Surface characterization using Friction Force Microscopy and the Jarzynski equality

Abstract

The Jarzynski equality is a fundamental result from non-equilibrium statistical mechanics that provides the difference in free energy between two states from the work done on the system by processes that can be carried out far from equilibrium. We evaluate the applicability of Jarzynski equality to map the potential energy of a model graphene surface using data from simulated Friction Force Microscopy (FFM). We model the scanning process of the FFM using the Prandtl-Tomlinson model and Langevin dynamics. By varying the simulation parameters, we verify the “stick–slip” and thermolubricity friction regimes, as well as the crossover between them. We then calculate the surface potential energy using the Jarzynski equality for these regimes. A new method for properly evaluating the free energy of the cantilever is introduced. We observe that the applicability of Jarzynski's equality is linked to the friction regimes: For thermolubricity, a very accurate potential energy curve is obtained for relatively few repetitions, but for the “stick–slip” movement, it is only possible to use Jarzynski’s equation in a small fraction of the scanning distance. For the crossover regime, it is possible to obtain a relatively accurate potential energy curve for a sufficiently large number of sampling repetitions.