Abstract
ABSTRACTThe Prandtl-Tomlinson (PT) model is the most widely used and successful minimalistic model to describe atomistic scale friction. It can describe the thermally activated, stress assistant process which shows stick-slip frictional behavior. The relationship between the energy barrier and lateral force is critical to determine how the frictional force depends on velocity and temperature. There is some confusion in the literature to derive such relationship. The underlying assumption and approximations are not stated in a clear way and the rigorous derivations are missing. This study discusses the asymptotic behavior of the energy barrier as the support-spring coupling lowers it to zero and gives a detailed derivation of the asymptotic expression of the energy barrier within the framework of PT model.
Highlights
Da Vinci, Amonton and Coulomb stated the fundamental law of friction as following: F 1⁄4 μN (1)where N is the normal force, F is frictional force, and μ is the friction coefficient
This study discusses the asymptotic behavior of the energy barrier as the support-spring coupling lowers it to zero and gives a detailed derivation of the asymptotic expression of the energy barrier within the framework of PT model
We can conclude: (1) friction is proportional to the applied load, (2) kinetic friction does not depend on the velocity, (3) friction is independent of the apparent contacting area between the two sliding objects [1,2]
Summary
Where N is the normal force, F is frictional force, and μ is the friction coefficient It works for static as well as kinetic friction. From this simple expression, we can conclude: (1) friction is proportional to the applied load, (2) kinetic friction does not depend on the velocity, (3) friction is independent of the apparent contacting area between the two sliding objects [1,2]. We can conclude: (1) friction is proportional to the applied load, (2) kinetic friction does not depend on the velocity, (3) friction is independent of the apparent contacting area between the two sliding objects [1,2] This law can describe a wide range of phenomenon commonly observed at the macroscopic scale. With the help of FFM measurements [4,6,7], people commonly believed that the nanoscale friction exhibits stick-slip behavior in a sawtooth pattern which is fundamentally different from macroscopic friction laws
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