Molecular Theory of Solutions

Molecular Theory of Solutions

by Arieh Ben-Naim
     
 

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

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Overview

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.

Product Details

ISBN-13:
9780199299706
Publisher:
Oxford University Press
Publication date:
10/05/2006
Pages:
400
Product dimensions:
9.60(w) x 6.70(h) x 0.70(d)

Table of Contents


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

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