Tribology on the small scale

A bottom up approach to friction, lubrication, and wear

C. Mathew Mate Hitachi San Jose Research Center

OXFORD UNIVERSITY PRESS

CONTENTS

Introduction 1 1.1 Why is it called tribology? 2 1.2 Economic and technological importance of tribology 3

1.2.1 Some tribology success stories 4 1.2.1.1 Reducing automotive friction 4 1.2.1.2 MEMS and solving adhesion in Digital

Micro-mirror Devices 5 1.2.1.3 Slider-disk interfaces in disk drives 7

1.3 A brief history of modern tribology 10 1.3.1 Scientific advances enabling nanoscale tribology 12 1.3.2 Breakthrough technologies relying on tribology

at the small scale 14 1.3.2.1 Nanoimprinting 16 1.3.2.2 IBM's millipede for high density storage 18 1.3.2.3 Nanotechnology 19

1.4 References 20

Characterizing surface roughness 24 2.1 Types of surface roughness 24 2.2 Roughness parameters 26

2.2.1 Variations in Z-height 26 2.2.2 Asperity summits roughness parameters 28

2.3 Surface height distributions 29 2.4 Measuring surface roughness 30

2.4.1 Atomic force microscopy (AFM) 30 2.4.2 Example: Disk surfaces in disk drives 33

2.5 References 37

Mechanical properties of solids and real area of contact 39 3.1 Atomic origins of deformation 39 3.2 Elastic deformation 43

3.2.1 Basic relations 43 3.2.2 Elastic deformation of a single asperity 44

3.2.2.1 Approximating a single asperity contact 44 3.2.2.2 Elastic contact area for a sphere on a flat 45

3.2.2.2.1 Example: Spherical steel particle sandwiched between two flat surfaces 46

V U l CONTENTS

3.3 Plastic deformation 48 3.3.1 Basic relations 48 3.3.2 Hardness 49

3.4 Real area of contact 50 3.4.1 Greenwood and Williamson model 51

3.4.1.1 Example: TiN contacts 53 3.4.1.2 Real area of contact using the

Greenwood and Williamson model 54 3.4.1.2.1 Example: Recording head on a laser

textured disk surface 55 3.5 Inelastic impacts 59 3.6 References 61

Friction 63 4.1 Amontons' and Coulomb's laws of friction 63 4.2 Adhesion and plowing in friction 66

4.2.1 Adhesive friction 66 4.2.2 Plowing friction 68 4.2.3 Work hardening 70 4.2.4 Junction growth 70

4.3 Static friction 72 4.3.1 Stick-slip 74

4.3.1.1 Velocity-controlled stick-slip 75 4.3.1.2 Time-controlled stick-slip 77 4.3.1.3 Displacement-controlled stick-slip 78

4.4 References 81

Surface energy and capillary pressure 82 5.1 Liquid surface tension 82 5.2 Capillary pressure 85

5.2.1 Capillary pressure in confined places 87 5.2.2 The Kelvin equation and capillary condensation 90

5.2.2.1 Example: Capillary condensation of water in a nanosized pore 91

5.2.2.2 Example: Capillary condensation of an organic vapor at a sphere-on-flat geometry 91

5.3 Interfacial energy and work of adhesion 92 5.4 Surface Energy of Solids 93

5.4.1 Why solids are not like liquids 93 5.4.2 Experimental determination of a solid's

surface energy 95 5.4.2.1 Contact angles 96

5.4.2.1.1 Estimating interfacial energies 97 5.4.2.1.2 Zisman method for estimating surface

energy for a solid 98 5.4.2.1.3 Types of wetting 101

CONTENTS ix

5.4.2.1.4 Contact angle measurements 101 5.4.2.1.5 Contact angle hysteresis 103

5.4.3 Adhesion hysteresis 104 5.5 References 110

Surface forces derived from surface energies 113 6.1 The Derjaguin approximation 113 6.2 Dry environment 114

