Amontons' law at the molecular level

One of the fundamental postulates of friction is that at the microscopic or molecular level, the "real" area of contact is proportional to the load applied over the macroscopic or "apparent" area. This has both theoretical and experimental support and has formed the basis of many theoretical analyses, including an explanation of one of the most basic observations of everyday friction, i.e., that the friction force F is proportional to the load L or weight of the moving object (Amontons' law) where the ratio of F to L defines the coefficient of friction mu = F/L. We have carried out friction experiments between two molecularly smooth non-adhering surfaces under conditions where all the relevant macroscopic and microscopic parameters were directly measured. We find that even at the microscopic level the friction force is proportional to the net applied load and not to the real area of contact. One implication of this finding is that Amontons' law is also obeyed directly at the molecular level and does not emerge indirectly because of some fortuitous correlation between the net applied load and the local contact area or shear strength, as is commonly supposed. A physical model, based on intermolecular forces and thermodynamic considerations, is offered to explain why the friction force is proportional to the net applied load, and why the case of adhering surfaces - where the friction force is found to be proportional to the molecular contact area - is quite different from that of non-adhering surfaces.