Preface ....................................................... vii
Acknowledgments ............................................... xix
List of Abbreviations ......................................... xxi
1 Survey of the Properties of Water Personal Introduction ...... 1
1.1 Introduction and Some Historical Notes .................. 2
1.2 Properties of Water in the Gaseous Phase ................ 4
1.2.1 The single water molecule ........................ 4
1.2.2 Interaction between two water molecules ......... 10
1.3 Properties of Water in the Solid Phase ................. 26
1.3.1 Ordinary ice .................................... 26
1.3.2 The residual entropy of ice ..................... 28
1.3.3 The phase diagram of water ...................... 33
1.4 Properties of Water in the Liquid Phase ................ 41
1.4.1 Some outstanding properties of water ............ 42
1.4.2 Molar volume of water and its temperature
dependence ...................................... 46
1.4.3 Heat capacity ................................... 48
1.4.4 Isothermal compressibility ...................... 51
1.4.5 The radial distribution function of water ....... 53
1.5 The Kirkwood-Buff Integral ............................. 67
1.5.1 Ideal gas ....................................... 75
1.5.2 Inert gases represented as Lennard-Jones
particles ....................................... 77
1.5.3 Water, methanol, and ethanol .................... 78
1.6 Solvation of Water in Water ............................ 83
1.7 The Importance of Water in Biological Systems .......... 88
2 Theoretical Approaches to the Study of Liquid Water
Personal Introduction ....................................... 96
2.1 Introduction ........................................... 99
2.2 The General Theoretical Framework ..................... 100
2.3 The Mixture-Model Approach to Liquid Water ............ 113
2.3.1 The origin of the mixture-model theory of
water .......................................... 113
2.3.2 Wada's two-structure model for water: The
success and the limitation of the MM
approach ....................................... 118
2.3.3 An exact MM approach to the theory of
liquids ........................................ 126
2.3.4 Application of an exact two-structure model .... 140
2.4 Lattice Models for Water .............................. 153
2.4.1 Introduction ................................... 153
2.4.2 The Pauling model and its solution ............. 154
2.4.3 The heat capacity and the isothermal
compressibility ................................ 166
2.5 A One-Dimensional Model for Water ..................... 167
2.5.1 Introduction ................................... 167
2.5.2 The primitive model and the corresponding
partition function ............................. 172
2.5.3 Selected illustrative results for the
primitive model ................................ 175
2.5.4 The primitive cluster model for water and its
partition function ............................. 193
2.5.5 Cluster's size distribution .................... 199
2.5.6 Selected results for the primitive cluster
model .......................................... 201
2.5.7 Some concluding remarks regarding the 1-D
model for water ................................ 206
2.6 A Two-Dimensional Model for Water ..................... 209
2.6.1 Introduction ................................... 209
2.6.2 The physical model of water-like particles in
two dimensions ................................. 211
2.6.3 The application of the Percus-Yevick equation
to the BN2D model .............................. 218
2.6.4 Simulated results .............................. 224
2.6.5 Further development of the 2-D model ........... 229
2.7 Three-Dimensional Models for Water .................... 230
2.7.1 Introduction: A new era of water research ...... 230
2.7.2 Effective pair potential for water ............. 232
2.7.3 Second virial coefficients of water ............ 241
2.7.4 Definition of the structure of water ........... 245
2.7.5 An approximate method of calculating the
structure of water ............................. 249
2.7.6 Solvation of water in pure water ............... 252
2.7.7 Distribution of species of water molecules ..... 259
2.7.8 Application of the Percus-Yevick equation ...... 266
2.7.9 Application of cluster expansion to water ...... 268
2.7.10 Simulated results .............................. 269
3 Water with One Simple Solute Personal Introduction ......... 280
3.1 Introduction and Some Historical Notes ................ 283
3.2 Survey of Some Properties of Simple Aqueous
Solutions ............................................. 288
3.3 Solvation and Conditional Solvation ................... 302
3.3.1 Definition of the solvation process ............ 304
3.3.2 Hydrophobic and hydrophilic solutes ............ 305
3.3.3 Why do we need solvation quantities? ........... 308
3.4 Statistical Mechanical Expressions for the Solvation
Thermodynamic Quantities .............................. 311
3.5 Application of the Mixture-Model Approach to Water .... 322
3.5.1 Application of a two-structure model (TSM) ..... 324
3.5.2 Generalization to any mixture model of water ... 334
3.6 Application of an Interstitial Model for Water to
Aqueous Solutions ..................................... 343
3.7 The Problem of Stabilization of the Structure of
