Liquid state physical chemistry fundamentals modeling and applications

Gijsbertus de With
Liquid-State Physical
Chemistry


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Gijsbertus de With

Liquid-State Physical Chemistry
Fundamentals, Modeling, and Applications


Author
Gijsbertus de With
Eindhoven Univ. of Technology
Dept. of Chemical Engineering
and Chemistry
Den Dolech 2
5612AZ Eindhoven
The Netherlands
Cover: Martijn de With: Disordered
order : an artist’s impression of
liquids, 2013.

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There are two quite different approaches to a theory of the liquid state which
in fact complement each other.
Henry Eyring, page 141 in Liquids: Structure, Properties, Solid Interactions,
T.J. Hughel ed., Elsevier Publ. Comp. Amsterdam, 1965.



VII

Contents
Preface XV
Acknowledgments XIX
List of Important Symbols and Abbreviations XXV
1
1.1
1.2
1.3
1.4

Introduction 1
The Importance of Liquids 1
Solids, Gases, and Liquids 2
Outline and Approach 5

Notation 8
References 9
Further Reading 9

2

Basic Macroscopic and Microscopic Concepts: Thermodynamics,
Classical, and Quantum Mechanics 11
Thermodynamics 11
The Four Laws 11
Quasi-Conservative and Dissipative Forces 15
Equation of State 16
Equilibrium 17
Auxiliary Functions 18
Some Derivatives and Their Relationships 20
Chemical Content 21
Chemical Equilibrium 24
Classical Mechanics 26
Generalized Coordinates 27
Hamilton’s Principle and Lagrange’s Equations 28
Conservation Laws 30
Hamilton’s Equations 33
Quantum Concepts 35
Basics of Quantum Mechanics 35
The Particle-in-a-Box 41
The Harmonic Oscillator 42
The Rigid Rotator 43

2.1
2.1.1

2.1.2
2.1.3
2.1.4
2.1.5
2.1.6
2.1.7
2.1.8
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
2.3.3
2.3.4


VIII

Contents

2.4
2.4.1
2.4.2
2.4.3

Approximate Solutions 44
The Born–Oppenheimer Approximation 44

The Variation Principle 45
Perturbation Theory 48
References 51
Further Reading 51

3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.7.1
3.7.2
3.7.3
3.8

Basic Energetics: Intermolecular Interactions 53
Preliminaries 53
Electrostatic Interaction 55
Induction Interaction 59
Dispersion Interaction 60
The Total Interaction 63
Model Potentials 65
Refinements 68
Hydrogen Bonding 68
Three-Body Interactions 70
Accurate Empirical Potentials 70
The Virial Theorem 72

References 72
Further Reading 73

4
4.1
4.2
4.3
4.3.1

Describing Liquids: Phenomenological Behavior 75
Phase Behavior 75
Equations of State 76
Corresponding States 79
Extended Principle 82
References 86
Further Reading 87

5

The Transition from Microscopic to Macroscopic: Statistical
Thermodynamics 89
Statistical Thermodynamics 89
Some Concepts 89
Entropy and Partition Functions 91
Fluctuations 99
Perfect Gases 101
Single Particle 101
Many Particles 102
Pressure and Energy 103
The Semi-Classical Approximation 104

A Few General Aspects 110
Internal Contributions 112
Vibrations 112
Rotations 115
Electronic Transitions 116

5.1
5.1.1
5.1.2
5.1.3
5.2
5.2.1
5.2.2
5.2.3
5.3
5.4
5.5
5.5.1
5.5.2
5.5.3


Contents

5.6
5.6.1
5.6.2
5.6.3
5.6.4
5.6.5

Real Gases 118
Single Particle 118
Interacting Particles 118
The Virial Expansion: Canonical Method 119
The Virial Expansion: Grand Canonical Method 121
Critique and Some Further Remarks 123
References 126
Further Reading 127

6
6.1
6.2
6.2.1
6.2.2
6.3
6.4
6.5
6.6

Describing Liquids: Structure and Energetics 129
The Structure of Solids 129
The Meaning of Structure for Liquids 132
Distributions Functions 132
Two Asides 136
The Experimental Determination of g(r) 138
The Structure of Liquids 140
Energetics 146
The Potential of Mean Force 150
References 154

Further Reading 154

7
7.1
7.2
7.2.1
7.2.2
7.2.3
7.2.4
7.2.5
7.2.6
7.2.7
7.3
7.4
7.4.1
7.4.2
7.4.3
7.5
7.6

