Molecular Theory of Capillarity

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