Tribology on the Small Scale: A Modern Textbook on Friction, Lubrication, and Wear

Carpick - Mate - Tribology at the small scale

In recent decades, tribology field has seen a great interest in friction and wear processes occurring at the micro- and nanoscale. This interest has led to the development of a new branch of tribology focusing on the small scale phenomena – nanotribology. With the development of this field, it became clear that the mysteries of lubrication, friction and wear at the macroscopic level can be studied via the processes at micro and nanoscale. Recently, a textbook devoted to tribology at the nanoscale was published: Tribology on the Small Scale: A Modern Textbook on Friction, Lubrication, and Wear. The book is written by Dr. Mathew Mate – a surface scientist and physicist from industry and Professor Robert Carpick – a physicist and (nano) tribologist – two well-known scientists in the field of tribology. The authors focus on micro- and nanoscale phenomena, and link the processes to the macroscopic tribological behavior. The new book is actually the second edition of a book that was written just over ten years ago by Mathew Mate (Tribology on the Small ScaleA Bottom Up Approach to Friction, Lubrication, and Wear). All the chapters have been extensively revised and updated with this new edition.

The book combines in one place the information that is necessary for a researcher or an engineer working on tribological problems at small scales, or when the small scale phenomena drive the macroscopic behavior. The textbook contains the theory, but also practical examples relevant to the field of tribology. On top of it, the book contains a valuable list of references for further details and a list of problems for practicing. The book can form an initial basis for those interested in research into atomic and molecular scale tribology.

The book is opened by the Introduction chapter – an overview of tribology science, its economic and technological importance, its history and perspectives. The authors discuss in detail successful application of tribology findings in reducing friction in automotive industry, solution of sticking issues in microelectromechanical systems (MEMS), improvements in hard disk drive devices. The chapter makes sure that the reader gets enthused with the topic of the book.

Since the 1950s it was recognized that the surface roughness plays a key role in friction, adhesion and wear phenomena. It is one of the main ingredients in all of the contact models dealing with the contact of rough surfaces, thus one cannot underestimate the importance of this topic for tribologists. The Surface Roughness chapter describes methods to measure the surface roughness, but also various ways to characterize the surfaces. The measurement methods include optical, electron microscopy, atomic force microscopy, contact profilometry and several other methods. The possibilities and the limitations of the methods are discussed in the chapter in detail. Besides the measurement techniques, surface roughness characterization is of the important topics for researchers and engineers dealing with tribology in industry. Various surface roughness parameters are described in the chapter, including  R_a, R_q and the Power Spectrum Density. Self-affine fractal surfaces are also discussed.

Figure 2.5. Roughness at different scales, [1].

The chapter Mechanical Properties of Solids and Real Area of Contact discusses the origin of deformations taking place in contacting bodies, covers elastic and plastic deformation regimes and introduces the concept of the real contact area – one of the most important yet debated concepts in tribology. The last part of the chapter is devoted to the contact mechanics of rough surfaces where the famous Greenwood and Williamson and Persson contact models for rough surfaces are introduced. These models allow one to link the surface roughness, the mechanical properties of the solids and the real area of contact together.


Friction is the source of energy losses in many mechanical components, and given the recently discussed impact of friction on the climate change, this area of tribological research has never been more important. The chapter Friction introduces the reader to the topic, covers the classical friction laws and classical views on the origins of friction. Discussion of the three classical laws of friction by Amonton and Coulomb opens the chapter and familiarizes the reader with the concept of friction coefficient and the factors that impact this parameter. The difference between the kinetic and static friction coefficients is explained from the perspective of atoms and molecules. Here a clear distinction is made between the dry and lubricated friction as they have different origins. The two primary mechanisms of dry friction are presented: adhesive and plowing.

Surface forces become significant at the nanoscale and Surface Energy and Capillary Pressure chapter covers the impact of these phenomena on friction and adhesion. It starts with the definitions of the surface energy, interfacial energy, surface tension, work of adhesion and capillary pressure. This part of the book also answers the question of why solids are not like liquids and how one could obtain (approximately) the surface energies of solids via contact angle measurements. The last part of the chapter is focused on the adhesion hysteresis and its mechanical and chemical origins.

Surface energies give rise to the surface forces. The chapter Surface Forces Derived from Surface Energies focuses on various theories relating these quantities in dry and wet environments. A typical contact of a sphere on flat is considered, and Derjaguin-Müller-Toporov as well as Johnson-Kendal-Roberts theories are presented and discussed. The second half of the chapter deals with capillary pressure and its impact on various natural phenomena. This includes the strength of sand castles, the mystery of Egyptians pouring water on sand during transport of heavy monuments in the desert and the ability of ordinary house flies to walk on ceilings.

Egyptians pouring water
Figure 6.12. Wall painting from the tomb of Djehutihotep from 1880 BC depicting a colossal statue being dragged across the desert by 172 men (Newberry 1895). Standing on the front edge of the sled is a man pouring a liquid in front of the sled, presumably a lubricant that reduces the friction forces on the bottom sled.

The chapter Physical Origins of Surface Forces considers the interactions of atoms. These interactions include van der Waals forces (orientation, induction and dispersion forces), liquid mediated forces between solids (solvation forces, electrostatic double-layer, hydration repulsion, hydrophobic attraction) and forces rising due to contact electrification and electrostatics. The origins of the forces are discussed in detail and the calculation examples are given for various cases, including the sphere on flat macroscopic case. The Hamaker constants and adhesion calculations using Hamaker constants are considered. The theories of contact electrification are presented and discussed.