Modeling the Structure of Liquids: The Integral Equation
Approach 155
The Vital Role of the Correlation Function 155
Integral Equations 156
The Yvon–Born–Green Equation 156
The Kirkwood Equation 158
The Ornstein–Zernike Equation 159
The Percus–Yevick Equation 161
The Hyper-Netted Chain Equation 162
The Mean Spherical Approximation 162

Comparison 163
Hard-Sphere Results 165
Perturbation Theory 168
The Gibbs–Bogoliubov Inequality 168
The Barker–Henderson Approach 170
The Weeks–Chandler–Andersen Approach 172
Molecular Fluids 174
Final Remarks 174
References 175
Further Reading 175

8
8.1
8.2
8.3

Modeling the Structure of Liquids: The Physical Model Approach 177
Preliminaries 177
Cell Models 178
Hole Models 187

IX


X

Contents

8.3.1
8.3.2

8.4
8.5

The Basic Hole Model 189
An Extended Hole Model 191
Significant Liquid Structures 194
Scaled-Particle Theory 200
References 202
Further Reading 202

9
9.1
9.2
9.3
9.4

Modeling the Structure of Liquids: The Simulation Approach 203
Preliminaries 203
Molecular Dynamics 205
The Monte Carlo Method 211
An Example: Ammonia 214
References 218
Further Reading 219

10
10.1
10.2
10.3
10.3.1
10.4

10.5
10.5.1
10.5.2
10.5.3

Describing the Behavior of Liquids: Polar Liquids
Basic Aspects 221
Towards a Microscopic Interpretation 223
Dielectric Behavior of Gases 224
Estimating μ and α 229
Dielectric Behavior of Liquids 231
Water 238
Models of Water 241
The Structure of Liquid Water 242
Properties of Water 245
References 249
Further Reading 250

11
11.1
11.1.1
11.1.2
11.2
11.2.1
11.2.2
11.3
11.4
11.5
11.5.1
11.5.2

11.5.3
11.6
11.6.1
11.6.2
11.7

Mixing Liquids: Molecular Solutions 251
Basic Aspects 251
Partial and Molar Quantities 251
Perfect Solutions 253
Ideal and Real Solutions 256
Raoult’s and Henry’s Laws 257
Deviations 258
Colligative Properties 260
Ideal Behavior in Statistical Terms 262
The Regular Solution Model 265
The Activity Coefficient 267
Phase Separation and Vapor Pressure 268
The Nature of w and Beyond 270
A Slightly Different Approach 272
The Solubility Parameter Approach 274
The One- and Two-Fluid Model 275
The Activity Coefficient for Other Composition Measures 277

221


Contents

11.8

11.9

Empirical Improvements 278
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
13.1
13.2
13.2.1
13.3
13.3.1
13.3.2
13.3.3
13.3.4
13.4
13.5
13.5.1
13.5.2
13.5.3
13.5.4
13.6

Mixing Liquids: Polymeric Solutions
Polymer Configurations 325
Real Chains in Solution 333
Temperature Effects 337
The Florry–Huggins Model 339

The Entropy 339
The Energy 342
The Helmholtz Energy 343
Phase Behavior 344
Solubility Theory 347
EoS Theories 352
A Simple Cell Model 352
The FOVE Theory 354
The LF Theory 356
The SS Theory 358
The SAFT Approach 361
References 368
Further Reading 369

325

XI


XII

Contents

14
14.1
14.2
14.2.1
14.2.2
14.2.3
14.3

14.4
14.5
14.6
14.7
14.7.1
14.7.2
14.7.3
14.7.4
14.8

Some Special Topics: Reactions in Solutions
Kinetics Basics 371
Transition State Theory 373
The Equilibrium Constant 373
Potential Energy Surfaces 374
The Activated Complex 376
Solvent Effects 379
Diffusion Control 381
Reaction Control 384
Neutral Molecules 385
Ionic Solutions 387
The Double-Sphere Model 388
The Single-Sphere Model 389
Influence of Ionic Strength 390
Influence of Permittivity 392
Final Remarks 392
References 393
Further Reading 393

371

15
15.1
15.2
15.3
15.4
15.5
15.6
15.6.1
15.6.2
15.6.3
15.7

Some Special Topics: Surfaces of Liquids and Solutions
Thermodynamics of Surfaces 395
One-Component Liquid Surfaces 402
Gradient Theory 409
Two-Component Liquid Surfaces 413
Statistics of Adsorption 415
Characteristic Adsorption Behavior 417
Amphiphilic Solutes 418
Hydrophobic Solutes 423
Hydrophilic Solutes 424
Final Remarks 425
References 425
Further Reading 427

