Defining Contact at the Atomic Scale

Contact area plays a central role in continuum theories of friction and adhesion, and there is growing interest in calculating it with atomic resolution. Molecular dynamics simulations are used to study definitions of contact area based on instantaneous and time-averaged forces or separations between atoms. Flat and spherical surfaces with different atomic geometries, adhesion, and temperatures are examined. In continuum theory, the fraction of two flat surfaces that is in contact rises sharply from zero to unity when a load is applied. This simple behavior is surprisingly difficult to reproduce with atomic scale definitions of contact. At typical temperatures, nonadhesive surfaces are held apart by a small fraction of atoms with large thermal fluctuations until the normal pressure is comparable to the ideal hardness. The contact area associated with atoms interacting at any instant rises linearly with load. Time averaging produces a monotonic increase in area with time interval that only converges to the sharp rise in continuum models for the special case of identical crystal surfaces. Except in this special case, the time-averaged contact area between adhesive surfaces also rises to full contact over a range of pressures comparable to the ideal hardness. Similar complications are encountered in defining contact areas for spherical tips. The fraction of atoms in contact rises linearly with local pressure, and the contact area based on time-averaged forces does not fit continuum theory. A simple harmonic mean-field theory provides a quantitative description of the simulation results and explains why the instantaneous forces on atoms are observed to have a universal exponential form. The results imply that continuum models of contact only apply to forces averaged over areas containing many atoms.