Contact mechanics and friction are topics of huge importance with many applications
in Nature andtec hnology. They are closely interconnected, so that understanding
friction requires a deep insight into the contact formation between two
solids. During university studies, students learn very early that the sliding friction
force 𝐹f is proportional to the normal force 𝐹N and independent of the relative sliding
velocity, 𝐹f = 𝜇𝐹N. The constant of proportionality 𝜇, the coefficient of friction,
depends on several parameters, such as the material combination, temperature and
surface roughness. Thus one may think that friction is a simple andw ell understood
subject. It is, in fact, one of the oldest topics in physics, and a vast amount of
work has been investedin order to gain insight into contact mechanics andfriction.
Despite all the theoretical and experimental effort, neither topic is well understood.
The importance of contact mechanics andfriction cannot be overestimated, as
they affect our every day life in countless situations. The reader of this manuscript,
for example, wouldb e unable to turn to the next page or walk to the coffee machine
in the absence of friction. The complex nature of friction results from its extreme
surface sensitivity; a single monolayer of interface atoms or molecules can change the
friction by an order of magnitude (or more). In addition, friction usually depends
on many decades in length scales, which can be illustrated by two examples. On the
nanometer scale, the coefficient of friction between two clean diamond surfaces in
ultrahigh vacuum is typically of order 1 or more, because of the strong interaction
between the surface dangling bonds. If these bonds are saturated with a hydrogen
monolayer, the coefficient of friction decreases rapidly to ≈ 0.05. This shows that
even a nanometer thick boundary layer can influence the friction greatly. On the
other hand, energy losses due to tidal forces cause the rotation of the earth to
slow by the order of 1.6 ⋅ 10−7 seconds per year. This is the reason why during the
Cambrian age, approximately 500 Million years ago, the day had only about 21
hours. How to account for all the relevant length scales remains an important and
open problem in physics
Boris Lorenz
Contact Mechanics Elastic Solids Rough Substrates