16
16.1
16.2

16.2.1
16.2.2
16.3
16.3.1
16.3.2
16.3.3
16.3.4
16.4
16.4.1

Some Special Topics: Phase Transitions 429
Some General Considerations 429
Discontinuous Transitions 434
Evaporation 435
Melting 437
Continuous Transitions and the Critical Point 437
Limiting Behavior 438
Mean Field Theory: Continuous Transitions 441
Mean Field Theory: Discontinuous Transitions 444
Mean Field Theory: Fluid Transitions 444
Scaling 447
Homogeneous Functions 447

395


Contents

16.4.2
16.4.3

16.5
16.6

Scaled Potentials 448
Scaling Lattices 449
Renormalization 451
Final Remarks 457
References 457
Further Reading 458

Appendix A Units, Physical Constants, and Conversion Factors
Basic and Derived SI Units 459
Physical Constants 460
Conversion Factors for Non-SI Units 460
Prefixes 460
Greek Alphabet 461
Standard Values 461

459

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

XIII


XIV

Contents

D.3

A Dipole in a Spherical Cavity
Further Reading 501

500

Appendix E Data 503
References 512
Appendix F

Numerical Answers to Selected Problems

Index

515

513


XV

Preface
For many processes and applications in science and technology a basic knowledge
of liquids and solutions is a must. However, the usual curriculum in chemistry,
physics, and materials science pays little or no attention to this subject. It must
be said that many books have been written on liquids and solutions. However,
only a few of them are suitable as an introduction (many of them are far too elaborate), and most of them have been published quite some time ago, apart from the
relatively recent book by Barrat and Hansen (2005). In spite of my admiration for
that book I feel that it is not suitable as an introduction for chemical engineers
and chemists.
In the present book a basic but as far as possible self-contained and integrated
treatment of the behavior of liquids and solutions and a few of their simplest
applications is presented. After introducing the fundamentals required, we try to
present an overview of models of liquids giving an approximately equal weight to
pure liquids, simple solutions, be it non-electrolyte, electrolyte, or polymeric solutions. Thereafter, we deal with a few special topics: reactions in solutions, surfaces,
and phase transitions. Obviously, not all topics can be treated and a certain initial
acquaintance with several aspects of physical chemistry is probably an advantage
for the reader.
A particular feature of this book is the attempt to provide a basic but balanced
presentation of the various aspects relevant to liquids and solutions, using the
regular solution concept as a guide. That does not imply that we “forget” more
modern approaches, but the concept is useful as a guide, in particular for engineering applications. To clarify the authors’ view on the subject a bit further, it may
be useful to quote Henry Eyrings’ statement, as printed on the title page, more

fully:
There are two quite different approaches to a theory of the liquid state which
in fact complement each other. In the deductive approach one proceeds as
far as possible strictly mathematically, and when the complications cause
this logical procedure to bog down, one resorts to some more or less defensible assumption such as Kirkwood’s superposition principle. In the other
approach one struggles to find a physical model of the liquid state which
is as faithful to reality as can be devised and yet be solvable. The solution


XVI

Preface

of the model may then proceed with considerable rigor. There are advantages and disadvantages to both procedures. In fact, either method expertly
enough executed will solve the problem.
Although rigorous approaches have advanced considerably since the time this
statement was made, the essence of this remark is still to the point in our view,
in spite of the rebuttal by Stuart Rice:
The second approach mentioned by professor Eyring depends on our ability
to make a very accurate guess about the structure and proper parameterization of the model or models chosen. It is the adequacy of our guesses as
representations of the real liquid which I question.
There is no doubt that rigorous approaches are important, much more so than in
the time Eyring made his remark but, in our opinion, understanding is still very
much served by using as simple as possible models.
The whole of topics the presented is conveniently described as physical chemistry or the chemical physics1) of liquids and solutions: it describes the physicochemical behavior of liquids and solutions with applications to engineering
problems and processes. Unfortunately, this description is wide, in fact too wide,
and we have to limit ourselves to those topics that are most relevant to chemical
engineers and chemists. This implies that we do not deal systematically with
quantum liquids, molten salts, or liquid metals. Obviously, it is impossible to
reflect these considerations exactly in any title so that we have chosen for a brief

