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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Seitenzahl: 461
Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Chapter 1: Classical Theory and Atomistics
1.1 Law of Friction
1.2 The Origin of Friction
1.3 Atomistics in Tribology
Chapter 2: Atomistic Models
2.1 Friction Models
2.2 Physical Essence of Mechanical Adiabaticity in Friction
Chapter 3: Atomistic Locking and Friction
3.1 Theoretical Preliminaries
3.2 Topological Description of Friction
3.3 A More Realistic Case: A Relaxed Upper Body
3.4 Quasi-static Friction of -Iron
Chapter 4: Atomistic Origin of Friction
4.1 Friction Model
4.2 Static Friction
4.3 Energy Dissipation in Dynamic Friction
4.4 Criterion for Friction Transition
Chapter 5: Superlubricity
5.1 A State of Vanishing Friction
5.2 How Does Friction Become Zero?
5.3 Nonadiabatic Motion of Atoms
5.4 Importance of High Dimensionality
Chapter 6: Atomistic Simulation of Friction
6.1 Computer Simulation
6.2 Atomic Structure and Electronic States
6.3 Cohesion of Solids
6.4 Crystal Binding
6.5 Interatomic Force and Interatomic Potential
6.6 Molecular Dynamics Method
6.7 Simple Atomistic Model
6.8 Energy Recurrence in Superlubricity
6.9 Realistic Systems
Chapter 7: Experimental Approach for Atomic Level Friction
7.1 Atomic Force Microscopy Techniques
7.2 Verification of Atomistic Theory
Chapter 8: Summary
8.1 Origin of Friction
8.2 Controlling Friction
Appendix A: Physical Preliminaries
A.1 Analytical Mechanics
A.2 Fundamentals of Statistical Mechanics
A.3 Classical Mechanics with Vector Analysis
A.4 Vibration and Wave
A.5 Lattice Vibration
Appendix B: Mathematical Supplement
B.1 Trigonometry
B.2 Taylor Expansion
B.3 Complex Exponential Function
B.4 Vectors and Geometry
B.5 Linear Algebra
Appendix C: Data Analysis
C.1 Fundamentals of Description of Physical Data
C.2 Signal Processing
Appendix D: Crystal Structure
D.1 Periodicity of Crystals
D.2 Crystal Structure
D.3 X-ray Diffraction
D.4 Various Crystal Data
Appendix E: The SI (mks) Unit System
E.1 Three Basic Units
E.2 The SI (mks) Unit System
E.3 The cgs System
Appendix F: Practice for Verlet Algorithm
Appendix G: Program Example of Molecular Dynamics for Atomistic Model
G.1 Annealing Program
G.2 Sliding Program
Appendix H: Table of Values
Appendix I: Table of Relative Atomic Weights
References
Afterword
Atomistics of Friction
Mechanical Engineering and Creation of Values
Young Generations
About the Author
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Classical Theory and Atomistics
Figure 1.1 History of tribology.
Figure 1.2 Tomlinson's single-pair atom model for explaining energy dissipation in friction [23].
Chapter 2: Atomistic Models
Figure 2.1 Atomistic friction models. (a) Solid A sliding across solid B. (b) Independent oscillator model (Tomlinson's model). (c) Frenkel–Kontorova model. Black part shows rigid body sliding toward the right [32].
Figure 2.2 The friction system consisting of four atoms numbered by 1, and 1, 2, and 3. All atoms are assumed to interact with each other. The atom 1, nonadiabatically (abruptly) changes its position during sliding. The nonadiabaticity leads to transforming the elastic energy into the vibrational or kinetic energy of the atom 1. The vibrational energy of the atom 1 may be considered to dissipate into the vibrational energies of the other atoms, that is, into the thermal energy. This picture involves the irreversible physical process, that is, the energy dissipation in its natural form.
Figure 2.3 The explanation of Tomlinson's mechanism using the potential surface. The shape of the potential surface depends on . The equilibrium position of the atom 2 is indicated by a circle, and another possible equilibrium position by the dotted circles. The left and the right local minima correspond to the equilibrium position of the atom 2 and that on the atom 3, respectively. In the processes from (a) to (d), continuously varies with . At the process in Figure 2.3(d), sites on the saddle point of the potential surface. When one proceeds further, changes discontinuously from the left minimum to the right one, as shown in (d) and (e). Then, the potential energy difference between two local minima transforms into the kinetic energy of the atom through the nonadiabatic change of the position of the atom 2. The kinetic energy may be consumed into exciting the vibrations of the surrounding atoms, that is, into the thermal energy. The ingredient of this process is an appearance of the discontinuity in the equilibrium positions of atoms.
Figure 2.4 The behaviors of the frictional system corresponding to the Figure shown in Figure 2.3.
Chapter 3: Atomistic Locking and Friction
Figure 3.1 General configuration where the primitive cell is spanned by primitive vectors and of the upper body and contacts a primitive cell spanned by primitive vectors and of the lower body with misfit vector .
Figure 3.2 Schematic illustrations of possible nonvanishing regions where the atoms of the upper body are projected onto a two-dimensional space spanned by and when is variant with . = for , or for , or for , and or or or for , where “” represents rationality and “” irrationality.
Figure 3.4 Schematic illustrations of possible nonvanishing regions where the atoms of the upper body are projected onto a two-dimensional space spanned by and when invariance with is restricted. = for , or for , for , and or for , where “” represents rationality and “” irrationality.
