Contents. Preface XI Symbols and Abbreviations XIII. 1 Introduction 1

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1 V Contents Preface XI Symbols and Abbreviations XIII 1 Introduction 1 2 Van der Waals Forces Van der Waals Forces Between Molecules Coulomb Interaction Monopole Dipole Interaction Dipole Dipole Interaction Keesom Interaction Debye Interaction London Dispersion Interaction The Van der Waals Force Between Macroscopic Solids Microscopic or Hamaker Approach Macroscopic Calculation: Lifshitz Theory Combining Relations for Hamaker Constants Surface Energy and Hamaker Constant The Derjaguin Approximation The General Equation Van der Waals Forces for Different Geometries Retarded Van der Waals Forces Screening of Van der Waals Forces in Electrolytes Measurement of Van der Waals Forces The Casimir Force Casimir Forces Between Metal Surfaces Critical Casimir Force Summary Exercises 53 Surface and Interfacial Forces. Hans-Jürgen Butt and Michael Kappl Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

2 VI Contents 3 Experimental Methods Surface Forces Apparatus Mica Multiple Beam Interferometry Friction Force Measurements Surface Modification Atomic Force Microscope Force Measurements with the AFM AFM Cantilevers Calibration of the Spring Constant Microfabricated Tips and Colloidal Probes Friction Forces Force Maps Dynamic Modes Optical Tweezers Calibration Multiple Traps Total Internal Reflection Microscopy Magnetic Tweezers Summary Exercises 92 4 Electrostatic Double-Layer Forces The Electric Double Layer Poisson Boltzmann Theory of the Diffuse Double Layer The Poisson Boltzmann Equation Planar Surfaces The Full One-Dimensional Case The Electric Double-layer Around a Sphere The Grahame Equation Capacity of the Diffuse Electric Double Layer Beyond Poisson Boltzmann Theory Limitations of the Poisson Boltzmann Theory The Stern Layer The Gibbs Energy of the Electric Double Layer The Electrostatic Double-Layer Force General Equations Electrostatic Interaction Between Two Identical Surfaces Electrostatic Interaction Between Different Surfaces The DLVO Theory Electrostatic Forces in Nonpolar Media Summary Exercises 125

3 Contents VII 5 Capillary Forces Equation of Young and Laplace Kelvin Equation and Capillary Condensation Capillary Condensation The Youngs Equation Capillary Forces Calculated with the Circular Approximation Capillary Force Between a Sphere and a Plane Two Different Spheres Other Geometries Assumptions and Limits Influence of Roughness Kinetics of Capillary Bridge Formation and Rupture Capillary Forces in Immiscible liquid Mixtures and Other Systems Lateral Forces Between Particles at a Fluid Interface Summary Exercises Hydrodynamic Forces Fundamentals of Hydrodynamics The Navier Stokes Equation Laminar and Turbulent Flow Creeping Flow Hydrodynamic Force between a Solid Sphere and a Plate Force in Normal Direction Force on a Sphere in Contact with a Plate in Linear Shear Flow Motion of a Sphere Parallel to a Wall Hydrodynamic Boundary Condition Gibbs Adsorption Isotherm Hydrodynamic Forces Between Fluid Boundaries Summary Exercises Interfacial Forces Between Fluid Interfaces and Across Thin Films Overview The Disjoining Pressure Drainage Vertical Foam Films Horizontal Foam Films Thin Film Balance Interfacial Forces Across Foam and Emulsion Films Shape of a Liquid Film Quasiequilibrium Rupture Thin Wetting Films Stability of Thin Films 212

4 VIII Contents Rupture of Thin Films Summary Exercises Contact Mechanics and Adhesion Surface Energy of Solids Relation Between Surface Energy and Adhesion Energy Determination of Surface Energies of Solids Contact Mechanics Elastic Contact for a Flat Punch Adherence of a Flat Punch (Kendall) Elastic Contact of Spheres: Hertz, Model Adhesion of Spheres: JKR Theory Adhesion of Spheres: DMT Theory Adhesion of Spheres: Maugis Theory Influence of Surface Roughness Adhesion Force Measurements Summary Exercises Friction Macroscopic Friction Dry Friction Amontons and Coulombs Law Sliding on Ice Static, Kinetic, and Stick Slip Friction Rolling Friction Friction and Adhesion Techniques to Measure Friction Lubrication Hydrodynamic Lubrication Elastohydrodynamic Lubrication Boundary Lubrication Microscopic Friction: Nanotribology Single Asperity Friction Atomic Stick Slip Velocity Dependence of Nanoscale Friction Superlubricity Thin Film Lubrication Summary Exercises Solvation Forces and Non-DLVO Forces in Water Solvation Forces Contact Theorem 294

5 Contents IX Solvation Forces in Simple Liquids Solvation Forces in Liquid Crystals Non-DLVO Forces in an Aqueous Medium Hydration Forces Hydrophobic Force The Hydrophobic Effect Hydrophobic Forces The Interaction Between Lipid Bilayers Lipids The Osmotic Stress Method Forces Between Lipid Bilayers Force Between Surfaces with Adsorbed Molecules Summary Exercises Surface Forces in Polymer Solutions and Melts Properties of Polymers Polymer Solutions Ideal Chains Real Chains in a Good Solvent Stretching Individual Chains Steric Repulsion Polymer-Induced Forces in Solutions Bridging Attraction Depletion and Structural Forces Interfacial Forces in Polymer Melts Summary Exercises Solutions to Exercises 363 Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter References 381 Index 417

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