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E-grāmata: Statistical Mechanics of Liquids and Solutions: Intermolecular Forces, Structure and Surface Interactions

4.00/5 (2 ratings by Goodreads)

Roland Kjellander (University of Gothenburg, Sweden)

Formāts: 544 pages
Izdošanas datums: 30-Jul-2019
Izdevniecība: CRC Press Inc
ISBN-13: 9781482244021

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Formāts: 544 pages
Izdošanas datums: 30-Jul-2019
Izdevniecība: CRC Press Inc
ISBN-13: 9781482244021

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The statistical mechanical theory of liquids and solutions is a fundamental area of physical sciences with important implications in other fields of science and for many industrial applications. This book introduces equilibrium statistical mechanics in general, and statistical mechanics of liquids and solutions in particular. A major theme is the intimate relationship between forces in a fluid and the fluid structure a relationship that is paramount for the understanding of the subject of interactions in dense fluids. Using this microscopic, molecular approach, the text emphasizes clarity of physical explanations for phenomena and mechanisms relevant to fluids, addressing the structure and behavior of liquids and solutions under various conditions. A notable feature is the authors treatment of forces between particles that include nanoparticles, macroparticles, and surfaces. The book provides an expanded, in-depth treatment of simple liquids and electrolytes in the bulk and in confinement.

Provides an introduction to statistical mechanics of liquids and solutions with special attention to structure and interactions.

Offers an extensive presentation starting with the basics of statistical mechanics to modern aspects of the theory of liquids and solutions, including intermolecular interactions in fluids.

Treats both homogeneous bulk fluids and inhomogeneous fluids near surfaces and in confinement.

Takes a microscopic, molecular approach that combines physical transparency, theoretical sharpness and a pedagogical and accessible style.

Gives explicit and clear textual explanations and physical interpretations for any mathematical relationships and derivations.

Goes deeper than the available texts on interactions in fluids, by taking the discussion beyond simple approximations and mean field approaches.

The book will be an invaluable resource for advanced undergraduate, graduate, and postgraduate students in physics, chemistry, soft matter science, surface and colloid science and related fields, as well as professionals and instructors in those areas of science.

Preface

Author

xix

Part I Basis of Equilibrium Statistical Mechanics

Chapter 1 Introduction

(30)

1.1 The Microscopic Definitions of Entropy and Temperature

(14)

1.1.1 A Simple Illustrative Example

(7)

1.1.2 Microscopic Definition of Entropy and Temperature for Isolated Systems

(5)

1.2 Quantum vs Classical Mechanical Formulations of Statistical Mechanics: An Example

(14)

1.2.1 The Monatomic Ideal Gas: Quantum Treatment

(9)

1.2.2 The Monatomic Ideal Gas: Classical Treatment

(4)

Appendix 1A: Alternative Expressions for the Entropy of an Isolated System

(2)

Chapter 2 Statistical Mechanics from a Quantum Perspective

(76)

2.1 Postulates and Some Basic Definitions

(5)

2.2 Isolated Systems: The Microcanonical Ensemble

(14)

2.3 Thermal Equilibria and the Canonical Ensemble

(14)

2.3.1 The Canonical Ensemble and Boltzmann's Distribution Law

(4)

2.3.2 Calculations of Thermodynamical Quantities; the Connection with Partition Functions

(10)

2.3.2.1 The Helmholtz Free Energy

(3)

2.3.2.2 Thermodynamical Quantities as Averages

(4)

2.3.2.3 Entropy in the Canonical Ensemble

(3)

2.4 Constant Pressure: The Isobaric-Isothermal Ensemble

(13)

2.4.1 Probabilities and the Isobaric-Isothermal Partition Function

(5)

2.4.2 Thermodynamical Quantities in the Isobaric-Isothermal Ensemble

(8)

2.4.2.1 The Gibbs Free Energy

(2)

2.4.2.2 Probabilities and Thermodynamical Quantities

(3)

2.4.2.3 The Entropy in the Isobaric-Isothermal Ensemble

(3)

2.5 Open Systems: Chemical Potential and the Grand Canonical Ensemble

(9)

2.5.1 Probabilities and the Grand Canonical Partition Function

(4)

2.5.2 Thermodynamical Quantities in the Grand Canonical Ensemble

(5)

2.6 Fluctuations in Thermodynamical Variables

(3)

2.6.1 Fluctuations in Energy in the Canonical Ensemble

(1)

2.6.2 Fluctuations in Number of Particles in the Grand Canonical Ensemble

(1)

2.6.3 Fluctuations in the Isobaric-Isothermal Ensemble

(1)

2.7 Independent Subsystems

(8)

2.7.1 The Ideal Gas and Single-Particle Partition Functions

(4)

2.7.2 Translational Single-Particle Partition Function

(4)

Appendix 2A: The Volume Dependence of S and Quasistatic Work

(4)

