Liquid–State Physical Chemistry: Fundamentals, Modeling, and Applications

This is the only comprehensive introduction to this central topic and thus a must-have for many chemists, chemical engineers and material scientists. 
The book describes the behavior of liquids and solutions and their simplest applications in a basic and self-contained way. 
The author has extensive experience from research in areas where the theoretical concepts of liquids are applied and adopts here a clear, well-structured approach to provide an excellent overview of pure liquids, simple non-electrolyte, electrolyte and polymeric solutions, as well as the most important types of reaction. 
Suitable as an introductory text as well as on an intermediate level, since the more advanced parts are clearly marked.

Preface XV

Acknowledgments XIX

List of Important Symbols and Abbreviations XXV

1 Introduction 1

1.1 The Importance of Liquids 1

1.2 Solids, Gases, and Liquids 2

1.3 Outline and Approach 5

1.4 Notation 8

References 9

Further Reading 9

2 Basic Macroscopic and Microscopic Concepts: Thermodynamics, Classical, and Quantum Mechanics 11

2.1 Thermodynamics 11

2.1.1 The Four Laws 11

2.1.2 Quasi-Conservative and Dissipative Forces 15

2.1.3 Equation of State 16

2.1.4 Equilibrium 17

2.1.5 Auxiliary Functions 18

2.1.6 Some Derivatives and Their Relationships 20

2.1.7 Chemical Content 21

2.1.8 Chemical Equilibrium 24

2.2 Classical Mechanics 26

2.2.1 Generalized Coordinates 27

2.2.2 Hamilton’s Principle and Lagrange’s Equations 28

2.2.3 Conservation Laws 30

2.2.4 Hamilton’s Equations 33

2.3 Quantum Concepts 35

2.3.1 Basics of Quantum Mechanics 35

2.3.2 The Particle-in-a-Box 41

2.3.3 The Harmonic Oscillator 42

2.3.4 The Rigid Rotator 43

2.4 Approximate Solutions 44

2.4.1 The Born–Oppenheimer Approximation 44

2.4.2 The Variation Principle 45

2.4.3 Perturbation Theory 48

References 51

Further Reading 51

3 Basic Energetics: Intermolecular Interactions 53

3.1 Preliminaries 53

3.2 Electrostatic Interaction 55

3.3 Induction Interaction 59

3.4 Dispersion Interaction 60

3.5 The Total Interaction 63

3.6 Model Potentials 65

3.7 Refi nements 68

3.7.1 Hydrogen Bonding 68

3.7.2 Three-Body Interactions 70

3.7.3 Accurate Empirical Potentials 70

3.8 The Virial Theorem 72

References 72

Further Reading 73

4 Describing Liquids: Phenomenological Behavior 75

4.1 Phase Behavior 75

4.2 Equations of State 76

4.3 Corresponding States 79

4.3.1 Extended Principle 82

References 86

Further Reading 87

5 The Transition from Microscopic to Macroscopic: Statistical Thermodynamics 89

5.1 Statistical Thermodynamics 89

5.1.1 Some Concepts 89

5.1.2 Entropy and Partition Functions 91

5.1.3 Fluctuations 99

5.2 Perfect Gases 101

5.2.1 Single Particle 101

5.2.2 Many Particles 102

5.2.3 Pressure and Energy 103

5.3 The Semi-Classical Approximation 104

5.4 A Few General Aspects 110

5.5 Internal Contributions 112

5.5.1 Vibrations 112

5.5.2 Rotations 115

5.5.3 Electronic Transitions 116

5.6 Real Gases 118

5.6.1 Single Particle 118

5.6.2 Interacting Particles 118

5.6.3 The Virial Expansion: Canonical Method 119

5.6.4 The Virial Expansion: Grand Canonical Method 121

5.6.5 Critique and Some Further Remarks 123

References 126

Further Reading 127

6 Describing Liquids: Structure and Energetics 129

6.1 The Structure of Solids 129

6.2 The Meaning of Structure for Liquids 132