Figure 3.3 Schematic illustrations of possible nonvanishing regions where the atoms of the upper body are projected onto a two-dimensional space spanned by and when is invariant with . = , where “” represents irrationality.
Figure 3.5 Disconnectedness of a pattern made by tiling periodically. (a) is the variant case, and (b) is the invariant case.
Figure 3.6 Schematic phase diagram representing whether friction force is finite or vanishing. Here, the invariant case is denoted as Inv-P, the restricted invariant case as R-Inv-P, and the variant case as V-P. Atomistic locking is denoted as “(A)”, and dynamic locking as “(D)”.
Figure 3.7 Atomic arrangements at the contact interfaces. The upper body with atoms is slid over a stationary lower body with atoms in the direction. is variant with in any direction for . is invariant only with in the direction for .
Figure 3.8 Calculated adiabatic potentials normalized by the contact area. The (0 0 1) plane of an -iron is slid over the same (0 0 1) plane for , and a (1 1 0) plane over a (0 0 1) plane for . Dashed lines represent the unrelaxed case and solid lines the relaxed one.
Chapter 4: Atomistic Origin of Friction
Figure 4.1 The atomistic picture for the origin of the static frictional force, shown for the one-dimensional frictional systems. The upper body is simply expressed by the linear chain where each atom interacts with each other. Each atom of the upper body feels the interaction of attraction from the lower body, which is represented by the potential curve. When we apply an external force to push the linear chain to the right, each atom rises to the mountain part of the interaction potential coherently or cooperatively. The drag against the applied force is the sum of the forces along the chain which each atom feels from the lower body.
Figure 4.2 Surface-roughness model. The contacting solid surfaces are so rough that surface asperities are mechanically locked against the gravitational force. It is necessary to apply an external force to slide one body against the other. This mechanical-locking mechanism concerns the origin of the static frictional force. The weakest point of the surface-roughness model is that basically it fails to explain an energy dissipation, that is, the origin of the dynamic frictional force since the gravitational force is an energy-conserving force.
Figure 4.3 Translational momentum as a function of in (a) and the internal momentum as a function of in (b) for the Frenkel–Kontorova frictional system. The dots stand for their values at every 1000 unit time intervals. The magnitude of of the spring describing the interaction between the upper body and the magnitude describing the adhesion are taken to be equal to 1 and 0.1, respectively. (b) implies that the system is ergodic, and so the host system works as an energy absorber, as seen from (a).
Figure 4.4 The atomistic picture for the origin of the dynamic frictional force, shown for the one-dimensional frictional system. For any given , the total interaction energy where the atoms are assumed to have their equilibrium positions for each is shown. Imagine we push the upper body to slide against the lower body. , the coordinate of the center of mass, begins to rise up a mountain of the potential, and reach the top of the mountain. When moves further to the right, the system lowers the potential energy, and so gains the kinetic energy. This is a process of increasing the kinetic energy of the translational motion. The available phase-space volume of the internal motions becomes much larger than that of the translational motion. The energy transfer from the translational motion to the internal motion occurs irreversibly. Therefore, the excess kinetic energy may be dissipated into the other internal motions in the body due to the mechanism.
Figure 4.5 The atoms sit on the lowest minima () of , when . When becomes a strong limit, the atoms occupy the positions for the lowest minima () of .
Figure 4.6 Topological property of the whole domain obtained by tiling the unit domain repeatedly. Domains are shown according to whether or not Tomlinson's mechanism occurs. is shown by a solid line, the domain for the nonoccurrence of Tomlinson's mechanism by the connected bold solid line, and that for the occurrence of Tomlinson's mechanism by the disconnected bold lines. In moving relatively, the atom can slide by continuously changing its equilibrium position. On the other hand, the atom can slide only by changing its equilibrium position discontinuously between two disconnected domains. The occurrence (or nonoccurrence) of Tomlinson's mechanism is studied by examining the topological property of the tiled unit domains.
Figure 4.7 Topological property of the whole domain, where the atom can take its equilibrium position. These Figure show the cases where the contacting surface of the lower body has the oblique-square crystalline symmetry. The point different from the one-dimensional case is that the sliding path where the atom can slide by continuously changing its equilibrium position depends on the direction of the sliding displacement vector . The atom can slide toward an arbitrary direction by continuously transforming its equilibrium position for the case shown in (a) and (b). In the case shown in (c), the atom can slide continuously in the -direction, but can slide in the -direction by discontinuous transformation. The atom can slide only by discontinuously changing its equilibrium position in any direction for the case shown in (d).
Figure 4.8 Model for friction transition. Symbols are upper body atoms, and symbols are lower body atoms. Symbol is the critical atom.
Figure 4.9 Calculated as a function of Morse potential parameter .
Figure 4.10 Representative distributions . (a) Shows distribution before relaxation. (b), (c), and (d) Show distributions after relaxation when = 10, 20, and 60.
Figure 4.11 Calculated as a function of the Morse potential parameter . Here, s are shown for the critical atoms giving the lowest values, that is, for the critical atoms on the contacting surface of the upper body. s are positive for all of the metals examined. This shows that Tomlinson's mechanism is unlikely to occur in the realistic systems. Tomlinson's mechanism does not occur even for the strong adhesion such as metallic bonding.
Chapter 5: Superlubricity
Figure 5.1 Diagrams representing the concept of a one-dimensional friction model. (a) Friction appears; (b) friction vanishes (superlubricity). The symbols and in the Figure indicate forces received by atoms.
