Friction laws at the nanoscale

Macroscopic laws of friction do not generally apply to nanoscale contacts. Although continuum mechanics models have been predicted to break down at the nanoscale(1), they continue to be applied for lack of a better theory. An understanding of how friction force depends on applied load and contact area at these scales is essential for the design of miniaturized devices with optimal mechanical performance(2,3). Here we use large-scale molecular dynamics simulations with realistic force fields to establish friction laws in dry nanoscale contacts. We show that friction force depends linearly on the number of atoms that chemically interact across the contact. By defining the contact area as being proportional to this number of interacting atoms, we show that the macroscopically observed linear relationship between friction force and contact area can be extended to the nanoscale. Our model predicts that as the adhesion between the contacting surfaces is reduced, a transition takes place from nonlinear to linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments(4-7). We demonstrate that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and show that roughness theories(8-10) of friction can be applied at the nanoscale.