Friction at the Atomic Level

Written by one of the most distinguished scientists and a pioneer in this field, this monograph represents a stand-alone, concise guide to friction at the atomic level. It brings together hitherto widely-scattered information in one single source, and is the first to explain the nature of friction in terms of atomistic mechanisms. In addition to his detailed description on modeling and simulation, the author stresses experimental approaches like AFM (Atomic Force Microscope) techniques for verification of theory. In this respect the book will benefit the whole nanotribology community, from graduate students who want to get the basics right up to researchers specializing in mechanical engineering, materials science, physics and chemistry.

Autorentext
Motohisa Hirano was born in 1957 in Gamagori City, Aichi, Japan. Following his graduation from the Graduate School of Engineering, Nagoya University, in 1982, he joined Nippon Telegraph and Telephone Public Corporation in the same year. After working for Nippon Telegraph and Telephone Corporation (1985-2003) and serving as a professor at the Faculty of Engineering, Gifu University (2003-2014), he has been serving as a professor at the faculty of Science and Engineering, Hosei University, since 2014.
He obtained doctoral degrees in engineering in 1989, from Nagoya University, and in science in 1998, from the University of Tokyo. Professor Hirano has authored over 200 scientific publications on engineering and science on the atomistics of friction and nanotribology. Laboratory HP: http://hirano-lab.ws.hosei.ac.jp/index\_j.html

Inhalt

Preface xiii

1 Classical Theory and Atomistics 1

1.1 Law of Friction 1

1.2 The Origin of Friction 4

1.3 Atomistics in Tribology 6

2 AtomisticModels 9

2.1 Friction Models 9

2.2 Physical Essence of Mechanical Adiabaticity in Friction 11

3 Atomistic Locking and Friction 15

3.1 Theoretical Preliminaries 15

3.1.1 Model 15

3.1.2 Expression for Adiabatic Potential 17

3.2 Topological Description of Friction 19

3.2.1 Adiabatic Potential 19

3.2.2 Atomic Configurations of Surfaces 19

3.2.2.1 Variant P;; (;;) Case 21

3.2.2.2 Invariant P;; (;;) Case 22

3.2.2.3 Restricted Invariant P;; (;;) Case 22

3.3 A More Realistic Case: A Relaxed Upper Body 22

3.4 Quasi-static Friction of -Iron 24

3.4.1 Case (a) 24

3.4.2 Case (b) 25

4 Atomistic Origin of Friction 29

4.1 Friction Model 29

4.2 Static Friction 31

4.3 Energy Dissipation in Dynamic Friction 32

4.4 Criterion for Friction Transition 35

5 Superlubricity 43

5.1 A State of Vanishing Friction 43

5.2 How Does Friction Become Zero? 44

5.3 NonadiabaticMotion of Atoms 45

5.4 Importance of High Dimensionality 46

6 Atomistic Simulation of Friction 49

6.1 Computer Simulation 49

6.2 Atomic Structure and Electronic States 51

6.2.1 Properties of Atoms 51

6.2.2 Electronic States 53

6.3 Cohesion of Solids 55

6.3.1 Cohesive Forces Between Molecules 55

6.3.2 Cohesive Forces in Solids 58

6.4 Crystal Binding 58

6.4.1 Ionic Crystals 59

6.4.2 Covalent Crystals 60

6.4.3 Metallic Crystals 61

6.4.4 Molecular Crystals 62

6.4.5 Hydrogen-Bonded Crystals 64

6.5 Interatomic Force and Interatomic Potential 66

6.6 Molecular Dynamics Method 68

6.6.1 Equations of Motion of Atoms 68

6.6.2 Numerical Integral 68

6.7 Simple Atomistic Model 69

6.7.1 Friction Model 69

6.7.2 Equation of Motion in Dimensionless Form 70

6.7.3 Friction Diagram 72

6.8 Energy Recurrence in Superlubricity 75

6.8.1 Energy Dissipation 75

6.8.2 Two-DimensionalModel Simulation 76

6.9 Realistic Systems 79

6.9.1 Friction Transition 79

6.9.2 Many-Body Interatomic Potentials 80

6.9.3 Stability of Superlubricity 82

7 Experimental Approach for Atomic Level Friction 85

7.1 Atomic Force Microscopy Techniques 85

7.2 Verification of AtomisticTheory 87

7.2.1 Static Friction Forces 87

7.2.2 Commensurability in Sliding Surfaces 88

8 Summary 99

8.1 Origin of Friction 99

8.2 Controlling Friction 100

A Physical Preliminaries 103

A.1 AnalyticalMechanics 103

A.1.1 Coordinates and Transformation of a Coordinate System 103

A.1.1.1 Cartesian Coordinate System 104

A.1.1.2 Expression of Velocity and Acceleration in Polar Coordinates 104

A.1.1.3 Three-Dimensional Polar Coordinate System 108

A.1.1.4 Cartesian Curvilinear Coordinates 111

A.1.1.5 Generalized Coordinates 113

A.1.1.6 Generalized Momentum and Canonical Conjugate Variable 116

A.1.1.7 Generalized Force 116

A.1.2 Lagrange Equation of Motion and Variational Principle 118

A.1.2.1 Lagrange Equation of Motion 118

A.1.2.2 Application of Lagrange's Equation of Motion 120

A.1.2.3 Variational Principle and EulerLagrange Equation 123

A.1.2.4 Principle of VirtualWork 126

A.1.3 Hamilton's Canonical Equation 129

A.1.3.1 Hamiltonian 129

A.1.3.2 Hamilton's Canonical Equation 132 A.1.3.3 Phase Space and Trajectory of Motion 132</p&gt...