INTRODUCTION TO LIQUID STATE PHYSICS

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Paperback | 19 August 2002

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This work provides an introduction to the liquid state. A qualitative description of liquid properties is first given, followed by detailed chapters on thermodynamics, liquid structure in relation to interaction forces and transport properties such as diffusion and viscosity. treatment of complex fluids such as anisotropic liquid crystals and polymers, and of technically important topics such as non-Newtonian and turbulent flows, is included. Surface properties and characteristics of the liquid-vapour critical point are also discussed. While the book focuses on classical liquids, the final chapter deals with quantal fluids.

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Non-Fiction Science Physics Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Thermodynamics & Heat Classical Mathematics Fluid Mechanics Applied Physics Chemical Physics Chemistry Physical Chemistry

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Published: 19th August 2002

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Preface	p. v
Qualitative Description of Liquid Properties	p. 1
Three Phases of Matter: pVT Behaviour of Pure Materials	p. 2
Critical isotherm	p. 4
Triple point	p. 4
Phase diagram of a pure material (e.g. argon)	p. 5
Phase change from gas to liquid	p. 6
A liquid open to the atmosphere	p. 7
Melting and Lindemann's Law	p. 8
Molecular Thermal Movements in the Liquid Phase: Brownian Motion	p. 9
Qualitative Considerations Continued: Flow Properties of Dense Liquids	p. 12
Ideal liquids and Bernoulli's equation	p. 13
Flow in real liquids: Introduction of viscosity	p. 15
Poiseuille's formula: Viscous flow through a tube	p. 15
Turbulence and Reynolds number	p. 16
Rigidity of Liquids	p. 17
Surface Properties	p. 18
Surface free energy and surface tension	p. 18
Surface energy versus surface free energy	p. 20
Contact angle	p. 20
Capillarity	p. 21
Energy for capillary rise	p. 23
Water and Ice Revisited	p. 24
Excluded Volume, Free Volume and Hard Sphere Packing	p. 29
Excluded Volume and Packing Problems	p. 29
Accessible Configuration Space	p. 30
Experiments on Random Packing Models	p. 31
Origins of Method of Molecular Dynamics	p. 33
Free-Volume Approximation	p. 36
Free Volume and Entropically Driven Freezing Transition	p. 36
Building on Hard Sphere Equation of State	p. 39
Hard-Particle Fluid Equation of State Using Nearest-Neighbour Correlations	p. 41
Free Volume Revisited in Hard Sphere Fluid	p. 42
Statistical geometry of high-density fluid	p. 43
Chemical potential in terms of statistical geometry	p. 44
Hard Particles in Low Dimensions	p. 45
Rods and disks	p. 46
Hard ellipses	p. 46
Equation of State of Hard-Body Fluids	p. 47
Hard Sphere Fluid in Narrow Cylindrical Pores	p. 48
Thermodynamics, Equipartition of Energy and Some Scaling Properties	p. 51
Thermodynamic Functions for a Fluid	p. 51
Thermodynamic identity and the first principle of thermodynamics	p. 53
Helmholtz free energy and variational principle	p. 54
Gibbs free energy	p. 56
Specific Heats and Compressibilities	p. 56
Specific heat at constant pressure	p. 57
Specific heat properties of liquid metals near freezing	p. 58
Compressibilities, both adiabatic and isothermal	p. 59
Fluctuation Phenomena	p. 59
Fluctuations in a perfect gas	p. 60
Effect of intermolecular forces	p. 61
Temperature fluctuations	p. 62
Clausius-Clapeyron Equation and Melting	p. 62
Free Energy from Partition Function	p. 64
Principle of Equipartition of Energy	p. 67
Internal energy and other thermodynamic functions of a perfect gas	p. 67
Harmonic oscillator revisited	p. 68
Thermodynamic and Other Properties of Hard Sphere Fluid	p. 68
Scaling of Thermodynamic Properties for Inverse-Power Repulsive Potentials	p. 70
Consequence for melting transition	p. 70
Analogues of the Clausius-Clapeyron Equation for Other Phase Transitions	p. 71
A magnetic system	p. 71
