Defining Contact at the Atomic Scale
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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.
KeywordsNanotribology Contact mechanics
This material is based upon study supported by the National Science Foundation under Grant No. DMR-0454947 and the Air Force Office of Scientific Research under Grant No. FA9550-0910232.
- 5.Bowden, F.P., Tabor, D.: The Friction and Lubrication of Solids. Clarendon Press, Oxford (1986)Google Scholar
- 13.Luan, B.Q.: Simulations of contact and friction: Connecting atomic and continuum descriptions. Ph.D. thesis, Johns Hopkins University, Baltimore (2006)Google Scholar
- 17.Harrison, J.A., Stuart, S.J., Brenner, D.W.: Atomic-scale simulation of tribological and related phenomena. In: Bhushan, B. (ed.) Handbook of Micro/Nanotribology, pp. 525–594. CRC Press, Boca Raton (1999)Google Scholar
- 18.Robbins, M.O., Müser, M.H.: Computer simulations of friction, lubrication and wear. In: Bhushan, B. (ed.) Handbook of Modern Tribology, pp. 717–765. CRC Press, Boca Raton (2000) (cond-mat/0001056)Google Scholar
- 28.Luan, B.Q., Hyun, S., Robbins, M.O., Bernstein, N.: Multiscale modeling of two dimensional rough surface contacts. In: Wahl, K.J., Huber, N., Mann, A.B., Bahr, D.F., Cheng, Y.T. (eds.) Fundamentals of Nanoindentation and Nanotribology, vol 841, pp. R74. Materials Research Society, Warrendale (2005)Google Scholar
- 36.D. Dowson, History of Tribology. Longman, New York (1979)Google Scholar
- 37.Israelachvili, J.N.: Intermolecular and Surface Forces, 2nd edn. Academic Press, London (1991)Google Scholar
- 41.Maugis, D.: In: Grunze, M., Kreuzer, H.J. (eds.) Adhesion and Friction, vol. 17, pp. 303. Springer, Berlin (1990)Google Scholar
- 43.Stevens, M.J., Robbins, M.O.: Melting of Yukawa systems: a test of phenomenological melting criteria. J. Chem. Phys. 98, 2319–2324 (1993)Google Scholar
- 44.Krim J., Palasantzas, G.: Experimental observation of self-affine scaling and kinetic roughening at sub-micron lengthscales. Int. J. Mod. Phys. B 9, 599–632 (1995)Google Scholar