one, trusting that potential users will read this preface (and the introduction) so
that they know what to expect. For brevity, therefore, we refer to the field as liquidstate physical chemistry.
We pay quite some attention to physical models since, despite all developments
in simulations, they are rather useful for providing a qualitative understanding of
molecular liquids and solutions. Moreover, they form the basis for a description
of the behavior of polymer solutions as presently researched, and last – but not
least – they provide to a considerable extent solvable models and therefore have a
substantial pedagogical value. Whilst, admittedly, this approach may be characterized by some as “old-fashioned,” in my opinion it is rather useful.
This book grew out of a course on the behavior of liquids and solutions, which
contained already all the essential ingredients. This course, which was conducted
at the Department of Chemical Engineering and Chemistry at Eindhoven University of Technology, originated from a total revision of the curriculum some 10
years ago and the introduction of liquid-state physical chemistry (or as said, equiva1) I refer here to the preface of Introduction to
Chemical Physics by J.C. Slater (1939), where
he states: “It is probably unfortunate that
physics and chemistry were ever separated.
Chemistry is the science of atoms and the way

they combine. Physics deals with the
interatomic forces and with the large-scale
properties of matter resulting from those forces.
. . . A wide range of study is common to both
subjects. The sooner we realize this, the better”.


Preface

lently, liquid-state chemical physics) some seven years ago. The overall set-up as
given here has evolved during the last few years, and hopefully both the balance
in topics and their presentation is improved. I am obliged to our students and
instructors who have followed and used this course and have provided many useful

remarks. In particular, I wish to thank my colleagues Dr Paul van der Varst, Dr
Jozua Laven, and Dr Frank Peters for their careful reading of, and commenting
on, several parts of the manuscript, and their discussions on many of the topics
covered. Hopefully, this has led to an improvement in the presentation. I realize
that a significant part of writing a book is usually done outside office hours, and
this inevitably interferes considerably with one’s domestic life. This text is no
exception: for my wife, this is the second experience along this line, and I hope
that this second book has “removed” less attention than the first. I am, therefore,
indebted to my wife Ada for her patience and forbearance. Finally, I would like to
thank Dr Martin Graf-Utzmann (Wiley-VCH, publisher) and Mrs Bernadette Cabo
(Toppan Best-set Premedia Limited, typesetter) for all their efforts during the
production of this book.
Obviously, the border between various classical disciplines is fading out nowadays. Consequently, it is hoped that these notes are useful not only for the original
target audience, chemists, and chemical engineers, but also for materials scientists, mechanical engineers, physicists, and the like. Finally, we fear that the text
will not be free from errors, and these are our responsibility. Hence, any comments, corrections, or indications of omissions will be appreciated.
January 2013

Gijsbertus de With

XVII



XIX

Acknowledgments
Wiley-VCH and the author have attempted to trace the copyright holders of all
material from various websites, journals, or books reproduced in this publication
to obtain permission to reproduce this material, and apologize herewith to copyright holders if permission to publish in this form has not been obtained.
Fig. 1.4a: Courtesy of Oak Ridge National Laboratory, U.S. Dept. of Energy:

/>Fig. 1.4b: Source: M. Maňas at Wikimedia Commons: i
media.org/wiki/File:3D_model_hydrogen_bonds_in_water.jpg
Fig. 1.5a: This image is from the Solubility article on the ellesmere-chemistry
Wikia and is under the Creative Commons Attibution-Share Alike License: http://
ellesmere-chemistry.wikia.com/wiki/File:Salt500.jpg#file
Fig. 1.5b: This image is from the YouTube movie Hydration Shell Dynamics of
a Hydrophobic Particle by hexawater and is under the Creative Commons Attibution-Share Alike License: />feature=related
Fig. 1.6a: This image is used with permission from J.T. Padding and W.J. Briels,
Computational Biophysics, University of Twente, the Netherlands, from their
website: />Fig. 1.6b: This image is used from Science, vol. 331, issue 6023, 18 March 2011,
cover page by D.R. Glowachi, School of Chemistry, University of Bristol. Reprinted
with permission from AAAS.
Fig. 4.1: Reprinted with permission from Thermal Physics, by C.B.P. Finn,
Chapman & Hall, London 1993 (fig. 9.1, page 166). Copyright 1993 Francis &
Taylor.
Fig. 4.2: This image is used from the Real Gases article by M. Gupta from the
website: />Fig. 4.4: Reprinted with permission from Q.J. Su (1946), Ind. Eng. Chem. Res.,
38, 803 (fig. 1). Copyright 1946 American Chemical Society.
Fig. 4.5: Reprinted from Thermodynamics: An Advanced Treatment for Chemists
and Physicists, by E.A. Guggenheim, North Holland, copyright 1967 (fig. 3.10, page
137 and fig. 3.11, page 138), with permission from Elsevier.
Problem 6.6: Reprinted from L.V. Woodcock (1971), Chem, Phys. Letters, 10,
257 (fig. 1), with permission from Elsevier.


