Introduction to Liquid State Physics

Norman H. March, M. P. Tosi9789810246396, 981-02-4639-0, 9810246528

This important book 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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Table of contents :
Contents……Page 8
Preface……Page 6
1 Qualitative Description of Liquid Properties……Page 19
1.1 Three Phases of Matter: pVT Behaviour of Pure Materials……Page 20
1.2 Melting and Lindemann’s Law……Page 26
1.3 Molecular Thermal Movements in the Liquid Phase: Brownian Motion……Page 27
1.4 Qualitative Considerations Continued: Flow Properties of Dense Liquids……Page 30
1.5 Rigidity of Liquids……Page 35
1.6 Surface Properties……Page 36
1.7 Water and Ice Revisited……Page 42
2.1 Excluded Volume and Packing Problems……Page 47
2.2 Accessible Configuration Space……Page 48
2.3 Experiments on Random Packing Models……Page 49
2.4 Origins of Method of Molecular Dynamics……Page 51
2.6 Free Volume and Entropically Driven Freezing Transition……Page 54
2.7 Building on Hard Sphere Equation of State: the Model of Longuet-Higgins and Widom……Page 57
2.8 Hard-Particle Fluid Equation of State Using Nearest-Neighbour Correlations……Page 59
2.9 Free Volume Revisited in Hard Sphere Fluid……Page 60
2.10 Hard Particles in Low Dimensions……Page 63
2.11 Equation of State of Hard-Body Fluids……Page 65
2.12 Hard Sphere Fluid in Narrow Cylindrical Pores……Page 66
3.1 Thermodynamic Functions for a Fluid……Page 69
3.2 Specific Heats and Compressibilities……Page 74
3.3 Fluctuation Phenomena……Page 77
3.4 Clausius-Clapeyron Equation and Melting……Page 80
3.5 Free Energy from Partition Function……Page 82
3.6 Principle of Equipartition of Energy……Page 85
3.7 Thermodynamic and Other Properties of Hard Sphere Fluid……Page 86
3.8 Scaling of Thermodynamic Properties for Inverse-Power Repulsive Potentials……Page 88
A3.1.1 A magnetic system……Page 89
A3.1.2 Higher-order phase transitions……Page 90
Appendix 3.2 Partition Function, Phase Space and Configurational Integral for Inverse Power Repulsive Potentials……Page 91
4.1 Pair Distribution Function g(r)……Page 93
4.2 Definition of Liquid Structure Factor S(k)……Page 94
4.3 Diffractive Scattering from a Liquid……Page 96
4.4 Salient Features of Liquid Structure Factor……Page 97
4.5 Internal Energy and Virial Equation of State with Pair Forces……Page 102
4.6 Ornstein-Zernike Direct Correlation Function c(r)……Page 103
4.7 Thermodynamic Consistency and Structural Theories……Page 110
4.8 Liquid-Vapour Critical Point……Page 113
4.9 Fluids at Equilibrium in a Porous Medium……Page 119
Appendix 4.1 Inhomogeneous Monatomic Fluids……Page 120
A4.1.1 Equilibrium conditions……Page 121
A4.1.2 Direct correlation function……Page 123
A4.1.3 Hypernetted-chain approximation in liquid-structure theory……Page 124
Appendix 4.2 The Dieterici Equation of State……Page 125
Appendix 4.3 Force Equation and Born-Green Theory of Liquid Structure……Page 126
5.1 Background: Magnitude of Diffusion Coefficients in Gases Contrasted with Liquids……Page 129
5.2 Fick’s Law and Diffusion Equation……Page 132
5.3 Solute Diffusion at High Dilution in Water and in Non-aqueous Solvents……Page 134
5.4 Summary of Techniques, Including Computer Simulation, for Determining Diffusion Coefficients……Page 136
5.5 Velocity Autocorrelation Function in Pure Dense Liquids……Page 143
5.6 Models of Velocity Autocorrelation Function……Page 149
6.1 Hydrodynamic Variables……Page 155
6.2 Stresses in a Newtonian Fluid and the Navier-Stokes Equation……Page 157
6.3 Laminar Flow and the Measurement of Shear Viscosity……Page 161
6.4 Creeping Flow Past an Obstacle……Page 164
6.5 Vorticity……Page 168
