Friction at small scales

The friction of a bow against the strings of a cello has to be just right to produce the desired sound.(**)
The friction of a bow against the strings of a cello has to be just right to produce the desired sound.(**)
Friction is important in everyday life and in the operation of all devices with moving parts, but it is still very poorly understood. Since the time of Leonardo da Vinci we know the phenomenological laws that describe how static friction is usually proportional to the load force, and kinetic friction tends to be smaller than the static friction. Nevertheless, we still do not fully understand these laws and their coefficients. As a result, attempts to engineer low-friction surfaces or effective lubricants are often based on trial and error. The last few decades, there have been enormous developments in experimental techniques for probing friction on large and small scales, such as the atomic force microscope (AFM). But theoretical understanding is lagging behind.

Transport properties in general, but friction in particular, are challenging theoretically, because there is no general formalism to describe them. To understand transport, we must link microscopic dynamics of particles to macroscopic averages. For equilibrium systems, such as a liquid that is completely stationary, the powerful formalisms of equilibrium statistical mechanics provide a framework for this. For systems with transport, which are out of equilibrium, we are stuck using ad-hoc approaches that are only valid in particular cases, and often we are forced to resort to numerical simulations.
This issue is what most of my research deals with, to develop general, theoretical models to connect microscopic nonlinear dynamics to transport of matter, energy, or momentum. At the moment, I focus on two types of systems: 1) molecules and nanoscale objects on surfaces, especially in the context of friction, and 2) gases and liquids of various levels of complexity.

Friction originates from dissipation of energy due to interactions between atoms at microscopic contacts.
Friction originates from dissipation of energy due to interactions between atoms at microscopic contacts.

Another reason why friction is such a challenging subject, is because many different effects occur at different scales. While two sliding surfaces appear flat on macroscopic scales, they are in fact almost never truly flat (see figure). On smaller scales, the roughness of the surfaces means that the actual contact area is small compared to the apparent contact area. The actual contacts are of the order of micrometer in size. Energy is dissipated in a variety of ways at these contacts by atomic interaction that occur on the scale of a nanometer. To understand friction on large, macroscopic scales, we must first understand friction on micro and nanometer scales. (The study of friction on very small scales is called nanotribology.)

When things get complicated, physicists develop simple models to describe them, and this is the case also for nano-scale friction. The simplicity normally helps focus on the modelling of isolated aspects of a complex problem. Recently, together with collaborators in Israel, the Netherlands, and Ukraine, I developed a simple model for friction in electrochemical systems such as salt solutions [1].

Our simple model contains just one important ingredient that was missing from previous models: the orientation of polar molecules is affected by external electric fields. Nevertheless, it captures some of the essence of the problem. It predicts that the friction peaks near values of the external potential when molecules on the surface go through a reorientation transition, and go from being flat on the surface to standing upright. When we started looking for an experimental group to confirm our predictions, we discovered that someone was
already seeing the effect. Experiments for pyridine in solution and on a gold substrate are being performed at the university of Bonn in Germany and they show exactly the peak in the friction that our model predicts.

[1] Nanoscopic friction under electrochemical control, A. S. de Wijn, A. Fasolino, A. Filippov, M. Urbakh, Phys. Rev. Lett. 112, 055502 (2014)
http://arxiv.org/abs/1309.6658

Astrid S. de Wijn (dewijn@fysik.su.se) – Researcher at the Physics Department

Astrid.SdeWijn

(**) Image source wikipedia CC

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