Figure 5.2 Motion of atoms at a contact surface. The white sections represent unstable areas in which atoms cannot stably exist and the shaded sections to stable areas in which they can stably exist. (a) One-dimensional system. (b) and (c) Two- and three-dimensional systems.
Chapter 6: Atomistic Simulation of Friction
Figure 6.1 Atomic model.
Figure 6.2 Number of energy levels. is the principal quantum number and is the azimuthal quantum number.
Figure 6.3 Electron density in the hydrogen molecule.
Figure 6.4 Energy of a hydrogen molecule as a function of interatomic spacing.
Figure 6.5 Binding energy due to a decrease in the energy of the outermost electrons.
Figure 6.6 Schematic view of interatomic potential.
Figure 6.7 Electron configurations in a pair of hydrogen atoms [56].
Figure 6.8 Two dipole harmonic oscillators [56].
Figure 6.9 Structure of ice.
Figure 6.10 Interatomic potential and interatomic force.
Figure 6.11 Frenkel–Kontorova atomistic friction model. is the lattice constant of the upper crystal. is the lattice constant of the lower crystal.
Figure 6.12 Mass center position moving with time ( = 0.2).
Figure 6.13 Friction phase diagram of Frenkel–Kontorova model.
Figure 6.14 Momentum of a solid versus mass center position.
Figure 6.15 State of atoms' momentum in phase space. represents state in which energy dissipates and friction appears for lattice misfit angle . represents state of superlubricity in which energy does not dissipate continuously as a result of recurrence phenomena for .
Figure 6.16 Atomistic model of Si(0 0 1) surface contacting against W(0 1 1) surface for evaluating friction transition.
Figure 6.17 Plots of (solid line) and versus for a range of structures of silicon, where and represent benzene and diamond, respectively [59].
Figure 6.18 Interface model for friction transition in realistic systems of Si(0 0 1) and W(0 1 1). The symbols such as and represent the atoms belonging to the upper Si surface and symbols such as + represent the atoms belonging to the lower W surface.
Figure 6.19 One-dimensional crystal model.
Chapter 7: Experimental Approach for Atomic Level Friction
Figure 7.1 Change in the measured static and dynamic friction forces as a function of the lattice misfit angle between two contacting mica lattices. The misfit angle is approximately when the two specimens are brought into commensurate contact without rotation of the lower specimen [90].
Figure 7.2 Average friction force versus rotation angle of the graphite sample around an axis normal to the sample surface [94].
Figure 7.3 Schematic illustration of the UHV-STM friction measurement system in an ultrahigh vacuum with a base pressure of 10 Pa. The inset shows an atomic illustration of the tip and surface. The measurement system was placed on a vibration isolation air platform, which had a resonance at 1.2 Hz. Clean Si(0 0 1) (n-type, 0.01 cm) was scanned one-dimensionally using a piezoelectric tube scanner against the W(0 1 1) surface on the top of a polycrystalline tungsten tip, while controlling the tunneling gap distance. The scanning was conducted under weak feedback control, that is, at an almost constant-height mode of operation. The silicon sample was transferred to appropriate positions when cleaning the samples and when performing LEED and AES measurements. The tungsten tip faced the silicon sample during friction measurements and faced a microchannel plate during FEM measurements. Since foreign gaseous elements in UHV are likely to stick to fresh tungsten surfaces, we performed friction measurements quickly, within about 10 min, of cleaning the tip. The time limit was determined by examining the degradation of FEM images with time in UHV. [84].
Figure 7.4 Fowler–Nordheim plot. is given in ampere and in volt.
Figure 7.5 (a) FEM image of a clean tungsten tip. (b) Lattice orientation of W(0 1 1). (c) LEED pattern of clean Si(0 0 1). (d) Lattice orientation of Si(0 0 1).
Figure 7.6 (a) Scanning in commensurate contact conditions. This indicates the tunneling current between the tungsten tip and Si(0 0 1), the deflection of the tip, and the scanning voltage applied for a piezoelectric tube scanner as a function of time. (b) Scanning in incommensurate contact conditions. This indicates the tunneling current between the tungsten wire and Si(0 0 1) and the deflection of the wire as a function of time.
Figure 7.7 Friction coefficient of MoS coatings versus environmental pressure.
Appendix A: Physical Preliminaries
Figure A.1 Cartesian coordinate system.
Figure A.2 Expression of planar motion in a polar coordinate.
Figure A.3 Representation of physical quantity in a polar coordinate system.
Figure A.4 Coordinate system in motion.
Figure A.5 Equation of motion in a plane in a polar coordinate system.
Figure A.6 Three-dimensional Cartesian coordinate system and polar coordinate system.
Figure A.7 Three-dimensional polar coordinate system and gravity.
Figure A.8 (a) Area element and (b) volume element.
Figure A.9 Orthogonal curvilinear coordinates.
Figure A.10 Constraint condition.
Figure A.11 Time-dependent constraints.
Figure A.12 Free fall.
Figure A.13 A one-dimensional simple harmonic oscillator.
Figure A.14 Motion of mass in two-dimensional plane.
Figure A.15 Path of motion.
Figure A.16 Stationary point.
Figure A.17 Free falling box.
Figure A.18 Single pendulum.
Figure A.19 Trajectory of a one-dimensional harmonic oscillator in phase space.
Figure A.20 Gas molecules colliding with a wall.
