Atomic Resolution from Friction Force Microscopy Using the Jarzynski Equality

Atomic resolution in Atomic Force Microscopy (AFM) has been achieved in a number of studies regarding surface properties in atomic scale. Most of these works are performed using the frequency-modulation analysis of the normal force. In the present work, we explore the possibility of achieving atomic resolution using Friction Force Microscopy (FFM). We simulate the scanning process using the Tomlinson model and Langevin dynamics. Tests are performed on the graphene surface, using different scanning speeds, temperatures and contact forces. By varying these parameters, it is possible to observe two distinct motion regimes of the tip of the microscope on the surface of sample: The “stick-and-slip” movement and the thermolubricity regime. We use the Jarzynski equality to map the potential energy of graphene in both cases. In the “stick-and-slip” case, it is only possible to use Jarzynski’s equation in a portion of the distance between two energy minima, but the whole potential curve can be extrapolated, with an energy barrier in agreement with the reference values. For the thermolubricity mode, we were able to obtain the surface potential for the entire scanning distance, which indicates it may be possible to apply these results in order to obtain FFM images with better resolution.