6.2.1 Force between a sphere and a flat 114 6.2.1.1 Example: Adhesion force between two

polystyrene spheres 115 6.2.1.2 Example: Adhesion force between a

polystyrene sphere and a PTFE Flat 115 6.2.1.3 Example: Adhesion force for an atomically

sharp asperity 116 6.2.2 Adhesion-induced deformation at a sphere-on-flat

contact 117 6.2.2.1 The Johnson-Kendall-Roberts (JKR) theory 117 6.2.2.2 The Derjaguin-Muller-Toporov (DMT)

theory 121 6.2.2.3 Adhesion deformation in nanoscale contacts 121

6.3 Wet environment 122 6.3.1 Force for a sphere-on-flat in a wet environment 122

6.3.1.1 Example: Lubricant meniscus force on an AFM tip 123

6.3.1.2 Solid-solid adhesion in the presence of a liquid meniscus 125

6.3.2 Water menisci in sand 126 6.3.3 Meniscus force for different wetting regimes at

contacting interfaces 128 6.3.3.1 Toe dipping regime 128

6.3.3.1.1 Example: Toe dipping adhesion with exponential distribution of summit heights 129

6.3.3.2 Pillbox and flooded regimes 131 6.3.3.3 Immersed regime 132

6.3.4 Example: Liquid adhesion of a microfabricated cantilever beam 133

6.4 References 135

Physical origins of surface forces 137 7.1 Normal force sign convention 137 7.2 Repulsive atomic potentials 138 7.3 Van der Waals forces 139

7.3.1 Van der Waals forces between molecules 139 7.3.1.1 Retardation effects for dispersion forces 142

CONTENTS

7.3.2 Van der Waals forces between macroscopic objects 142 7.3.2.1 Molecule-flat surface interaction 142 7.3.2.2 Flat-Flat interaction 144 7.3.2.3 Sphere-flat interaction 145

7.3.3 The Hamaker constant 145 7.3.3.1 Determining Hamaker constants from

Lifshitz's theory 146 7.3.3.2 Example: Van der Waals force on a polystyrene

sphere above a Teflon flat 151 7.3.4 Surface energies arising from van der Waals interactions 152 7.3.5 Van der Waals adhesive pressure 153 7.3.6 Van der Waals interaction between contacting

rough surfaces 154 7.3.6.1 Example: Stuck microcantilevers 156

7.3.7 Example: Gecko adhesion 158 7.3.8 Van der Waals contribution to the disjoining

pressure of a liquid film 160 7.4 Liquid-mediated forces between solids 162

7.4.1 Solvation forces 162 7.4.1.1 Example: Squalane between smooth

mica surfaces 164 7.4.1.2 Oscillatory solvation forces at sharp

AFM contacts 166 7.4.2 Forces in aqueous medium 167

7.4.2.1 Electrostatic double-layer force 167 7.4.2.2 Hydration repulsion and hydrophobic

attraction 169 7.5 Contact electrification 171

7.5.1 Mechanisms of contact electrification 172 7.5.1.1 Conductor-conductor contact 172

7.5.1.1.1 Example: Recording head slider flying over a disk in a disk drive 175

7.5.1.2 Metal-insulator and insulator-insulator Contacts 177

7.5.2 AFM studies of contact electrification 179 7.6 References 181

Measuring surface forces 186 8.1 Surface force apparatus 188 8.2 Atomic force microscope 192 8.3 Examples of forces acting on AFM tips 195

