Molecular Theory of Solutions

by Ben-Naim, Arieh

• ISBN13: 9780199299706
• ISBN10: 0199299706
• Format: Paperback
• Copyright: 2006-10-05
• Publisher: Oxford University Press

Summary

This book presents new and updated developments in the molecular theory of mixtures and solutions. It is based on the theory of Kirkwood and Buff which was published more than fifty years ago. This theory has been dormant for almost two decades. It has recently become a very powerful and general tool to analyze, study and understand any type of mixtures from the molecular, or the microscopic point of view. The traditional approach to mixture has been, for many years, based on the study of excess thermodynamic quantities. This provides a kind of global information on the system. The new approach provides information on the local properties of the same system. Thus, the new approach supplements and enriches our information on mixtures and solutions.

Author Biography

Arieh Ben-Naim is a Professor of Physical Chemistry at The Hebrew University, Israel.

Table of Contents

List of Abbreviations	p. xvii
Introduction	p. 1
Notation regarding the microscopic description of the system	p. 1
The fundamental relations between statistical thermodynamics and thermodynamics	p. 3
Fluctuations and stability	p. 9
The classical limit of statistical thermodynamics	p. 12
The ideal gas and small deviation from ideality	p. 16
Suggested references on general thermodynamics and statistical mechanics	p. 20
Molecular distribution functions	p. 21
The singlet distribution function	p. 21
The pair distribution function	p. 28
The pair correlation function	p. 31
Conditional probability and conditional density	p. 33
Some general features of the radial distribution function	p. 35
Theoretical ideal gas	p. 35
Very dilute gas	p. 36
Slightly dense gas	p. 38
Lennard-Jones particles at moderately high densities	p. 40
Molecular distribution functions in the grand canonical ensemble	p. 48
Generalized molecular distribution functions	p. 50
The singlet generalized molecular distribution function	p. 50
Coordination number	p. 51
Binding energy	p. 53
Volume of the Voronoi polyhedron	p. 54
Combination of properties	p. 56
Potential of mean force	p. 56
Molecular distribution functions in mixtures	p. 61
Potential of mean force in mixtures	p. 73
Thermodynamic quantities expressed in terms of molecular distribution functions	p. 76
Average values of pairwise quantities	p. 77
Internal energy	p. 80
The pressure equation	p. 83
The chemical potential	p. 85
Introduction	p. 85
Insertion of one particle into the system	p. 87
Continuous coupling of the binding energy	p. 89
Insertion of a particle at a fixed position: The pseudochemical potential	p. 92
Building up the density of the system	p. 94
Some generalizations	p. 95
First-order expansion of the coupling work	p. 97
The compressibility equation	p. 99
Relations between thermodynamic quantities and generalized molecular distribution functions	p. 105
The Kirk wood-Buff theory of solutions	p. 112
Introduction	p. 112
General derivation of the Kirkwood-Buff theory	p. 114
Two-component systems	p. 120
Inversion of the Kirkwood-Buff theory	p. 124
Three-component systems	p. 127
Dilute system of Sin A and B	p. 130
Application of the KB theory to electrolyte solutions	p. 131
Ideal solutions	p. 136
Ideal-gas mixtures	p. 136
Symmetrical ideal solutions	p. 140
Very similar components: A sufficient condition for SI solutions	p. 141
Similar components: A necessary and sufficient condition for SI solutions	p. 145
Dilute ideal solutions	p. 150
Summary	p. 154
Deviations from ideal solutions	p. 156
Deviations from ideal-gas mixtures	p. 156
Deviations from SI Behavior	p. 158
Deviations from dilute ideal solutions	p. 160
Explicit expressions for the deviations from IG, SI, and DI behavior	p. 164
First-order deviations from ideal-gas mixtures	p. 165
One-dimensional model for mixtures of hard "spheres"	p. 169
The McMillan-Mayer theory of solutions	p. 171
Stability condition and miscibility based on first-order deviations from SI solutions	p. 176
Analysis of the stability condition based on the Kirkwood-Buff theory	p. 183
The temperature dependence of the region of instability: Upper and lower critical solution temperatures	p. 187
Solvation thermodynamics	p. 193
Why do we need solvation thermodynamics?	p. 194
Definition of the solvation process and the corresponding solvation thermodynamics	p. 197
Extracting the thermodynamic quantities of solvation from experimental data	p. 201
Conventional standard Gibbs energy of solution and the solvation Gibbs energy	p. 203
Other thermodynamic quantities of solvation	p. 210
Entropy	p. 210
Enthalpy	p. 212
Volume	p. 213
Further relationships between solvation thermodynamics and thermodynamic data	p. 215
Very dilute solutions of s in /	p. 215
Concentrated solutions	p. 216
Pure liquids	p. 219
Stepwise solvation processes	p. 221
Stepwise coupling of the hard and the soft parts of the potential	p. 222
Stepwise coupling of groups in a molecule	p. 225
Conditional solvation and the pair correlation function	p. 227
Solvation of a molecule having internal rotational degrees of freedom	p. 230
Solvation of completely dissociable solutes	p. 238
Solvation in water: Probing into the structure of water	p. 244
Definition of the structure of water	p. 245
General relations between solvation thermodynamics and the structure of water	p. 248
Isotope effect on solvation Helmholtz energy and structural aspects of aqueous solutions	p. 251
Solvation and solubility of globular proteins	p. 254
Local composition and preferential solvation	p. 262
Introduction	p. 263
Definitions of the local composition and the preferential solvation	p. 265
Preferential solvation in three-component systems	p. 270
Local composition and preferential solvation in two-component systems	p. 276
Local composition and preferential solvation in electrolyte solutions	p. 279
Preferential solvation of biomolecules	p. 281
Some illustrative examples	p. 283
Lennard-Jones particles having the same [epsilon] but different diameter [sigma]	p. 283
Lennard-Jones particles with the same [sigma] but with different [epsilon]	p. 285
The systems of argon-krypton and krypton-xenon	p. 286
Mixtures of water and alcohols	p. 288
Mixtures of Water: 1,2-ethanediol and water-glycerol	p. 290
Mixture of water and acetone	p. 291
Aqueous mixtures of 1-propanol and 2-propanol	p. 292
Appendices	p. 295
A brief summary of some useful thermodynamic relations	p. 297
Functional derivative and functional Taylor expansion	p. 301
The Ornstein-Zernike relation	p. 307
The Percus-Yevick integral equation	p. 312
Numerical solution of the Percus-Yevick equation	p. 316
Local density fluctuations	p. 318
The long-range behavior of the pair correlation function	p. 323
Thermodynamics of mixing and assimilation in ideal-gas systems	p. 333
Mixing and assimilation in systems with interacting particles	p. 339
Delocalization process, communal entropy and assimilation	p. 345
A simplified expression for the derivative of the chemical potential	p. 347
On the first-order deviations from SI solutions	p. 352
Lattice model for ideal and regular solutions	p. 354
Elements of the scaled particle theory	p. 357
Solvation volume of pure components	p. 365
Deviations from SI solutions expressed in terms of [rho Delta subscript AB] and in terms of [Characters not reproducible]	p. 368
References	p. 372
Index	p. 379
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