Rolling and sliding of a nanorod between two planes: Tribological regimes and control of friction

The motion of a cylindrical crystalline nanoparticle sandwiched between two crystalline planes, one stationary and the other pulled at a constant velocity and pressed down by a normal load, is considered theoretically using a planar model. The results of our model calculations show that, depending on load and velocity, the nanoparticle can be either rolling or sliding. At sufficiently high normal loads, several sliding states characterized by different friction forces can coexist, corresponding to different orientations of the nanoparticle, and allowing one to have low or high friction at the same pulling velocity and normal load.Comment: 5 figure

Thermally Activated Contact Strengthening Explains Nonmonotonic Temperature and Velocity Dependence of Atomic Friction

Evstigneev M, Reimann P. Thermally Activated Contact Strengthening Explains Nonmonotonic Temperature and Velocity Dependence of Atomic Friction. Physical Review X. 2013;3(4): 041020.While the well-established Prandtl-Tomlinson (PT) model of atomic friction predicts that the friction force decreases with temperature and grows with velocity, several recent experiments reported that a nonmonotonic temperature dependence and a decreasing velocity dependence may also occur. We propose a minimal extension of the PT model, incorporating the possibility of thermally activated contact strengthening and providing one common framework to quantitatively explain all those "anomalous'' experimental findings, as well as the previously known "normal'' (PT-like) behavior

Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments

Evstigneev M. Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments. PHYSICAL REVIEW E. 2008;78(1): 11118.The dynamics of a number of experimental systems can be described as thermally activated escape out of a metastable state over a potential barrier, whose height is being constantly reduced in time by an increasing external force. In such systems, one can distinguish two loading regimes: for slow loading, the distribution of the force values at which escape occurs is a monotonically decreasing function, while for fast loading, the escape-force distribution has a maximum at some nonzero force value. In this work, an approximate relation between the most probable escape force and the first two moments thereof is derived for fast loading, and the expression for the first two force moments vs loading rate is obtained for slow loading. Then, for a special but physically well-motivated functional form of the escape rate, the most probable escape force is found analytically as a function of the loading rate. The high accuracy of these expressions is confirmed by comparing them with numerical results for realistic parameter values

Description of atomic friction as forced Brownian motion

Reimann P, Evstigneev M. Description of atomic friction as forced Brownian motion. NEW JOURNAL OF PHYSICS. 2005;7:25.A theoretical description of friction force microscopy experiments in terms of a forced Brownian motion model is derived on the basis of microscopic considerations. Particular emphasis is put on the discussion of the relevant state variables/collective coordinates and on a realistic description of dissipation and inertia effects by means of comparison with experimental findings. The main new prediction of the model is a non-monotonic dependence of the friction force upon the pulling velocity of the AFM-tip relative to an atomically flat surface. The region around the force maximum can be approximately described by a universal scaling law and should be observable under experimentally realistic conditions

Refined force-velocity relation in atomic friction experiments

Evstigneev M, Reimann P. Refined force-velocity relation in atomic friction experiments. PHYSICAL REVIEW B. 2006;73(11): 113401.The stick slip motion of an atomic-force-microscopy tip in contact with a uniformly moving surface consists of the stick phases when the tip is confined to one of the moving surface sites and thermally activated slips of the tip from one site to the next. The stick phase is associated with the increase of the elastic deformation of the cantilever spring, the tip apex, and the surface in the contact region. The corresponding spring constant is experimentally determined from the rate of increase of the elastic force. By taking into account the effect of the tip-surface interaction potential, we refine the expression for the experimentally measured spring constant and show that it weakly depends on the pulling velocity. We incorporate this expression into the force-velocity relation obtained previously within the rate theory and demonstrate that such a refinement leads to a notable improvement of the accuracy of this relation

Rate description of the stick-slip motion in friction force microscopy experiments

Evstigneev M, Reimann P. Rate description of the stick-slip motion in friction force microscopy experiments. PHYSICAL REVIEW E. 2005;71(5): 056119.During the stick-slip motion of an atomic force microscope tip contacting with a uniformly moving atomically clean surface, the force developed in the cantilever spring performs random sawtoothlike oscillations resulting from the thermally activated transitions of the tip from one surface site to the next. Using escape rate theory, the probability distribution of forces is calculated numerically to deduce the time-average lateral force as a function of pulling velocity. A transcendental equation for the average force is proposed and its approximate solution is obtained. The accuracy of this analytic approximation is demonstrated via comparison with the numerical results. The analogous force-velocity relations existing in the literature are shown to be the limiting cases of low and high cantilever spring constants of our analytic approximation

Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation

Evstigneev M, Reimann P. Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation. Journal of Physics Condensed Matter. 2015;27(12): 125004.Friction force microscopy and single-molecule force spectroscopy are experimental methods to explore multistable energy landscapes by means of a controlled reduction of the energy barriers between adjacent potential minima. This affects the system's interstate transition rates proportional to e-(Delta E(f)/kBT), with Delta E(f) being the barrier height, k(B)T the thermal energy, and f the elastic force applied. It is often assumed that, at large forces, the barrier height scales as (f(c)-f)(3/2), where f(c) is the critical force, at which the barrier vanishes. We show that, for the elastic forces produced by a pulling device of finite stiffness., this scaling relation is actually incorrect. Rather, the barrier is a double-valued function of force of the form Delta E(f) alpha (kappa/kappa(c) +/- root 1-f/f(0))(3), where f(0) is the maximal force that the system potential can generate, and the characteristic stiffness kappa(c) is not necessarily much larger than.. In particular, for finite kappa, the barrier vanishes at a certain force f(kappa) 0 limit of our more general result, but becomes increasingly worse as grows. We introduce a new data analysis method that allows one to quantitatively characterize the system potential and evaluate the stiffness of the pulling device, kappa, which is usually not known beforehand. We demonstrate the feasibility of our method by analyzing the results of a numerical experiment based on the standard Prandtl-Tomlinson model of nanoscale friction

Pulsating potential ratchet

Reimann P, Evstigneev M. Pulsating potential ratchet. Europhysics Letters. 2007;78(5): 50004.We consider Brownian motion in a periodic array of potential wells. The potential barriers between adjacent wells are spatially symmetric and pulsating periodically in time. While the modulation amplitude is the same for all barriers, the spatial symmetry is broken by sequentially alternating the respective pulsation frequencies among three different incommensurate values. The result is a net motion ( ratchet effect), whose direction depends in an intriguing way on the detailed choice of parameters. Copyright (C) EPLA, 2007

Dynamic force spectroscopy: Optimized data analysis

Evstigneev M, Reimann P. Dynamic force spectroscopy: Optimized data analysis. PHYSICAL REVIEW E. 2003;68(4): 45103.The forced rupture of single chemical bonds in biomolecular compounds (e.g., ligand-receptor systems) as observed in dynamic force spectroscopy experiments is addressed. An optimized method of data analysis is proposed. This method significantly outperforms the current standard one when applied to data from an idealized numerical computer simulation of an experiment with realistic parameter values. In particular, the force-free dissociation rate can be inferred with a considerably smaller statistical uncertainty and without the systematic overestimation of about 30%, which is shown to be inherent in the standard method