We theoretically investigated the image of atomic-scale friction of graphite in atomic-force microscopy ͑AFM͒, based on numerical simulation for a static model. We performed systematic calculations of lateral force images of AFM aiming to clarify the effects of cantilever stiffness, scan direction, anisotropy of the cantilever, and surface deformation. The simulation is performed for a simple atomistic model with a singleatom tip connected with the cantilever spring scanned on a monolayer graphite surface. The process in which the conservative lateral force becomes a nonconservative frictional force is clarified. ''Stick regions'' of the tip atom are also discussed in relation to the cantilever stiffness. Calculated frictional-force image patterns are in good agreement with experimental ones. We also find the supercell frictional-force images and discuss their mechanisms.

Effects of the tip-induced nonconservative processes of the tip or surface atom on the cantilever dynamics of noncontact atomic force microscopy (nc-AFM) are theoretically analyzed based on the time-averaging perturbation theory. The typical order of the magnitude of the Q value due to such nonconservative processes is estimated to be on the order of 104, which is comparable to the intrinsic dissipation of the cantilever free oscillation. The additional frequency shift due to the hysteresis loop of the force curve is estimated to be on the order of 10 Hz. This part of the frequency shift sets in like a step function when the tip turning point approaches the surface within a certain threshold height. This feature explains the experimental observation of the discontinuous frequency shift at chemical reactive sites.

An ultralubricated system is reported which confines a C60 monolayer between graphite plates. C60 molecules act as molecular bearings, assisted by the nanogears of six-membered carbon rings between C60 molecules and graphite, in which the mean dynamical frictional forces are zero up to a high load of 100 nanonewtons. A stick-slip rolling model with a step rotation of a C60 molecule is proposed. This ultralubricated system, very promising for the realization of nano- and micromachines, is expected to open a new field of molecular bearings.

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