Toward Understanding Low Surface Friction on Quasiperiodic Surfaces

In a 2005 article in Science, Park et al. measured in vacuum the friction between a coated atomic-force- microscope tip and the clean two-fold surface of an AlNiCo quasicrystal. Because the two-fold surface is periodic in one direction and aperiodic (with a quasiperiodicity related to the Fibonacci sequence) in the perpendicular direction, frictional anisotropy is not unexpected; however, the magnitude of that anisotropy in the Park experiment, a factor of eight, is unprecedented. By eliminating chemistry as a variable, the experiment also demonstrated that the low friction of quasicrystals must be tied in some way to their quasiperiodicity. Through various models, we investigate generic geometric mechanisms that might give rise to this anisotropy.