8.3.1 Van der Waals forces under vacuum conditions 195 8.3.2 Capillary condensation of contaminants and

water vapor 197

CONTENTS XI

8.3.3 Bonded and unbonded perfluoropolyether polymer films 200

8.3.4 Electrostatic double-layer force 202 8.4 References 204

Lubrication 207 9.1 Lubrication regimes 207 9.2 Viscosity 209

9.2.1 Definition and units 209 9.2.2 Non-Newtonian behavior and shear degradation 211 9.2.3 Temperature dependence 214

9.3 Fluid film flow in confined geometries 214 9.4 Slippage at liquid-solid interfaces 216

9.4.1 Definition of slip length 217 9.4.2 Measuring slip at liquid-solid interfaces 218

9.4.2.1 Pressure drop versus flow rate method 218 9.4.2.2 Drainage versus viscous force 219

9.4.3 Mechanisms for slip at liquid-solid interfaces 220 9.4.3.1 Molecular slip 220

9.4.3.1.1 Molecular slip at low energy surfaces 220

9.4.3.1.2 Slippage of polymers melts 222 9.4.3.2 Apparent slip 222

9.4.4 Example: Shear stress in the presence of slip 225 9.4.5 Why does the no-slip boundary condition work

so well? 225 9.5 Fluid film lubrication 226

9.5.1 Hydrodynamic lubrication 228 9.5.1.1 Inclined plane bearing 229 9.5.1.2 Rayleigh step bearing 229 9.5.1.3 Journal bearings 230

9.5.2 Gas bearings 232 9.5.2.1 Slip flow in gas bearings 234

9.5.3 Elastohydrodynamic lubrication 235 9.5.3.1 Pressure dependence of viscosity 235 9.5.3.2 Pressure-induced elastic deformation 236 9.5.3.3 Example: Minimum film thickness

between sliding gear teeth 238 9.5.3.4 Experimental measurements of

elastohydrodynamic lubrication 239 9.6 Important physical and chemical properties of lubricants 241

9.6.1 Surface tension 241 9.6.2 Thermal properties 242

9.7 References 243

CONTENTS

10 Lubrication in tight spots 246 10.1 Confined liquids 246 10.2 Boundary lubrication 255

10.2.1 Molecular mechanisms of boundary lubrication 256 10.2.2 Molecularly thin liquid boundary lubricant layers 260

10.2.2.1 Example of the importance of end-groups in a liquid lubricant film 262

10.3 Capillary and disjoining pressures 265 10.3.1 Disjoining pressure 265 10.3.2 Distribution of a liquid film around a pore opening 267

10.3.2.1 Example: Measurement of the disjoining pressure of a perfluoropolyether lubricant 269

10.3.3 Lubricant distribution between contacting surfaces 270 10.3.4 Meniscus force 272

10.3.4.1 Example: Stiction of a recording head slider 272 10.3.4.2 Calculating meniscus force 273

10.3.4.2.1 Example: Calculation of stiction force of disk drive sliders in the pillbox regime 275

10.3.4.2.2 Padded or stiction-free slider 276 10.3.5 Liquid menisci at high speeds 278

10.4 References 279

11 Atomistic origins of friction 284 11.1 Simple models for adhesive friction 284 11.2 Atomistic models for static friction 286

11.2.1 Prenkel-Kontorova model 287 11.2.1.1 Experimental realizations of ultra-low friction

in incommensurate sliding systems 289 11.2.2 Tomlinson model 290

11.2.2.1 Example: An AFM tip sliding across an NaCl crystal at ultra-low loads 291

11.2.3 Molecular dynamic simulations 295 11.2.4 Example: Cold welding 295 11.2.5 Why static friction occurs in real-life situations 295

11.3 Atomic origins of kinetic friction 297 11.3.1 Sliding isolated molecules and monolayers across

surfaces 297 11.3.2 Quartz crystal microbalance 299

11.3.2.1 Example: Xe on Ag( l l l ) 300 11.3.3 Movement of a liquid film on a surface with the

blow-off technique 301 11.3.3.1 Example: Wind-driven flow of perfluoropolyether

lubricants on silicon wafers 302

CONTENTS хш

12

11.3.4 Pinning of an absorbed layer 11.4 References

Wear 12.1 Simple model for sliding wear 12.2 Major influences on wear rates

12.2.1 Wear maps 12.3 Mechanisms of wear

12.3.1 Wear from plastic deformation 12.3.2 Adhesive wear

12.3.2.1 Example: An atomic level simulation of adhesive wear

12.3.3 Abrasive wear 12.3.4 Oxidative wear

12.3.4.1 Metals 12.3.4.2 Carbon overcoats 12.3.4.3 Ceramics

12.4 Plasticity at the nanoscale 12.5 References

Index

307 308

313 314 317 318 319 319 320

321 321 325 325 326 326 327 329 331