-Aligned Nematic Film | p. 157 |
| External Field Effects: Characteristic Lengths and Frederiks Transitions | p. 161 |
| Standard Applications of the Elasticity of Smectics | p. 164 |
| Smectic Phase with Small Deformations | p. 164 |
| Smectic Phase with Large Deformations and Topological Deformations | p. 167 |
| Thermodynamic Fluctuations | p. 170 |
| Thermodynamic Fluctuations in Nematics | p. 171 |
| Thermodynamic Fluctuations in Smectics | p. 173 |
| One-Dimensional Variational Problem | p. 174 |
| Fixed Boundary Conditions | p. 174 |
| Soft Boundary Conditions | p. 176 |
| Formulae for Fourier Transforms | p. 177 |
| Dynamics of Isotropic and Anisotropic Fluids | p. 184 |
| Velocity Field and Stress Tensor | p. 185 |
| Material Derivatives and Components of Fluid Motion | p. 185 |
| Body and Surface Forces. Stress Tensor | p. 187 |
| Isotropic Fluid in Motion | p. 189 |
| Conservation of Mass: Contunuity Equation | p. 189 |
| Linear Momentum Equation | p. 189 |
| Energy Balance Equation | p. 191 |
| Entropy Production Equation | p. 192 |
| Viscous Stress Tensor | p. 195 |
| Navier-Stokes Equations. Reynolds Number. Laminar and Turbulent Flow | p. 196 |
| Nematodynamics in Ericksen-Leslie Model | p. 198 |
| Angular Momentum Equation | p. 199 |
| Energy Balance Equation | p. 200 |
| Entropy Production Equation | p. 200 |
| Nondissipative Dynamics | p. 202 |
| Dissipative Dynamics | p. 202 |
| Nematodynamics in Harvard Theory | p. 205 |
| Director Dynamics and Dissipative Stress Tensor | p. 205 |
| Summary of Nematodynamics | p. 206 |
| Applications of Nematodynamics | p. 210 |
| Nematic Viscosimetry | p. 210 |
| Flow-Aligning and Tumbling Nematics with Director in the Shear Plane | p. 213 |
| Instabilities with the Director Field Perpendicular to the Shear Plane | p. 217 |
| Hydrodynamic Modes | p. 218 |
| Fractals and Growth Phenomena | p. 223 |
| Basic Fractal Concepts | p. 224 |
| Length of a Line | p. 224 |
| Koch Curve | p. 225 |
| Self-Similarity | p. 227 |
| Estimating Fractal Dimensions | p. 228 |
| Deterministic and Stochastic Fractals | p. 230 |
| Brownian Motion and Random Walks | p. 232 |
| Pair Correlation Function | p. 233 |
| Inner and Outer Cutoffs | p. 235 |
| Percolation | p. 235 |
| Geometrical Percolation | p. 235 |
| Percolation and Second-Order Phase Transitions | p. 239 |
| Finite Clusters at the Percolation Threshold | p. 240 |
| Fractal Dimension of the Percolation Cluster | p. 242 |
| Percolation on Bethe Lattice | p. 243 |
| Percolation and the Renormalization Group | p. 245 |
| Aggregation | p. 247 |
| Cluster-Cluster Aggregation | p. 249 |
| The Witten-Sander Model of Diffusion-Limited Aggregation | p. 249 |
| Continuum Laplacian Model | p. 250 |
| Viscous Fingering in the Hele-Shaw Cell | p. 252 |
| Flow in Thin Cells | p. 254 |
| Instability of Interface | p. 254 |
| Dislocations in Solids. Plastic Relaxation | p. 261 |
| Elasticity of Dislocations | p. 261 |
| Linear Elasticity: A Summary | p. 261 |
| Applied Stresses and Internal Stresses | p. 264 |
| Volterra Dislocations | p. 264 |
| Definitions | p. 264 |
| Elastic Observables Related to Volterra Defects | p. 266 |
| Simple Topological Characteristics of Dislocations | p. 269 |
| Equivalent Circuits | p. 269 |
| Dislocations in Crystals | p. 270 |
| Imperfect Dislocations. Stacking Faults and Twins | p. 272 |
| Some Remarks on the Elastic Energy of a Dislocation | p. 272 |
| Stability | p. 272 |
| Image Forces; Peach and Kohler Forces | p. 273 |
| Line Tension | p. 276 |
| Frank and Read Mechanism | p. 276 |
| The Dislocation Core | p. 278 |
| Mobility of a Dislocation | p. 279 |
| Elementary Movements of a Dislocation | p. 279 |
| Glide and Peierls Stress | p. 281 |
| Point Defects and Climb | p. 285 |
| Vacancies and Interstitials | p. 286 |
| Diffusion of Point Defects and Autodiffusion | p. 287 |
| Creep | p. 291 |
| Ensembles of Dislocations | p. 293 |
