We investigate the dependence of solid friction on the number of surface atoms in a unit cell under periodic boundary conditions. A two-dimensional friction model between a single asperity and an elastic solid surface is examined. The solid surface is modeled using a coupled-oscillator lattice that consists of an infinite number of inner solid atoms; the dynamics are simulated by the recently proposed semi-infinite dynamic lattice Green's function method. A significant dependence of the friction on the number of surface atoms is observed. The dependence is attributed to the requirement for a large number of surface atoms for the excitation of the energy-dissipative surface phonons with nonzero wave numbers. In order to eliminate the problematic dependence, a correction method combined with the continuum contact theory is developed to evaluate friction in the limit of the infinite surface atoms. In addition, we found a relationship between the friction and the power spectrum of the temporal fluctuation in the force; the latter quantity does not significantly depend on the number of surface atoms.

• Received 25 November 2011

DOI:https://doi.org/10.1103/PhysRevB.86.075453