Higher-order phase transitions	p. 72
Partition Function, Phase Space and Configurational Integral for Inverse Power Repulsive Potentials	p. 73
Structure, Forces and Thermodynamics	p. 75
Pair Distribution Function g(r)	p. 75
Definition of Liquid Structure Factor S(k)	p. 76
Diffractive Scattering from a Liquid	p. 78
Salient Features of Liquid Structure Factor	p. 79
Long wavelength limit and connection with thermodynamic fluctuations	p. 79
The Hansen-Verlet freezing criterion	p. 80
Relation between the main features of the peak in the structure factor	p. 81
Verlet's rule related to Lindemann's melting criterion	p. 83
Internal Energy and Virial Equation of State with Pair Forces	p. 84
Ornstein-Zernike Direct Correlation Function	p. 85
Direct correlation function from Percus-Yevick theory for hard spheres	p. 87
Softness corrections to the hard sphere potential	p. 90
Small angle scattering from liquid argon near triple point	p. 91
Thermodynamic Consistency and Structural Theories	p. 92
Consistency of virial and fluctuation compressibility: Consequences for c(r)	p. 92
A route to thermodynamic consistency in liquid-structure theory	p. 93
Liquid-Vapour Critical Point	p. 95
Critical constants for insulating fluids and expanded alkali metals	p. 95
Ornstein-Zernike theory and critical exponents	p. 98
Scaling relations	p. 99
X-ray critical scattering from fluids	p. 100
Fluids at Equilibrium in a Porous Medium	p. 101
Inhomogeneous Monatomic Fluids	p. 102
Equilibrium conditions	p. 103
Direct correlation function	p. 105
Hypernetted-chain approximation in liquid-structure theory	p. 106
The Dieterici Equation of State	p. 107
Force Equation and Born-Green Theory of Liquid Structure	p. 108
Diffusion	p. 111
Background: Magnitude of Diffusion Coefficients in Gases	p. 111
Practical consequences of "slow" diffusion in dense liquids	p. 113
Fick's Law and Diffusion Equation	p. 114
Examples of diffusion across a thin film	p. 115
Solute Diffusion at High Dilution in Water and in Non-aqueous Solvents	p. 116
Stokes-Einstein and semiempirical estimates of solute diffusion	p. 116
Summary of Techniques, Including Computer Simulation, for Determining	p. 118
Incoherent neutron scattering	p. 119
Dynamic light scattering	p. 121
Nuclear magnetic resonance	p. 122
Computer simulation of mean square displacement	p. 123
Velocity Autocorrelation Function in Pure Dense Liquids	p. 125
Frequency spectrum and long-time tails	p. 126
The Nernst-Einstein relation	p. 129
Models of Velocity Autocorrelation Function	p. 131
The Zwanzig model	p. 132
Wallace's independent atom model	p. 134
Generalisation of Stokes-Einstein relation	p. 135
Viscosity	p. 137
Hydrodynamic Variables	p. 137
Stresses in a Newtonian Fluid and the Navier-Stokes Equation	p. 139
Viscosity stress tensor	p. 139
Bulk and shear viscosity	p. 141
The Navier-Stokes equation	p. 141
Viscous dissipation	p. 142
Laminar Flow and the Measurement of Shear Viscosity	p. 143
Oscillating disk viscometer	p. 145
Couette viscometer	p. 145
Hydrodynamic lubrication	p. 146
Creeping Flow Past an Obstacle	p. 146
Stokes' law revisited	p. 147
The viscosity of suspensions	p. 149
Percolation	p. 150
Vorticity	p. 150
Vorticity diffusion	p. 151
The Magnus force	p. 152
Models of Viscosity	p. 152
Shear and bulk viscosity of hard sphere fluid	p. 153
Temperature dependence of shear viscosity	p. 155
Green-Kubo formulae for viscosity	p. 156
Computer simulation of shear viscosity in a Lennard-Jones fluid	p. 157
Transverse Currents and Sound Propagation in Isothermal Conditions	p. 157
Linearised Navier-Stokes equation	p. 157
Bulk viscosity	p. 159
Brillouin light scattering	p. 160
Microscopic Density Fluctuations and Inelastic Scattering	p. 160
Inelastic neutron scattering from liquids	p. 161
Inelastic photon scattering from liquids	p. 165
Fast sound in water	p. 167
Kinetic Calculation of Shear Viscosity for Hard Spheres	p. 168
Heat Transport	p. 171
Fourier's Law	p. 171
Studies of Heat Conduction by Molecular Dynamics	p. 174
Green-Kubo formula	p. 175