Figure A.21 Phase space representative point of the system.
Figure A.22 Energy of the coupled system.
Figure A.23 Ensemble of a system.
Figure A.24 Trajectory of mass point in motion.
Figure A.25 Moment of force around point O.
Figure A.26 Angular velocity vector.
Figure A.27 Outer product.
Figure A.28 (a) Mode and (b) traveling wave.
Figure A.29 Harmonic oscillation and circular motion.
Figure A.30 Expression of harmonic oscillation with complex number.
Figure A.31 Travelling wave expressed by the form of .
Figure A.32 Travelling wave expressed by the form of .
Figure A.33 Vibration of strings represented by two-variable function .
Figure A.34 External force applied to minute parts of a string.
Figure A.35 Solid line shows the dispersion relation as . Dashed line shows the dispersion relation as .
Figure A.36 A traveling wave with a beat.
Figure A.37 Plane wave: point source and observer.
Figure A.38 Coordinates describing plane waves.
Figure A.39 Plane wave: equation of plane.
Figure A.40 Einstein model and Debye model.
Figure A.41 A one-dimensional crystal model.
Figure A.42 Continuum approximation of a lattice displacement.
Figure A.43 Dispersion relation.
Figure A.44 Wave number of lattice vibration. The wave with a wavelength smaller than interatomic distance , shown by the solid line, gives the same atomic vibration as the wave having the longer wavelength, shown by the dashed line. The wave represented by the solid line conveys no information. Only wavelengths longer than 2 are needed to represent the atomic motion.
Figure A.45 One-dimensional crystals containing two atoms per unit cell. in lattice constant.
Figure A.46 Dispersion relation for a diatomic linear lattice, showing optical and acoustical branches.
Figure A.47 The particle displacements in a diatomic linear lattice having two atoms per primitive basis are illustrated for (a) acoustical and (b) optical waves.
Figure A.48 Dispersion curve of potassium bromide (KBr). TA, transverse acoustical; TO, transverse optical; LA, longitudinal acoustical; LO, longitudinal optical.
Appendix B: Mathematical Supplement
Figure B.1 General angle and sine and cosine.
Figure B.2 Graphs of trigonometric functions such as sine, cosine, and tangent.
Figure B.3 on the complex plane.
Figure B.4 Equation of a line.
Figure B.5 Equation of a plane.
Figure B.6 A plane passing through three points.
Figure B.7 A plane perpendicular to vector
and passing point B.
Figure B.8 Equation of a spherical surface.
Figure B.9 Equation of a tangential plane.
Figure B.10 Interior division of line segments.
Figure B.11 Center of gravity of the triangle.
Appendix D: Crystal Structure
Figure D.1 Lattice vector and two-dimensional lattice.
Figure D.2 The simple cubic crystal structure.
Figure D.3 The face-centered cubic crystal structure.
Figure D.4 Tight stacking of atomic layers.
Figure D.5 The hexagonal closed-packed crystal structure.
Figure D.6 The sodium chloride crystal structure.
Figure D.7 The cesium chloride crystal structure.
Figure D.8 The diamond crystal structure. The primitive basis of the diamond structure has two identical atoms at coordinate (0, 0, 0) and .
Figure D.9 Superposition of scattered waves.
Figure D.10 Plot of function .
Figure D.11 Relationship between lattice plane spacing and reciprocal lattice vector.
Figure D.12 Bragg's diffraction condition.
List of Tables
Chapter 6: Atomistic Simulation of Friction
Table 6.1 Quantum numbers
Table 6.3 Binding energy of crystals
Table 6.2 Distances between neighboring ions and ionic radii in Å
Table 6.4 Heat of fusion and heat of evaporation (kcal/mol)
Table 6.5 Calculation conditions (values are dimensionless)
Table 6.6 Potential parameters of Si, W, and W–Si
Chapter 8: Summary
Table 8.1 Comparison of the present model with other models for friction
Appendix D: Crystal Structure
Table D.1 Ionic crystal
Table D.2 Covalent crystal
Table D.3 Metalic crystal
Table D.4 Molecular crystal (fcc)
Appendix E: The SI (mks) Unit System
Table E.1 SI base units
Table E.2 SI supplementary units
Table E.3 Some SI derived units with special names
Table E.4 Some SI derived units
Table E.5 AccepTable non-SI units
Table E.6 SI prefixes
Table E.7 CGS units with special names
Table E.8 Other units
Friction at the Atomic Level
Atomistic Approaches in Tribology
Motohisa Hirano
Author
Prof. Dr. Motohisa Hirano
Hosei University
Faculty of Science and Engineering
Department of Mechanical Engineering
3-7-2, Kajino, Koganei
Tokyo
Japan
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Preface
How much do we know about friction? We actually know how to utilize friction surprisingly well. Although we are not consciously aware of it in our daily lives, we are very familiar with the ways to deal with it. Whenever we turn the pages of a book, or slide a heavy corrugated carton across the floor, we are employing naturally learned tricks to cope with friction. Even the people in ancient Egypt in 2000 B.C. knew how to use rollers and oil to transport large rocks when constructing pyramids. We also know that friction comes in various degrees; we are very careful when climbing up or down wet steps while going out in the rain; and we learn the hard way when we slip and fall in leather shoes on a sudden snowy day. Friction is extremely sensitive to small changes: One drop of lubricant can dramatically improve the performance of a machine. In professional sports, controlling friction can make the crucial difference between winning and losing. Athletes, who have put their heart and soul into winning, must exercise extreme care in waxing their ski boards, putting for win in golf, and judging the crucial moment to exchange suitable tires during Formula One automobile races.
