Statistical Physics of Fluids Basic Concepts and Applications

✍ Scribed by V.I. Kalikmanov

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 269
• Series: Theoretical and Mathematical Physics
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

The focus is on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others.

✦ Table of Contents

Statistical Physics of Fluids......Page 1
Preface......Page 4
Contents......Page 6
Notion of a phase space......Page 10
Statistical ensemble and Liouville's theorem......Page 14
Microcanonical ensemble......Page 15
Canonical ensemble......Page 20
Grand canonical ensemble......Page 30
n-particle distribution function......Page 38
Calculation of thermal averages......Page 39
n-particle correlation function......Page 40
The structure factor......Page 43
Energy equation......Page 46
Pressure (virial) equation......Page 47
Compressibility equation......Page 48
Hard spheres......Page 50
Virial expansion......Page 53
Law of corresponding states......Page 56
Thermodynamics of the interface......Page 58
Statistical mechanical calculation of surface tension......Page 61
Van der Waals theory......Page 66
First-order perturbation theories......Page 71
Weeks-Chandler-Andersen theory......Page 74
Song and Mason theory......Page 79
Perturbation approach to surface tension......Page 84
Algebraic method of Ruelle......Page 86
Classification of phase transitions......Page 92
Phase equilibrium and stability conditions......Page 95
Critical point......Page 98
Universality hypothesis and critical exponents......Page 99
Critical behavior of the van der Waals fluid......Page 104
Landau theory of second-order phase transitions......Page 106
Basic principles of Monte Carlo. Original capabilities and typical drawbacks......Page 112
Computer simulation of randomness......Page 115
Simulation of 'observations of random variables' for statistical ensembles......Page 121
Metropolis algorithm for canonical ensemble......Page 123
Simulation of boundary conditions for canonical ensemble......Page 125
Grand ensemble simulation......Page 126
Simulation of lattice systems......Page 134
Some advanced Monte Carlo techniques to simulate microcanonical ensemble......Page 137
Bogolubov-Born-Green-Kirkwood-Yvon hierarchy......Page 142
Ornstein-Zernike equation......Page 146
Foundations of the density functional theory......Page 160
Intrinsic free energy......Page 166
Surface tension......Page 169
Nonlocal density functional theories......Page 172
10. Real gases......Page 178
Fisher droplet model......Page 179
Thermodynamics of a spherical interface......Page 192
Tolman length......Page 195
Semiphenomenological theory of the Tolman length......Page 199
Algebraic perturbation theory of a polar fluid......Page 204
Dielectric constant......Page 208
Generalization of basic concepts......Page 218
One-fluid approximation......Page 221
Density functional theory for mixtures......Page 222
Surface tension......Page 224
14. Ferrofluids......Page 232
Cell model of a ferrofluid......Page 233
Magnetic subsystem in a low field. Algebraic perturbation theory......Page 237
Magnetic subsystem in an arbitrary field. High-temperature approximation......Page 242
Perturbation approach for the solvent......Page 246
A. Empirical correlations for macroscopic properties of argon, benzene and n-nonane......Page 248
B. Angular dipole integrals......Page 250
C. De Gennes-Pincus integral......Page 252
D. Calculation of yD and yd in the algebraic perturbation theory......Page 254
Calculation of yD......Page 255
Calculation of yd......Page 257
Pressure......Page 260
Chemical potentials......Page 261
References......Page 262
Index......Page 266