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.
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
1. Classical theory of friction
1.1 Law of friction
1.2 Surface roughness model
1.3 Cohesive energy and adhesion model
1.4 Mechanical adiabaticity of atomic motion and energy dissipation in friction
2. Atomistic model of friction
2.1 Single atom model: Tomlinson model
2.2 Many atom model: Frenkel-Kontorova model
2.3 Realistic model and interatomic potentials
3. Topological description of friction -static and dynamic friction-
3.1 Theoretical preliminaries
3.2 The case of unrelaxed upper body
3.3 A more realistic case: A relaxed upper body
3.4 Friction transition and Tomlinson model
4. Atomistic origin of friction
4.1 Friction model
4.2 Static friction
4.3 Dynamic friction and energy dissipation
5. Superlubricity: a state of vanishing friction
5.1 Adiabatic motion of atoms and atomic arrangements at surfaces
5.2 Importance of high dimensionality
5.3 Energy recurrence phenomena
6. Friction diagram
6.1 Friction diagram of Frenkel-Kontorova model
6.4 Atomic-scale sliding friction of realistic model
7. Experimental approach for atomic-scale friction
7.1 Atomic force microscopy techniques for measuring friction
7.2 Verification of atomistic theory of friction by atomic force microscopy
Appendix A. Adiabatic theorem
Appendix B. Calculation of static friction force
Appendix C. Molecular dynamics
Appendix D. Chaos and atomistic friction
Appendix E. Lattice vibration
Classical 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 . 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 . 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 , 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 . 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  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 . 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 .
As the mechanics of Isaac Newton5 was being systematized in the seventeenth and eighteenth centuries , 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 . 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 . 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 .
Charles Augustin de Coulomb was born in Angouleme, France in 1736. He made contributions of particular note in the fields of electromagnetism and mechanics . 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 . 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...