Theory of Simple Liquids (eBook)

front cover 1
copyright 5
front matter 6
Preface to the Third Edition 6
Preface to the Second Edition 7
Preface to the First Edition 9
Contents 10
Introduction 14
The liquid state 14
Intermolecular forces and model potentials 16
Experimental methods 22
Notes and References 23
body 24
Statistical Mechanics 24
Time evolution and kinetic equations 24
Time averages and ensemble averages 30
Canonical and isothermal-isobaric ensembles 33
The grand canonical ensemble 36
Particle densities and distribution functions 41
Particle densities in the grand canonical ensemble 46
Computer simulation: molecular dynamics and Monte Carlo 48
Notes and References 57
Static Properties of Liquids: Thermodynamics and Structure 59
A fluid in an external field 59
Functionals and functional differentiation 63
Functional derivatives of the grand potential 66
Density-functional theory 68
Direct correlation functions 70
The density response function 75
Diagrammatic methods 78
Diagrammatic expansions of the direct correlation functions 84
Virial expansion of the equation of state 87
Notes and References 90
Distribution-function Theories 91
The static structure factor 91
The YBG hierarchy and the Born-Green equation 96
Functional expansions and integral equations 98
The Percus-Yevick equation 103
The mean spherical approximation 108
Diagrammatic expansions of the pair functions 110
Extensions of integral equations 116
Notes and References 120
Perturbation Theory 122
Introduction: the van der Waals model 122
The lambda-expansion 124
Soft-core reference systems 129
An example: the Lennard-Jones fluid 134
Treatment of attractive forces 137
Mean-field theory of liquid-vapour coexistence 145
Scaling concepts and hierarchical reference theory 152
Notes and References 158
Inhomogeneous Fluids 160
Liquids at interfaces 160
Approximate free-energy functionals 164
The liquid-vapour interface 169
Fundamental-measure theory 172
Confined fluids 178
Density-functional theory of freezing 183
Notes and References 189
Time-dependent Correlation and Response Functions 191
General properties of time-correlation functions 191
The velocity autocorrelation function and self-diffusion 196
Brownian motion and the generalised Langevin equation 203
Correlations in space and time 208
Inelastic neutron scattering 214
Linear-response theory 219
Applications of the linear-response formalism 226
Notes and References 231
Hydrodynamics and Transport Coefficients 232
Thermal fluctuations at long wavelengths and low frequencies 232
Space-dependent self motion 234
The Navier-Stokes equation and hydrodynamic collective modes 238
Transverse-current correlations 243
Longitudinal collective modes 247
Generalised hydrodynamics 254
Long-time tails in time-correlation functions 258
Dynamics of supercooled liquids 263
Notes and References 267
Theories of Time-correlation Functions 268
The projection-operator formalism 268
Self correlation functions 274
Transverse collective modes 279
Density fluctuations 283
Mode-coupling theory I. the velocity autocorrelation function 290
Mode-coupling theory II. the kinetic glass transition 295
Notes and References 302
Ionic Liquids 304
Classes and models of ionic liquids 304
Screening and charge ordering 308
Integral-equation theories 315
Frequency-dependent electric response 320
Microscopic dynamics in molten salts 327
The electric double layer 331
Effective interactions between colloidal particles 338
Liquid metals: electrons and ions 343
Ionic dynamics in liquid metals 349
Notes and References 352
Molecular Liquids 354
The molecular pair distribution function 354
Expansions of the pair distribution function 356
Site-site distribution functions 359
Correlation-function expansions for simple polar fluids 366
The static dielectric constant 370
Integral-equation approximations for dipolar hard spheres 375
Interaction-site diagrams 381
Interaction-site models: the RISM equations 384
Angular correlations and the RISM formalism 388
Associating liquids 391
Reorientational time-correlation functions 397
Notes and References 403
back matter 406
Fluctuations 406
Two theorems in density-functional theory 408
Lemmas on diagrams 411
Solution of the PY equation for hard spheres 415
Scaled-particle theory 419
Index 422