Stochastic Modeling and Rate Theory of Atomic Friction

Abstract

Atomic friction involves objects whose dynamics is strongly influenced by thermal fluctuations. In stochastic modeling, one focuses on a few relevant degrees of freedom, whereas the atomistic ones are taken into account by introducing dissipation and noise. We review applications of this approach to atomic friction, namely, the basic Prandtl-Thomlinson model, some of its multidimensional generalizations, and the rate approximation, which allows one to obtain analytical results not easily accessible by other methods.

On the Origin of Frictional Energy Dissipation

“…In fact, the motion for each atom was obtained by simply integrating Newton's equations along the x-, y-, and z-directions, i.e., along [100], [010] and [001], in response to the forces exerted on the atom by its direct and next-nearest neighbors. No velocity-related terms entered this description [14]. Also, we have left out all other 'hidden' forms of damping, for example via a thermostat in the calculation or via absorbing boundary conditions [20,21] (see Appendix 3 for more details).…”

“…Such strong damping is predicted theoretically only for the vibrations of isolated adsorbate atoms on a semi-infinite solid [2], but is not characteristic for the surface or interior of the solid itself. Near-critical damping [14][15][16] also forms an essential ingredient in the interpretation of friction force microscopy (FFM) images, in which atomic stick-slip patterns are routinely observed [15][16][17], with occasional slips of the FFM tip over two or more lattice spacings [17][18][19]. Again, details of the materials and their structural perfection, both for the tip and the substrate, seem not to be of critical importance.…”