Friction has always been thought to exist constantly and eternally, but can friction disappear? Recent studies are beginning to explore a world outside our common sense. A theory in which superlubricity with zero friction appears during certain types of contact between surfaces has been proposed, bringing a new vista in research on friction. Experiments are being conducted worldwide, and international workshops on superlubricity are being held in various venues. Experiments to find how losses from friction can be minimized are now being conducted from the viewpoints of atomistic theory.
The author began his research shortly after his graduation when he joined a team that was developing an artificial satellite. Outer space is an extremely severe environment for machines. To complete the mission for the artificial satellite, it was essential that friction be minimized. At that time in 1985, the approach of comet Halley after around 76 years had been a popular topic in the mass media (Next approaching date will be July 29 in 2061). After the end of the astronomical show, a simple and naive question came to mind: “Why does friction occur?” Research into this question has a long history, dating back at least to experiments by Leonardo da Vinci in the fifteenth century Italian Renaissance. The French physicist, Coulomb, and the German, Hertz are best known for their work in electromagnetics and for SI units (LeSystè me International d 'Unitès), but they and other famous physicists also studied friction. However, they found no clear answer to its fundamental cause. In olden times, people thought that friction occurred as the result of rough asperities on the surfaces mechanically locking with each other, but this was when the existence of atoms was not yet known. At present, it is thought that friction is caused by the interactions between atoms that become prominent when two smooth surfaces are brought together. Larger friction is observed when the surfaces are smoother, which may seem opposite to our normal perception. The source of this misunderstanding can be found in elementary textbooks on Newtonian mechanics. In problems in high-school-level mechanics, a surface without friction is described as a smooth surface and a surface with friction, a rough surface. On the other hand, smooth surfaces can cause serious problems in industrial products because they have large friction. Under the vacuum environment of outer space, smooth surfaces can become adhered spontaneously when they come together. It also seems that the question of the static friction coefficient being larger than the dynamic friction coefficient has not been solved. We must search on the atomic level for a clear interpretation of the friction phenomenon.
This book has been written on the basis of atomistics, which proves that all substances are composed of atoms. Atomistics was established after a long history of controversy surrounding the atomic hypothesis, that is, the question of whether the structure of substances is continuous or discontinuous; this controversy began in the Greek era, around 500 B.C. The purpose of this book is to provide the necessary knowledge for young researchers to understand the theory of friction on the atomic level, that is, the atomistics of friction, and to further advance the theory of friction. Just as in most fields of study, an enormous amount of effort is required in order to set up a new research theme in any new field of science for which the intrinsic understanding is still developing, and to achieve a deep understanding of the problem. The resolve to learn and study from an interdisciplinary viewpoint including both basic sciences such as physics, chemistry and biophysics, and applied sciences such as mechanics, electronics, and instrumentation is essential. I hope the young generations will challenge unknown fields. I realize this anew. Basics and motivation are most important in anything. They are essential for achieving one's goals. Whether the field is research or art, attaining the basic skills through continued basic training and having a strong motivation become the focus of one's activities. Athletes focus on the importance of having motivation more and more emphatically in interviews after the games. I believe that motivation is important, and that repetition of motivation, execution, and earning a sense of achievement will lead to progress.
Chapter 1Classical Theory and Atomistics
Many research workers have pursued the friction law. Behind the fruitful achievements, we found enormous amounts of efforts by workers in every kind of research field. Friction research has crossed more than 500 years from its beginning to establish the law of friction, and the long story of the scientific history of friction research is introduced here.
1.1 Law of Friction
Coulomb's friction law1 was established at the end of the eighteenth century [1]. Before that, from the end of the seventeenth century to the middle of the eighteenth century, the basis or groundwork for research had already been done by Guillaume Amontons2 [2]. The very first results in the science of friction were found in the notes and experimental sketches of Leonardo da Vinci.3 In his experimental notes in 1508 [3], da Vinci evaluated the effects of surface roughness on the friction force for stone and wood, and, for the first time, presented the concept of a coefficient of friction.
Coulomb's friction law is simple and sensible, and we can readily obtain it through modern experimentation. This law is easily verified with current experimental techniques, but during the Renaissance era in Italy, it was not easy to carry out experiments with sufficient accuracy to clearly demonstrate the universality of the friction law. For that reason, 300 years of history passed after the beginning of the Italian Renaissance in the fifteenth century before the friction law was established as Coulomb's law.
The progress of industrialization in England between 1750 and 1850, which was later called the Industrial Revolution, brought about a major change in the production activities of human beings in Western society and later on a global scale. Research and development of machines necessary for various manufacturing industries was promoted. Improvement in the performance of lubrication technology was required together with machine design technology and machine processing technology.
The laws of friction can be described as the following empirical laws.
1.
The friction force is proportional to the force acting in the direction perpendicular to the surface of friction regardless of the apparent area of contact.
2.
The dynamic friction force is independent of the speed of sliding motion.
3.
The static friction force is greater than the dynamic friction force.
We can see friction at work in the various mechanical phenomena that surround us, and Coulomb's law can explain most of the nature of the dry friction of solid objects. For mechanical technology that supports industry, it goes without saying that friction is an important problem to be overcome. In the study of mechanical engineering, mechanical design that takes friction and contact phenomena into account ensures the efficiency of machinery. That fact made a detailed understanding of the nature of friction essential and motivated the research for the laws of friction.
