Filippov, Vanossi, and Urbakh Reply:

Abstract

Filippov, Vanossi, and Urbakh Reply: We thank McLaughlin, Rabson, and Thiel [1] for their interest in our original work [2] and for their attentive reading.Based on a 2D generalized Prandtl-Tomlinson model, the main conclusion of our Letter [2] is ''that the difference between the length scales of potential corrugation in the periodic and aperiodic directions is the main source of the observed anisotropy of friction on the Al-Ni-Co quasicrystal surface.'' The Prandtl-Tomlinson model demonstrates that the friction force along a given direction is mainly defined by the maximal gradient of the potential in that direction, which is dictated, besides the amplitudes of the substrate potential, by the length scales of potential corrugation. The length scales of potential corrugation depend, in turn, in a correlated way, on both lattice periodicity of the substrate and on the widths of the Gaussian functions used to mimic the potential. We do certainly agree with McLaughlin, Rabson, and Thiel that both these interrelated features are important, and their careful analysis highlights this issue.Notwithstanding the theoretical interest of this ''parametric'' study, we did not play systematically in our work

The physics of atomic‐scale friction: Basic considerations and open questions

“…Another consequence of the two-dimensional nature of the motion is the possibility of so-called "friction anisotropy," which is the dependence of the sliding motion and friction force on the sliding direction with respect to the main crystallographic directions (see, e.g., [12] and references therein). Interesting complications arise when friction is studied on the inherently non-periodic surfaces of quasi-crystals [96,97]. Friction anisotropy is emphasized on surfaces with steps [98].…”

“…We close this section by briefly mentioning the coupling with the rotational coordinate that has been considered experimentally and in computer simulations in relation to the geometry of graphite flakes sheared over a graphite surface [99]. Even when the sum of all forces on the carbon atoms in the flake is close to zero and the flake can be translated without stick-slip instabilities, the torques on all carbon atoms can still add up to a significant total torque, especially when the flake has been twisted out of registry with the substrate only over a modest angle.…”

“…Even when the sum of all forces on the carbon atoms in the flake is close to zero and the flake can be translated without stick-slip instabilities, the torques on all carbon atoms can still add up to a significant total torque, especially when the flake has been twisted out of registry with the substrate only over a modest angle. If the flake is free to rotate and respond to the torques to which it is subjected, it will tend to rotate into registry [99]. During the translational motion, the flake may be frequently thrown out of registry, but in its rotational random walk, it displays a significant preference for aligned geometries.…”

Graphene nanoribbons on gold: understanding superlubricity and edge effects

“…When deposited on a clean flat crystal surface, nano-sized objects usually provide a welldefined mechanical contact. For this and other reasons, systems of this kind have been the subject of extensive nanofriction investigation in recent years both in experiments [1,2,3,4,5,6,7,8,9,10,11,12] and in simulations [13,14,15,16,17,18,19,20,21,22]. The gold-graphite interface constitutes an especially smooth and lubric contact, characterized by tenuous lateral forces, which make it an ideal workhorse system for basic tribological studies.…”

Friction and nonlinear dynamics

“…The nature of two problems -earthquakes and friction -is very similar: differences are restricted to their spatial-temporal scales: kilometers and years to millenia in geology compared to nanometers and seconds to hours in tribology. The EQ model, also known as the spring-and-block model or the multi-contact model, has been successfully used in many studies of friction [141,[210][211][212][213][214][215][216][217]; similar schemes have been used also to model the failure of fiber bundles and faults [218][219][220].…”