Surface and Interfacial Forces

Hans-Jürgen Butt studied physics in Hamburg and Göttingen, Germany. Then he went to the Max-Planck-Institute of Biophysics in Frankfurt. After receiving his PhD in 1989 he went as a post-doc to Santa Barbara, California, using the newly developed atomic force microscope. From 1990–95 he spent as a researcher back in Germany at the Max-Planck-Institute for Biophysics. In 1996 he became associate professor for physical chemistry at the University Mainz, three years later full professor at the University of Siegen. Two years later he joined the Max-Planck-Institute of Polymer Research in Mainz and became director for Experimental Physics.Michael Kappl received his PhD thesis from the Max-Planck-Institute of Biophysics in Frankfurt and worked at the University of Mainz and Siegen. Since 2002 he is group leader at the MPIP, working in the fields of surface forces, wetting and characterization of mechanical properties on the micro- and nanoscale.

• Preface xiList of Symbols xiii1 Introduction 12 Experimental Methods 52.1 Surface Forces Apparatus 62.1.1 Mica 82.1.2 Multiple Beam Interferometry 92.1.3 Friction Force Measurements 122.1.4 Surface Modification 132.2 Atomic Force Microscope 132.2.1 Force Measurements with the AFM 142.2.2 AFM Cantilevers 162.2.3 Calibration of the Spring Constant 182.2.4 Microfabricated Tips and Colloidal Probes 212.2.5 Friction Forces 222.2.6 Force Maps 242.2.7 Dynamic Modes 252.3 Optical Tweezers 262.3.1 Calibration 302.3.2 Multiple Traps 322.4 Total Internal Reflection Microscopy 332.5 Magnetic Tweezers 362.6 Summary 402.7 Exercises 413 van der Waals Forces 433.1 van der Waals Forces between Molecules 433.1.1 Coulomb Interaction 433.1.2 Monopole–Dipole Interaction 443.1.3 Dipole–Dipole Interaction 473.1.3.1 Keesom Interaction 483.1.3.2 Debye Interaction 493.1.3.3 London Dispersion Interaction 503.2 The van der Waals Force between Macroscopic Solids 523.2.1 Microscopic or Hamaker Approach 523.2.2 Macroscopic Calculation: Lifshitz Theory 573.2.3 Hamaker Constants 643.2.3.1 Calculation of Hamaker Constants 643.2.3.2 Combining Relations for Hamaker Constants 703.2.3.3 Table of Hamakar Constants 713.2.4 Surface Energy and Hamaker Constant 713.3 The Derjaguin Approximation 783.3.1 The General Equation 783.3.2 van der Waals Forces for Different Geometries 813.4 Retarded van der Waals Forces 823.4.1 Screening of van der Waals Forces in Electrolytes 843.5 Measurement of van der Waals Forces 853.6 The Casimir Force 883.6.1 Casimir Forces between Metal Surfaces 883.6.1.1 The Effect of Temperature 903.6.1.2 Finite Conductivity of Real Metals 903.6.1.3 Surface Roughness 913.6.1.4 Casimir Force for Nontrivial Geometries 923.6.2 Measurements of Casmir Forces 923.6.3 Critical Casimir Force 943.7 Summary 973.8 Exercises 984 Electrostatic Double-Layer Forces 994.1 The Electric Double Layer 994.2 Poisson–Boltzmann Theory of the Diffuse Double Layer 1004.2.1 The Poisson–Boltzmann Equation 1004.2.2 Planar Surfaces 1014.2.3 The Full One-Dimensional Case 1044.2.4 The Electric Double Layer around a Sphere 1064.2.5 The Grahame Equation 1074.2.6 Capacity of the Diffuse Electric Double Layer 1084.3 Beyond Poisson–Boltzmann Theory 1094.3.1 Limitations of the Poisson–Boltzmann Theory 1094.3.2 The Stern Layer 1114.4 The Gibbs Energy of the Electric Double Layer 1124.5 The Electrostatic Double-Layer Force 1144.5.1 General Equations 1154.5.2 Electrostatic Interaction between Two Identical Surfaces 1174.5.3 Electrostatic Interaction between Different Surfaces 1184.6 The DLVO Theory 1204.7 Electrostatic Forces in Nonpolar Media 1234.8 Summary 1284.9 Exercises 1295 Capillary Forces 1315.1 Equation of Young and Laplace 1325.2 Kelvin Equation 1355.2.1 Capillary Condensation 1375.3 Young’s Equation 1385.4 Capillary Forces Calculated with the Circular Approximation 1395.4.1 Capillary Force between a Sphere and a Plane 1405.4.2 Two Different Spheres 1445.4.3 Other Geometries 1465.4.4 Assumptions and Limits 1485.5 Influence of Roughness 1505.6 Kinetics of Capillary