XX

Acknowledgments

Fig. 6.2: Reprinted from Mechanics of Materials, by M.A. Meyers, R.W. Armstrong, H.O.K. Kirchner, Chapter 7: Rate processes in plastic deformation of

crystalline and noncrystalline solids by A.S. Argon (fig. 7.20, page 204), J. Wiley,
NY 1999. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with
permission.
Fig. 6.3: Reprinted from Mechanics of Materials, by M.A. Meyers, R.W. Armstrong, H.O.K. Kirchner, Chapter 7: Rate processes in plastic deformation of
crystalline and noncrystalline solids by A.S. Argon (fig. 7.21, page 205), J. Wiley,
NY 1999. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with
permission.
Fig. 6.6: Reprinted from Physics of Simple Liquids, by H.N.V. Temperley, J.S.
Rowlinson, G.S. Rushbrooke, Chapter 10: Structure of simple liquids by X-ray
diffraction, by C.J. Pings, North Holland, Amsterdam 1968 (fig. 2, page 406), with
permission from Elsevier.
Fig. 6.7a: Reprinted from The Liquid State, by J.A. Pryde, Hutchinson University
Library, London 1966 (fig. 3.2, page 42).
Fig. 6.7b: Reprinted with permission from J.L. Yarnell et al. (1973), Phys.
Rev. A7 [6] 2130, APS (fig. 4). Copyright 1973 American Physical Society.
Fig. 6.8a: Reprinted with kind permission from J. Phys. Soc. Japan, 64 [8] (1995)
2886, Y. Tatuhiro (fig. 3).
Fig. 6.8b: With kind permission from Springer Science+Business Media: Il
Nuovo Cimento D 12 (1990) 543, J.C. Dore (fig. 2).
Fig. 6.10: With kind permission from Springer Science+Business Media: Il
Nuovo Cimento D 12 (1990) 543, J.C. Dore (fig. 4 and fig. 5).
Fig. 6.11: Reprinted from The Liquid State, by J.A. Pryde, Hutchinson University
Library, London 1966 (fig 8.3, page 139).
Fig. 7.1: Reprinted from Liquid State Chemical Physics, by R.O. Watts, I.J. McGee,
Wiley, NY 1976 (fig. 5.1, page 137). Copyright Wiley-VCH Verlag GmbH & Co.
KGaA. Reproduced with permission.
Fig. 7.2a: Reprinted from Physical Chemistry – an Advanced Treatise – vol. VIIIA/
Liquid State, by H. Eyring, D. Henderson, W. Jost, Chapter 4: Distribution functions, by R.J. Baxter, Academic Press, New York and London 1971 (fig. 7, page
297), with permission from Elsevier.
Fig. 7.2b: Reprinted from Liquid State Chemical Physics, by R.O. Watts, & I.J.

McGee, Wiley, NY 1976 (fig. 5.2, page 140). Copyright Wiley-VCH Verlag GmbH
& Co. KGaA. Reproduced with permission.
Fig. 7.5: Reprinted with permission from J.A. Barker, D. Hendersson (1967), J.
Chem. Phys., 47, 4714 (fig. 5 and fig. 6). Copyright 1967 American Institute of
Physics.
Fig. 7.6: From D. Chandler, J.D. Weeks (1983), Science, 220, 787. Reprinted with
permission from AAAS.
Fig. 7.7: Reprinted with permission from J.A. Barker, D. Henderson (1971), Acc.
Chem. Res., 4, 3031 (fig. 4). Copyright 1971 American Chemical Society.
Fig. 8.1: Reprinted with kind permission from B.A. Dasannacharya, K.R. Rao,
Phys. Rev., 137 (1965) A417 (fig. 9). Copyright 1965 by American Physical Society.


