Introduction to liquid state physics / N.H. March, M.P. Tosi.

Format:

Book

Author/Creator:

March, Norman H. (Norman Henry), 1927-

Contributor:

Tosi, M. P.

Language:

English

Subjects (All):

Liquids.

Thermodynamics.

Statistical mechanics.

Physical Description:

xvii, 431 pages : illustrations ; 24 cm

Other Title:

Liquid state physics.

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, [2002]

Summary:

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.

Contents:

1 Qualitative Description of Liquid Properties 1

1.1 Three Phases of Matter: pVT Behaviour of Pure Materials 2

1.1.1 Critical isotherm 4

1.1.2 Triple point 4

1.1.3 Phase diagram of a pure material (e.g. argon) 5

1.1.4 Phase change from gas to liquid 6

1.1.5 A liquid open to the atmosphere 7

1.2 Melting and Lindemann's Law 8

1.3 Molecular Thermal Movements in the Liquid Phase: Brownian Motion 9

1.4 Qualitative Considerations Continued: Flow Properties of Dense Liquids 12

1.4.1 Ideal liquids and Bernoulli's equation 13

1.4.2 Flow in real liquids: Introduction of viscosity 15

1.4.3 Poiseuille's formula: Viscous flow through a tube 15

1.4.4 Turbulence and Reynolds number 16

1.5 Rigidity of Liquids 17

1.6 Surface Properties 18

1.6.1 Surface free energy and surface tension 18

1.6.2 Surface energy versus surface free energy 20

1.6.3 Contact angle 20

1.6.4 Capillarity 21

1.6.5 Energy for capillary rise 23

1.7 Water and Ice Revisited 24

2 Excluded Volume, Free Volume and Hard Sphere Packing 29

2.1 Excluded Volume and Packing Problems 29

2.2 Accessible Configuration Space 30

2.3 Experiments on Random Packing Models 31

2.4 Origins of Method of Molecular Dynamics 33

2.5 Free-Volume Approximation 36

2.6 Free Volume and Entropically Driven Freezing Transition 36

2.7 Building on Hard Sphere Equation of State 39

2.8 Hard-Particle Fluid Equation of State Using Nearest-Neighbour Correlations 41

2.9 Free Volume Revisited in Hard Sphere Fluid 42

2.9.1 Statistical geometry of high-density fluid 43

2.9.2 Chemical potential in terms of statistical geometry 44

2.10 Hard Particles in Low Dimensions 45

2.10.1 Rods and disks 46

2.10.2 Hard ellipses 46

2.11 Equation of State of Hard-Body Fluids 47

2.12 Hard Sphere Fluid in Narrow Cylindrical Pores 48

3 Thermodynamics, Equipartition of Energy and Some Scaling Properties 51

3.1 Thermodynamic Functions for a Fluid 51

3.1.1 Thermodynamic identity and the first principle of thermodynamics 53

3.1.2 Helmholtz free energy and variational principle 54

3.1.3 Gibbs free energy 56

3.2 Specific Heats and Compressibilities 56

3.2.1 Specific heat at constant pressure 57

3.2.2 Specific heat properties of liquid metals near freezing 58

3.2.3 Compressibilities, both adiabatic and isothermal 59

3.3 Fluctuation Phenomena 59

3.3.1 Fluctuations in a perfect gas 60

3.3.2 Effect of intermolecular forces 61

3.3.3 Temperature fluctuations 62

3.4 Clausius-Clapeyron Equation and Melting 62

3.5 Free Energy from Partition Function 64

3.6 Principle of Equipartition of Energy 67

3.6.1 Internal energy and other thermodynamic functions of a perfect gas 67

3.6.2 Harmonic oscillator revisited 68

3.7 Thermodynamic and Other Properties of Hard Sphere Fluid 68

3.8 Scaling of Thermodynamic Properties for Inverse-Power Repulsive Potentials 70

3.8.1 Consequence for melting transition 70

Appendix 3.1 Analogues of the Clausius-Clapeyron Equation for Other Phase Transitions 71

