Self-organization at the interface (self-healing, self-lubrication, self-cleaning)


Friction is usually thought of as a process that leads to irreversible dissipation of energy while wear leads to irreversible deterioration. Many scientists and engineers do not realize that under certain conditions friction can lead to the formation of new structures at the interface, including in-situ tribofilms, and various patterns at the interface. Friction-induced self-organization was studied mostly by scholars in Eastern Europe in the 1970-1990s although the field remains exotic to many tribologists in other countries.

Friction-induced instabilities are related to friction-induced self-organization. Friction is usually thought of as a stabilizing factor; however, sometimes friction leads to the instability of sliding, in particular when friction is coupled with another process. For example, thermoelastic instabilities were studied extensively by J. R. Barber. These instabilities arise from the fact that friction is coupled with heat generation, which, in turn, is coupled with material expansion, creating a positive feedback. If friction increases locally due to a random fluctuation, more heat is generated, leading to higher local normal pressures at the interface and, in turn, to increased friction. Thus a random fluctuation has a tendency to grow, signifying the instability.

A similar situation occurs when the coefficient of friction decreases with the increasing sliding velocity: a small random increase of the sliding velocity leads to a decrease of the frictional resistance and to the further increasing of velocity. It was discovered in the 1990s that frictional elastodynamic instabilities (the Adams instabilities) occur even in the case when the coefficient of friction is constant. Instabilities are related to self-organization because they constitute the main mechanism for pattern formation. At first, a stationary structure loses its stability; after that, vibrations with increasing amplitude occur, leading to a limit cycle corresponding to a periodic pattern.

We discuss a general variational stability criterion of the stationary state of frictional sliding, δ^2(dS/dt)>0, where dS/dt is the rate of entropy production and δ^2 is the second variation. The criterion is very powerful since it allows combining very diverse mechanisms of frictional instabilities within one general theory. The entropy S can include pure mechanical, thermodynamic, heat and mass transfer, chemical reactions, and other terms. Variations of the relevant parameters (physically corresponding to small random fluctuation) can either be suppressed or expand. The stability criterion captures this trend. For the case of the constant temperature T, sliding velocity V, and normal load W, the criterion can be significantly simplified.

Furthermore, we wanted to combine the mechanical and thermodynamic methods in tribology. From the thermodynamic point of view, friction and wear are two sides of the same phenomenon: irreversible energy dissipation and material deterioration during sliding. As with any irreversibility, both friction and wear are the consequences of the second law of thermodynamics. It would be therefore logical to expect that the laws of friction and wear (such as the Coulomb and Archard laws) are deduced from the thermodynamic principles of irreversibility. However, in practice this is difficult to achieve. We suggest a procedure on how this can be done using Onsager’s linearized laws of irreversible thermodynamics combined with the asymptotic transition from the bulk to the interface. Non-equilibrium (irreversible) thermodynamics is also useful for the study of friction-induced self-organization. In general, the place of thermodynamic methods in tribology is growing.

The area of friction-induced self-organization is related to novel biomimetic materials, such as self-lubricating, self-cleaning, and self-healing materials. These “smart ” materials have the embedded capacity for self-organization, leading to their unusual properties. Understanding the structure-property relationships leading to self-organization is the key to designing these novel materials. It is noted that these materials often have hierarchical organization, which makes them similar to biological materials.

All this background information caused us to look at friction, as a physical phenomenon, from a different perspective. For most conventional textbooks on mechanics, Coulomb’s dry friction is quite an external phenomenon, which is postulated in the form of laws of friction (usually, the Coulomb-Amontons laws) introduced in an arbitrary and ad hoc manner in addition to the constitutive laws of mechanics. Furthermore, the very compatibility of the Coulomb friction laws with the laws of mechanics is questionable due to the existence of the so-called frictional paradoxes or logical contradictions in the mechanical problems with friction. The Coulomb-Amontons law is not considered a fundamental law of nature, but an approximate empirical rule, whereas friction is perceived as a collective name for various unrelated effects of different nature and mechanisms, such as adhesion, fracture, and deformation, lacking any internal unity or universality.

Despite this artificial character of friction laws in mechanics, Coulomb friction is a fundamental and universal phenomenon that is observed for all classes of materials and for loads ranging from nanonewtons in nanotribology to millions of tons in seismology. There is a contradiction between the generality and universality of friction and the artificial manner of how the friction laws are postulated in mechanics and physics. Is it by chance that all these diverse conditions and mechanisms lead to the same (or at least similar) laws of friction? If a thermodynamic approach is used consistently, the laws of friction and wear can be introduced in a much more consistent way.

These reflections about the fundamental nature of friction and its status in physics caused us also to examine with great attention the role of friction in physics throughout the history of science. In the days of Aristotle’s “Physics,” friction was seen as a fundamental force having the same status as inertia force (nothing would move without inertia, nothing would stop without friction). The problem of inertia force was one of the central issues of physics throughout the middle ages, until it was finally resolved by Galileo, leading to the foundation of modern mechanics by Newton in the late 17th century. In contrast, friction force was not usually seen as a fundamental force of nature and became somewhat marginal in modern mechanics. In order to discover the inertia, one had first to recognize the existence of friction as a force which resists the motion by inertia. Consequently, friction was viewed only as a phenomenon which contaminates pure experiments rather than as a fundamental force. For centuries, friction was marginalized by physicists and it was studied mostly by engineers and material scientists. Hopefully, the awareness of these facts will help to restore the interests towards friction and its central role in many phenomena.


M. Nosonovsky & V. Mortazavi. Friction-Induced Vibrations and Self-Organization: Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact (CRC Press/Taylor & Francis, 2013)

M. Nosonovsky, “Entropy in Tribology: in Search for Applications” Entropy, 12:1345-1390 (2010)

M. Nosonovsky, “Self-organization at the frictional interface” Phil. Trans. Royal. Soc. A., (2010), Vol. 368:4755-4774