Non-equilibrium methods	p. 176
Transient time correlation formula	p. 176
Electronic Contribution to Heat Conduction in Liquid Metals	p. 178
Thermodynamics with Mass Motion and Entropy Production	p. 180
Thermodynamic relations	p. 180
Entropy production	p. 181
Constitutive relations	p. 182
The Effect of Heat Flow on Sound Wave Propagation	p. 183
Hydrodynamic modes	p. 183
Light scattering	p. 185
Sound propagation in the critical region	p. 186
Binary Fluids	p. 187
Thermodiffusion	p. 187
Hydrodynamic modes	p. 189
Superfluid Helium	p. 189
Transport properties of superfluid [superscript 4]He	p. 191
Inelastic neutron scattering from superfluid [superscript 4]He	p. 193
Kinetic Theory of Thermal and Electrical Conductivity	p. 196
Hydrodynamics of Superfluid Helium in the Two-Fluid Model	p. 198
Chemical Short-Range Order: Molten Salts and Some Metal Alloys	p. 201
Classical One-Component Plasma: Static and Dynamic Screening	p. 201
Debye screening	p. 202
Dynamic screening and plasma excitation	p. 204
Structure and dynamics of the strongly coupled OCP	p. 204
Macroscopic Properties of Molten Salts	p. 205
Selected macroscopic data for chlorides	p. 206
Melting parameters	p. 207
Alkali halide vapours and critical behaviour of ionic fluids	p. 208
Structural Functions for Multicomponent Fluids	p. 209
Number-concentration structure factors	p. 210
Coulomb Ordering in Monohalides and Dihalides	p. 212
Alkali halides	p. 212
Noble-metal halides	p. 213
Fluorite-type superionic conductors	p. 214
Tetrahedral-network structure in ZnCl[subscript 2]	p. 214
Structure of Trivalent-Metal Halides	p. 216
Octahedral-network formation in lanthanide chlorides	p. 217
Ionic-to-molecular melting in AlCl[subscript 3] and FeCl[subscript 3]	p. 217
Liquid haloaluminates	p. 218
Molecular-to-molecular melting in GaCl[subscript 3] and SbCl[subscript 3]	p. 218
Transport and Dynamics in Molten Salts	p. 219
Ionic transport	p. 219
Viscosity	p. 221
Dynamics of density fluctuations	p. 223
Chemical Short-Range Order in Liquid Alloys	p. 224
The CsAu compound	p. 224
Other alkali-based alloys with chemical short-range order	p. 225
Bonds, Rings and Chains	p. 227
Outline	p. 227
Elemental Molecular Liquids	p. 228
Nitrogen	p. 228
Phase diagram of carbon: Especially liquid-liquid transformation	p. 229
Selenium and sulphur: Especially liquid-liquid transitions	p. 231
Structure of liquid boron	p. 232
Orientational Pair Correlation Function from Diffraction Experiments	p. 234
Use of generalised rotation matrices	p. 235
Example of orientational structure in water	p. 236
Polymers	p. 238
The isolated polymer molecule	p. 238
Polymer solutions	p. 239
Polymer blends	p. 242
Polymeric materials	p. 243
Liquid Crystal Phases	p. 244
Smectic phase	p. 245
Nematic phase	p. 245
Cholesteric phase	p. 246
Nematic Liquid Crystals and their Phase Transitions	p. 247
Landau-de Gennes theory	p. 248
Molecular mean-field theory of isotropic-nematic transition	p. 250
The isotropic-nematic-smecticA transition	p. 251
Model potentials for molecular liquid and liquid crystals	p. 252
Melting and Orientational Disorder	p. 253
Crystallisation from Solution	p. 254
Supercooling and the Glassy State	p. 255
Macroscopic Characteristics of a Glass	p. 255
Kinetics of Nucleation and Phase Changes	p. 259
Homogeneous nucleation and crystal growth	p. 259
The critical cooling rate for glass formation	p. 261
Superheating and vapour condensation	p. 261
The Structure of Amorphous Solids	p. 262
Network and modified-network glasses	p. 263
Molten and amorphous semiconductors	p. 264
Thermodynamic Aspects and Free Energy Landscape	p. 266
A topographic view of supercooled liquids	p. 267
Atomic Motions in the Glassy State	p. 269
Relaxation processes	p. 269
Strong and fragile liquids	p. 271
Annealing and aging	p. 273
Anharmonicity and boson peaks	p. 274
Supercooled and Glassy Materials	p. 274
Hard sphere statistics on the amorphous branch	p. 274
Supercooled water	p. 276
Metallic glasses	p. 277
Superionic glasses	p. 278
Glassy polymers	p. 279