Acknowledgments

Fig. 8.2: Reprinted from The Liquid State, by J.A. Pryde, Hutchinson University
Library, London 1966 (fig. 6.1. page 99).
Fig. 8.3: Reprinted with permission from W.G. Hoover, F.H. Ree (1968), J.
Chem. Phys. 49, 3609 (fig. 2 and fig. 4). Copyright 1968 American Institute of
Physics.
Fig. 8.4: Reprinted with permission from D. Henderson (1962), J. Chem. Phys.,
37, 631 (fig. 1 and fig. 2). Copyright 1962 American Institute of Physics.
Fig. 8.5: Reprinted with permission from The Dynamic Liquid State, by A.F.M.
Barton, Longman, New York 1974 (fig. 12.1, page 109). Copyright 1974 Pearson.
Fig. 8.6: Reprinted with permission from H. Eyring, R.P. H., Marchi (1963), J.
Chem. Ed., 40, 562 (fig. 1). Copyright 1963 American Chemical Society.
Fig. 8.7: Reprinted with permission from T.S. Ree et al. (1965), J. Phys. Chem.,
69, 3322 (fig. 2 and fig. 3). Copyright 1965 American Chemical Society.
Fig. 9.1a: Reprinted from Properties of Liquids and Solutions, by J.N. Murrell, A.D.
Jenkins, Wiley, Chichester 1994 (fig. 3.3, page 54). Copyright Wiley-VCH Verlag

GmbH & Co. KGaA. Reproduced with permission.
Fig. 9.1b: Reprinted from A Course on Statistical Mechanics, by H.L. Friedman,
Prentice-Hall, Englewood Cliffs, NJ 1985 (fig. 5.2, page 95). Copyright Wiley-VCH
Verlag GmbH & Co. KGaA. Reproduced with permission.
Fig. 9.2: Reprinted with permission from T. Wainwright, B.J. Alder (1958), Il
Nuovo Cimento 9 [1] Supplement, 116 (fig. 6 and fig. 7). Copyright 1958 Springer.
Fig. 9.3: Reprinted from A Course on Statistical Mechanics, by H.L. Friedman,
Prentice-Hall, Englewood Cliffs, NJ 1985 (fig. 5.3, page 100 and fig. 5.5, page 107).
Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.
Fig. 9.4: Reprinted with permission from S. Hannongbua (2000), J. Chem.
Phys., 113, 4707 (fig. 1). Copyright 2000 American Institute of Physics.
Fig. 9.5: Reprinted with permission from S. Hannongbua (2000), J. Chem.
Phys., 113, 4707 (fig. 3). Copyright 2000 American Institute of Physics.
Fig. 9.6: Reprinted with permission from S. Hannongbua (2000), J. Chem.
Phys., 113, 4707 (fig. 5). Copyright 2000 American Institute of Physics.
Fig. 9.7: Reprinted with permission from S. Hannongbua (2000), J. Chem.
Phys., 113, 4707 (fig. 2). Copyright 2000 American Institute of Physics.
Fig. 10.1: Reprinted from Polar Molecules, P. Debye, The Chemical Catalog
Company Inc., New York 1929 (fig. 9, page 38 and fig. 10, page 39).
Fig. 10.4: This image is from the Colors from Vibrations article on the Causes of
Color exhibition, M. Douma, curator, and is under the Creative Commons Attibution-Share Alike License. />Fig. 10.5: Reprinted with permission from J.A. Odutola, T.R. Dyke (1980), J.
Chem. Phys., 72, 5062 (fig. 4). Copyright 1980 American Institute of Physics.
Fig. 10.6: Reprinted with permission from Principles of Modern Chemistry, 5th
ed. by D.W. Oxtoby, M.P. Gillis, N.H. Nachtrieb (fig. 5.19, page 145). Copyright
2003 Cengage/Nelson.
Fig. 10.7a: Reprinted from Biophysical Chemistry, vol. 1, by J.T. Edsall, J. Wyman,
Academic Press Inc. Publishers, NY 1958 (fig. 3, page 31), with permission from
Elsevier.