6.2.1 Distributions Functions 132

6.2.2 Two Asides 136

6.3 The Experimental Determination of g(r) 138

6.4 The Structure of Liquids 140

6.5 Energetics 146

6.6 The Potential of Mean Force 150

References 154

Further Reading 154

7 Modeling the Structure of Liquids: The Integral Equation Approach 155

7.1 The Vital Role of the Correlation Function 155

7.2 Integral Equations 156

7.2.1 The Yvon–Born–Green Equation 156

7.2.2 The Kirkwood Equation 158

7.2.3 The Ornstein–Zernike Equation 159

7.2.4 The Percus–Yevick Equation 161

7.2.5 The Hyper-Netted Chain Equation 162

7.2.6 The Mean Spherical Approximation 162

7.2.7 Comparison 163

7.3 Hard-Sphere Results 165

7.4 Perturbation Theory 168

7.4.1 The Gibbs–Bogoliubov Inequality 168

7.4.2 The Barker–Henderson Approach 170

7.4.3 The Weeks–Chandler–Andersen Approach 172

7.5 Molecular Fluids 174

7.6 Final Remarks 174

References 175

Further Reading 175

8 Modeling the Structure of Liquids: The Physical Model Approach 177

8.1 Preliminaries 177

8.2 Cell Models 178

8.3 Hole Models 187

8.3.1 The Basic Hole Model 189

8.3.2 An Extended Hole Model 191

8.4 Signifi cant Liquid Structures 194

8.5 Scaled-Particle Theory 200

References 202

Further Reading 202

9 Modeling the Structure of Liquids: The Simulation Approach 203

9.1 Preliminaries 203

9.2 Molecular Dynamics 205

9.3 The Monte Carlo Method 211

9.4 An Example: Ammonia 214

References 218

Further Reading 219

10 Describing the Behavior of Liquids: Polar Liquids 221

10.1 Basic Aspects 221

10.2 Towards a Microscopic Interpretation 223

10.3 Dielectric Behavior of Gases 224

10.3.1 Estimating μ and α 229

10.4 Dielectric Behavior of Liquids 231

10.5 Water 238

10.5.1 Models of Water 241

10.5.2 The Structure of Liquid Water 242

10.5.3 Properties of Water 245

References 249

Further Reading 250

11 Mixing Liquids: Molecular Solutions 251

11.1 Basic Aspects 251

11.1.1 Partial and Molar Quantities 251

11.1.2 Perfect Solutions 253

11.2 Ideal and Real Solutions 256

11.2.1 Raoult’s and Henry’s Laws 257

11.2.2 Deviations 258

11.3 Colligative Properties 260

11.4 Ideal Behavior in Statistical Terms 262

11.5 The Regular Solution Model 265

11.5.1 The Activity Coefficient 267

11.5.2 Phase Separation and Vapor Pressure 268

11.5.3 The Nature of w and Beyond 270

11.6 A Slightly Different Approach 272

11.6.1 The Solubility Parameter Approach 274

11.6.2 The One- and Two-Fluid Model 275

11.7 The Activity Coefficient for Other Composition Measures 277

11.8 Empirical Improvements 278

11.9 Theoretical Improvements 281

References 283

Further Reading 284

12 Mixing Liquids: Ionic Solutions 285

12.1 Ions in Solution 285

12.1.1 Solubility 286

12.2 The Born Model and Some Extensions 289

12.3 Hydration Structure 293

12.3.1 Gas-Phase Hydration 293

12.3.2 Liquid-Phase Hydration 294

12.4 Strong and Weak Electrolytes 300

12.5 Debye–Hückel Theory 303

12.5.1 The Activity Coefficient and the Limiting Law 306

12.5.2 Extensions 307

12.6 Structure and Thermodynamics 308

12.6.1 The Correlation Function and Screening 308

12.6.2 Thermodynamic Potentials 310

12.7 Conductivity 311

12.7.1 Mobility and Diffusion 315

12.8 Conductivity Continued 317

12.8.1 Association 320

12.9 Final Remarks 323

References 323

Further Reading 324

13 Mixing Liquids: Polymeric Solutions 325

13.1 Polymer Configurations 325

13.2 Real Chains in Solution 333

