Factors influencing the calculation of friction of two-dimensional materials using the Lennard-Jones potential*

To understand friction at the nanoscale, either short-range chemical interactions or long-range van der Waals interactions have been considered depending on the surface termination states of sliding bodies. Lennard-Jones (LJ) potential has been used to explain the frictional characteristics of two-dimensional (2D) materials in molecular dynamics simulations studies. LJ potential includes the van der Waals interactions and well describes the essential features of interactions between atoms and molecules. Two particles do not interact at infinity, repel each other when they get very close, and attract when they are at moderate distances. When applying the LJ potential in realistic systems, an approximation is made for convenience: the LJ potential is defined as zero outside the cut-off radius. The cut-off radius in various systems generally uses a value of 2.5σ, where σ corresponds to the distance at which the LJ potential energy between atoms becomes zero.

In a situation where a single atom slides on a 2D sample surface, we have calculated the LJ potential experienced by the atom as a function of position at various cut-off radii to estimate the frictional force. Based on our calculations, we explore whether the generally considered 2.5σ cut-off standard applies to 2D materials.