The temperature dependence of the Tomlinson/Prandtl model for nanoscale sliding friction is analyzed by considering the properties of the initial and final states between which the tip can move, as well as the energy barrier between them, for various sliding regimes defined by the value of the corrugation factor γ. When γ < 1, the friction force tends to zero, defining a so-called superlubricious regime. The most commonly observed behavior is found for γ > 4.603, where the friction force increases monotonically with increasing sliding velocity up to a critical value equal to the value of F * (lateral force at T = 0) and monotonically decreases with temperature from F * at T = 0. However, completely different behavior is found when 1 < γ < 4.603. The temperature dependence of the lateral force in this regime is investigated using Monte Carlo simulations. The friction force still tends to F * as T approaches 0 K, but in contrast to the behavior found when γ > 4.603, the friction force increases with increasing temperature from F *, reaches a maximum value, and then decreases monotonically as the temperature rises further. Such behavior has been observed in atomic force microscopy friction measurements.
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Tomlinson, G.A.: A molecular theory of friction. Philos. Mag. 7, 905–937 (1929)
Prandtl, L.: Ein Gedankenmodell zur kinetischen Theorie der festen Körper. Z. Angew. Math. Mech. 8, 85 (1928)
Gnecco, E., Bennewitz, R., Gyalog, T., Meyer, E.: Friction experiments on the nanometre scale. J. Phys. Condens. Matter 13, R619–R642 (2001)
Szlufarska, I., Chandross, M., Carpick, R.W.: Recent advances in single-asperity nanotribology. J. Phys. D Appl. Phys. 41, 123001 (2008)
Dong, Y., Vadakkepatt, A., Martini, A.: Analytical models for atomic friction. Tribol. Lett. 44, 367–386 (2011)
Gnecco, E., Bennewitz, R., Gyalog, T., Loppacher, C., Bammerlin, M., Meyer, E., Güntherodt, H.H.: Velocity dependence of atomic friction. Phys. Rev. Lett. 84, 1172–1175 (2000)
Riedo, E., Gnecco, E., Bennewitz, R., Meyer, E., Brune, H.: Interaction potential and hopping dynamics governing sliding friction. Phys. Rev. Lett. 91, 084502 (2003)
Sang, Y., Dubé, M., Grant, M.: Thermal effects on atomic friction. Phys. Rev. Lett. 87, 174301 (2001)
Jansen, L., Hölscher, H., Fuchs, H., Schirmeisen, A.: Temperature dependence of atomic-scale stick–slip friction. Phys. Rev. Lett. 104, 256101 (2010)
Li, Q., Dong, Y., Perez, D., Martini, A., Carpick, R.W.: Speed dependence of atomic stick–slip friction in optimally matched experiments and molecular dynamics simulations. Phys. Rev. Lett. 106, 126101 (2011)
Zhao, X., Phillpot, S.R., Sawyer, W.G., Sinnott, S.B., Perry, S.S.: Transition from thermal to athermal friction under cryogenic conditions. Phys. Rev. Lett. 102, 186102 (2009)
Greiner, C., Felts, J.R., Dai, Z., King, W.P., Carpick, R.W.: Controlling nanoscale friction through the competition between capillary adsorption and thermally-activated sliding. ACS Nano 6, 4305–4313 (2012)
Barel, I., Urbakh, M., Jansen, L., Schirmeisen, A.: Unexpected temperature and velocity dependencies of atomic-scale stick–slip friction. Phys. Rev. B 84, 115417 (2011)
Barel, I., Urbakh, M., Jansen, L., Schirmeisen, A.: Multibond dynamics of nanoscale friction: the role of temperature. Phys. Rev. Lett. 104, 066104 (2010)
Dong, Y., Gao, H., Martini, A.: Suppression of atomic friction under cryogenic conditions: the role of athermal instability in AFM measurements. EPL 98, 16002 (2012)
Socoliuc, A., Bennewitz, R., Gnecco, E., Meyer, E.: Transition from stick–slip to continuous sliding in atomic friction: entering a new regime of ultralow friction. Phys. Rev. Lett. 92, 134301 (2004)
Medyanik, S.N., Liu, W.K., Sung, I., Carpick, R.W.: Predictions and observations of multiple slip modes in atomic-scale friction. Phys. Rev. Lett. 97, 136106 (2006)
Gnecco, E., Roth, R., Baratoff, A.: Analytical expressions for the kinetic friction in the Prandtl–Tomlinson model. Phys. Rev. B 86, 035443 (2012)
Müser, M.H.: Velocity dependence of kinetic friction in the Prandtl–Tomlinson model. Phys. Rev. B 84, 125419 (2011)
Furlong, O.J., Manzi, S.J., Pereyra, V.D., Bustos, V., Tysoe, W.T.: Kinetic Monte Carlo theory of sliding friction. Phys. Rev. B 80, 153408 (2009)
Furlong, O.J., Manzi, S.J., Pereyra, V.D., Bustos, V., Tysoe, W.T.: Monte Carlo simulations for Tomlinson sliding models for non-sinusoidal periodic potentials. Tribol. Lett. 39, 177–180 (2010)
Sales, J.L., Uñac, R.O., Gargiulo, M.V., Bustos, V., Zgrablich, G.: Monte Carlo simulation of temperature programmed desorption spectra: a guide through the forest for monomolecular adsorption on a square lattice. Langmuir 12, 95–100 (1996)
We gratefully acknowledge the National Science Foundation under Grant Number CMMI 0826151, the CONICET (Argentina) for support of this work, and Prof. Victor Pereyra for helpful discussions.
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Manzi, S.J., Tysoe, W.T. & Furlong, O.J. Temperature Dependences in the Tomlinson/Prandtl Model for Atomic Sliding Friction. Tribol Lett 55, 363–369 (2014). https://doi.org/10.1007/s11249-014-0360-x
- Tomlinson/Prandtl model
- Monte Carlo simulations
- Periodic sliding potentials
- Temperature dependence