Leonardo da Vinci conceived of friction experiments out of his own interest in science and interest in the shipbuilding technology of his day. His experimental records pointed to the material of the objects and surface roughness as factors that affect friction. Those experimental results founded the conjecture that friction is caused by mechanical locking of roughness on the surfaces of the objects. da Vinci also discovered that the friction force of dry solids is proportional to the weight of the object, which is perpendicular to friction force, and is independent of the area of contact far before the establishment of Coulomb's law. That proportionality of friction force and weight is linked to coming up with the concept of a coefficient of friction [4]. da Vinci also considered the difference between sliding friction and rolling friction. He thus revealed facts and laws that were entirely unknown before his research. After his work, the research on the origin of the appearance of friction had to wait for the appearance of an understanding based on atomistic theory and nanotechnology [5] for experimenting at the atomic level. Thus, for the next 200 years, the study of friction did not take the center stage in scientific research. The history of tribology and its related topics are shown in Figure 1.1.
Figure 1.1 History of tribology.
The friction laws were established in the seventeenth and eighteenth centuries in France. At that time, shipbuilding, flower milling, and other industries thrived, and advances in mechanical design made the study of friction and mechanical components such as gears and bearings essential. On the foundation of advanced experimental techniques, the study of friction moved forward from the work of Amontons, Coulomb, and others, resulting in a deeper understanding of the nature of friction and the laws that describe it.
Amontons explained the lawful behavior of friction and the friction laws suggested by da Vinci through meticulous experimentation in 1699, proceeding with research to clarify why the friction laws hold by determining the causes [2]. Among the issues that Amontons tackled was the difficult problem of clarifying whether friction force is proportional to contact area. The common sense of the time was that friction force is proportional to the area of contact. In fact, there were experimental results that the friction force is proportional to the contact surface area when the surface is coated with a film of oil or other lubricant. Philippe de la Hire,4 who lived in the same generation as Amontons, approached that problem with precise experimentation and showed that the friction force is proportional only to weight and is unrelated to the contact surface area in 1706 [6].
As the mechanics of Isaac Newton5 was being systematized in the seventeenth and eighteenth centuries [7], there were attempts to incorporate friction force into the dynamics. At that time, friction force was a new force that was not dealt with in dynamics. Antonie Parent6 solved the problem of an object taking friction force into account as a static equilibrium problem and published a paper in 1704 describing the concepts of the friction angle and friction cone [4]. Using Newton's mechanics as the foundation, Leonhard Euler7 solved the problem of the sliding motion of an object with friction and provided the first theoretical basis in dynamics for the static friction coefficient being larger than the dynamic friction coefficient. The fact that the friction during sliding is often smaller than static friction could be explained by assuming that the asperities on one surface could jump part of the way over the gap between asperities on the other [8]. Euler solved the problem of belts and ropes wrapped around a cylinder as a dynamics problem, showing that very large force is necessary for slippage of wrapped belts or ropes [4].
Charles Augustin de Coulomb was born in Angouleme, France in 1736. He made contributions of particular note in the fields of electromagnetism and mechanics [1]. In electromagnetics, he is well known for deriving the law of static electrical force. In the fields of physics and mechanical engineering, too, he is known for his great achievement in establishing the Coulomb's law of friction. The eighteenth century in France was an era in which culture, economics, and industry reached full maturity. There were strong gains in machine performance and durability, and overcoming friction was a major obstacle for those achievements. Before Coulomb, there were limits to the conditions that could be set in laboratory experiments, but advancement in the rapidly developing mechanical technology made it possible to obtain highly reliable practical data from actual machines. The French Academy of Sciences offered an award for excellent, highly practical research on friction. To meet the expectations, Coulomb submitted excellent research results for various types of friction, including flat surface friction, rope friction, pivot bearing friction, and rolling friction. Coulomb accurately solved the problem of flat surface friction and compiled dry friction experiments and theory to demonstrate the principles behind the friction law.
1.2 The Origin of Friction
The Japanese scientist Norimune Sota8 wrote an interesting article on the scientific history of friction research [4]. The science of friction started in Italy during the Renaissance period in the fifteenth century. Leonardo da Vinci carefully observed and experimented on stones and wood found in daily life and introduced the concept of the friction coefficient. More than 200 years passed without any progress in friction research, until much discussion of the laws regarding friction and the origin of friction started to happen in the seventeenth to eighteenth centuries. The results of research were applied to engineering in the form of lubrication technology during the Industrial Revolution in the eighteenth century, and research by Coulomb and others were summarized as laws of friction.
The principles of how friction happens at contacting surfaces were discussed from the end of the seventeenth century to around the middle of the eighteenth century as mentioned, and Coulomb completed his surface-roughness model. Although surface roughness still sometimes could be an explanation of frictional behavior, the surface-roughness model basically fails to explain energy dissipation because of the gravitational force being the conservative force, as pointed out by John Leslie9 in 1804 [9].