| Frank Network | p. 293 |
| Sub-Boundaries | p. 294 |
| Large Misorientations, Twin and Epitaxy Dislocations, Martensitic Transformations | p. 296 |
| Dislocations in Smectic and Columnar Phases | p. 300 |
| Static Dislocations in Smectics | p. 300 |
| Edge Dislocations | p. 300 |
| Screw Dislocation | p. 308 |
| Line Tension of a Screw Dislocation | p. 313 |
| Stresses in an SmA and Peach and Kohler Forces | p. 313 |
| Dislocations in Columnar Phases | p. 315 |
| Longitudinal Edge Dislocations | p. 315 |
| Edge Transversal Dislocations | p. 316 |
| Screw Dislocations | p. 318 |
| Free Fluctuations of Longitudinal Dislocations | p. 320 |
| Hydrodynamics of a Smectic Phase | p. 321 |
| Dynamic Modes in Smectics | p. 326 |
| Movement of Isolated Dislocations in an SmA Phase | p. 327 |
| Edge Dislocation | p. 327 |
| Screw Dislocation | p. 330 |
| Collective Behavior of Dislocations and Instabilities | p. 331 |
| General Remarks | p. 331 |
| Collective Climb of Dislocations in SmA | p. 332 |
| Multiplication of Edge Dislocations | p. 333 |
| Curvature Defects in Smectics and Columnar Phases | p. 337 |
| Curvature in Solid Crystals | p. 338 |
| Curvature in Liquid Crystals: Some General Remarks | p. 339 |
| Curvature in Smectics | p. 340 |
| Historical Remarks | p. 340 |
| Congruences of Straight Normals and Focal Conic Domains | p. 341 |
| Congruences of Normals, Variations of Perfect Focal Conic Domains | p. 343 |
| Focal Conic Domains | p. 345 |
| The Analytical Approach: Basic Formulae | p. 345 |
| Different Species of Focal Conic Domains | p. 347 |
| Curvature Energy of FCDs | p. 351 |
| FCD-I: Negative Gaussian Curvature | p. 352 |
| Toric FCD with Negative Gaussian Curvature | p. 354 |
| Parabolic FCD with Negative Gaussian Curvature | p. 355 |
| FCD-II: Positive Gaussian Curvature | p. 358 |
| Curvature Defects in Columnar Phases | p. 359 |
| General Considerations | p. 359 |
| Developable Domains | p. 361 |
| Classification of Developable Domains | p. 363 |
| FCDs in Lyotropic Lamellar Phases: Oily Streaks and Spherulites | p. 365 |
| Oily Streaks | p. 365 |
| Spherulites | p. 367 |
| Grain Boundaries and Space Filling with FCDs | p. 368 |
| Focal Conic Domains of the First Species | p. 369 |
| Focal Conic Domains of the Second Species | p. 377 |
| Rheophysics of FCDs | p. 378 |
| Global Viscoelastic Behavior and Alignment Under Shear | p. 379 |
| Textures | p. 380 |
| Disclinations and Topological Point Defects. Fluid Relaxation | p. 388 |
| Lines and Points in Uniaxial Nematics: Static Properties | p. 389 |
| Wedge Disclinations in Nematics | p. 389 |
| Nonsingular Disclinations | p. 394 |
| Twist Disclinations | p. 399 |
| Defect Lines in LCPs | p. 400 |
| Singular Points | p. 400 |
| Confinement-Induced Twists | p. 402 |
| Cholesterics | p. 404 |
| Elastic Theory at Different Scales | p. 405 |
| Weak Twist Deformations: Double Twist | p. 406 |
| Disclinations [lambda, tau], and X | p. 408 |
| Dislocations | p. 410 |
| Other Effects of the Layer Structure | p. 412 |
| Beyond the Volterra Process: First Step | p. 414 |
| Dislocations and Disclinations Densities in Relation with Disclinations | p. 414 |
| Extension to Finite Dislocations | p. 418 |
| Core Structure and Physical Properties | p. 418 |
| Dynamical Properties: General Features, Instabilities | p. 419 |
| General Features | p. 420 |
| Instabilities of Initially Defect-Free Samples | p. 421 |
| Dynamics of Defects | p. 426 |
| Isolated Disclination, Drag Force | p. 426 |
| Interaction and Annihilation of Line and Point Defects | p. 427 |
| Coarsening of Disclination Networks | p. 430 |
| Topological Theory of Defects | p. 434 |
| Basic Concepts of the Topological Classification | p. 435 |
| Topological Charges Illustrated with Mobius Strips | p. 435 |
| DNA and Twisted Strips, a Digression | p. 436 |
| Groups: Basic Definitions | p. 438 |
| General Scheme of the Topological Classification of Defects | p. 439 |
