The Tomlinson model, also known as the Prandtl–Tomlinson Model, is one of the most popular models in
nanotribology
Nanotribology is the branch of tribology that studies friction, wear, adhesion and lubrication phenomena at the Nanoscopic scale, nanoscale, where atomic interactions and quantum effects are not negligible. The aim of this discipline is characteriz ...
widely used as the basis for many investigations of
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
al mechanisms on the
atomic scale
Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. In solid materials, the ato ...
. 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 ''V
0'' and periodicity ''a'' then
:
where ''k'' is the spring constant.
If ''η''<1, the tip slides continuously across the landscape (
superlubricity
In physics (specifically tribology), superlubricity is a regime of motion in which friction vanishes or very nearly vanishes. What is a "vanishing" friction level is not clear, which makes the term quite vague. As an ''ad hoc'' definition, a ki ...
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
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of ...
who suggested in 1928 this model to describe the plastic deformations in crystals as well as the dry friction. In the meantime, many researchers still call this model the "Prandtl–Tomlinson Model".
In
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
this model was introduced by the
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
physicists
Yakov Frenkel
__NOTOC__
Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...
and T. Kontorova. The
Frenkel defect
In crystallography, a Frenkel defect is a type of point defect in crystalline solids, named after its discoverer Yakov Frenkel. The defect forms when an atom or smaller ion (usually cation) leaves its place in the lattice, creating a vacancy a ...
became firmly fixed in the physics of solids and liquids. In the 1930s, this research was supplemented with works on the theory of
plastic deformation
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
. Their theory, now known as the
Frenkel–Kontorova model The Frenkel–Kontorova model, also known as the FK model, is a fundamental model of low-dimensional nonlinear physics.
The generalized FK model describes a chain of classical particles with nearest neighbor interactions and subjected to a periodic ...
, is important in the study of
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
s.
[O. M. Braun, "The Frenkel-Kontorova model: concepts, methods and applications", Springer, 2004.]
References
External links
''The Tomlinson mechanism''* 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 its translation into English''Description of the basic properties of the Prandtl-Tomlinson Model
Nanotechnology
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