Molecular Theory of Capillarity

Tracing the history of thought on the molecular origins of surface phenomena, this volume offers a critical and detailed examination and assessment of modern theories.
The opening chapters survey the earliest efforts to recapture these phenomena by using crude mechanical models of liquids as well as subsequent quasi-thermodynamic methods. A discussion of statistical mechanics leads to the application of results in mean-field approximation to some tractable but artificial model systems. More realistic models are portrayed both by computer simulation and by approximation to some portrayed both by computer simulation and by approximations of the precise statistical equations. Emphasis throughout the text is consistently placed on the liquid-gas surface, with a focus on liquid-liquid surfaces in the final two chapters.
Students, teachers, and professionals will find in this volume a comprehensive account of the field: theorists will encounter novel problems to which to apply the basic principles of thermodynamics, and industrial scientists will deem it an invaluable guide to understanding and predicting the properties of the interfacial region. Its extensive cross-referencing effectively assembles many diverse topics and theoretical approaches, making this book indispensable to all those engaged in research into interfaces in fluid-phase equilibria.

Principal symbols
1 MECHANICAL MOLECULAR MODELS
1.1 Introduction
1.2 Molecular mechanics
1.3 Capillary phenomena
1.4 The internal energy of a liquid
1.5 The continuous surface profile
1.6 The mean molecular field
2 THERMODYNAMCIS
2.1 Thermodynamics and kinetic theory
2.2 The thermodynamics of the surface
2.3 Surface functions
2.4 The spherical surface
2.5 Quasi-thermodynamics-a first look
3 THE THEORY OF VAN DER WAALS
3.1 Introduction
3.2 The surface tension
3.3 Independently variable densities
3.4 Gibbs adsorption equation in the van der Waals theory
3.5 Constraints on the range of fluctuations
4 STATISTICAL MECHANICS OF THE LIQUID-GAS SURFACE
4.1 Introduction
4.2 Distribution and correlation functions
4.3 The pressure tensor
4.4 The virial route to the surface tension
4.5 Functionals of the distribution functions
4.6 The surface tension from the direct correlation function
4.7 Equivalence of the two expressions for the surface tension
4.8 The spherical surface
4.9 Density fluctuations and their correlation
4.10 Local thermodynamic functions
5 MODEL FLUIDS IN THE MEAN-FIELD APPROXIMATION
5.1 Introduction: mean-field theory of a homogeneous fluid of attracting hard spheres
5.2 Liquid-gas interface in the model of attracting hard spheres
5.3 Lattice-gas model: one component
5.4 Lattice-gas model: two components
5.5 Penetrable-sphere model: theory
5.6 Penetrable-sphere model: applications
5.7 Penetrable-sphere model: spherical surfaces
6 COMPUTER SIMULATION OF THE LIQUID-GAS SURFACE
6.1 The experimental background
6.2 The methods of computer simulation
6.3 The density profile
6.4 The surface tension
6.5 Further work
7 CALCULATION OF THE DENSITY PROFILE
7.1 Introduction
7.2 Solution of the YBG equation
7.3 Approximations for the direct correlation function
7.4 Modified van der Waals theories
7.5 Perturbation theories
7.6 Surface tensions
8 THREE-PHASE EQUILIBRIUM
8.1 Introduction
8.2 Contact angles and Neumann's triangle
8.3 Spreading and Antonow's rule
8.4 The ay interface
8.5 Phase transitions in interfaces. The Cahn transition
8.6 Three-phrase line and line tension
9 INTERFACES NEAR CRITICAL POINTS
9.1 Introduction: mean-field approximation
9.2 Digression on the Ornstein-Zernike theory of the pair-correlation function
9.3 Digression on critical-point exponents
9.4 Van der Waals theory with non-classical exponents
9.5 Tricritical points
9.6 Non-critical interface near a critical endpoint
9.7 Renormalization-group theory; field-theoretical models
APPENDIX 1 Thermodynamics
APPENDIX 2 Dirac's delta-function
NAME INDEX
SUBJECT INDEX