| Order Parameter Space. Groups That Describe Transformations of the Order Parameter | p. 440 |
| Homotopy Groups | p. 441 |
| Point Defects in a Two-Dimensional Nematic Phase | p. 444 |
| Point Dislocations in a Two-Dimensional Crystal | p. 447 |
| The Fundamental Group of the Order Parameter Space. Linear Defects | p. 452 |
| Unstable Disclinations in a Three-Dimensional Isotropic Ferromagnet | p. 453 |
| Stable Disclinations in a Three-Dimensional Uniaxial Nematic Phase | p. 454 |
| Disclinations in Biaxial Nematic and Cholesteric Phases | p. 455 |
| The Second Homotopy Group of the Order Parameter Space and Point Defects | p. 459 |
| Point Defects in a Three-Dimensional Ferromagnet | p. 460 |
| Topological Charges of Point Defects | p. 461 |
| Point Defects in a Three-Dimensional Nematic Phase | p. 463 |
| Solitons | p. 464 |
| Planar Solitons | p. 464 |
| Linear Solitons | p. 466 |
| Particlelike Solitons | p. 467 |
| Surface Phenomena | p. 472 |
| Surface Phenomena in Isotropic Media | p. 472 |
| Surface Tension and Thermodynamics of Flat Interfaces | p. 472 |
| Adsorption | p. 475 |
| Curved Interfaces | p. 479 |
| Surface Tension and Nucleation of the New Phase | p. 483 |
| Wetting | p. 485 |
| Surface Phenomena in Anisotropic Media | p. 489 |
| Equilibrium Shape (Wulff Shape) of Solid Crystals | p. 489 |
| Surface Anchoring in Nematic Liquid Crystals | p. 493 |
| Field Effects Under Finite Anchoring | p. 496 |
| Thin Liquid Crystal Films; Casimir Interactions | p. 500 |
| Topological Defects in Large Liquid Crystal Droplets | p. 501 |
| Smectic A Droplets | p. 510 |
| Stability of Colloidal Systems | p. 519 |
| Interactions Between Rigid Charged Surfaces | p. 520 |
| The Poisson-Boltzmann Equation | p. 520 |
| Fundamental Lengths in the Poisson-Boltzmann Problem | p. 522 |
| Free Energy and Maxwell Stress Tensor | p. 524 |
| Weak Electrolyte Solutions | p. 526 |
| Strong Electrolyte Solutions | p. 528 |
| The DLVO Theory: van der Waals versus Electrostatic Interactions | p. 530 |
| Interactions in Lamellar Flexible Systems | p. 531 |
| Elasticity of Neutral Membranes | p. 533 |
| Flexible Layers and Excluded Volume | p. 540 |
| The Lamellar, Sponge, and Cubic Phases; Microemulsions | p. 546 |
| Solutions of Colloidal Particles; Stability Properties | p. 547 |
| Brownian Flocculation | p. 549 |
| Depletion Flocculation | p. 550 |
| Stability Under Shear; Rheological Properties | p. 551 |
| Order versus Disorder | p. 553 |
| Measurements of Interactions in Colloidal Systems | p. 555 |
| Polymers: Structural Properties | p. 560 |
| Ideal and Flory Chains | p. 561 |
| Single-chain Conformations | p. 563 |
| The Ideal (or Gaussian) Chain | p. 564 |
| Pair Correlation Function and Radius of Gyration | p. 567 |
| The Flory Chain | p. 568 |
| Chains in Interaction | p. 572 |
| The Mean Field Approach | p. 573 |
| Scaling Laws for Athermal Solutions | p. 577 |
| Phase Separation in Polymer Solutions and Polymer Blends | p. 580 |
| Liquid Equilibrium States versus Nonequilibrium States | p. 580 |
| First-Order Phase Transitions: An Overview | p. 582 |
| Polymer Blends | p. 586 |
| Microscopic Phase Separation into Block Copolymers | p. 588 |
| Rigid and Semiflexible Polymers | p. 590 |
| Rigid Rods | p. 590 |
| Semiflexible Polymers | p. 591 |
| Chirality | p. 593 |
| The Central Limit Theorem | p. 593 |
| Isothermal Compressibility and Density Fluctuations; Static Linear Response | p. 595 |
| Table of Constants | p. 604 |
| Name Index | p. 605 |
| Subject Index | p. 617 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
ISBN: 9780387952673
ISBN-10: 0387952675
Series: Partially Ordered Systems
Published: 1st October 2002
Format: Hardcover
Language: English
Number of Pages: 672
Audience: General Adult
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 24.77 x 19.05 x 3.18
Weight (kg): 1.11
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