Comparison of molecular binding engeries
Figure 7.1. Comparison of molecular binding engeries, [1]

Since surface forces play an important role in the tribological contacts, these forces need to be measured. The Measuring Surface Forces chapter covers the basic concept of measuring these forces using a force-displacement approach. The method allows to measure both normal and tangential forces in a similar fashion. The Surface Force Apparatus (SFA) and Atomic Force Microscopy (AFM) techniques are discussed in detail starting with principles of operation and design. The tips and tricks in measuring using these two most popular devices are listed. The modes of AFM operation, as well as the examples of AFM measurements are described. The last part of the chapter illustrates the measurement of various forces using AFM, such as van der Waals, short-range, capillary and frictional forces to name a few.

The lubricants have been used for friction reduction since ages. The Lubrication chapter covers this classical tribological topic. In the first part of the chapter, the basic lubrication concepts are considered: lubrication regimes, the Stribeck curve, types of lubrication. Viscosity and shear-thinning and its impact on lubrication are considered as well. A large part of the chapter is devoted to the slip of lubricants near the solid walls. Finally, several types of bearings are discussed.


The chapter Lubrication in the Tight Spots concentrates on the more recent concepts in the lubrication theory. When the space between the sliding surfaces becomes very small – in the range of several molecular layers – behavior of the lubricants changes. In particular, three scenarios are considered: confined liquids, boundary lubrication and presence of capillary and disjoining pressures. Confined liquids exhibit transition of properties from that of bulk to enhanced viscosity and solid-like liquid. As discussed in the chapter, these transitions occur due to ordering of the liquid molecules and lead to increase of the viscosity up to 10^6 times. With respect to boundary lubrication mechanisms, the origin of this lubrication regime is considered from the molecular point of view. In addition, the impact of anti-wear additives and the mechanisms of their function are covered. In the last section of the chapter, the rise of  a lubricant menisci due to capillary forces is considered. The balance of the capillary and disjoining pressures provides the equilibrium, and lays a way of calculating the radius of curvature of the menisci.

The Atomistic Origins of Friction considers the mechanisms of energy dissipation leading to friction at the atomic scale. Various friction models are considered: cobblestone, Frenkel-Kontorova, Prandtl-Tomlinson models. These models can be used to describe frictional contacts at the atomic scale. Frenkel-Kontorova model, for example, predicted the existence of frictionless sliding, which is called superlubricity. The state of superlubricity can only be achieved if there is no wear, no chemical reactions and no cold-welding, and consequently, cannot be achieved in industrial settings. In the chapter, several examples of superlubricity are covered. Additionally several friction mechanisms are discussed: phononic and electronic friction.

Tribology at the small scale
Figure 12.12 Schematic for atomic wear of Si tip and Diamond substrate, reproduced with permission from: Imaging and Understanding Atomic-Scale Adhesion and Wear: Quantitative investigations Using in situ TEM, Tevis Jacobs, PhD Thesis, pg. 151.

The closing chapter of the book is devoted to Wear. It is opened with the definition of the term and with several examples of wear consequences: from catastrophic failures to the technology used to polish silicon wafers down to a roughness of a few angstroms in semiconductor industry. It was identified that there are more than 182 equations to model wear, however, most of them are empirical. One of the most common models is Archard’s model. The model is derived in the chapter. Further in this section of the book various mechanisms of wear are covered: delamination wear, wear from plastic deformation, adhesiveabrasive and oxidative wear processes are described. These processes are the most commonly encountered in practice. Atomic attrition – atom-by-atom wear process, and transition state theory of wear are the more recently studied theories. Atomic attrition can be well studied using Atomic Force Microscopy. Finally the chapter is closed by the discussion of hardness, plasticity and fracture at nanoscale.


  1. Tribology on the Small Scale: A Modern Textbook on Friction, Lubrication, and Wear, Second Edition, C. Mathew Mate and Robert W. Carpick, Oxford University Press, 2019.
  2. Imaging and Understanding Atomic-Scale Adhesion and Wear: Quantitative investigations Using in situ TEM, Tevis Jacobs, PhD Thesis, University of Pennsylvania, 2013.

Founder of TriboNet, Editor, PhD (Tribology), Tribology Scientist at ASML, The Netherlands. Expertise in lubrication, friction, wear and contact mechanics with emphasis on modeling. Creator of Tribology Simulator.

1 Comment

  1. Dr. Aydar Akchurin has done a commendable job of defining various tribological interactions in his concise article, “Tribology on the Small Scale: …” However, the field of tribology has traditionally been presented in terms of disparate regimes, but this method of classification lacked sufficient rigor.
    I kindly suggest, the author to browse through the related book [Ref-1]. This book, explores the phenomenon of continuum spectrum as applied to new tribo-particulate lubrication technology, from nano to macro scales. It explains that characterization and treatment of any one regime may require the simultaneous accounting of several different modalities that are present in a particular mode of operation. Based on experimental and theoretical work, this text shows how the interdependence of solid partials (powder) and hydrodynamic lubrication exemplifies that perpetuity in tribological processes.

    Kind Regards
    [1] – “Tribology of Interface Layers,” Book, Heshmat, H., 2010

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