The velocity dependence of point-contact friction is studied by means of friction force microscopy of different carbon compounds (diamond, graphite, amorphous carbon). The measured frictional force is found to be constant over a wide range of sliding velocities [nm/s to µm/s]. This result is substantiated by a simple mechanical model, where the frictional forces are shown to be constant at sliding velocities well below the slip velocity.Although frictional phenomena are familiar from daily life and the study of friction is one of the oldest topics in physics because of its technological relevance [1], there has been only little success in deriving an exact description of friction since the time the following phenomenological laws of dry friction were established by Amontons and Coulomb 200 years ago. These laws are: (i) the frictional force is proportional to the normal load; (ii) the frictional force is independent of the (apparent) contact area of the sliding surfaces; (iii) sliding friction is independent of the sliding velocity. These three laws of friction hold surprisingly well at the macroscopic scale, but cannot be explained by first principles. Nevertheless, with the advent of new experimental tools such as the surface force apparatus, the quartz crystal microbalance, and the friction force microscope, the expanding field of nanotribology has been established where the tribological properties of contacts with well-defined geometries are studied on the nanometer scale [2].By using the friction force microscope (FFM) [3], which is an extension of the scanning force microscope (SFM) [4], it is possible to examine the frictional properties of an (approximate) point contact at the nanometer scale. The observed frictional behavior differs significantly from the behavior expected from the macroscopic friction laws introduced above. In particular, it is found that frictional forces are proportional to the true area of contact, which is generally not proportional to the loading force [5]. Consequently, the laws (i) and (ii) are no longer valid at the nanometer scale. * Corresponding author In this study, we examine the validity of law (iii) for point contacts by using a friction force microscope. It is found that the frictional forces are independent of the sliding velocity in a wide range. This result is substantiated by a simple mechanical model based on the Tomlinson [6] and the independent oscillator [7, 8] models.
Experiment
SamplesIn order to investigate the velocity dependence of frictional forces in point-contact friction, three different modifications of carbon were studied as examples. (i) A diamond film deposited by chemical vapor deposition on a silicon (001) substrate which exhibited crystallites with flat, {100} oriented surfaces. The surfaces of individual crystallites were typically several 100 nm 2 up to somewhat more than 1 µm 2 . (ii) Highly oriented pyrolytic graphite (HOPG) with 99.99% purity [9]. The sample was cleaved each time right before measurement along its (0001) plane by using Scotch...