13.2.1 Temperature Effects 337

13.3 The Florry–Huggins Model 339

13.3.1 The Entropy 339

13.3.2 The Energy 342

13.3.3 The Helmholtz Energy 343

13.3.4 Phase Behavior 344

13.4 Solubility Theory 347

13.5 EoS Theories 352

13.5.1 A Simple Cell Model 352

13.5.2 The FOVE Theory 354

13.5.3 The LF Theory 356

13.5.4 The SS Theory 358

13.6 The SAFT Approach 361

References 368

Further Reading 369

14 Some Special Topics: Reactions in Solutions 371

14.1 Kinetics Basics 371

14.2 Transition State Theory 373

14.2.1 The Equilibrium Constant 373

14.2.2 Potential Energy Surfaces 374

14.2.3 The Activated Complex 376

14.3 Solvent Effects 379

14.4 Diffusion Control 381

14.5 Reaction Control 384

14.6 Neutral Molecules 385

14.7 Ionic Solutions 387

14.7.1 The Double-Sphere Model 388

14.7.2 The Single-Sphere Model 389

14.7.3 Influence of Ionic Strength 390

14.7.4 Influence of Permittivity 392

14.8 Final Remarks 392

References 393

Further Reading 393

15 Some Special Topics: Surfaces of Liquids and Solutions 395

15.1 Thermodynamics of Surfaces 395

15.2 One-Component Liquid Surfaces 402

15.3 Gradient Theory 409

15.4 Two-Component Liquid Surfaces 413

15.5 Statistics of Adsorption 415

15.6 Characteristic Adsorption Behavior 417

15.6.1 Amphiphilic Solutes 418

15.6.2 Hydrophobic Solutes 423

15.6.3 Hydrophilic Solutes 424

15.7 Final Remarks 425

References 425

Further Reading 427

16 Some Special Topics: Phase Transitions 429

16.1 Some General Considerations 429

16.2 Discontinuous Transitions 434

16.2.1 Evaporation 435

16.2.2 Melting 437

16.3 Continuous Transitions and the Critical Point 437

16.3.1 Limiting Behavior 438

16.3.2 Mean Field Theory: Continuous Transitions 441

16.3.3 Mean Field Theory: Discontinuous Transitions 444

16.3.4 Mean Field Theory: Fluid Transitions 444

16.4 Scaling 447

16.4.1 Homogeneous Functions 447

16.4.2 Scaled Potentials 448

16.4.3 Scaling Lattices 449

16.5 Renormalization 451

16.6 Final Remarks 457

References 457

Further Reading 458

Appendix A Units, Physical Constants, and Conversion Factors 459

Basic and Derived SI Units 459

Physical Constants 460

Conversion Factors for Non-SI Units 460

Prefixes 460

Greek Alphabet 461

Standard Values 461

Appendix B Some Useful Mathematics 463

B.1 Symbols and Conventions 463

B.2 Partial Derivatives 463

B.3 Composite, Implicit, and Homogeneous Functions 465

B.4 Extremes and Lagrange Multipliers 467

B.5 Legendre Transforms 468

B.6 Matrices and Determinants 469

B.7 Change of Variables 471

B.8 Scalars, Vectors, and Tensors 473

B.9 Tensor Analysis 477

B.10 Calculus of Variations 480

B.11 Gamma Function 481

B.12 Dirac and Heaviside Function 482

B.13 Laplace and Fourier Transforms 482

B.14 Some Useful Integrals and Expansions 484

Further Reading 486

Appendix C The Lattice Gas Model 487

C.1 The Lattice Gas Model 487

C.2 The Zeroth Approximation or Mean Field Solution 488

C.3 The First Approximation or Quasi-Chemical Solution 490

C.3.1 Pair Distributions 491

C.3.2 The Helmholtz Energy 492

C.3.3 Critical Mixing 493

C.4 Final Remarks 494

References 494

Appendix D Elements of Electrostatics 495

D.1 Coulomb, Gauss, Poisson, and Laplace 495

D.2 A Dielectric Sphere in a Dielectric Matrix 498

D.3 A Dipole in a Spherical Cavity 500

Further Reading 501

Appendix E Data 503

References 512

Appendix F Numerical Answers to Selected Problems 513

Index 515