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Fig. 10.7b: This image is used with permission from the Ice Structure article on
The Interactive Library of EdInformatics.com: />interactive_molecules/ice.htm
Fig. 10.7c: This image is used with permission from the Water Molecule Structure
article on the Water Structure and Science webpage of M. Chaplin: http://www.
lsbu.ac.uk/water/molecule.html
Fig. 10.8a: Reprinted from Properties of Liquids and Solutions, by J.N. Murrell,
A.D. Jenkins, Wiley, Chichester 1994 (fig. 8.7, page 172). Copyright Wiley-VCH
Verlag GmbH & Co. KGaA. Reproduced with permission.
Fig. 10.8b: This image is used with permission from Dr L. Ojamäe, Linköpings
University, Department of Physics, Chemistry and Biology, Computational
Chemistry, Linköping, Sweden from his webpage on Molecular Dynamics Simulation of Liquid Water on the website: />liquid.html
Fig. 10.9: Reprinted from Properties of Liquids and Solutions, by J.N. Murrell, A.D.
Jenkins, Wiley, Chichester 1994 (fig. 8.9, page 175). Copyright Wiley-VCH Verlag
GmbH & Co. KGaA. Reproduced with permission.
Fig. 10.10: Reprinted from Springer: F. Franks (ed.), Water – A Comprehensive
Treatise, Vol. 1: The Physics and Physical Chemistry of Water, Chapter 5: Raman and
infrared spectral investigation of water structure, by G.E. Walraten (fig. 11, page
177, fig. 12, page 178, fig. 15, page 182). Copyright 1972 Plenum Press, with kind
permission from Springer Science+Business Media B.V.
Fig. 10.11a: Reprinted with permission from J. Morgan, B.E. Warren (1938), J.
Chem. Phys., 6, 666 (fig. 4). Copyright 1938 American Institute of Physics.
Fig. 10.11b: Reprinted from Springer: F. Franks (ed.) Water – A Comprehensive
Treatise, Vol. 1: The Physics and Physical Chemistry of Water, Chapter 8: Liquid
water: scattering of X-rays, by H. Narten, H.A. Levy (fig. 5, page 326). Copyright

1972 Plenum Press, with kind permission from Springer Science+Business
Media B.V.
Fig. 10.12: Reprinted with permission from G.C. Lie, E. Clementi (1975), J.
Chem. Phys., 62, 2195 (fig. 4). Copyright 1975 American Institute of Physics.
Fig. 10.13: Reprinted from Properties of Liquids and Solutions, by J.N. Murrell,
A.D. Jenkins, Wiley, Chichester 1994 (fig. 8.15, page 183). Copyright Wiley-VCH
Verlag GmbH & Co. KGaA. Reproduced with permission.
Fig.10.14: Reprinted with permission from The Nature of Chemical Bond, 3rd
ed., by L. Pauling, Cornell University Press, Ithaca, NY 1960 (fig. 12.3, page 456
and fig. 12.2, page 455). Copyright 1960 Cornell University Press.
Fig. 11.2: Reprinted from J. Zawidsky, Z. Phys. Chem., 35 (1900), 129 (fig. 7,
fig. 8, fig. 14 and fig. 15).
Fig. 11.3: This image is used with permission from Dortmund Data Base: http://
www.ddbst.com
Fig. 11.5: Reprinted from Thermodynamics: An Advanced Treatment for Chemists
and Physicists, by E.A. Guggenheim, North Holland. Copyright 1967 (fig. 4.8 and
fig. 4.9, page 199), with permission from Elsevier.


Acknowledgments

Fig. 11.6: Reprinted with permission from D. Henderson, P.J. Leonard, Proc.
Nat. Acad. Sci. USA, 68 (1971) 632 (fig. 1 and fig. 2). Copyright 1971 National
Academy of Sciences of the United States of America.
Fig. 12.3: Reprinted from Ions in Solutions, by J. Burgess, Ellis Horwood, Chicester 1988 (fig. 2.2, page 31). Copyright Wiley-VCH Verlag GmbH & Co. KGaA.
Reproduced with permission.
Fig. 12.4: Reprinted from Springer: F. Franks (ed.) Water – A Comprehensive
Treatise, Vol. 6: Recent Advances, Chapter 1: X-ray and neutron scattering by electrolytes, by J.E. Enderby, G.W. Neilson, G. Plenum Press, London and New York
1979 (fig. 5, page 28, fig. 8, page 31, fig. 12, page 35), with kind permission from
Springer Science+Business Media B.V.