In contrast, John Theophilus Desaguliers10 was aware of the importance of intermolecular force [10]. His idea, which is the root of the molecular theory, is the complete opposite of the popular roughness theory, around the middle of the eighteenth century. After Desaguliers, during the 100 years until the nineteenth century, only one British physicist Samuel Vince11 committed to Desaguliers' idea. The molecular theory considers the atomistic origin of friction to be the interaction of molecular forces at the surfaces where friction appears, as pointed out by James Alfred Ewing12 in 1877 [11]. Accordingly, this theory claims that a smoother surface means that the friction surfaces come together, increasing the interference between surface forces. Desaguliers extracted a few millimeter-sized pieces from a lead sphere, and found in 1725 that strongly pressing such pieces against each other resulted in strong bonding between the pieces [10]. Further observation of the remains after separation showed that only a fraction of the pressed surface had actually been in contact. This finding in 1725 gave rise to the prediction that “friction ultimately increases if surfaces are fully polished to very flat.” This prediction was proved by William Bate Hardy13 in 1919 with improvements in surface processing technologies [12]. He is also well known as the first person to use the term boundary lubrication. He carried out experiments on the friction of glass surfaces and showed that glass surfaces that are polished very carefully such as those in lenses have greater friction than glass with rough surfaces. He also found that tracks of wear caused by friction are initially about 1 m wide, and as friction gradually increases wear, the width increases to about 50 . This experiment refuted the roughness theory and proved that friction is not only a problem of energy loss from the interaction of molecular forces but also is a phenomenon in materials science that accompanies fracture of the surface. The experiment done by Ragnar Holm14 in 1936 demonstrated that the friction between clean surfaces is high under high vacuum and that minute amounts of gas molecule adsorption significantly decrease friction [13]. The modern ultrahigh-vacuum experiment of clean metal surfaces by Buckley showed a correlation with electronic properties such as the number of d-electrons [14]. Strang's experiment [15] done in 1949 proved that measured up-and-down motion of a solid in sliding was very small, and the corresponding work for the up-and-down motion was only 3–7% of the total work consumed by friction. These results showed the work for up-and-down motion stemming from the surface roughness was negligible. Thus, molecular theory gained evidence and became the foundation of the atomistics of friction.
On the other hand, regarding the friction model of actual surfaces, the contact model was refined through the concept of real area of contact proposed by Holm and Mises's material yield theory in plastic deformation [16]. Relations between friction forces and materials properties such as plasticity were investigated in detail in terms of adhesion theory based on shear models at the truly contacting and adhesive element [17–20]. A pair of contact asperities can be approximated as two spheres making elastic contact, that is, Hertzian contact by Hertz by15 [21]. The findings resulted in today's lubrication technologies for head-disk interfaces in contact start-stop-type magnetic information storage disk devices, and lubrication technologies on the small scale [22] will become even more important in miniature precision devices in the future.
1.3 Atomistics in Tribology
The work done by friction has a very different nature from the work done by gravity [4]. Work by gravity happens when objects are moved against gravity, which is always acting on objects. In contrast, friction is the force required to slide objects perpendicular to the direction of gravity. Once sliding motion starts, friction appears as resistance against the sliding motion and results in work by friction. Therefore, friction has the interesting property that it appears when objects start sliding and disappears when objects stop. Even in interatomic forces, no work by friction is generated as long as the combined interatomic force is perpendicular to the sliding direction. Leslie did not agree with Desaguliers' atomistic idea. Ewing stated in 1877, as mentioned, that friction force stems from molecular interaction at contacting surfaces. The British physicist Tomlinson [23] was the first to explain the energy dissipation stemming from molecular interaction at the start of the twentieth century, in 1929. He should have been inspired by the modern atomistics established by the British chemist John Dalton.16
Modern atomistics was established after physics reached the level of atoms in the nineteenth century. Physics started to consider atoms around the mid-nineteenth century, although the original concept of atomistics itself, which is that matter consists of atoms, is thought to have emerged in ancient Greece as particle philosophy. The British physicist–chemist Robert Boyle17 tried to use particle philosophy as the foundation of chemistry, and his attempt to build chemistry upon particle philosophy materialized in the early nineteenth century as Dalton's atomistics. Dalton postulated that objects with sizes that are touched daily, regardless of whether the objects are in gas, liquid, or solid state, consist of a vast number of very minute particles or atoms bound together by force. He thought that there is attraction and repulsion between atoms and that the balance between these opposing forces results in the three states of gas, liquid, and solid. The attraction and repulsion between atoms was later explained on the basis of the concept of electron energy levels and electron states in quantum mechanics. Dalton's atomistics was improved through corrections by Amedeo Carlo Avogadro18 and others. Although there were opponents to atomistics, it explained many experimental findings about the materials properties of gases, Boyle's law, diffusion and viscosity of gases, laws on heat conductivity, and the law of increasing entropy. Atomistics later provided an important foundation for problems regarding the nature of heat. Physicists such as Hermann von Helmholtz19 came to believe that atoms govern thermal motion. Tomlinson's paper states early on that “friction is generally recognized to happen because of interactions between molecules that are very close to each other” [23]. He theoretically investigated the forces that appear in the relative motion of atoms in the field of interatomic interactions at the contact surface, and succeeded in rationally explaining the problem of how friction arises from interatomic interactions at the contact surface, or how mechanical energy dissipates into heat energy due to friction, by introducing the concept of mechanical adiabaticity, thereby opening the door to the atomic theory of friction. Figure 1.2 shows the original model in the paper. It has been considered that two solid bodies in contact and with relative sliding motion, and, for simplicity, a single atom D forming part of a body which is moving in the direction of EF past another body, of which B and C form two atoms in the state of equilibrium characteristic of a solid. Let us suppose that the atom D in moving past B along the line EF approaches B to within a distance of the attraction field but outside the range of the repulsion. The passage of D causes a slight disturbance in the position of B, which moves away from C, supposing C to be fixed. The atom D in proceeding further along EF then withdraws from B, which returns to its original position. It is conceivable that B arrives back to its original position with some appreciable velocity and therefore with some added energy, the aggregate of which might correspond to the loss of energy in friction. How does a loss of energy occur in friction? The energy dissipation mechanisms are described in Chapters 2 and 4.
