Tomlinson model
Encyclopedia
Also: Prandtl-Tomlinson-Model. One of the most popular models in nanotribology widely used as the basis for many investigations of frictional mechanisms on the atomic scale. Essentially, a nanotip is dragged by a spring over a corrugated energy landscape. A "frictional parameter" η can be introduced to describe the ratio between the energy corrugation and the elastic energy stored in the spring. If the tip-surface interaction is described by a sinusoidal potential with amplitude V0 and periodicity a:
where k is the spring constant.
If η<1 the tip slides continuously across the landscape (superlubricity
regime). If η>1 the tip motion consists in abrupt jumps between the minima of the energy landscape (stick-slip regime).
The name "Tomlinson model" is, however, historically incorrect: The paper by Tomlinson that is often cited in this context did not contain the model known as the "Tomlinson model" and suggests an adhesive contribution to friction. In reality it was Ludwig Prandtl who suggested in 1928 this model to describe the plastic deformations in crystals as well as the dry friction. In the meantime, many researchers therefore call this model the "Prandtl-Tomlinson-Model".
In Russia
this model was introduced by the Soviet physicists Yakov Frenkel
and T. Kontorova. The Frenkel defect
became firmly fixed in the physics of solids and liquids. In the 1930s, his research was supplemented with works on the theory of plastic deformation. Their theory, now known as the Frenkel-Kontorova model, is important in the study of dislocation
s.
where k is the spring constant.
If η<1 the tip slides continuously across the landscape (superlubricity
Superlubricity
Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes.Superlubricity may occur when two crystalline surfaces slide over each other in dry incommensurate contact...
regime). If η>1 the tip motion consists in abrupt jumps between the minima of the energy landscape (stick-slip regime).
The name "Tomlinson model" is, however, historically incorrect: The paper by Tomlinson that is often cited in this context did not contain the model known as the "Tomlinson model" and suggests an adhesive contribution to friction. In reality it was Ludwig Prandtl who suggested in 1928 this model to describe the plastic deformations in crystals as well as the dry friction. In the meantime, many researchers therefore call this model the "Prandtl-Tomlinson-Model".
In Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
this model was introduced by the Soviet physicists Yakov Frenkel
Yakov Frenkel
Yakov Il'ich Frenkel, was a Soviet physicist renowned for his works in the field of solid-state physics. He is also known as Jacov Frenkel....
and T. Kontorova. The Frenkel defect
Frenkel defect
The Frenkel Defect is shown by ionic solids. The smaller ion is displaced from its lattice position to an interstitial site. It creates a vacancy defect at its original site and an interstitial defect at its new location.-Definition:...
became firmly fixed in the physics of solids and liquids. In the 1930s, his research was supplemented with works on the theory of plastic deformation. Their theory, now known as the Frenkel-Kontorova model, is important in the study of dislocation
Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...
s.
External links
- The Tomlinson mechanism
- Frenkel-Kontorova-Tomlinson Model
- Michael Weiss, Franz-Josef Elmer: Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties, Zeitschrift für Physik B 104 (1997).
- The complete text of the original paper by Ludwig Prandtl describing the "Tomlinson" model as well as it translation into English
- Description of the basic properties of the Prandtl-Tomlinson-Model