Contents Preface, xi Overview of Contents, xv Author, xix PART I Basis of Equilibrium Statistical Mechanics CHAPTER 1 Introduction 3 1.1 The Microscopic Definitions of Entropy and Temperature 3 1.1.1 A Simple Illustrative Example 5 1.1.2 Microscopic Definition of Entropy and Temperature for Isolated Systems 12 1.2 Quantum vs Classical Mechanical Formulations of Statistical Mechanics: An Example 17 1.2.

1 The Monatomic Ideal Gas: Quantum Treatment 18 1.2.2 The Monatomic Ideal Gas: Classical Treatment 27 Appendix 1A: Alternative Expressions for the Entropy of an Isolated System 31 CHAPTER 2 Statistical Mechanics from a Quantum Perspective 33 2.1 Postulates and Some Basic Definitions 33 2.2 Isolated Systems: The Microcanonical Ensemble 38 2.3 Thermal Equilibria and the Canonical Ensemble 52 2.3.1 The Canonical Ensemble and Boltzmann''s Distribution Law 52 2.

3.2 Calculations of Thermodynamical Quantities; the Connection with Partition Functions 56 2.3.2.1 The Helmholtz Free Energy 56 2.3.2.2 Thermodynamical Quantities as Averages 59 2.

3.2.3 Entropy in the Canonical Ensemble 63 2.4 Constant Pressure: The Isobaric-Isothermal Ensemble 66 2.4.1 Probabilities and the Isobaric-Isothermal Partition Function 66 2.4.2 Thermodynamical Quantities in the Isobaric-Isothermal Ensemble 71 2.

4.2.1 The Gibbs Free Energy 71 2.4.2.2 Probabilities and Thermodynamical Quantities 73 2.4.2.

3 The Entropy in the Isobaric-Isothermal Ensemble 76 2.5 Open Systems: Chemical Potential and the Grand Canonical Ensemble 79 2.5.1 Probabilities and the Grand Canonical Partition Function 79 2.5.2 Thermodynamical Quantities in the Grand Canonical Ensemble 83 2.6 Fluctuations in Thermodynamical Variables 88 2.6.

1 Fluctuations in Energy in the Canonical Ensemble 88 2.6.2 Fluctuations in Number of Particles in the Grand Canonical Ensemble 89 2.6.3 Fluctuations in the Isobaric-Isothermal Ensemble 90 2.7 Independent Subsystems 91 2.7.1 The Ideal Gas and Single-Particle Partition Functions 91 2.

7.2 Translational Single-Particle Partition Function 95 Appendix 2A: The Volume Dependence of S and Quasistatic Work 99 Appendix 2B: Stricter Derivations of Probability Expressions 103 CHAPTER 3 Classical Statistical Mechanics 109 3.1 Systems with N Spherical Particles 110 3.2 The Canonical Ensemble 112 3.3 The Grand Canonical Ensemble 122 3.4 Real Gases 125 CHAPTER 4 Illustrative Examples from Some Classical Theories of Fluids 131 4.1 The Ising Model 131 4.2 The Ising Model Applied to Lattice Gases and Binary Liquid Mixtures 134 4.

2.1 Ideal Lattice Gas 135 4.2.2 Ideal Liquid Mixture 136 4.2.3 The Bragg-William Approximation 138 4.2.3.

1 Regular Solution Theory 138 4.2.3.2 Some Applications of Regular Solution Theory 142 4.2.3.3 Flory-Huggins Theory for Polymer Solutions 151 PART II Fluid Structure and Interparticle Interactions CHAPTER 5 Interaction Potentials and Distribution Functions 165 5.1 Bulk Fluids of Spherical Particles.

The Radial Distribution Function 166 5.2 Number Density Distributions: Density Profiles 172 5.3 Force Balance and the Boltzmann Distribution for Density: Potential of Mean Force 175 5.4 The Relationship to Free Energy and Chemical Potential 181 5.5 Distribution Functions of Various Orders for Spherical Particles 184 5.5.1 Singlet Distribution Function 184 5.5.

2 Pair Distribution Function 185 5.5.3 Distribution Functions in the Canonical Ensemble 188 5.6 The structure factor for homogeneous and inhomogeneous fluids 192 5.7 Thermodynamical Quantities from Distribution Functions 199 5.8 Microscopic density distributions and density-density correlations 212 5.9 Distribution Function Hierarchies and Closures, Preliminaries 215 5.10 Distribution Functions in the Grand Canonical Ensemble 218 5.

11 The Born-Green-Yvon Equations 222 5.12 Mean Field Approximations for Bulk Systems 225 5.13 Computer Simulations and Distribution Functions 227 5.13.1 General Background 227 5.13.1.1 Basics of Molecular Dynamics Simulations 228 5.

13.1.2 Basics of Monte Carlo Simulations 231 5.13.2 Bulk Fluids 235 5.13.2.1 Boundary Conditions 235 5.

13.2.2 Distribution Functions 237 5.13.2.3 Thermodynamical Quantities 242 5.13.3 Inhomogeneous Fluids 250 5.

13.3.1 Density Profiles Outside Macroparticles or Near Planar Surfaces 250 5.13.3.2 Pair Distribution Functions 252 Appendix 5A: The Dirac Delta Function 255 CHAPTER 6 Interactions and Correlations in Simple Bulk Electrolytes 257 6.1 The Poisson-Boltzmann (PB) Approximation 258 6.1.