Figure 1.2 Tomlinson's single-pair atom model for explaining energy dissipation in friction [23].
Tomlinson 1929. Reproduced with permission of Taylor and Francis.
However, very little research on the atomistics of friction followed because of the difficulty in handling the complexity of actual non-well-defined surfaces based on the theory. Friction research has been innovated with recent advances in nanotechnology [5]. Friction research in ideal systems where many factors of friction are identified has been difficult for experimental technology reasons; however, recent measurement technologies, including scanning probe microscopy (SPM) [24–27] and technologies to control very clean well-defined surfaces under ultrahigh vacuum, have enabled direct comparison between theoretical models and experiments [28, 29]. Theory can investigate in detail the fundamental properties of interatomic interactions and the mechanism for the appearance of friction generation using computational experiments on atomistic models [30]. Therefore, ideal friction experiments, where the origin of friction are accurately identified, can be combined with atomic-scale friction simulations, and thus the adequacy of atomic-scale friction theory can now be directly verified. For example, atomic force microscopy (AFM) can accurately measure the friction between the surface of a very sharp tip attached to the end of a cantilever and the surface of a sample using the optical lever method [31], which is a displacement measurement method. The latest experimental devices have enabled the first observations of friction without wear or damage [26]. The adhesion theory cannot be used to investigate such friction without wear, and therefore it was necessary to clarify the origins of friction in terms of atomistics [32].
1
Charles Augustin de Coulomb, 1736–1806, France.
2
Guillaume Amontons, 1633–1705, France.
3
Leonardo da Vinci, 1452–1519, Italy.
4
Philippe de la Hire, 1640–1718, France.
5
Isaac Newton, 1642–1727, United Kingdom.
6
Antonie Parent, 1666–1716, France.
7
Leonhard Euler, 1707–1783, Switzerland.
8
Norimune Sota, 1911–1995, Japan.
9
John Leslie, 1766–1832, United Kingdom.
10
John Theophilus Desaguliers, 1683–1744, United Kingdom.
11
Samuel Vince, 1749–1821, United Kingdom.
12
James Alfred Ewing, 1855–1935, United Kingdom.
13
William Bate Hardy, 1864–1934, United Kingdom.
14
Ragnar Holm, 1879–1970, Germany.
15
Heinrich Rudolf Hertz, 1857–1894, Germany.
16
John Dalton, 1766–1844.
17
Robert Boyle, 1627–1691, United Kingdom.
18
Amedeo Carlo Avogadro, 1776–1856, Italy.
19
Hermann von Helmholtz, 1821–1894, Germany.
Chapter 2Atomistic Models
Several models have been proposed to explain the origin of friction force. Some relate to the mechanical locking of surface asperities and others to the atomistic origin, that is, the molecular interactions between the constituent atoms of solids. A solution to the problems in understanding friction mechanisms in real systems is achieved from the viewpoint of phenomenology by a priori assuming that frictional force exists. The experimental data usually measured in real systems contains many unknown factors: surface roughness and poisoning by various contaminants. It is difficult, therefore, to study the origin of friction force from the experimental data available at present. Recent experimental studies, on the other hand, try to exclude many of the unknown factors by preparing well-defined surfaces. The purity and completion of such surfaces can be detected by current surface analysis techniques such as scanning tunneling microscopy (STM). This chapter considers the atomistic origin of friction force on clean surfaces by discussing the atomistic models.
2.1 Friction Models
Uncovering the principles of energy dissipation in friction has been recognized as an important problem for a long time. For friction phenomena caused by adhesion at the true contact area, which has been observed the most, friction energy has been considered to dissipate by plastic deformation at the true contact area [13, 18, 19]. This is the basic concept of adhesion theory, which postulates that bumps on the surface dig into the other surfaces and cause wear debris because of plastic deformation and the subsequent fracture, and the accumulation of such behavior results in energy dissipation. The principle is the same as the idea that the energy necessary for the deformation of bulk materials at the macroscopic scale is due to the dissipation by motion of dislocations and propagation of cracks in the material. However, friction experiments at the atomic scale mentioned in the previous section revealed new friction phenomena that do not accompany plastic deformation or wear, that is, wear-free friction [26], and thus the problem of energy dissipation in friction regained attention in relation to atomistics.
Figure 2.1 Atomistic friction models. (a) Solid A sliding across solid B. (b) Independent oscillator model (Tomlinson's model). (c) Frenkel–Kontorova model. Black part shows rigid body sliding toward the right [32].
McClelland 1989. Reproduced with permission of Springer.
McClelland [32] built an atomistic model in which infinite planes slide against each other to investigate the problem of energy dissipation in a wear-free friction model (Figure 2.1a). Atoms of an upper body do not interact with each other in the independent oscillator model in Figure 2.1b, and so the model is fundamentally the same as Tomlinson's model (Figure 1.2). Figure 2.1