Appendix 2B: Stricter Derivations of Probability Expressions

103

(6)

Chapter 3 Classical Statistical Mechanics

109

(22)

3.1 Systems with N Spherical Particles

110

(2)

3.2 The Canonical Ensemble

112

(10)

3.3 The Grand Canonical Ensemble

122

(3)

3.4 Real Gases

125

(6)

Chapter 4 Illustrative Examples from Some Classical Theories of Fluids

131

(34)

4.1 The Ising Model

131

(3)

4.2 The Ising Model Applied to Lattice Gases and Binary Liquid Mixtures

134

(31)

4.2.1 Ideal Lattice Gas

135

(1)

4.2.2 Ideal Liquid Mixture

136

(2)

4.2.3 The Bragg-William Approximation

138

(46)

4.2.3.1 Regular Solution Theory

138

(4)

4.2.3.2 Some Applications of Regular Solution Theory

142

(9)

4.2.3.3 Flory-Huggins Theory for Polymer Solutions

151

(14)

Part II Fluid Structure and Interparticle Interactions

Chapter 5 Interaction Potentials and Distribution Functions

165

(92)

5.1 Bulk Fluids of Spherical Particles. The Radial Distribution Function

166

(6)

5.2 Number Density Distributions: Density Profiles

172

(3)

5.3 Force Balance and the Boltzmann Distribution for Density: Potential of Mean Force

175

(6)

5.4 The Relationship to Free Energy and Chemical Potential

181

(3)

5.5 Distribution Functions of Various Orders for Spherical Particles

184

(8)

5.5.1 Singlet Distribution Function

184

(1)

5.5.2 Pair Distribution Function

185

(3)

5.5.3 Distribution Functions in the Canonical Ensemble

188

(4)

5.6 The structure factor for homogeneous and inhomogeneous fluids

192

(7)

5.7 Thermodynamical Quantities from Distribution Functions

199

(13)

5.8 Microscopic density distributions and density-density correlations

212

(3)

5.9 Distribution Function Hierarchies and Closures, Preliminaries

215

(3)

5.10 Distribution Functions in the Grand Canonical Ensemble

218

(4)

5.11 The Born-Green-Yvon Equations

222

(3)

5.12 Mean Field Approximations for Bulk Systems

225

(2)

5.13 Computer Simulations and Distribution Functions

227

(28)

5.13.1 General Background

227

(8)

5.13.1.1 Basics of Molecular Dynamics Simulations

228

(3)

5.13.1.2 Basics of Monte Carlo Simulations

231

(4)

5.13.2 Bulk Fluids

235

(15)

5.13.2.1 Boundary Conditions

235

(2)

5.13.2.2 Distribution Functions

237

(5)

5.13.2.3 Thermodynamical Quantities

242

(8)

5.13.3 Inhomogeneous Fluids

250

(8)

5.13.3.1 Density Profiles Outside Macroparticles or Near Planar Surfaces

250

(2)

5.13.3.2 Pair Distribution Functions

252

(3)

Appendix 5A: The Dirac Delta Function

255

(2)

Chapter 6 Interactions and Correlations in Simple Bulk Electrolytes

257

(96)

6.1 The Poisson-Boltzmann (PB) Approximation

258

(46)

6.1.1 Bulk Electrolytes, Basic Treatment

258

(17)

6.1.2 Decay of Electrostatic Potential and Effective Charges of Particles

275

(15)

6.1.2.1 The Concept of Effective Charge

275

(3)

6.1.2.2 Electrostatic Potential from Nonspherical Particles

278

(5)

6.1.2.3 The Decay of Electrostatic Potential from Spherical and Nonspherical Particles

283

(7)

6.1.3 Interaction between two Particles Treated on an Equal Basis

290

(4)

6.1.3.1 Background

290

(1)

6.1.3.2 The Decay of Interaction between Two Nonspherical Macroions

291

(3)

6.1.4 The Interaction between Two Macroions for all Separations

294

(5)

6.1.4.1 Poisson-Boltzmann Treatment

294

(3)

6.1.4.2 Electrostatic Part of Pair Potential of Mean Force, General Treatment

297

(2)

6.1.5 One Step beyond PB: What Happens When all Ions are Treated on an Equal Basis?

299

(5)

6.2 Electrostatic Screening in Simple Bulk Electrolytes, General Case

304

(41)

6.2.1 Electrostatic Interaction Potentials

306

(12)

6.2.1.1 Polarization Response and Nonlocal Electrostatics

307

(4)

6.2.1.2 The Potential of Mean Force and Dressed Particles

311

(2)

6.2.1.3 Screened Electrostatic Interactions

313

(5)

6.2.2 The Decay Behavior and the Screening Decay Length

318

(21)

6.2.2.1 Oscillatory and Monotonic Exponential Decays: Explicit Examples

318

(2)

