Thermal effects on atomic friction

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at non-zero temperatures. We find that stick-slip motion occurs and that the average frictional force follows $|\ln v|^{2/3}$, where $v$ is the tip velocity. This compares well to recent experimental work (Gnecco et al, PRL 84, 1172), permitting the quantitative extraction of all microscopic parameters. We calculate the scaled form of the average frictional force's dependence on both temperature and tip speed as well as the form of the friction-force distribution function.Comment: Accepted for publication, Physical Review Letter

Mode-locking of incommensurate phase by quantum zero point energy in the Frenkel-Kontorova model

In this paper, it is shown that a configuration modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero point energy is taken into account. It is also found that the specific heat for an incommensurate phase shows different parameter-dependence in sliding phase and pinning phase. These findings provide a possible way for experimentalists to verify the phase transition by breaking of analyticity.Comment: 6 pages in Europhys style, 3 eps figure

A simple variational approach to the quantum Frenkel-Kontorova model

We present a simple and complete variational approach to the one-dimensional quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle is adopted together with a Hatree-type many-body trial wavefunction for the atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We obtain an effective classical Hamiltonian for the system which is simple enough for a complete numerical solution for the static ground state of the model. Numerical results show that our simple approach captures the essence of the quantum effects first observed in quantum Monte Carlo studies.Comment: 12 pages, 2 figure

Defect-induced perturbations of atomic monolayers on solid surfaces

We study long-range morphological changes in atomic monolayers on solid substrates induced by different types of defects; e.g., by monoatomic steps in the surface, or by the tip of an atomic force microscope (AFM), placed at some distance above the substrate. Representing the monolayer in terms of a suitably extended Frenkel-Kontorova-type model, we calculate the defect-induced density profiles for several possible geometries. In case of an AFM tip, we also determine the extra force exerted on the tip due to the tip-induced de-homogenization of the monolayer.Comment: 4 pages, 2 figure

Friction between atomically flat surfaces

We investigate the mechanism of atomic friction between two infinitely extended atomically flat surfaces within a two-dimensional Frenkel-Kontorova-Tomlinson model. The surfaces are identical but are rotated with respect to each other through an arbitrary misfit angle. The misfit gives rise to the formation of domains where every potential valley contains exactly one particle. They are separated by two sets of shift lines, crossing each other in topological defects. During quasistatic sliding, the whole domain pattern moves perpendicular to the driving force. Dissipation and friction hysteresis in the quasistatic limit are caused by irreversible jumps of these topological defects, which are the two-dimensional analogues of discommensurations occurring in the one-dimensional case of friction between chains with different lattice constants. Critical spring constants for the occurrence of instabilities can be derived. Friction shows strong dependence on both the misfit angle and the pulling direction. The relevance of the theoretical study for friction experiments on the nanoscale is discussed

Friction experiments on the nanometre scale

In this review, we present various results obtained by friction force microscopy in the last decade. Starting with material-specific contrast, commonly observed in friction force maps, we discuss how the load dependence of friction and the area of contact have been estimated and compared to elasticity theories. The features observed in a sliding process on the atomic scale can be, interpreted within the Tomlinson model. An extension of the model, including thermal effects, predicts a smooth velocity dependence of friction, which recent experiments have confirmed. Other subjects like anisotropy of friction, role of environment, topographical effects, electronic friction and tip modifications are also discussed. The growing importance of molecular dynamics simulations in the study of tribological processes on the atomic scale is outlined