The area of molecular contact between surfaces plays a central role in friction and adhesion. Traditionally it is calculated using continuum contact mechanics, which is known to break down as the contact width approaches atomic dimensions. Yet contact mechanics is being applied at ever smaller lengths, even to atomic force microscope (AFM) tips containing a few atoms. Molecular simulations are used to test the limits of contact mechanics under ideal non-adhesive and adhesive conditions. A simple geometry of sphere-on-flat is considered. One surface is an atomically flat crystal and is deformable. The approximately spherical curved surface is rigid and is produced by bending a crystal, or cutting a crystal or amorphous material. While these methods of producing the curved surface differ only in the amount of atomic-scale roughness, they produce very different behavior in some quantities. The normal stiffness is affected very little, the contact area can be modified by a factor of two, and the friction and lateral stiffness can be modified by an order of magnitude. The implications for AFM experiments are discussed.

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