6.2.2.2 Roles of Effective Charges, Effective Dielectric Permittivities and the Decay Parameter K

320

(10)

6.2.2.3 The Significance of the Asymptotic Decays: Concrete Examples

330

(9)

6.2.3 Density-Density, Charge-Density and Charge-Charge Correlations

339

(6)

Appendix 6A: The Orientational Variable ω

345

(1)

Appendix 6B: Variations in Density Distribution When the External Potential is Varied; the First Yvon Equation

346

(3)

Appendix 6C: Definitions of the HNN, HQN and HQQ Correlation Functions

349

(4)

Chapter 7 Inhomogeneous and Confined Simple Fluids

353

(68)

7.1 Electric Double-Layer Systems

354

(38)

7.1.1 The Poisson-Boltzmann (Gouy-Chapman) Theory

355

(11)

7.1.1.1 The Poisson-Boltzmann Equation for Planar Double Layers

355

(3)

7.1.1.2 The Case of Symmetric Electrolytes

358

(4)

7.1.1.3 Effective Surface Charge Densities and the Decay of the Electrostatic Potential

362

(4)

7.1.2 Electrostatic Screening in Electric Double-Layers, General Case

366

(6)

7.1.2.1 Decay of the Electrostatic Potential Outside a Wall

367

(2)

7.1.2.2 Decay of Double-Layer Interactions: Macroion-Wall and Wall-Wall

369

(3)

7.1.3 Ion-Ion Correlation Effects in Electric Double-Layers: Explicit Examples

372

(7)

7.1.4 Electric Double-Layers with Surface Polarizations (Image Charge Interactions)

379

(6)

7.1.5 Electric Double-Layers with Dispersion Interactions

385

(7)

7.2 Structure of Inhomogeneous Fluids on the Pair Distribution Level

392

(23)

7.2.1 Inhomogeneous Simple Fluids

393

(13)

7.2.1.1 Lennard-Jones Fluids

393

(3)

7.2.1.2 Hard Sphere Fluids

396

(10)

7.2.2 Primitive Model Electrolytes

406

(15)

7.2.2.1 Pair Distributions in the Electric Double-Layer

406

(4)

7.2.2.2 Ion-Ion Correlations Forces: Influences on Density Profiles

410

(5)

Appendix 7A: Solution of PB Equation for a Surface in Contact with a Symmetric Electrolyte

415

(1)

Appendix 7B: Electric Double-Layers with Ion-Wall Dispersion Interactions in Linearized PB Approximation

416

(5)

Chapter 8 Surface Forces

421

(58)

8.1 General Considerations

421

(6)

8.1.1 The Disjoining Pressure and the Free Energy of Interaction

422

(2)

8.1.2 Electric Double-Layer Interactions, Some General Matters

424

(3)

8.2 Poisson-Boltzmann Treatment of Electric Double-Layer Interactions

427

(13)

8.2.1 Equally Charged Surfaces

428

(7)

8.2.2 Arbitrarily Charged Surfaces

435

(4)

8.2.3 Electrostatic part of double-layer interactions, general treatment

439

(1)

8.3 Surface Forces and Pair Correlations, General Considerations

440

(7)

8.4 Structural Surface Forces

447

(4)

8.5 Electric Double-Layer Interactions with lon-lon Correlations

451

(9)

8.5.1 Counterions between Charged Surfaces

451

(8)

8.5.2 Equilibrium with Bulk Electrolyte

459

(1)

8.6 Van der Waals Forces and Image Interactions in Electric Double-Layer Systems

460

(12)

8.6.1 Van der Waals Interactions and Mean Field Electrostatics: The DLVO Theory

461

(2)

8.6.2 The Effects of Ion-Ion Correlations on Van der Waals Interactions. Ionic Image Charge Interactions

463

(4)

8.6.3 The Inclusion of Dispersion Interactions for the Ions

467

(5)

Appendix 8A: Solution of PB Equation for Counterions between Two Surfaces

472

(2)

Appendix 8B: Proofs of Two Expressions for Pslit

474

(5)

List of Symbols,

479

(8)

Index,

487

Roland Kjellander acquired a masters degree in chemical engineering, a Ph.D. in physical chemistry, and the title of docent in physical chemistry from the Royal Institute of Technology, Stockholm, Sweden. He is currently a professor emeritus of physical chemistry in the Department of Chemistry and Molecular Biology at the University of Gothenburg, Sweden. His previous appointments include roles in various academic and research capacities at the University of Gothenburg, Sweden; Australian National University, Canberra; Royal Institute of Technology, Stockholm, Sweden; Massachusetts Institute of Technology, Cambridge, USA; and Harvard Medical School, Boston, USA. He was awarded the 2004 Pedagogical Prize from the University of Gothenburg, Sweden, and the 2007 Norblad-Ekstrand Medal from the Swedish Chemical Society. Professor Kjellanders field of research is statistical mechanics, in particular liquid state theory.

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