Fig. 12.5: Reprinted from Ions in Solutions, by J. Burgess, Ellis Horwood Chicester 1988 (fig. 3.5 and fig. 3.6, page 42). Copyright Wiley-VCH Verlag GmbH & Co.
KGaA. Reproduced with permission.
Fig. 12.6: Reprinted with permission from Pitzer, K.D. (1977), Acc. Chem. Res.,
10, 371 (fig. 2 and fig. 3). Copyright 1977 American Chemical Society.
Fig. 12.9: This image is used with permission from the Grotthuss Mechanism
article on the Water Structure and Science webpage of M. Chaplin: http://www.
lsbu.ac.uk/water/grotthuss.html#r160
Fig. 13.1: Reprinted from Microstructure and Wear of Materials, by K.-H. zum
Gahr, Elsevier, Amsterdam 1987 (fig. 2.5, page 13), with permission of Elsevier.
Fig. 13.4: Reprinted with permission from R.H. Boyd, P.J. Phillips (1993), The
Science of Polymer Molecules (fig. 6.15, page 215). Copyright 1993 Cambridge University Press.
Fig. 13.6: These two images are used with permission from the Thermodynamic
Considerations for Polymer Solubility article on the Polymer Science Learning Center
webpage of Prof. L.J. Mathias; University of Southern Mississippi, Department of
Polymer Science: />Fig. 13.7: Reprinted from E.F. Casassa (1976), J. Polymer Sci. Part C: Polymer
Symposia, 54, 53. Copyright 1976 Wiley. This material is reproduced with permission of John Wiley & Sons. Inc.
Fig. 13.8a: Reprinted with permission from P.J. Flory (1970), Disc. Far. Soc., 49,
7 (fig. 1). Copyright 1970 Royal Society of Chemistry.
Fig. 13.8b: Reprinted with permission from I.C. Sanchez, R.H. Lacombe
(1978), Macromolecules, 11, 1145 (fig. 6). Copyright 1978 American Chemical
Society.
Fig. 13.9: Reprinted from H. Xie, E. Nies, A. Stroeks, R. Simha (1992), Pol. Eng.
Sci., 32, 1654 (fig. 3 and fig. 9). Copyright 1992 John Wiley & Sons.
Fig. 13.10a: Reprinted from C.S. Wu, Y.P. Chen Y.P. (1994), Fluid Phase Equilibria, 100, 103 (fig. 4), with permission from Elsevier.
Fig. 13.10b: Reprinted with permission from I.G. Economou (2002), Ind. Eng.
Chem. Res., 41, 953 (fig. 5). Copyright 2002 American Chemical Society.
Fig. 13.11a: Reprinted with permission from J. Gross, G. Sadowski (2001), Ind.
Eng. Chem. Res., 40, 1244 (fig. 3). Copyright 2001 American Chemical Society.

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Fig. 13.11b: Reprinted from N. von Solms et al. (2006), Fluid Phase Equilibria
241, 344 (fig. 1), with permission from Elsevier.
Fig. 14.1: Reprinted from Physical Chemistry, 3rd ed., by R.J. Silbey, R.A. Alberty,
J. Wiley & Sons, NY 2001 (fig. 19.2, page 709). This material is reproduced with
permission of John Wiley & Sons. Inc.
Fig. 14.4: Reprinted from The Theory of Rate Processes, by S. Glasstone, K.J.
Laidler and H. Eyring, McGraw-Hill, NY 1941 (fig. 105 and fig. 106, page 420),
with permission of McGraw-Hill Higher Education.
Fig. 14.6: Reprinted from The Theory of Rate Processes, by S. Glasstone, K.J.
Laidler and H. Eyring, McGraw-Hill, NY 1941 (fig. 108, page 429 and fig. 109,
page 431), with permission of McGraw-Hill Higher Education.
Fig. 15.4: Reprinted with permission from R.F. Crul, K. Pitzer (1958), Ind. Eng.
Chem., 50, 265 (fig. 4). Copyright 1958 American Chemical Society.
Fig. 16.3: This image is from the ChemEd DL video on- Critical Point of Benzene.
Video from JCE Web Software, Chemistry Comes Alive: Copyright ACS Division
of Chemical Education, Inc. Used with permission. />Fig. 16.6: Reprinted with permission from P. Heller (1967), Rep. Prog. Phys.,
30, 731 (fig. 10). Copyright 1967 IOP Science.
Fig. 16.7: Reprinted with permission from P. Heller (1967), Rep. Prog. Phys.,
30, 731 (fig. 18). Copyright 1967 IOP Science.
Fig. 16.11: Reprinted from H.E. Stanley (1971), Introduction to Phase Transistions
and Critical Phenomena, Oxford University Press (fig. 1.5, page 7), with permission
from Oxford University Press, USA.
Fig. 16.12: This image is used with permission from M.R. Foster from
the percolation article on his website: />Percolation.pdf

Fig. App. C2: Reprinted from Statististical Mechanics and Dynamics, 2nd ed., by
H. Eyring, D. Henderson, B.J. Stover, E. M. Eyring, Wiley-Interscience, Chichester
1982 (fig. 2, page 474 and fig. 1, page 473). This material is reproduced with permission of John Wiley & Sons Inc.