Introduction to Liquid State Physics

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......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 Contents 8 Preface 6 1 Qualitative Description of Liquid Properties 19 1.1 Three Phases of Matter: pVT Behaviour of Pure Materials 20 1.2 Melting and Lindemann's Law 26 1.3 Molecular Thermal Movements in the Liquid Phase: Brownian Motion 27 1.4 Qualitative Considerations Continued: Flow Properties of Dense Liquids 30 1.5 Rigidity of Liquids 35 1.6 Surface Properties 36 1.7 Water and Ice Revisited 42 2 Excluded Volume, Free Volume and Hard Sphere Packing 47 2.1 Excluded Volume and Packing Problems 47 2.2 Accessible Configuration Space 48 2.3 Experiments on Random Packing Models 49 2.4 Origins of Method of Molecular Dynamics 51 2.5 Free-Volume Approximation 54 2.6 Free Volume and Entropically Driven Freezing Transition 54 2.7 Building on Hard Sphere Equation of State: the Model of Longuet-Higgins and Widom 57 2.8 Hard-Particle Fluid Equation of State Using Nearest-Neighbour Correlations 59 2.9 Free Volume Revisited in Hard Sphere Fluid 60 2.10 Hard Particles in Low Dimensions 63 2.11 Equation of State of Hard-Body Fluids 65 2.12 Hard Sphere Fluid in Narrow Cylindrical Pores 66 3 Thermodynamics, Equipartition of Energy and Some Scaling Properties 69 3.1 Thermodynamic Functions for a Fluid 69 3.2 Specific Heats and Compressibilities 74 3.3 Fluctuation Phenomena 77 3.4 Clausius-Clapeyron Equation and Melting 80 3.5 Free Energy from Partition Function 82 3.6 Principle of Equipartition of Energy 85 3.7 Thermodynamic and Other Properties of Hard Sphere Fluid 86 3.8 Scaling of Thermodynamic Properties for Inverse-Power Repulsive Potentials 88 Appendix 3.1 Analogues of the Clausius-Clapeyron Equation for Other Phase Transitions 89 A3.1.1 A magnetic system 89 A3.1.2 Higher-order phase transitions 90 Appendix 3.2 Partition Function, Phase Space and Configurational Integral for Inverse Power Repulsive Potentials 91 4 Structure, Forces and Thermodynamics 93 4.1 Pair Distribution Function g(r) 93 4.2 Definition of Liquid Structure Factor S(k) 94 4.3 Diffractive Scattering from a Liquid 96 4.4 Salient Features of Liquid Structure Factor 97 4.5 Internal Energy and Virial Equation of State with Pair Forces 102 4.6 Ornstein-Zernike Direct Correlation Function c(r) 103 4.7 Thermodynamic Consistency and Structural Theories 110 4.8 Liquid-Vapour Critical Point 113 4.9 Fluids at Equilibrium in a Porous Medium 119 Appendix 4.1 Inhomogeneous Monatomic Fluids 120 A4.1.1 Equilibrium conditions 121 A4.1.2 Direct correlation function 123 A4.1.3 Hypernetted-chain approximation in liquid-structure theory 124 Appendix 4.2 The Dieterici Equation of State 125 Appendix 4.3 Force Equation and Born-Green Theory of Liquid Structure 126 5 Diffusion 129 5.1 Background: Magnitude of Diffusion Coefficients in Gases Contrasted with Liquids 129 5.2 Fick's Law and Diffusion Equation 132 5.3 Solute Diffusion at High Dilution in Water and in Non-aqueous Solvents 134 5.4 Summary of Techniques, Including Computer Simulation, for Determining Diffusion Coefficients 136 5.5 Velocity Autocorrelation Function in Pure Dense Liquids 143 5.6 Models of Velocity Autocorrelation Function 149 6 Viscosity 155 6.1 Hydrodynamic Variables 155 6.2 Stresses in a Newtonian Fluid and the Navier-Stokes Equation 157 6.3 Laminar Flow and the Measurement of Shear Viscosity 161 6.4 Creeping Flow Past an Obstacle 164 6.5 Vorticity 168 6.6 Models of Viscosity 170 6.7 Transverse Currents and Sound Propagation in Isothermal Conditions 175 6.8 Microscopic Density Fluctuations and Inelastic Scattering 178 Appendix 6.1 Kinetic Calculation of Shear Viscosity for Hard Spheres 186 7 Heat Transport 189 7.1 Fourier's Law 189 7.2 Studies of