Path Selection Mechanism of Graphene Nanofriction under Transverse Elastic Constraints

The classical Prandtl-Tomlinson (PT) model is inherently one-dimensional, whereas nanofriction between two-dimensional (2D) materials is 2D in nature, which raises the question of how the sliding path is selected. Using graphene as an example, in the work we employed molecular dynamics simulation and theoretical analysis to study how an underexplored variable, i.e., the transverse spring stiffness used to stabilize the sliding tip, changes the sliding path and nanofriction. Our simulation results reveal that with increasing elastic constraint, the nanofriction exhibits path change from the conventional minimum energy path (MEP) with minimal energy barriers to non-MEP. To address this path selection mechanism, we propose that the transverse elastic constraint reconstructs the intrinsic potential energy surface (PES) from the substrate, and we indeed found that the tip motion trajectory corresponds to the conventional MEP on the total PES but not on the intrinsic PES. This leads us to propose a friction path selection mechanism for the sliding tip under transverse elastic constraints: the selected path ensures that the transverse elastic restoring force is balanced by the transverse gradient force of the intrinsic PES. Our simulation results also indicate that although transverse elastic constraints exert a significant influence in path selection, it is the path-dependent energy barriers from the intrinsic PES that dominate the magnitude of friction force.