We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the experimental conditions and time scales. The overall behavior can be described in terms of two Deborah numbers.

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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

We demonstrate that lateral vibrations of a substrate can dramatically increase surface diffusivity and mobility and reduce friction at the nanoscale. Dilatancy is shown to play an essential role in the dynamics of a nanometer-size tip which interacts with a vibrating surface. We find an abrupt dilatancy transition from the state with a small tip-surface separation to the state with a large separation as the vibration frequency increases. Atomic force microscopy experiments are suggested which can test the predicted effects.

While formation of capillary bridges significantly contributes to the adhesion and friction at micro- and nanoscales, many key aspects of dynamics of capillary condensation and its effect on friction forces are still not well understood. Here, by analytical model and numerical simulations, we address the origin of reduction of friction force with velocity and increase of friction with temperature, which have been experimentally observed under humid ambient conditions. These observations differ significantly from the results of friction experiments carried out under ultrahigh vacuum, and disagree with predictions of thermal Prandtl-Tomlinson model of friction. Our calculations demonstrate what information on the kinetics of capillary condensation can be extracted from measurements of friction forces and suggest optimal conditions for obtaining this information.

The driven underdamped chain of anharmonically interacting atoms in the sinusoidal external potential is studied. It is shown that due to the interatomic interaction the system exhibits hysteresis for any nonzero rate of changing of the dc driving force. Before the transition to the running state the system passes through the traffic-jam inhomogeneous state. The system behavior is explained with the help of two simple models, the discrete lattice-gas model with two states of atoms, and the continuum mean-field model based on the FokkerPlanck equation. ͓S1063-651X͑98͒10507-X͔ PACS number͑s͒: 05.40.ϩj, 05.70.Ln, 46.10.ϩz, 82.20.Mj

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We propose a theoretical model of friction under electrochemical conditions focusing on the interaction of a force microscope tip with adsorbed polar molecules of which the orientation depends on the applied electric field. We demonstrate that the dependence of friction force on the electric field is determined by the interplay of two channels of energy dissipation: (i) the rotation of dipoles and (ii) slips of the tip over potential barriers. We suggest a promising strategy to achieve a strong dependence of nanoscopic friction on the external field based on the competition between long range electrostatic interactions and short range chemical interactions between tip and adsorbed polar molecules. PACS numbers:Control of friction during sliding is extremely important for a large variety of applications [1,2]. A unique path to control and ultimately manipulate the forces between material surfaces is through an applied electric field. By varying the applied potential, the electrode surface can quickly and reversibly be modified either with adsorbed (sub)monolayer or multilayers, or via the oxidation and reduction of surfaces, or deposition of ultrathin films [3,4]. Thus, friction force microscopy (FFM) measurements under electrochemical conditions [5-10] may offer significant advantages in comparison to those between dry surfaces.Several experimental and theoretical studies of electrochemical interfaces demonstrated that the orientation of polar molecules adsorbed at electrode surfaces is potential dependent. Water molecules at electrode/electrolyte interfaces reorient from "oxygen-up" to "oxygen-down" as the potential on the electrode changes from negative to positive [11][12][13][14]. Another extensively studied system is pyridine adsorbed on gold electrodes [15,16]. Recent FFM measurements combined with cyclic voltammetry [17] have shown that friction depends strongly on the orientation of the molecules and is five times higher when the molecules are parallel to the substrate compared to their vertical orientation. The molecule orientation can be changed either by changing their concentration or by an external field. In the latter case, the friction shows an intense peak around values of the field where the change of orientation takes place. Recent FFM measurements in UHV have also shown strong sensitivity of nanoscopic friction to the orientation of surface molecules [18]. Investigating the impact of potentialdependent orientation of adsorbed molecules on friction offers a new perspective on active control of friction forces through reversible molecular reorientation.In spite of the first successful experimental studies of nanoscopic friction under potential control [5][6][7][8][9][10], so far there have been no theoretical or numerical studies of the effect of electric fields on friction. We do not know what the mechanism is behind the observed variation of friction with electrostatic potential, nor in which systems significant reversible variation of the friction can be achieved.In this Letter we propose a m...