6.6 Models of Viscosity……Page 170
6.7 Transverse Currents and Sound Propagation in Isothermal Conditions……Page 175
6.8 Microscopic Density Fluctuations and Inelastic Scattering……Page 178
Appendix 6.1 Kinetic Calculation of Shear Viscosity for Hard Spheres……Page 186
7.1 Fourier’s Law……Page 189
7.2 Studies of Heat Conduction by Molecular Dynamics……Page 192
7.3 Electronic Contribution to Heat Conduction in Liquid Metals……Page 196
7.4 Thermodynamics with Mass Motion and Entropy Production……Page 198
7.5 The Effect of Heat Flow on Sound Wave Propagation……Page 201
7.6 Binary Fluids……Page 205
7.7 Superfluid Helium……Page 207
Appendix 7.1 Kinetic Theory of Thermal and Electrical Conductivity……Page 214
Appendix 7.2 Hydrodynamics of Superfluid Helium in the Two-Fluid Model……Page 216
8.1 Classical One-Component Plasma: Static and Dynamic Screening……Page 219
8.2 Macroscopic Properties of Molten Salts……Page 223
8.3 Structural Functions for Multicomponent Fluids……Page 227
8.4 Coulomb Ordering in Monohalides and Dihalides……Page 230
8.5 Structure of Trivalent-Metal Halides……Page 234
8.6 Transport and Dynamics in Molten Salts……Page 237
8.7 Chemical Short-Range Order in Liquid Alloys……Page 242
9.1 Outline……Page 245
9.2 Elemental Molecular Liquids……Page 246
9.3 Orientational Pair Correlation Function from Diffraction Experiments……Page 252
9.4 Polymers……Page 256
9.5 Liquid Crystal Phases……Page 262
9.6 Nematic Liquid Crystals and their Phase Transitions……Page 265
Appendix 9.1 Melting and Orientational Disorder……Page 271
Appendix 9.2 Crystallisation from Solution……Page 272
10.1 Macroscopic Characteristics of a Glass and the Glass Transition……Page 273
10.2 Kinetics of Nucleation and Phase Changes……Page 277
10.3 The Structure of Amorphous Solids……Page 280
10.4 Thermodynamic Aspects and Free Energy Landscape……Page 284
10.5 Atomic Motions in the Glassy State……Page 287
10.6 Supercooled and Glassy Materials……Page 292
11.1 Introduction to Non-Newtonian Flow Behaviour……Page 301
11.2 Viscosity in Uniaxial Liquid……Page 305
11.3 Flow Birefringence and Flow Alignment……Page 308
11.4 Non-Newtonian Behaviour in Polymeric Liquids……Page 309
11.5 Flow in Nematic Liquid Crystals……Page 312
11.6 Colloidal Dispersions and Suspensions……Page 318
11.7 Surfactant Systems……Page 323
12.1 Introduction……Page 327
12.2 Instabilities in Fluids……Page 329
12.3 Evolution of Bénard Convection with Increasing Rayleigh Number……Page 334
12.4 Energy Cascade in Homogeneous Turbulence……Page 337
12.5 Diffusion in Homogeneous Turbulence……Page 342
12.6 Turbulent Shear Flows……Page 346
12.7 Turbulence in Compressible Fluids……Page 350
12.8 Turbulent Behaviour of Non-Newtonian Fluids……Page 351
Appendix 12.1 Navier-Stokes Equation: Analogy with Maxwell’s Equations……Page 353
Appendix 12.2 Series Solution of Navier-Stokes Equation……Page 355
13.1 Background and Empirical Correlations……Page 357
13.2 Definition of a Surface and its Thermodynamic Properties……Page 360
13.3 Phenomenology……Page 363
13.4 Microscopic Theories: Direct Correlation Function……Page 366
13.5 Microscopic Theories: Two-Particle Distribution Function……Page 373
13.6 Interfacial Dynamics……Page 375
13.7 Interfacial Transport and Rheology……Page 379
14.1 Ideal Fermi and Bose Gases……Page 383
14.2 Boson Fluids……Page 386
14.3 Normal Fermion Fluids……Page 393
14.4 BCS Superconductivity and Superfluidity in Fermion Fluids……Page 402
14.5 Electron Theory of Liquid Metals……Page 407
14.6 Liquid Hydrogen Plasmas and the Giant Planets……Page 413
Appendix 14.1 Density Profiles in the Perturbed Electron Gas……Page 415
References……Page 417
Index……Page 437