A3.1.1 A magnetic system 71

A3.1.2 Higher-order phase transitions 72

Appendix 3.2 Partition Function, Phase Space and Configurational Integral for Inverse Power Repulsive Potentials 73

4 Structure, Forces and Thermodynamics 75

4.1 Pair Distribution Function g(r) 75

4.2 Definition of Liquid Structure Factor S(k) 76

4.3 Diffractive Scattering from a Liquid 78

4.4 Salient Features of Liquid Structure Factor 79

4.4.1 Long wavelength limit and connection with thermodynamic fluctuations 79

4.4.2 The Hansen-Verlet freezing criterion 80

4.4.3 Relation between the main features of the peak in the structure factor 81

4.4.4 Verlet's rule related to Lindemann's melting criterion 83

4.5 Internal Energy and Virial Equation of State with Pair Forces 84

4.6 Ornstein-Zernike Direct Correlation Function 85

4.6.1 Direct correlation function from Percus-Yevick theory for hard spheres 87

4.6.2 Softness corrections to the hard sphere potential 90

4.6.3 Small angle scattering from liquid argon near triple point 91

4.7 Thermodynamic Consistency and Structural Theories 92

4.7.1 Consistency of virial and fluctuation compressibility: Consequences for c(r) 92

4.7.2 A route to thermodynamic consistency in liquid-structure theory 93

4.8 Liquid-Vapour Critical Point 95

4.8.1 Critical constants for insulating fluids and expanded alkali metals 95

4.8.2 Ornstein-Zernike theory and critical exponents 98

4.8.3 Scaling relations 99

4.8.4 X-ray critical scattering from fluids 100

4.9 Fluids at Equilibrium in a Porous Medium 101

Appendix 4.1 Inhomogeneous Monatomic Fluids 102

A4.1.1 Equilibrium conditions 103

A4.1.2 Direct correlation function 105

A4.1.3 Hypernetted-chain approximation in liquid-structure theory 106

Appendix 4.2 The Dieterici Equation of State 107

Appendix 4.3 Force Equation and Born-Green Theory of Liquid Structure 108

5 Diffusion 111

5.1 Background: Magnitude of Diffusion Coefficients in Gases 111

5.1.1 Practical consequences of "slow" diffusion in dense liquids 113

5.2 Fick's Law and Diffusion Equation 114

5.2.1 Examples of diffusion across a thin film 115

5.3 Solute Diffusion at High Dilution in Water and in Non-aqueous Solvents 116

5.3.1 Stokes-Einstein and semiempirical estimates of solute diffusion 116

5.4 Summary of Techniques, Including Computer Simulation, for Determining 118

5.4.1 Incoherent neutron scattering 119

5.4.2 Dynamic light scattering 121

5.4.3 Nuclear magnetic resonance 122

5.4.4 Computer simulation of mean square displacement 123

5.5 Velocity Autocorrelation Function in Pure Dense Liquids 125

5.5.1 Frequency spectrum and long-time tails 126

5.5.2 The Nernst-Einstein relation 129

5.6 Models of Velocity Autocorrelation Function 131

5.6.1 The Zwanzig model 132

5.6.2 Wallace's independent atom model 134

5.6.3 Generalisation of Stokes-Einstein relation 135

6 Viscosity 137

6.1 Hydrodynamic Variables 137

6.2 Stresses in a Newtonian Fluid and the Navier-Stokes Equation 139

6.2.1 Viscosity stress tensor 139

6.2.2 Bulk and shear viscosity 141

6.2.3 The Navier-Stokes equation 141

6.2.4 Viscous dissipation 142

6.3 Laminar Flow and the Measurement of Shear Viscosity 143

6.3.1 Oscillating disk viscometer 145

6.3.2 Couette viscometer 145

