A Note on the Two-Spring Tomlinson Model

Tribology Letters - Tập 43 - Trang 73-76 - 2011
Pin Lu1, Yee Chong Loke1, Xiaosong Tang1, Sunil S. Kushvaha1, Sean J. O’Shea1
1Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), Singapore, Singapore

Tóm tắt

In this note, quasistatic solutions of a two-mass-two-spring Tomlinson model for atomic force microscopy are derived, and are compared with the corresponding results of the single-spring Tomlinson model. It is clarified that the solutions of the two models are equivalent provided that the effective spring constant is correctly defined. It is also shown that modeling the onset of stick-slip motion in terms of the criteria defined by explicit tip and cantilever stiffness is the most convenient to investigate the effects of the tip-flexibility on the stick-slip motion.

Tài liệu tham khảo

Maier, S., Sang, Y., Filleter, T., Grant, M., Bennewitz, R., Gnecco, E., Meyer, E.: Fluctuations and jump dynamics in atomic friction experiments. Phys. Rev. B 72, 245418 (2005) Reimann, P., Evstigneev, M.: Description of atomic friction as forced Brownian motion. New J. Phys. 7, 25 (2005) Krylov, S.Y., Dijksman, J.A., van Loo, W.A., Frenken, J.W.M.: Stick-slip motion in spite of a slippery contact: do we get what we see in atomic friction? Phys. Rev. Lett. 97, 166103 (2006) Abel, D., Krylov, S.Y., Frenken, J.W.M.: Evidence for contact delocalization in atomic scale friction. Phys. Rev. Lett. 99, 166102 (2007) Krylov, S.Y., Frenken, J.W.M.: Thermal contact delocalization in atomic scale friction: a multitude of friction regimes. New J. Phys. 9, 398 (2007) Johnson, K.L., Woodhouse, J.: Stick–slip motion in the atomic force microscope. Tribol. Lett. 5, 155–160 (1998) Gnecco, E., Bennewitz, R., Gyalog, T., Meyer, E.: Friction experiments on the nanometre scale. J. Phys. Condens. Matter 13, R619–R642 (2001) Gnecco, E., Socoliuc, A., Meyer, E.: Atomic-scale investigation of superlubricity on insulating surfaces. In: Erdemir, S., Martin, J.M. (eds.) Superlubricity, pp. 147–160. Elsevier, Amsterdam (2007) Holscher, H., Schirmeisen, A., Schwarz, U.D.: Principles of atomic friction: from sticking atoms to superlubric sliding. Philos. Trans. R. Soc. A 366, 1383–1404 (2008) Carpick, R.W., Ogletree, D.F., Salmeron, M.: Lateral stiffness: a new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl. Phys. Lett. 70, 1548–1550 (1997) Lantz, M.A., O’Shea, S.J., Welland, M.E., Johnson, K.L.: Atomic-force-microscope study of contact area and friction on NbSe2. Phys. Rev. B 55, 10776 (1997) Krylov, S.Y., Frenken, J.W.M.: The crucial role of temperature in atomic scale friction. J. Phys. Condens. Matter 20, 354003 (2008) Tshiprut, Z., Filippov, A.E., Urbakh, M.: Effect of tip flexibility on stick–slip motion in friction force microscopy experiments. J. Phys. Condens. Matter 20, 354002 (2008) Conley, W.G., Krousgrill, C.M., Raman, A.: Stick-slip motions in the friction force microscope: effects of tip compliance. Tribol. Lett. 29, 23–32 (2008) Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Dover Publications, New York (1972)