Heat Conduction by Molecular Dynamics 192 7.3 Electronic Contribution to Heat Conduction in Liquid Metals 196 7.4 Thermodynamics with Mass Motion and Entropy Production 198 7.5 The Effect of Heat Flow on Sound Wave Propagation 201 7.6 Binary Fluids 205 7.7 Superfluid Helium 207 Appendix 7.1 Kinetic Theory of Thermal and Electrical Conductivity 214 Appendix 7.2 Hydrodynamics of Superfluid Helium in the Two-Fluid Model 216 8 Chemical Short-Range Order: Molten Salts and Some Metal Alloys 219 8.1 Classical One-Component Plasma: Static and Dynamic Screening 219 8.2 Macroscopic Properties of Molten Salts 223 8.3 Structural Functions for Multicomponent Fluids 227 8.4 Coulomb Ordering in Monohalides and Dihalides 230 8.5 Structure of Trivalent-Metal Halides 234 8.6 Transport and Dynamics in Molten Salts 237 8.7 Chemical Short-Range Order in Liquid Alloys 242 9 Bonds, Rings and Chains 245 9.1 Outline 245 9.2 Elemental Molecular Liquids 246 9.3 Orientational Pair Correlation Function from Diffraction Experiments 252 9.4 Polymers 256 9.5 Liquid Crystal Phases 262 9.6 Nematic Liquid Crystals and their Phase Transitions 265 Appendix 9.1 Melting and Orientational Disorder 271 Appendix 9.2 Crystallisation from Solution 272 10 Supercooling and the Glassy State 273 10.1 Macroscopic Characteristics of a Glass and the Glass Transition 273 10.2 Kinetics of Nucleation and Phase Changes 277 10.3 The Structure of Amorphous Solids 280 10.4 Thermodynamic Aspects and Free Energy Landscape 284 10.5 Atomic Motions in the Glassy State 287 10.6 Supercooled and Glassy Materials 292 11 Non-Newtonian Fluids 301 11.1 Introduction to Non-Newtonian Flow Behaviour 301 11.2 Viscosity in Uniaxial Liquid 305 11.3 Flow Birefringence and Flow Alignment 308 11.4 Non-Newtonian Behaviour in Polymeric Liquids 309 11.5 Flow in Nematic Liquid Crystals 312 11.6 Colloidal Dispersions and Suspensions 318 11.7 Surfactant Systems 323 12 Turbulence 327 12.1 Introduction 327 12.2 Instabilities in Fluids 329 12.3 Evolution of Bénard Convection with Increasing Rayleigh Number 334 12.4 Energy Cascade in Homogeneous Turbulence 337 12.5 Diffusion in Homogeneous Turbulence 342 12.6 Turbulent Shear Flows 346 12.7 Turbulence in Compressible Fluids 350 12.8 Turbulent Behaviour of Non-Newtonian Fluids 351 Appendix 12.1 Navier-Stokes Equation: Analogy with Maxwell's Equations 353 Appendix 12.2 Series Solution of Navier-Stokes Equation 355 13 Liquid-Vapour Interface 357 13.1 Background and Empirical Correlations 357 13.2 Definition of a Surface and its Thermodynamic Properties 360 13.3 Phenomenology 363 13.4 Microscopic Theories: Direct Correlation Function 366 13.5 Microscopic Theories: Two-Particle Distribution Function 373 13.6 Interfacial Dynamics 375 13.7 Interfacial Transport and Rheology 379 14 Quantum Fluids 383 14.1 Ideal Fermi and Bose Gases 383 14.2 Boson Fluids 386 14.3 Normal Fermion Fluids 393 14.4 BCS Superconductivity and Superfluidity in Fermion Fluids 402 14.5 Electron Theory of Liquid Metals 407 14.6 Liquid Hydrogen Plasmas and the Giant Planets 413 Appendix 14.1 Density Profiles in the Perturbed Electron Gas 415 References 417 Index 437 March (Oxford U., UK) and Tosi (Scuola Normale Superiore, Italy) offer a more general treatment of this subject than in their earlier books, reflecting current trends applicable to diverse disciplines and the computer capability now available to calculate liquid state properties. Directed to advanced undergraduate/ graduate-level students and scientists, they describe such phase, surface, and thermodynamic properties of liquids as Brownian motion, viscosity, turbulence, heat transport, and supercooling. The final chapter covers quantum fluids. There are 542 references. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)