6.3.3 Hydrodynamic lubrication 146

6.4 Creeping Flow Past an Obstacle 146

6.4.1 Stokes' law revisited 147

6.4.2 The viscosity of suspensions 149

6.4.3 Percolation 150

6.5 Vorticity 150

6.5.1 Vorticity diffusion 151

6.5.2 The Magnus force 152

6.6 Models of Viscosity 152

6.6.1 Shear and bulk viscosity of hard sphere fluid 153

6.6.2 Temperature dependence of shear viscosity 155

6.6.3 Green-Kubo formulae for viscosity 156

6.6.4 Computer simulation of shear viscosity in a Lennard-Jones fluid 157

6.7 Transverse Currents and Sound Propagation in Isothermal Conditions 157

6.7.1 Linearised Navier-Stokes equation 157

6.7.2 Bulk viscosity 159

6.7.3 Brillouin light scattering 160

6.8 Microscopic Density Fluctuations and Inelastic Scattering 160

6.8.1 Inelastic neutron scattering from liquids 161

6.8.2 Inelastic photon scattering from liquids 165

6.8.3 Fast sound in water 167

Appendix 6.1 Kinetic Calculation of Shear Viscosity for Hard Spheres 168

7 Heat Transport 171

7.1 Fourier's Law 171

7.2 Studies of Heat Conduction by Molecular Dynamics 174

7.2.1 Green-Kubo formula 175

7.2.2 Non-equilibrium methods 176

7.2.3 Transient time correlation formula 176

7.3 Electronic Contribution to Heat Conduction in Liquid Metals 178

7.4 Thermodynamics with Mass Motion and Entropy Production 180

7.4.1 Thermodynamic relations 180

7.4.2 Entropy production 181

7.4.3 Constitutive relations 182

7.5 The Effect of Heat Flow on Sound Wave Propagation 183

7.5.1 Hydrodynamic

modes 183

7.5.2 Light scattering 185

7.5.3 Sound propagation in the critical region 186

7.6 Binary Fluids 187

7.6.1 Thermodiffusion 187

7.6.2 Hydrodynamic modes 189

7.7 Superfluid Helium 189

7.7.1 Transport properties of superfluid [superscript 4]He 191

7.7.2 Inelastic neutron scattering from superfluid [superscript 4]He 193

Appendix 7.1 Kinetic Theory of Thermal and Electrical Conductivity 196

Appendix 7.2 Hydrodynamics of Superfluid Helium in the Two-Fluid Model 198

8 Chemical Short-Range Order: Molten Salts and Some Metal Alloys 201

8.1 Classical One-Component Plasma: Static and Dynamic Screening 201

8.1.1 Debye screening 202

8.1.2 Dynamic screening and plasma excitation 204

8.1.3 Structure and dynamics of the strongly coupled OCP 204

8.2 Macroscopic Properties of Molten Salts 205

8.2.1 Selected macroscopic data for chlorides 206

8.2.2 Melting parameters 207

8.2.3 Alkali halide vapours and critical behaviour of ionic fluids 208

8.3 Structural Functions for Multicomponent Fluids 209

8.3.1 Number-concentration structure factors 210

8.4 Coulomb Ordering in Monohalides and Dihalides 212

8.4.1 Alkali halides 212

8.4.2 Noble-metal halides 213

8.4.3 Fluorite-type superionic conductors 214

8.4.4 Tetrahedral-network structure in ZnCl[subscript 2] 214

8.5 Structure of Trivalent-Metal Halides 216

8.5.1 Octahedral-network formation in lanthanide chlorides 217

8.5.2 Ionic-to-molecular melting in AlCl[subscript 3] and FeCl[subscript 3] 217

8.5.3 Liquid haloaluminates 218

8.5.4 Molecular-to-molecular melting in GaCl[subscript 3] and SbCl[subscript 3] 218

8.6 Transport and Dynamics in Molten Salts 219

8.6.1 Ionic transport 219

8.6.2 Viscosity 221

8.6.3 Dynamics of density fluctuations 223

8.7 Chemical Short-Range Order in Liquid Alloys 224