Non-Newtonian Fluids	p. 283
Introduction to Non-Newtonian Flow Behaviour	p. 283
Linear visco-elasticity	p. 285
Viscosity in Uniaxial Liquid	p. 287
Flow Birefringence and Flow Alignment	p. 290
Non-Newtonian Behaviour in Polymeric Liquids	p. 291
Reptation in concentrated polymer systems	p. 292
Macroscopic flow phenomena in polymeric liquids	p. 293
Flow in Nematic Liquid Crystals	p. 294
Curvature elasticity and the Freedericksz transition	p. 295
Macroscopic flow and disclinations in nematics	p. 297
Colloidal Dispersions and Suspensions	p. 300
Flow properties of colloidal dispersions	p. 301
The rheology of field-responsive suspensions	p. 304
Surfactant Systems	p. 305
Turbulence	p. 309
Introduction	p. 309
Instabilities in Fluids	p. 311
The Rayleigh-Taylor instability	p. 311
Thermal convection and the Rayleigh-Benard instability	p. 312
The Kelvin-Helmholtz instability	p. 314
Evolution of Benard Convection with Increasing Rayleigh Number	p. 316
Energy Cascade in Homogeneous Turbulence	p. 319
Energy cascade and Kolmogorov microscales	p. 320
Kinetic energy spectrum	p. 322
Energy spectra from renormalisation group approach	p. 324
Diffusion in Homogeneous Turbulence	p. 324
Time and length scales in diffusion	p. 324
Stochastic modelling of turbulent diffusion	p. 325
Eddy diffusivity	p. 327
Turbulent Shear Flows	p. 328
Length scales of momentum transport	p. 328
Reynolds stresses	p. 329
Lattice Boltzmann computing	p. 331
Turbulence in Compressible Fluids	p. 332
Turbulent Behaviour of Non-Newtonian Fluids	p. 333
Navier-Stokes Equation: Analogy with Maxwell's Equations	p. 335
Series Solution of Navier-Stokes Equation	p. 337
Liquid-Vapour Interface	p. 339
Background and Empirical Correlations	p. 339
Relation between surface tension and bulk properties: Organic liquids near 298 K	p. 340
Definition of a Surface and its Thermodynamic Properties	p. 342
Gibbs surface	p. 342
Surface tension	p. 343
Surface entropy	p. 344
Phenomenology	p. 345
Free energy from inhomogeneity	p. 346
Density gradient contribution to free energy	p. 347
Extension to binary alloys and surface segregation	p. 347
Microscopic Theories: Direct Correlation Function	p. 348
Density profile and surface tension	p. 349
Density gradient expansion: Pressure through interface	p. 350
Critical behaviour of surface tension	p. 351
Application to nucleation theory	p. 352
Microscopic Theories: Two-Particle Distribution Function	p. 355
Tangential pressure deficit and surface tension	p. 355
The Fowler approximation: Relation of surface tension to shear viscosity	p. 356
Computer studies: Role of interatomic forces in condensed rare-gas elements	p. 357
Interfacial Dynamics	p. 357
Surface waves	p. 357
Capillary waves and surface fluctuations	p. 359
Interface reflectivity and diffuse interface in a critical fluid mixture	p. 360
Interfacial Transport and Rheology	p. 361
Quantum Fluids	p. 365
Ideal Fermi and Bose Gases	p. 365
The Fermi surface	p. 366
Bose-Einstein condensation	p. 367
Boson Fluids	p. 368
The weakly interacting Bose gas (WIBG)	p. 368
Superfluid liquid [superscript 4]He	p. 370
Bose-Einstein condensates	p. 373
Normal Fermion Fluids	p. 375
Liquid [superscript 3]He in the normal state	p. 375
Electron fluids	p. 379
Wigner crystallisation	p. 383
BCS Superconductivity and Superfluidity in Fermion Fluids	p. 384
The superconducting state	p. 384
Flux quantisation and Josephson effects	p. 386
Superfluidity in liquid [superscript 3]He	p. 388
Electron Theory of Liquid Metals	p. 389
Interatomic forces from liquid structure factor S(k)	p. 390
Diffractive scattering from two-component plasmas	p. 391
Transport coefficients	p. 393
Liquid Hydrogen Plasmas and the Giant Planets	p. 395
Exploring the phase diagram of hydrogen	p. 395
Hydrogen-helium mixtures and the constitution of giant planets	p. 396
Density Profiles in the Perturbed Electron Gas	p. 397
References	p. 399
Table of Contents provided by Ingram. All Rights Reserved.

INTRODUCTION TO LIQUID STATE PHYSICS

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