PR O O F METHODS PAPER1 2 Analytical Models for Atomic Friction

6 Abstract In this methods article, we describe application 7 of Prandtl–Tomlinson models and their extensions to 8 interpret dry atomic-scale friction. The goal is to provide a 9 practical overview of how to use these models to study 10 frictional phenomena. We begin with the fundamental 11 equations and build on them step-by-step—from the simple 12 quasistatic one-spring, one-mass model for predicting 13 transitions between friction regimes to the two-dimensional 14 and multi-atom models for describing the effect of contact 15 area. The intention is to bridge the gap between theoretical 16 analysis, numerical implementation, and predicted physical 17 phenomena. In the process, we provide an introductory 18 manual with example computer programs for newcomers 19 to the field, and an illustration of the significant potential 20 for this approach to yield new fundamental understanding 21 of atomic-scale friction