1 Bulk Electrolytes, Basic Treatment 258 6.1.2 Decay of Electrostatic Potential and Effective Charges of Particles 275 6.1.2.1 The Concept of Effective Charge 275 6.1.2.

2 Electrostatic Potential from Nonspherical Particles 278 6.1.2.3 The Decay of Electrostatic Potential from Spherical and Nonspherical Particles 283 6.1.3 Interaction between two Particles Treated on an Equal Basis 290 6.1.3.

1 Background 290 6.1.3.2 The Decay of Interaction between Two Nonspherical Macroions 291 6.1.4 The Interaction between Two Macroions for all Separations 294 6.1.4.

1 Poisson-Boltzmann Treatment 294 6.1.4.2 Electrostatic Part of Pair Potential of Mean Force, General Treatment 297 6.1.5 One Step beyond PB:What HappensWhen all Ions are Treated on an Equal Basis? 299 6.2 Electrostatic Screening in Simple Bulk Electrolytes, General Case 304 6.2.

1 Electrostatic Interaction Potentials 306 6.2.1.1 Polarization Response and Nonlocal Electrostatics 307 6.2.1.2 The Potential of Mean Force and Dressed Particles 311 6.2.

1.3 Screened Electrostatic Interactions 313 6.2.2 The Decay Behavior and the Screening Decay Length 318 6.2.2.1 Oscillatory and Monotonic Exponential Decays: Explicit Examples 318 6.2.

2.2 Roles of Effective Charges, Effective Dielectric Permittivities and the Decay Parameter κ 320 6.2.2.3 The Significance of the Asymptotic Decays: Concrete Examples 330 6.2.3 Density-Density, Charge-Density and Charge-Charge Correlations 339 Appendix 6A: The Orientational Variable ω 345 Appendix 6B: Variations in Density Distribution When the External Potential is Varied; the First Yvon Equation 346 Appendix 6C: Definitions of the HNN, HQN and HQQ Correlation Functions 349 CHAPTER 7 Inhomogeneous and Confined Simple Fluids 353 7.1 Electric Double-Layer Systems 354 7.

1.1 The Poisson-Boltzmann (Gouy-Chapman) Theory 355 7.1.1.1 The Poisson-Boltzmann Equation for Planar Double Layers 355 7.1.1.2 The Case of Symmetric Electrolytes 358 7.

1.1.3 Effective Surface Charge Densities and the Decay of the Electrostatic Potential 362 7.1.2 Electrostatic Screening in Electric Double-Layers, General Case 366 7.1.2.1 Decay of the Electrostatic Potential Outside aWall 367 7.

1.2.2 Decay of Double-Layer Interactions: Macroion-Wall andWall-Wall 369 7.1.3 Ion-Ion Correlation Effects in Electric Double-Layers: Explicit Examples 372 7.1.4 Electric Double-Layers with Surface Polarizations (Image Charge Interactions) 379 7.1.

5 Electric Double-Layers with Dispersion Interactions 385 7.2 Structure of Inhomogeneous Fluids on the Pair Distribution Level 392 7.2.1 Inhomogeneous Simple Fluids 393 7.2.1.1 Lennard-Jones Fluids 393 7.2.

1.2 Hard Sphere Fluids 396 7.2.2 Primitive Model Electrolytes 406 7.2.2.1 Pair Distributions in the Electric Double-Layer 406 7.2.

2.2 Ion-Ion Correlations Forces: Influences on Density Profiles 410 Appendix 7A: Solution of PB Equation for a Surface in Contact with a Symmetric Electrolyte 415 Appendix 7B: Electric Double-Layers with Ion-Wall Dispersion Interactions in Linearized PB Approximation 416 CHAPTER 8 Surface Forces 421 8.1 General Considerations 421 8.1.1 The Disjoining Pressure and the Free Energy of Interaction 422 8.1.2 Electric Double-Layer Interactions, Some General Matters 424 8.2 Poisson-Boltzmann Treatment of Electric Double-Layer Interactions 427 8.

2.1 Equally Charged Surfaces 428 8.2.2 Arbitrarily Charged Surfaces 435 8.2.3 Electrostatic part of double-layer interactions, general treatment 439 8.3 Surface Forces and Pair Correlations, General Considerations 440 8.4 Structural Surface Forces 447 8.

5 Electric Double-Layer Interactions with Ion-Ion Correlations 451 8.5.1 Counterions between Charged Surfaces 451 8.5.2 Equilibrium with Bulk Electrolyte 459 8.6 Van der Waals Forces and Image Interactions in Electric Double-Layer Systems 460 8.6.1 Van derWaals Interactions and Mean Field Electrostatics: The DLVO Theory 461 8.

6.2 The Effects of Ion-Ion Correlations on Van derWaals Interactions. Ionic Image Charge Interactions 463 8.6.3 The Inclusion of Dispersion Interactions for the Ions 467 Appendix 8A: Solution of PB Equation for Counterions between Two Surfaces 472 Appendix 8B: Proofs of Two Expressions for P sl.