Bridge Formation and Rupture 1525.7 Capillary Forces in Immiscible Liquid Mixtures and Other Systems 1555.8 Normal Forces Acting on a Particle at a Liquid Interface 1575.9 Lateral Forces between Particles at a Fluid Interface 1605.10 Summary 1645.11 Exercises 1656 Hydrodynamic Forces 1676.1 Fundamentals of Hydrodynamics 1676.1.1 The Navier–Stokes Equation 1676.1.2 Laminar and Turbulent Flow 1706.1.3 Creeping Flow 1716.2 Hydrodynamic Force between a Solid Sphere and a Plate 1726.2.1 Force in Normal Direction 1726.2.2 Force on a Sphere in Contact with a Plate in Linear Shear Flow 1786.2.3 Motion of a Sphere Parallel to a Wall 1796.3 Hydrodynamic Boundary Condition 1826.4 Gibbs Adsorption Isotherm 1836.5 Hydrodynamic Forces between Fluid Boundaries 1856.6 Summary 1896.7 Exercises 1907 Interfacial Forces between Fluid Interfaces and across Thin Films 1917.1 Overview 1917.2 The Disjoining Pressure 1937.3 Drainage 1947.3.1 Vertical Foam Films 1947.3.2 Horizontal Foam Films 1977.4 Thin Film Balance 1997.5 Interfacial Forces across Foam and Emulsion Films 2027.5.1 Shape of a Liquid Film 2027.5.2 Quasiequilibrium 2037.5.3 Rupture 2077.6 Thin Wetting Films 2087.6.1 Stability of Thin Films 2127.6.2 Rupture of Thin Films 2147.7 Summary 2167.8 Exercises 2178 Contact Mechanics and Adhesion 2198.1 Surface Energy of Solids 2208.1.1 Relation between Surface Energy and Adhesion Energy 2228.1.2 Determination of Surface Energies of Solids 2238.2 Contact Mechanics 2258.2.1 Elastic Contact for a Flat Punch 2268.2.2 Adherence of a Flat Punch (Kendall) 2298.2.3 Elastic Contact of Spheres: Hertz Model 2308.2.4 Adhesion of Spheres: JKR Theory 2328.2.5 Adhesion of Spheres: DMT Theory 2368.2.6 Adhesion of Spheres: Maugis Theory 2398.3 Influence of Surface Roughness 2428.4 Elastocapillarity 2448.4.1 Surface Patterns for Soft Materials 2448.4.2 Drop on deformable surface 2448.4.3 Contact of spheres to soft surfaces 2458.5 Adhesion Force Measurements 2458.6 Summary 2488.7 Exercises 2499 Friction 2519.1 Macroscopic Friction 2529.1.1 Dry Friction 2529.1.1.1 Amontons’ and Coulomb’s Law 2529.1.1.2 Sliding on Ice 2599.1.1.3 Static, Kinetic, and Stick–Slip Friction 2609.1.2 Friction and Adhesion 2629.1.3 Rubber Friction 2639.1.4 Rolling Friction 2699.1.5 Techniques to Measure Friction 2719.2 Lubrication 2729.2.1 Hydrodynamic Lubrication 2739.2.1.1 Elastohydrodynamic Lubrication 2769.2.2 Boundary Lubrication 2799.3 Microscopic Friction: Nanotribology 2809.3.1 Single Asperity Friction 2809.3.2 Atomic Stick–Slip 2829.3.3 Velocity Dependence of Nanoscale Friction 2899.3.4 Superlubricity 2909.3.4.1 Structural Superlubricity 2919.3.4.2 Static Superlubricity 2929.3.4.3 Dynamic Superlubricity 2929.3.4.4 Thermal Superlubricity 2939.3.5 Thin Film Lubrication 2939.4 Summary 2959.5 Exercises 29610 Solvation Forces and Non-DLVO Forces in Water 29710.1 Solvation Forces 29710.1.1 Contact Theorem 29710.1.2 Solvation Forces in Simple Liquids 29810.1.3 Solvation Forces in Liquid Crystals 30210.2 Non-DLVO Forces in an Aqueous Medium 30410.2.1 Hydration Forces 30510.2.2 Hydrophobic Force 30810.2.2.1 The Hydrophobic Effect 30810.2.2.2 Hydrophobic Forces 31010.3 The Interaction between Lipid Bilayers 31610.3.1 Lipids 31610.3.2 The Osmotic Stress Method 31810.3.3 Forces between Lipid Bilayers 32010.3.3.1 Undulation Forces 32110.3.3.2 Protrusion Forces 32310.4 Force between Surfaces with Adsorbed Molecules 32510.5 Summary 32710.6 Exercises 32811 Surface Forces in Polymer Solutions and Melts 32911.1 Properties of Polymers 32911.2 Polymer Solutions 33411.2.1 Ideal Chains 33411.2.2 Real Chains in a Good Solvent 33611.2.3 Stretching Individual Chains 33811.3 Steric Repulsion 34011.4 Polymer-Induced Forces in Solutions 34911.5 Bridging Attraction 35311.6 Depletion and Structural Forces 35711.7 Interfacial Forces in Polymer Melts 35911.8 Summary 36111.9 Exercises 36212 Solutions to Exercises 363Chapter 2 363Chapter 3 364Chapter 4 365Chapter 5 367Chapter 6 370Chapter 7 372Chapter 8 373Chapter 9 374Chapter 10 375Chapter 11 377Bibliography 381Index 431