Water ................................................. 353
3.7.1 The concept of structural temperature .......... 353
3.7.2 Formulation of the problem within the
mixture-model approach ......................... 354
3.7.3 The application of the Kirkwood-Buff theory .... 358
3.7.4 An exact argument for a hard-point solute ...... 367
3.7.5 An approximate measure of the structural
change induced by the solute ................... 370
3.7.6 An empirical estimate of the structural
changes induced by the solute on the
solvation entropy .............................. 376
3.8 Application of the Scaled Particle Theory ............. 378
3.9 Application of a One-Dimensional Model ................ 381
3.9.1 Introduction ................................... 381
3.9.2 Solvation of hard rods in the primitive model
for water ...................................... 383
3.9.3 Application of the primitive cluster model
for dilute solutions of inert solutes .......... 388
3.9.4 Results for HR solute in dilute solutions
of the primitive cluster model ................. 396
3.10 Applications of Two-Dimensional Models ................ 406
3.11 Applications of Three-Dimensional Models .............. 408
4 Water with Two Solute Molecules; Hydrophobic Hydrophilic
Phenomena Persona I Introduction ........................... 411
4.1 Introduction .......................................... 415
4.2 The Experimental Evidence ............................. 419
4.3 Redefinition of the НøО Interaction ................... 426
4.4 A Simple Measure of the Strength of the "Pure" НøО
Interaction ........................................... 432
4.4.1 Some experimental data on the strength of НøО
interactions ................................... 442
4.4.2 НøО interaction among m identical spherical
non-polar solute particles ..................... 451
4.4.3 Attaching a methyl group to various
hydrocarbons ................................... 458
4.4.4 Attaching an ethyl group to various molecules .. 460
4.4.5 The hydrophobic interaction at zero
separation ..................................... 461
4.4.6 The hydrophobic interaction at contact
distance between the two solutes ............... 466
4.4.7 An improved approximate measure of the НøО
interaction .................................... 468
4.5 Intramolecular НøО Interactions ....................... 474
4.5.1 A simple measure of the intramolecular НøО
interaction .................................... 477
4.5.2 Mixed НøО-Нø1 interactions ..................... 483
4.6 Application of the Scaled Particle Theory ............. 489
4.7 Temperature and Pressure Dependence ................... 499
4.7.1 Some experimental values of the entropy,
enthalpy, and volume changes associated with
the НøО interaction ............................ 501
4.7.2 Formal statistical mechanical expressions for
δG, δS, δH, and δV for the НøО process ......... 503
4.7.3 Hydrophobic interaction and structural
changes in the solvent ......................... 506
4.7.4 A measure of the amount of structural changes
in the solvent ................................. 511
4.8 Solvent Induced Interactions Between Two Hydrophilic
Нø1 Groups ............................................ 513
4.8.1 The Нø1 interaction at R1 ≈ 2.76 Å ........... 515
4.8.2 The Нø1 interaction at R2 = 4.5 Å .............. 519
4.8.3 Intramolecular Нø1 interactions ................ 523
4.9 Application of One-Dimensional Models to Study
Hydrophobic Interactions .............................. 528
4.10 Application of Two-Dimensional Models ................. 535
4.11 Application of Three-Dimensional Models ............... 540
4.12 Hydrophobic or Hydrophilic? That is the Question! ..... 545
4.12.1 A short history of the rise and fall of
hydrophobia and hydrophilia .................... 545
4.12.2 The decline of the hydrophilic effect .......... 547
4.12.3 The rise of the НøО effect ..................... 549
4.12 A The resurgence of the Нø1 effects ................... 558
Appendices .................................................... 564
Appendix A: The Tetrahedral Geometry .......................... 564
Appendix B: Calculation of the Residual Entropy of Water ...... 565
Appendix C: The Kirkwood-Buff Integrals for an Ideal Gas ...... 568
Appendix D: The Equivalence Between the One-Component and
the Mixture-Model Views of the Same System ................. 570
Appendix E: The Generalized Euler Theorem ..................... 576
Appendix F: Some Identities in the Mixture-Model Approach ..... 580
Appendix G: The Statistical Mechanical Expression for the
Solvation Gibbs Energy of Hard Spheres and the Work of
Cavity Formation ........................................... 584
Appendix H: The Solubility of a Simple Solute in Water and
Structural Changes Induced in the Solvent .................. 586
Appendix I: An Estimate of the Strength of Hydrophilic
Interaction at R = 4.5 Å ................................... 591
Appendix J: Calculated Data on Нø1 Interactions ............... 596
Appendix K: Experimental Evidence for the
Entropy-Enthalpy Compensation .............................. 598
Appendix L: Solutions to Selected Exercises ................... 600
References .................................................... 611
Index ......................................................... 625
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