Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions Volume I

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Overview of Contents
Author
Part I: Basis of Equilibrium StatisticalMechanics
	Chapter 1: Introduction
		1.1 The Microscopic Definitions of Entropy and Temperature
			1.1.1 A Simple Illustrative Example
			1.1.2 Microscopic Definition of Entropy and Temperature for Isolated Systems
		1.2 Quantum vs Classical Mechanical Formulations of Statistical Mechanics: An Example
			1.2.1 The Monatomic Ideal Gas: Quantum Treatment15
			1.2.2 The Monatomic Ideal gas: Classical Treatment
		Appendix 1A: Alternative Expressions for the Entropy of an Isolated System
	Chapter 2: Statistical Mechanics from a Quantum Perspective
		2.1 Postulates and Some Basic Definitions
		2.2 Isolated Systems: the Microcanonical Ensemble
		2.3 Thermal Equilibria and the Canonical Ensemble
			2.3.1 The Canonical Ensemble and Boltzmann’s Distribution Law
			2.3.2 Calculations of Thermodynamical Quantities; the Connection with Partition Functions
				2.3.2.1 The Helmholtz Free Energy
				2.3.2.2 Thermodynamical Quantities as Averages
				2.3.2.3 Entropy in the Canonical Ensemble
		2.4 Constant Pressure: the Isobaric-Isothermal Ensemble
			2.4.1 Probabilities and the Isobaric-Isothermal Partition Function
			2.4.2 Thermodynamical Quantities in the Isobaric-Isothermal Ensemble
				2.4.2.1 The Gibbs Free Energy
				2.4.2.2 Probabilities and Thermodynamical Quantities
				2.4.2.3 The Entropy in the Isobaric-Isothermal Ensemble
		2.5 Open Systems: Chemical Potential and the Grand Canonical Ensemble
			2.5.1 Probabilities and the Grand Canonical Partition Function
			2.5.2 Thermodynamical Quantities in the Grand Canonical Ensemble
		2.6 Fluctuations in Thermodynamical Variables
			2.6.1 Fluctuations in Energy in the Canonical Ensemble
			2.6.2 Fluctuations in Number of Particles in the Grand Canonical Ensemble
			2.6.3 Fluctuations in the Isobaric-Isothermal Ensemble
		2.7 Independent Subsystems
			2.7.1 The Ideal Gas and Single-Particle Partition Functions
			2.7.2 Translational Single-Particle Partition Function
		Appendix 2A: The Volume Dependence Of S and Quasistatic Work
		Appendix 2B: Stricter Derivations of Probability Expressions
	Chapter 3: Classical Statistical Mechanics
		3.1 Systems With N Spherical Particles
		3.2 The Canonical Ensemble
		3.3 The Grand Canonical Ensemble
		3.4 Real Gases
	Chapter 4: Illustrative Examples from Some Classical Theories of Fluids
		4.1 The Ising Model
		4.2 The Ising Model Applied to Lattice Gases and Binary Liquid Mixtures
			4.2.1 Ideal Lattice Gas
			4.2.2 Ideal Liquid Mixture
			4.2.3 The Bragg-William Approximation
				4.2.3.1 Regular Solution Theory
				4.2.3.2 Some Applications of Regular Solution Theory
				4.2.3.3 Flory-Huggins Theory for Polymer Solutions
Part II: Fluid Structure and Interparticle Interactions
	Chapter 5: Interaction Potentials and Distribution Functions
		5.1 Bulk Fluids Of Spherical Particles the Radial Distribution Function
		5.2 Number Density Distributions: Density Profiles
		5.3 Force Balance and the Boltzmann Distribution for Density: Potential Of Mean Force
		5.4 The Relationship To Free Energy and Chemical Potential
		5.5 Distribution Functions of Various Orders for Spherical Particles
			5.5.1 Singlet Distribution Function
			5.5.2 Pair Distribution Function
			5.5.3 Distribution Functions in the Canonical Ensemble
		5.6 The Structure Factor for Homogeneous and Inhomogeneous Fluids
		5.7 Thermodynamical Quantities From Distribution Functions
		5.8 Microscopic Density Distributions and Density-Density Correlations
		5.9 Distribution Function Hierarchies and Closures, Preliminaries
		5.10 Distribution Functions in the Grand Canonical Ensemble
		5.11 The Born-Green-Yvon Equations
		5.12 Mean Field Approximations for Bulk Systems
		5.13 Computer Simulations and Distribution Functions
			5.13.1 General Background
				5.13.1.1 Basics of Molecular Dynamics Simulations
				5.13.1.2 Basics of Monte Carlo Simulations
			5.13.2 Bulk Fluids
				5.13.2.1 Boundary Conditions
				5.13.2.2 Distribution Functions
				5.13.2.3 Thermodynamical Quantities
			5.13.3 Inhomogeneous Fluids
				5.13.3.1 Density Profiles Outside Macroparticles or Near Planar Surfaces
				5.13.3.2 Pair Distribution Functions
