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9789810246525
Introduction To Liquid State Physics available in Hardcover, Paperback
Introduction To Liquid State Physics
by Norman H March, Mario P Tosi
Norman H March
- ISBN-10:
- 9810246528
- ISBN-13:
- 9789810246525
- Pub. Date:
- 08/19/2002
- Publisher:
- World Scientific Publishing Company, Incorporated
- ISBN-10:
- 9810246528
- ISBN-13:
- 9789810246525
- Pub. Date:
- 08/19/2002
- Publisher:
- World Scientific Publishing Company, Incorporated
Introduction To Liquid State Physics
by Norman H March, Mario P Tosi
Norman H March
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Overview
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.
Product Details
| ISBN-13: | 9789810246525 |
|---|---|
| Publisher: | World Scientific Publishing Company, Incorporated |
| Publication date: | 08/19/2002 |
| Edition description: | New Edition |
| Pages: | 452 |
| Product dimensions: | 6.00(w) x 8.80(h) x 0.80(d) |
Table of Contents
| Preface | v | |
| 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 |
| 9.1 | Outline | 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 th
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