8.7.1 The CsAu compound 224

8.7.2 Other alkali-based alloys with chemical short-range order 225

9 Bonds, Rings and Chains 227

9.2 Elemental Molecular Liquids 228

9.2.1 Nitrogen 228

9.2.2 Phase diagram of carbon: Especially liquid-liquid transformation 229

9.2.3 Selenium and sulphur: Especially liquid-liquid transitions 231

9.2.4 Structure of liquid boron 232

9.3 Orientational Pair Correlation Function from Diffraction Experiments 234

9.3.1 Use of generalised rotation matrices 235

9.3.2 Example of orientational structure in water 236

9.4 Polymers 238

9.4.1 The isolated polymer molecule 238

9.4.2 Polymer solutions 239

9.4.3 Polymer blends 242

9.4.4 Polymeric materials 243

9.5 Liquid Crystal Phases 244

9.5.1 Smectic phase 245

9.5.2 Nematic phase 245

9.5.3 Cholesteric phase 246

9.6 Nematic Liquid Crystals and their Phase Transitions 247

9.6.1 Landau-de Gennes theory 248

9.6.2 Molecular mean-field theory of isotropic-nematic transition 250

9.6.3 The isotropic-nematic-smecticA transition 251

9.6.4 Model potentials for molecular liquid and liquid crystals 252

Appendix 9.1 Melting and Orientational Disorder 253

Appendix 9.2 Crystallisation from Solution 254

10 Supercooling and the Glassy State 255

10.1 Macroscopic Characteristics of a Glass 255

10.2 Kinetics of Nucleation and Phase Changes 259

10.2.1 Homogeneous nucleation and crystal growth 259

10.2.2 The critical cooling rate for glass formation 261

10.2.3 Superheating and vapour condensation 261

10.3 The Structure of Amorphous Solids 262

10.3.1 Network and modified-network glasses 263

10.3.2 Molten and amorphous semiconductors 264

10.4 Thermodynamic Aspects and Free Energy Landscape 266

10.4.1 A topographic view of supercooled liquids 267

10.5 Atomic Motions in the Glassy State 269

10.5.1 Relaxation processes 269

10.5.2 Strong and fragile liquids 271

10.5.3 Annealing and aging 273

10.5.4 Anharmonicity and boson peaks 274

10.6 Supercooled and Glassy Materials 274

10.6.1 Hard sphere statistics on the amorphous branch 274

10.6.2 Supercooled water 276

10.6.3 Metallic glasses 277

10.6.4 Superionic glasses 278

10.6.5 Glassy polymers 279

11 Non-Newtonian Fluids 283

11.1 Introduction to Non-Newtonian Flow Behaviour 283

11.1.1 Linear visco-elasticity 285

11.2 Viscosity in Uniaxial Liquid 287

11.3 Flow Birefringence and Flow Alignment 290

11.4 Non-Newtonian Behaviour in Polymeric Liquids 291

11.4.1 Reptation in concentrated polymer systems 292

11.4.2 Macroscopic flow phenomena in polymeric liquids 293

11.5 Flow in Nematic Liquid Crystals 294

11.5.1 Curvature elasticity and the Freedericksz transition 295

11.5.2 Macroscopic flow and disclinations in nematics 297

11.6 Colloidal Dispersions and Suspensions 300

11.6.1 Flow properties of colloidal dispersions 301

11.6.2 The rheology of field-responsive suspensions 304

11.7 Surfactant Systems 305

12 Turbulence 309

12.2 Instabilities in Fluids 311

12.2.1 The Rayleigh-Taylor instability 311

12.2.2 Thermal convection and the Rayleigh-Benard instability 312

12.2.3 The Kelvin-Helmholtz instability 314

12.3 Evolution of Benard Convection with Increasing Rayleigh Number 316

12.4 Energy Cascade in Homogeneous Turbulence 319