		Appendix 5A: THE DIRAC DELTA FUNCTION
	Chapter 6: Interactions and Correlations in Simple Bulk Electrolytes
		6.1 The Poisson-Boltzmann (Pb) Approximation
			6.1.1 Bulk Electrolytes, Basic Treatment
			6.1.2 Decay of Electrostatic Potential and Effective Charges of Particles
				6.1.2.1 The Concept of Effective Charge
				6.1.2.2 Electrostatic Potential from Nonspherical Particles
				6.1.2.3 The Decay of Electrostatic Potential from Spherical and Nonspherical Particles
			6.1.3 Interaction between two Particles Treated on an Equal Basis
				6.1.3.1 Background
				6.1.3.2 The Decay of Interaction between Two Nonspherical Macroions
			6.1.4 The Interaction between Two Macroions for all Separations
				6.1.4.1 Poisson-Boltzmann Treatment
				6.1.4.2 Electrostatic Part of Pair Potential of Mean Force, General Treatment
			6.1.5 One Step beyond PB: What Happens When all Ions are Treated on an Equal Basis?
		6.2 Electrostatic Screening in Simple Bulk Electrolytes, General Case
			6.2.1 Electrostatic Interaction Potentials
				6.2.1.1 Polarization Response and Nonlocal Electrostatics
				6.2.1.2 The Potential of Mean Force and Dressed Particles
				6.2.1.3 Screened Electrostatic Interactions
			6.2.2 The Decay Behavior and the Screening Decay Length
				6.2.2.1 Oscillatory and Monotonic Exponential Decays: Explicit Examples
				6.2.2.2 Roles of Effective Charges, Effective Dielectric Permittivities and the Decay Parameter
				6.2.2.3 The Significance of the Asymptotic Decays: Concrete Examples
			6.2.3 Density-Density, Charge-Density and Charge-Charge Correlations
			Appendix 6A: The Orientational Variable
			Appendix 6B: Variations in Density Distribution When the External Potential is Varied; The First Yvon Equation
			Appendix 6C: Definitions of The HNN, HQN and HQQ Correlation Functions
	Chapter 7: Inhomogeneous and Confined Simple Fluids
		7.1 Electric Double-Layer Systems
			7.1.1 The Poisson-Boltzmann (Gouy-Chapman) Theory
				7.1.1.1 The Poisson-Boltzmann Equation for Planar Double Layers
				7.1.1.2 The Case of Symmetric Electrolytes
				7.1.1.3 Effective Surface Charge Densities and the Decay of the Electrostatic Potential
			7.1.2 Electrostatic Screening in Electric Double-Layers, General Case
				7.1.2.1 Decay of the Electrostatic Potential Outside a Wall
				7.1.2.2 Decay of Double-Layer Interactions: Macroion-Wall and Wall-Wall
			7.1.3 Ion-Ion Correlation Effects in Electric Double-Layers: Explicit Examples
			7.1.4 Electric Double-Layers with Surface Polarizations (Image Charge Interactions)
			7.1.5 Electric Double-Layers with Dispersion Interactions
		7.2 Structure of Inhomogeneous Fluids on the Pair Distribution Level
			7.2.1 Inhomogeneous Simple Fluids
				7.2.1.1 Lennard-Jones Fluids
				7.2.1.2 Hard Sphere Fluids
			7.2.2 Primitive Model Electrolytes
				7.2.2.1 Pair Distributions in the Electric Double-Layer
				7.2.2.2 Ion-Ion Correlations Forces: Influences on Density Profiles
		Appendix 7A: Solution of PB Equation for a Surface in Contact With a Symmetric Electrolyte
		Appendix 7B: Electric Double-Layers With Ion-Wall Dispersion Interactions in Linearized PB Approximation
	Chapter 8: Surface Forces
		8.1 General Considerations
			8.1.1 The Disjoining Pressure and the Free Energy of Interaction
			8.1.2 Electric Double-Layer Interactions, Some General Matters
		8.2 Poisson-Boltzmann Treatment Of Electric Double-Layer Interactions
			8.2.1 Equally Charged Surfaces
			8.2.2 Arbitrarily Charged Surfaces
			8.2.3 Electrostatic Part of Double-Layer Interactions, General Treatment
		8.3 SUrface Forces and Pair Correlations, General Considerations
		8.4 Structural Surface Forces
		8.5 Electric Double-Layer Interactions With Ion-Ion Correlations
			8.5.1 Counterions between Charged Surfaces
			8.5.2 Equilibrium with Bulk Electrolyte
		8.6 Van Der Waals Forces and Image Interactions In Electric Double-Layer Systems
			8.6.1 Van der Waals Interactions and Mean Field Electrostatics: The DLVO Theory
			8.6.2 The Effects of Ion-Ion Correlations on Van der Waals Interactions. Ionic Image Charge Interactions
			8.6.3 The Inclusion of Dispersion Interactions for the Ions
		Appendix 8A: Solution Of PB Equation for Counterions Between Two Surfaces
		Appendix 8B: Proofs of Two Expressions for Pslit
List of Symbols
Index