Amontons' Friction Law: Statistical Analysis of MD Simulations

Amontons' law, stating that the friction force (F) is directly proportional to the (normal) applied load ( L), F=μ L, with μ independent of the contact area, and sliding velocity, has no satisfactory theoretical explanation, to date. We report on molecular dynamics (MD) simulations of the friction between atomically rough or smooth surfaces lubricated by a thin alkane film. The simulations exhibit Amontons law behavior, and show trends consistent with surface-force-apparatus and atomic-force-microscope experiments. A new methodology is introduced, where the analysis of the MD trajectories is based on evaluation of the statistical distribution functions of the local friction and normal load forces, calculated as short-time averages acting on local areas with dimensions of a few interatomic distances. We find that only the averaged friction and load forces, obtained as first moments of the statistical distributions, are related linearly, i.e. obey Amontons law, while the corresponding local quantities do not. Interestingly, the much discussed concept of "area of contact", assumed in various models of friction, does not enter our analysis.