Preface to the Third Edition .................................... v
Preface to the Second Edition .................................. vi
Preface to the First Edition ................................. viii
Chapter 1. Introduction
1.1 The liquid state ........................................... 1
1.2 Intermolecular forces and model potentials ................. 3
1.3 Experimental methods ....................................... 9
Notes and References ........................................... 10
Chapter 2. Statistical Mechanics
2.1 Time evolution and kinetic equations ...................... 11
2.2 Time averages and ensemble averages ....................... 17
2.3 Canonical and isothermal-isobaric ensembles ............... 20
2.4 The grand canonical ensemble .............................. 23
2.5 Particle densities and distribution functions ............. 28
2.6 Particle densities in the grand canonical ensemble ........ 33
2.7 Computer simulation: molecular dynamics and Monte Carlo ... 35
Notes and References ........................................... 44
Chapter 3. Static Properties of Liquids: Thermodynamics and
Structure
3.1 A fluid in an external field .............................. 46
3.2 Functionals and functional differentiation ................ 50
3.3 Functional derivatives of the grand potential ............. 53
3.4 Density-functional theory ................................. 55
3.5 Direct correlation functions .............................. 57
3.6 The density response function ............................. 62
3.7 Diagrammatic methods ...................................... 65
3.8 Diagrammatic expansions of the direct correlation
functions ................................................. 71
3.9 Virial expansion of the equation of state ................. 74
Notes and References ........................................... 77
Chapter 4. Distribution-function Theories
4.1 The static structure factor ............................... 78
4.2 The YBG hierarchy and the Born-Green equation ............. 83
4.3 Functional expansions and integral equations .............. 85
4.4 The Percus-Yevick equation ................................ 90
4.5 The mean spherical approximation .......................... 95
4.6 Diagrammatic expansions of the pair functions ............. 97
4.7 Extensions of integral equations ......................... 103
Notes and References .......................................... 107
Chapter 5. Perturbation Theory
5.1 Introduction: the van der Waals model .................... 109
5.2 The λ-expansion .......................................... 111
5.3 Soft-core reference systems .............................. 116
5.4 An example: the Lennard-Jones fluid ...................... 121
5.5 Treatment of attractive forces ........................... 124
5.6 Mean-field theory of liquid-vapour coexistence ........... 132
5.7 Scaling concepts and hierarchical reference theory ....... 139
Notes and References .......................................... 145
Chapter 6. Inhomogeneous Fluids
6.1 Liquids at interfaces .................................... 147
6.2 Approximate free-energy functionals ...................... 151
6.3 The liquid-vapour interface .............................. 156
6.4 Fundamental-measure theory ............................... 159
6.5 Confined fluids .......................................... 165
6.6 Density-functional theory of freezing .................... 170
Notes and References .......................................... 176
Chapter 7. Time-dependent Correlation and Response
Functions
7.1 General properties of time-correlation functions ......... 178
7.2 An illustration: the velocity autocorrelation function
and self-diffusion ....................................... 183
7.3 Brownian motion and the generalised Langevin equation .... 190
7.4 Correlations in space and time ........................... 195
7.5 Inelastic neutron scattering ............................. 201
7.6 Linear-response theory ................................... 206
7.7 Applications of the linear-response formalism ............ 213
Notes and References .......................................... 218
Chapter 8. Hydrodynamics and Transport Coefficients
8.1 Thermal fluctuations at long wavelengths and low
frequencies .............................................. 219
8.2 Space-dependent self motion .............................. 221
8.3 The Navier-Stokes equation and hydrodynamic collective
modes .................................................... 225
8.4 Transverse-current correlations .......................... 230
8.5 Longitudinal collective modes ............................ 234
8.6 Generalised hydrodynamics ................................ 241
8.7 Long-time tails in time-correlation functions ............ 245
8.8 Dynamics of supercooled liquids .......................... 250
Notes and References .......................................... 254
Chapter 9. Theories of Time-correlation Functions
9.1 The projection-operator formalism ........................ 255
9.2 Self correlation functions ............................... 261
9.3 Transverse collective modes .............................. 266
9.4 Density fluctuations ..................................... 270
9.5 Mode-coupling theory I. The velocity autocorrelation
function ................................................. 277
9.6 Mode-coupling theory II. The kinetic glass transition .... 282
Notes and References .......................................... 289
Chapter 10. Ionic Liquids
10.1 Classes and models of ionic liquids ...................... 291
10.2 Screening and charge ordering ............................ 295
10.3 Integral-equation theories ............................... 302
10.4 Frequency-dependent electric response .................... 307
10.5 Microscopic dynamics in molten salts ..................... 314
10.6 The electric double layer ................................ 318
10.7 Effective interactions between colloidal particles ....... 325
10.8 Liquid metals: electrons and ions ........................ 330
10.9 Ionic dynamics in liquid metals .......................... 336
Notes and References .......................................... 339
Chapter 11. Molecular Liquids
11.1 The molecular pair distribution function ................. 341
11.2 Expansions of the pair distribution function ............. 343
11.3 Site-site distribution functions ......................... 346
11.4 Correlation-function expansions for simple polar
fluids ................................................... 353
11.5 The static dielectric constant ........................... 357
11.6 Integral-equation approximations for dipolar hard
spheres .................................................. 362
11.7 Interaction-site diagrams ................................ 368
11.8 Interaction-site models: the RISM equations .............. 371
11.9 Angular correlations and the RISM formalism .............. 375
11.10 Associating liquids ..................................... 378
11.11 Reorientational time-correlation functions .............. 384
Notes and References .......................................... 390
Appendix A. Fluctuations ...................................... 393
Appendix B. Two theorems in density-functional theory ......... 395
Appendix С. Lemmas on diagrams ................................ 398
Appendix D. Solution of the PY equation for hard spheres ...... 402
Appendix E. Scaled-particle theory ............................ 406
Index ......................................................... 409
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