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In this methods article, we describe application of Prandtl-Tomlinson models and their extensions to interpret dry atomic-scale friction. The goal is to provide a practical overview of how to use these models to study frictional phenomena. We begin with the fundamental equations and build on them step-by-step-from the simple quasistatic one-spring, one-mass model for predicting transitions between friction regimes to the two-dimensional and multi-atom models for describing the effect of contact area. The intention is to bridge the gap between theoretical analysis, numerical implementation, and predicted physical phenomena. In the process, we provide an introductory manual with example computer programs for newcomers to the field, and an illustration of the significant potential for this approach to yield new fundamental understanding of atomic-scale friction. [ABSTRACT FROM AUTHOR]

Friction between a nanoscale tip and a reconstructed Au(111) surface is investigated both by atomic force microscopy (AFM) and molecular statics calculations. Lateral force AFM images exhibit atomic lattice stick-slip behavior with a superstructure corresponding to the herringbone reconstruction pattern. However, the superstructure contrast is not primarily due to variations in the local frictional dissipation (which corresponds to the local width of the friction loop). Rather, the contrast occurs primarily because the local centerline position of the friction loop is periodically shifted from its usual value of zero. Qualitatively, similar behavior is reproduced in atomistic simulations of an AFM tip sliding on the reconstructed Au(111) substrate. In both simulations and experiments, this centerline modulation effect is not observed on unreconstructed surfaces. Similarly, using a topographically flat surface as a hypothetical control system, the simulations show that the centerline modulation is not caused by variations in the reconstructed surface's topography. Rather, we attribute it to the long-range variation of the local average value of the tip-sample interaction potential that arises from the surface reconstruction. In other words, surface atoms located at unfavorable sites, i.e., in the transition between face-centered-cubic (FCC) and hexagonal-close-packed (HCP) regions, have a higher surface free energy. This leads to a varying conservative force which locally shifts the centerline position of the friction force. This demonstrates that stick-slip behavior in AFM can serve as a rather sensitive probe of the local energetics of surface atoms, with an attainable lateral spatial resolution of a few nanometers. [ABSTRACT FROM AUTHOR]

We introduce a model AFM tip/substrate system that includes full atomistic detail as well as system compliance to study the transitions between three regimes of atomic friction: smooth sliding, stick-single slip, and stick-multiple slip. We characterize these atomic friction regimes in terms of static and dynamic effects, and investigate how the slip modes affect the mean friction. Molecular statics calculations show that reduced-order model predictions of possible transitions between slip regimes are generally adequate for a fully atomistic system, even for complex reaction coordinates. However, molecular dynamics simulations demonstrate that, while static features of the system govern possible slip regimes, dynamic effects ultimately determine actual transitions between slip regimes. [ABSTRACT FROM AUTHOR]

A recent note by Lu et al. presented a theoretical study of atomic friction using a two-spring Tomlinson model. In this comment, we argue that the conclusion of the note can be understood in a simple manner, and that the discussion of the criterion for the onset of stick-slip is unnecessarily complicated and potentially misleading. [ABSTRACT FROM AUTHOR]