12.4.1 Energy cascade and Kolmogorov microscales 320

12.4.2 Kinetic energy spectrum 322

12.4.3 Energy spectra from renormalisation group approach 324

12.5 Diffusion in Homogeneous Turbulence 324

12.5.1 Time and length scales in diffusion 324

12.5.2 Stochastic modelling of turbulent diffusion 325

12.5.3 Eddy diffusivity 327

12.6 Turbulent Shear Flows 328

12.6.1 Length scales of momentum transport 328

12.6.2 Reynolds stresses 329

12.6.3 Lattice Boltzmann computing 331

12.7 Turbulence in Compressible Fluids 332

12.8 Turbulent Behaviour of Non-Newtonian Fluids 333

Appendix 12.1 Navier-Stokes Equation: Analogy with Maxwell's Equations 335

Appendix 12.2 Series Solution of Navier-Stokes Equation 337

13 Liquid-Vapour Interface 339

13.1 Background and Empirical Correlations 339

13.1.1 Relation between surface tension and bulk properties: Organic liquids near 298 K 340

13.2 Definition of a Surface and its Thermodynamic Properties 342

13.2.1 Gibbs surface 342

13.2.2 Surface tension 343

13.2.3 Surface entropy 344

13.3 Phenomenology 345

13.3.1 Free energy from inhomogeneity 346

13.3.2 Density gradient contribution to free energy 347

13.3.3 Extension to binary alloys and surface segregation 347

13.4 Microscopic Theories: Direct Correlation Function 348

13.4.1 Density profile and surface tension 349

13.4.2 Density gradient expansion: Pressure through interface 350

13.4.3 Critical behaviour of surface tension 351

13.4.4 Application to nucleation theory 352

13.5 Microscopic Theories: Two-Particle Distribution Function 355

13.5.1 Tangential pressure deficit and surface tension 355

13.5.2 The Fowler approximation: Relation of surface tension to shear viscosity 356

13.5.3 Computer studies: Role of interatomic forces in condensed rare-gas elements 357

13.6 Interfacial Dynamics 357

13.6.1 Surface waves 357

13.6.2 Capillary waves and surface fluctuations 359

13.6.3 Interface reflectivity and diffuse interface in a critical fluid mixture 360

13.7 Interfacial Transport and Rheology 361

14 Quantum Fluids 365

14.1 Ideal Fermi and Bose Gases 365

14.1.1 The Fermi surface 366

14.1.2 Bose-Einstein condensation 367

14.2 Boson Fluids 368

14.2.1 The weakly interacting Bose gas (WIBG) 368

14.2.2 Superfluid liquid [superscript 4]He 370

14.2.3 Bose-Einstein condensates 373

14.3 Normal Fermion Fluids 375

14.3.1 Liquid [superscript 3]He in the normal state 375

14.3.2 Electron fluids 379

14.3.3 Wigner crystallisation 383

14.4 BCS Superconductivity and Superfluidity in Fermion Fluids 384

14.4.1 The superconducting state 384

14.4.2 Flux quantisation and Josephson effects 386

14.4.3 Superfluidity in liquid [superscript 3]He 388

14.5 Electron Theory of Liquid Metals 389

14.5.1 Interatomic forces from liquid structure factor S(k) 390

14.5.2 Diffractive scattering from two-component plasmas 391

14.5.3 Transport coefficients 393

14.6 Liquid Hydrogen Plasmas and the Giant Planets 395

14.6.1 Exploring the phase diagram of hydrogen 395

14.6.2 Hydrogen-helium mixtures and the constitution of giant planets 396

Appendix 14.1 Density Profiles in the Perturbed Electron Gas 397.

Notes:

Includes bibliographical references (pages 399-418) and index.

ISBN:

9810246390

9810246528

OCLC:

50754158